Physics’s pangolin

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Physics’s pangolin

Illustration by Claire Scully

Trying to resolve the stubborn paradoxes of their field, physicists craft ever more mind-boggling visions of reality

Margaret Wertheim is an Australian-born science writer and director of the Institute For Figuring in Los Angeles. Her latest book is Physics on the Fringe (2011).

4800 4,800 words
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Theoretical physics is beset by a paradox that remains as mysterious today as it was a century ago: at the subatomic level things are simultaneously particles and waves. Like the duck-rabbit illusion first described in 1899 by the Polish-born American psychologist Joseph Jastrow, subatomic reality appears to us as two different categories of being.

But there is another paradox in play. Physics itself is riven by the competing frameworks of quantum theory and general relativity, whose differing descriptions of our world eerily mirror the wave-particle tension. When it comes to the very big and the extremely small, physical reality appears to be not one thing, but two. Where quantum theory describes the subatomic realm as a domain of individual quanta, all jitterbug and jumps, general relativity depicts happenings on the cosmological scale as a stately waltz of smooth flowing space-time. General relativity is like Strauss — deep, dignified and graceful. Quantum theory, like jazz, is disconnected, syncopated, and dazzlingly modern.

Physicists are deeply aware of the schizophrenic nature of their science and long to find a synthesis, or unification. Such is the goal of a so-called ‘theory of everything’. However, to non-physicists, these competing lines of thought, and the paradoxes they entrain, can seem not just bewildering but absurd. In my experience as a science writer, no other scientific discipline elicits such contradictory responses.

In string cosmology, the totality of existing universes exceeds the number of particles in our universe by more than 400 orders of magnitude

This schism was brought home to me starkly some months ago when, in the course of a fortnight, I happened to participate in two public discussion panels, one with a cosmologist at Caltech, Pasadena, the other with a leading literary studies scholar from the University of Southern Carolina. On the panel with the cosmologist, a researcher whose work I admire, the discussion turned to time, about which he had written a recent, and splendid, book. Like philosophers, physicists have struggled with the concept of time for centuries, but now, he told us, they had locked it down mathematically and were on the verge of a final state of understanding. In my Caltech friend’s view, physics is a progression towards an ever more accurate and encompassing Truth. My literary theory panellist was having none of this. A Lewis Carroll scholar, he had joined me for a discussion about mathematics in relation to literature, art and science. For him, maths was a delightful form of play, a ludic formalism to be admired and enjoyed; but any claims physicists might make about truth in their work were, in his view, ‘nonsense’. This mathematically based science, he said, was just ‘another kind of storytelling’.

On the one hand, then, physics is taken to be a march toward an ultimate understanding of reality; on the other, it is seen as no different in status to the understandings handed down to us by myth, religion and, no less, literary studies. Because I spend my time about equally in the realms of the sciences and arts, I encounter a lot of this dualism. Depending on whom I am with, I find myself engaging in two entirely different kinds of conversation. Can we all be talking about the same subject?

Many physicists are Platonists, at least when they talk to outsiders about their field. They believe that the mathematical relationships they discover in the world about us represent some kind of transcendent truth existing independently from, and perhaps a priori to, the physical world. In this way of seeing, the universe came into being according to a mathematical plan, what the British physicist Paul Davies has called ‘a cosmic blueprint’. Discovering this ‘plan’ is a goal for many theoretical physicists and the schism in the foundation of their framework is thus intensely frustrating. It’s as if the cosmic architect has designed a fiendish puzzle in which two apparently incompatible parts must be fitted together. Both are necessary, for both theories make predictions that have been verified to a dozen or so decimal places, and it is on the basis of these theories that we have built such marvels as microchips, lasers, and GPS satellites.

Quite apart from the physical tensions that exist between them, relativity and quantum theory each pose philosophical problems. Are space and time fundamental qualities of the universe, as general relativity suggests, or are they byproducts of something even more basic, something that might arise from a quantum process? Looking at quantum mechanics, huge debates swirl around the simplest situations. Does the universe split into multiple copies of itself every time an electron changes orbit in an atom, or every time a photon of light passes through a slit? Some say yes, others say absolutely not.

Theoretical physicists can’t even agree on what the celebrated waves of quantum theory mean. What is doing the ‘waving’? Are the waves physically real, or are they just mathematical representations of probability distributions? Are the ‘particles’ guided by the ‘waves’? And, if so, how? The dilemma posed by wave-particle duality is the tip of an epistemological iceberg on which many ships have been broken and wrecked.

Undeterred, some theoretical physicists are resorting to increasingly bold measures in their attempts to resolve these dilemmas. Take the ‘many-worlds’ interpretation of quantum theory, which proposes that every time a subatomic action takes place the universe splits into multiple, slightly different, copies of itself, with each new ‘world’ representing one of the possible outcomes.

When this idea was first proposed in 1957 by the American physicist Hugh Everett, it was considered an almost lunatic-fringe position. Even 20 years later, when I was a physics student, many of my professors thought it was a kind of madness to go down this path. Yet in recent years the many-worlds position has become mainstream. The idea of a quasi-infinite, ever-proliferating array of universes has been given further credence as a result of being taken up by string theorists, who argue that every mathematically possible version of the string theory equations corresponds to an actually existing universe, and estimate that there are 10 to the power of 500 different possibilities. To put this in perspective: physicists believe that in our universe there are approximately 10 to the power of 80 subatomic particles. In string cosmology, the totality of existing universes exceeds the number of particles in our universe by more than 400 orders of magnitude.

Nothing in our experience compares to this unimaginably vast number. Every universe that can be mathematically imagined within the string parameters — including ones in which you exist with a prehensile tail, to use an example given by the American string theorist Brian Greene — is said to be manifest somewhere in a vast supra-spatial array ‘beyond’ the space-time bubble of our own universe.

What is so epistemologically daring here is that the equations are taken to be the fundamental reality. The fact that the mathematics allows for gazillions of variations is seen to be evidence for gazillions of actual worlds.

Perhaps what we are encountering here is not so much the edge of reality, but the limits of the physicists’ category system

This kind of reification of equations is precisely what strikes some humanities scholars as childishly naive. At the very least, it raises serious questions about the relationship between our mathematical models of reality, and reality itself. While it is true that in the history of physics many important discoveries have emerged from revelations within equations — Paul Dirac’s formulation for antimatter being perhaps the most famous example — one does not need to be a cultural relativist to feel sceptical about the idea that the only way forward now is to accept an infinite cosmic ‘landscape’ of universes that embrace every conceivable version of world history, including those in which the Middle Ages never ended or Hitler won.

In the 30 years since I was a student, physicists’ interpretations of their field have increasingly tended toward literalism, while the humanities have tilted towards postmodernism. Thus a kind of stalemate has ensued. Neither side seems inclined to contemplate more nuanced views. It is hard to see ways out of this tunnel, but in the work of the late British anthropologist Mary Douglas I believe we can find a tool for thinking about some of these questions.

On the surface, Douglas’s great book Purity and Danger (1966) would seem to have nothing do with physics; it is an inquiry into the nature of dirt and cleanliness in cultures across the globe. Douglas studied taboo rituals that deal with the unclean, but her book ends with a far-reaching thesis about human language and the limits of all language systems. Given that physics is couched in the language-system of mathematics, her argument is worth considering here.

In a nutshell, Douglas notes that all languages parse the world into categories; in English, for instance, we call some things ‘mammals’ and other things ‘lizards’ and have no trouble recognising the two separate groups. Yet there are some things that do not fit neatly into either category: the pangolin, or scaly anteater, for example. Though pangolins are warm-blooded like mammals and birth their young, they have armoured bodies like some kind of bizarre lizard. Such definitional monstrosities are not just a feature of English. Douglas notes that all category systems contain liminal confusions, and she proposes that such ambiguity is the essence of what is seen to be impure or unclean.

Whatever doesn’t parse neatly in a given linguistic system can become a source of anxiety to the culture that speaks this language, calling forth special ritual acts whose function, Douglas argues, is actually to acknowledge the limits of language itself. In the Lele culture of the Congo, for example, this epistemological confrontation takes place around a special cult of the pangolin, whose initiates ritualistically eat the abominable animal, thereby sacralising it and processing its ‘dirt’ for the entire society.

‘Powers are attributed to any structure of ideas,’ Douglas writes. We all tend to think that our categories of understanding are necessarily real. ‘The yearning for rigidity is in us all,’ she continues. ‘It is part of our human condition to long for hard lines and clear concepts’. Yet when we have them, she says, ‘we have to either face the fact that some realities elude them, or else blind ourselves to the inadequacy of the concepts’. It is not just the Lele who cannot parse the pangolin: biologists are still arguing about where it belongs on the genetic tree of life.

As Douglas sees it, cultures themselves can be categorised in terms of how well they deal with linguistic ambiguity. Some cultures accept the limits of their own language, and of language itself, by understanding that there will always be things that cannot be cleanly parsed. Others become obsessed with ever-finer levels of categorisation as they try to rid their system of every pangolin-like ‘duck-rabbit’ anomaly. For such societies, Douglas argues, a kind of neurosis ensues, as the project of categorisation takes ever more energy and mental effort. If we take this analysis seriously, then, in Douglas’ terms, might it be that particle-waves are our pangolins? Perhaps what we are encountering here is not so much the edge of reality, but the limits of the physicists’ category system.

In its modern incarnation, physics is grounded in the language of mathematics. It is a so-called ‘hard’ science, a term meant to imply that physics is unfuzzy — unlike, say, biology whose classification systems have always been disputed. Based in mathematics, the classifications of physicists are supposed to have a rigour that other sciences lack, and a good deal of the near-mystical discourse that surrounds the subject hinges on ideas about where the mathematics ‘comes from’.

According to Galileo Galilei and other instigators of what came to be known as the Scientific Revolution, nature was ‘a book’ that had been written by God, who had used the language of mathematics because it was seen to be Platonically transcendent and timeless. While modern physics is no longer formally tied to Christian faith, its long association with religion lingers in the many references that physicists continue to make about ‘the mind of God’, and many contemporary proponents of a ‘theory of everything’ remain Platonists at heart.

It’s a startling thought, in an age when we can read the speed of our cars from our digitised dashboards, that somebody had to discover ‘velocity’

In order to articulate a more nuanced conception of what physics is, we need to offer an alternative to Platonism. We need to explain how the mathematics ‘arises’ in the world, in ways other than assuming that it was put there there by some kind of transcendent being or process. To approach this question dispassionately, it is necessary to abandon the beautiful but loaded metaphor of the cosmic book — and all its authorial resonances — and focus, not the creation of the world, but on the creation of physics as a science.

When we say that ‘mathematics is the language of physics’, we mean that physicists consciously comb the world for patterns that are mathematically describable; these patterns are our ‘laws of nature’. Since mathematical patterns proceed from numbers, much of the physicist’s task involves finding ways to extract numbers from physical phenomena. In the 16th and 17th centuries, philosophical discussion referred to this as the process of ‘quantification’; today we call it measurement. One way of thinking about modern physics is as an ever more sophisticated process of quantification that multiplies and diversifies the ways we extract numbers from the world, thus giving us the raw material for our quest for patterns or ‘laws’. This is no trivial task. Indeed, the history of physics has turned on the question of what can be measured and how.

Stop for a moment and take a look around you. What do you think can be quantified? What colours and forms present themselves to your eye? Is the room bright or dark? Does the air feel hot or cold? Are birds singing? What other sounds do you hear? What textures do you feel? What odours do you smell? Which, if any, of these qualities of experience might be measured?

In the early 14th century, a group of scholarly monks known as the calculatores at the University of Oxford began to think about this problem. One of their interests was motion, and they were the first to recognise the qualities we now refer to as ‘velocity’ and ‘acceleration’ — the former being the rate at which a body changes position, the latter, the rate at which the velocity itself changes. It’s a startling thought, in an age when we can read the speed of our cars from our digitised dashboards, that somebody had to discover ‘velocity’.

Yet despite the calculatores’ advances, the science of kinematics made barely any progress until Galileo and his contemporaries took up the baton in the late-16th century. In the intervening time, the process of quantification had to be extracted from a burden of dreams in which it became, frankly, bogged down. For along with motion, the calculatores were also interested in qualities such as sin and grace and they tried to find ways to quantify these as well. Between the calculatores and Galileo, students of quantification had to work out what they were going to exclude from the project. To put it bluntly, in order for the science of physics to get underway, the vision had to be narrowed.

How, exactly, this narrowing was to be achieved was articulated by the 17th-century French mathematician and philosopher René Descartes. What could a mathematically based science describe? Descartes’s answer was that the new natural philosophers must restrict themselves to studying matter in motion through space and time. Maths, he said, could describe the extended realm — or res extensa. Thoughts, feelings, emotions and moral consequences, he located in the ‘realm of thought’, or res cogitans, declaring them inaccessible to quantification, and thus beyond the purview of science. In making this distinction, Descartes did not divide mind from body (that had been done by the Greeks), he merely clarified the subject matter for a new physical science.

So what else apart from motion could be quantified? To a large degree, progress in physics has been made by slowly extending the range of answers. Take colour. At first blush, redness would seem to be an ineffable and irreducible quale. In the late 19th century, however, physicists discovered that each colour in the rainbow, when diffracted through a prism, corresponds to a different wavelength of light. Red light has a wavelength of around 700 nanometres, violet light around 400 nanometres. Colour can be correlated with numbers — both the wavelength and frequency of an electromagnetic wave. Here we have one half of our duality: the wave.

The discovery of electromagnetic waves was in fact one of the great triumphs of the quantification project. In the 1820s, Michael Faraday noticed that, if he sprinkled iron filings around a magnet, the fragments would spontaneously assemble into a pattern of lines that, he conjectured, were caused by a ‘magnetic field’. Physicists today accept fields as a primary aspect of nature but at the start of the Industrial Revolution, when philosophical mechanism was at its peak, Faraday’s peers scoffed. Invisible fields smacked of magic. Yet, later in the 19th century, James Clerk Maxwell showed that magnetic and electric fields were linked by a precise set of equations — today known as Maxwell’s Laws — that enabled him to predict the existence of radio waves. The quantification of these hitherto unsuspected aspects of our world — these hidden invisible ‘fields’ — has led to the whole gamut of modern telecommunications on which so much of modern life is now staged.

Turning to the other side of our duality – the particle – with a burgeoning array of electrical and magnetic equipment, physicists in the late 19th and early 20th centuries began to probe matter. They discovered that atoms were composed from parts holding positive and negative charge. The negative electrons, were found to revolve around a positive nucleus in pairs, with each member of the pair in a slightly different state, or ‘spin’. Spin turns out to be a fundamental quality of the subatomic realm. Matter particles, such as electrons, have a spin value of one half. Particles of light, or photons, have a spin value of one. In short, one of the qualities that distinguishes ‘matter’ from ‘energy’ is the spin value of its particles.

We have seen how light acts like a wave, yet experiments over the past century have shown that under many conditions it behaves instead like a stream of particles. In the photoelectric effect (the explanation of which won Albert Einstein his Nobel Prize in 1921), individual photons knock electrons out of their atomic orbits. In Thomas Young's infamous double-slit experiment of 1805, light behaves simultaneously like waves and particles. Here, a stream of detectably separate photons are mysteriously guided by a wave whose effect becomes manifest over a long period of time. What is the source of this wave and how does it influence billions of isolated photons separated by great stretches of time and space? The late Nobel laureate Richard Feynman — a pioneer of quantum field theory — stated in 1965 that the double-slit experiment lay at ‘the heart of quantum mechanics’. Indeed, physicists have been debating how to interpret its proof of light’s duality for the past 200 years.

Just as waves of light sometimes behave like particles of matter, particles of matter can sometimes behave like waves. In many situations, electrons are clearly particles: we fire them from electron guns inside the cathode-ray tubes of old-fashioned TV sets and each electron that hits the screen causes a tiny phosphor to glow. Yet, in orbiting around atoms, electrons behave like three-dimensional waves. Electron microscopes put the wave-quality of these particles to work; here, in effect, they act like short-wavelengths of light.

physics is not just another story about the world: it is a qualitatively different kind of story to those told in the humanities, in myths and religions

Wave-particle duality is a core feature of our world. Or rather, we should say, it is a core feature of our mathematical descriptions of our world. The duck-rabbits are everywhere, colonising the imagery of physicists like, well, rabbits. But what is critical to note here is that however ambiguous our images, the universe itself remains whole and is manifestly not fracturing into schizophrenic shards. It is this tantalising wholeness in the thing itself that drives physicists onward, like an eternally beckoning light that seems so teasingly near yet is always out of reach.

Instrumentally speaking, the project of quantification has led physicists to powerful insights and practical gain: the computer on which you are reading this article would not exist if physicists hadn’t discovered the equations that describe the band-gaps in semiconducting materials. Microchips, plasma screens and cellphones are all byproducts of quantification and, every decade, physicists identify new qualities of our world that are amendable to measurement, leading to new technological possibilities. In this sense, physics is not just another story about the world: it is a qualitatively different kind of story to those told in the humanities, in myths and religions. No language other than maths is capable of expressing interactions between particle spin and electromagnetic field strength. The physicists, with their equations, have shown us new dimensions of our world.

That said, we should be wary of claims about ultimate truth. While quantification, as a project, is far from complete, it is an open question as to what it might ultimately embrace. Let us look again at the colour red. Red is not just an electromagnetic phenomenon, it is also a perceptual and contextual phenomenon. Stare for a minute at a green square then look away: you will see an afterimage of a red square. No red light has been presented to your eyes, yet your brain will perceive a vivid red shape. As Goethe argued in the late-18th century, and Edwin Land (who invented Polaroid film in 1932) echoed, colour cannot be reduced to purely prismatic effects. It exists as much in our minds as in the external world. To put this into a personal context, no understanding of the electromagnetic spectrum will help me to understand why certain shades of yellow make me nauseous, while electric orange fills me with joy.

Descartes was no fool; by parsing reality into the res extensa and res cogitans he captured something critical about human experience. You do not need to be a hard-core dualist to imagine that subjective experience might not be amenable to mathematical law. For Douglas, ‘the attempt to force experience into logical categories of non-contradiction’ is the ‘final paradox’ of an obsessive search for purity. ‘But experience is not amenable [to this narrowing],’ she insists, and ‘those who make the attempt find themselves led into contradictions.’

Quintessentially, the qualities that are amenable to quantification are those that are shared. All electrons are essentially the same: given a set of physical circumstances, every electron will behave like any other. But humans are not like this. It is our individuality that makes us so infuriatingly human, and when science attempts to reduce us to the status of electrons it is no wonder that professors of literature scoff.

Douglas’s point about attempting to corral experience into logical categories of non-contradiction has obvious application to physics, particularly to recent work on the interface between quantum theory and relativity. One of the most mysterious findings of quantum science is that two or more subatomic particles can be ‘entangled’. Once particles are entangled, what we do to one immediately affects the other, even if the particles are hundreds of kilometres apart. Yet this contradicts a basic premise of special relativity, which states that no signal can travel faster than the speed of light. Entanglement suggests that either quantum theory or special relativity, or both, will have to be rethought.

More challenging still, consider what might happen if we tried to send two entangled photons to two separate satellites orbiting in space, as a team of Chinese physicists, working with the entanglement theorist Anton Zeilinger, is currently hoping to do. Here the situation is compounded by the fact that what happens in near-Earth orbit is affected by both special and general relativity. The details are complex, but suffice it to say that special relativity suggests that the motion of the satellites will cause time to appear to slow down, while the effect of the weaker gravitational field in space should cause time to speed up. Given this, it is impossible to say which of the photons would be received first at which satellite. To an observer on the ground, both photons should appear to arrive at the same time. Yet to an observer on satellite one, the photon at satellite two should appear to arrive first, while to an observer on satellite two the photon at satellite one should appear to arrive first. We are in a mire of contradiction and no one knows what would in fact happen here. If the Chinese experiment goes ahead, we might find that some radical new physics is required.

To say that every possible version of their equations must be materially manifest strikes me as a kind of berserk literalism

You will notice that the ambiguity in these examples focuses on the issue of time — as do many paradoxes relating to relativity and quantum theory. Time indeed is a huge conundrum throughout physics, and paradoxes surround it at many levels of being. In Time Reborn: From the Crisis in Physics to the Future of the Universe (2013) the American physicist Lee Smolin argues that for 400 years physicists have been thinking about time in ways that are fundamentally at odds with human experience and therefore wrong. In order to extricate ourselves from some of the deepest paradoxes in physics, he says, its very foundations must be reconceived. In an op-ed in New Scientist in April this year, Smolin wrote:
The idea that nature consists fundamentally of atoms with immutable properties moving through unchanging space, guided by timeless laws, underlies a metaphysical view in which time is absent or diminished. This view has been the basis for centuries of progress in science, but its usefulness for fundamental physics and cosmology has come to an end.

In order to resolve contradictions between how physicists describe time and how we experience time, Smolin says physicists must abandon the notion of time as an unchanging ideal and embrace an evolutionary concept of natural laws.

This is radical stuff, and Smolin is well-known for his contrarian views — he has been an outspoken critic of string theory, for example. But at the heart of his book is a worthy idea: Smolin is against the reflexive reification of equations. As our mathematical descriptions of time are so starkly in conflict with our lived experience of time, it is our descriptions that will have to change, he says.

To put this into Douglas’s terms, the powers that have been attributed to physicists’ structure of ideas have been overreaching. ‘Attempts to force experience into logical categories of non-contradiction’ have, she would say, inevitably failed. From the contemplation of wave-particle pangolins we have been led to the limits of the linguistic system of physicists. Like Smolin, I have long believed that the ‘block’ conception of time that physics proposes is inadequate, and I applaud this thrilling, if also at times highly speculative, book. Yet, if we can fix the current system by reinventing its axioms, then (assuming that Douglas is correct) even the new system will contain its own pangolins.

In the early days of quantum mechanics, Niels Bohr liked to say that we might never know what ‘reality’ is. Bohr used John Wheeler's coinage, calling the universe ‘a great smoky dragon’, and claiming that all we could do with our science was to create ever more predictive models. Bohr’s positivism has gone out of fashion among theoretical physicists, replaced by an increasingly hard-core Platonism. To say, as some string theorists do, that every possible version of their equations must be materially manifest strikes me as a kind of berserk literalism, reminiscent of the old Ptolemaics who used to think that every mathematical epicycle in their descriptive apparatus must represent a physically manifest cosmic gear.

We are veering here towards Douglas’s view of neurosis. Will we accept, at some point, that there are limits to the quantification project, just as there are to all taxonomic schemes? Or will we be drawn into ever more complex and expensive quests — CERN mark two, Hubble, the sequel — as we try to root out every lingering paradox? In Douglas’s view, ambiguity is an inherent feature of language that we must face up to, at some point, or drive ourselves into distraction.

Read more essays on history of ideas, philosophy of science, physics and quantum theory


  • Lester

    This is wonderful.

    The problem of measurement and categorisation as an objective and disinterested phenomena has never existed in any field without collapsing into a subjective and possessed phenomena.

    It seems, and science is no exception regardless of it's supposed built-in structurally objective nature, that ownership of concepts and the right to possess "truth" is of greater value to humans than the content of the concepts and truths.

    Echoing Mary Douglas, this is precisely what David Bohm is getting at in "On Dialogue" where he deftly suggests that it is the thought process itself, rather than the content of the thoughts, that needs addressing if we are to make that oft cited and possibly never experienced myth called Progress.

    When Religion is vanquished with its heavily belittled conjecture of never provable other worldly beings forever beyond our reach by Sciences triumphant hypothesis of never provable other worlds forever beyond our reach one begins to wonder if the content is always subordinate to the structure on which it is pinned.

    • Toronto

      John Wheeler's game of twenty questions -- one person leaves the room, and the rest agree while she is gone that they will start with no answer, but however the first question is answered by one of them, all subsequent answers have to fit into the answer to the previous question -- is a good approximation to the situation......

      • Lester

        Except, and please correct me if I am wrong, I imagined Wheelers "it from bit" to be an analogy aimed at reaching an ultimate description of how the interaction between physical "reality" and consciousness and the formation of "reality".

        Whereas I'm suggesting that the capacity for human thought (not conscious experience per se) is limited to structures that seem to disable reasonable objectivity.

        • Margaret Wertheim

          Lester - thanks for the Bohmian comments on my piece. I think Bohm also was trying to put physics into a wider system of thought. Its interesting that these days so many physicists regard philosophy as a contentless species of speculation, yet they cannot see that their own science has itself become highly speculative. Einstein insisted that studying philosophy had led him to relativity, and in the great German tradition of education it would be unthinkable for a scientist not to be exposed to serious philosophical ideas. Bohm understood that philosophy and theoretical physics go hand-in-hand. Why have we become so resistant in the sciences to philosophical reflection on our own epistemology?

          • Lester

            Excellent point Margaret. I agree with your careful overview of the public face of science as well. Nicely put.

          • Felix Erwin

            We can thank Galileo for objectivity and Godel for pressing the reset button with his incompleteness theorem. Mathematics does not serve us well at the limits of science (and vice versa).

            Condensation of energy is the order of the Universe at this special time and place, and entropy is our vector. I think we can agree on the ghostly spectre of stars in the sky, the almost incomprehensible vastness of the cosmos, and our incredulity of the most populous forms of energy and matter.

            I find great irony in the fact that it may be the thing that we (apparently) least comprehend that may help us on this, our greatest quest. Perhaps a definitive understanding of QM is overdue. Thank you.

      • Lester

        Sorry - leapt off a little prematurely there - I just wanted to add that Wheeler (and lot's of others of course) seemed to imagine that not only was/is there an Answer to find, but that we would find it. That might be an unfair characterisation though considering in his less guarded moments he also imagined that the world was entirely a figment of the imagination.

        I'm more of the mind that imagines that not only is there never going to be an Answer, but that all we can hope for is an accommodation with a process of Questions. Never a product only a process, and limited by our own limitations.

        But I'm comfortable with that at least :)

    • drokhole

      Great comment on a great essay.

    • stevegbrown

      Sciences triumphant hypothesis of never provable other worlds forever beyond our reach one begins to wonder if the content is always subordinate to the structure on which it is pinned.
      Sounds like the physicists' "many worlds" theory. Where's the evidence? [Unlike the planes flown (1 at high altittude, the other at sea level) with synchronized atomic clocks that validated Relativity.]

  • andacar

    Of all things, this reminded me of nothing so much as a remarkably well written character in a recent animated film. In "Justice League: Crisis on Two Earths," Owlman is Batman's evil counterpart. He has discovered that there is virtually an infinite number of alternative Earths. Since as far as he can tell every possible action a person could take has been taken on some other Earth, life is meaningless. He becomes a nihilist and decides to destroy all possible universes simply because it is "the only action one can take that has any meaning."

    While I hope nobody goes that far, the conclusions of modern theoretical physics can lead us down a very dark rabbit hole like the one Owlman found if we aren't careful. HP Lovecraft said it best:

    "The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age."

    I hope some of the puzzling conclusions mentioned in this article aren't like that.

    • Nat Scientist

      The sciences, each straining in its own direction, have hitherto harmed
      us little; but some day the piecing together of dissociated knowledge
      will open up such terrifying vistas of reality, and of our frightful
      position therein, that we shall either go mad from the revelation or
      flee from the deadly light into the peace and safety of a new dark age."

      Your either/or choices describe your fear of hitherto science, but not your opportunities. 'terrifying' vistas indeed in your set of self-limiting suckful choices. You have plenty of company right now fleeing from the 'deadly' light.

  • rameshraghuvanshi

    That is why Einstein famously told God is not playing dice and dispiritedly struggle to search united theory of all thing. History proved that God is really playing dice.

    • Terry A Davis

      God controls dice and everything else.

      Some people admire hitchhikers infinite improbability engine. I think that's for niggers. God exists and I'm not a nigger -- there are not 400 gazillion orders of magnitude more realities.

      • beachcomber

        Your "nigger" comment is disgusting - I request the moderators to ban you from this forum.

  • Margaret Wertheim

    Thanks andacar for the beautiful quote by Lovecraft. Its amazing how prescient he was. My main purpose with this piece is to get people thinking about the limits of all ways of knowing, and thus to consider the prospect that we need many epistemological systems in our lives. Science is a fantastic way of knowing but it is not going to solve all our philosophical or practical problems - we need to learn to value other ways of investigating reality at the same time that we celebrate and support science.

    • Derek Roche


    • orthorim

      Science represents the pinnacle of thought. But as all human beings discover sooner or later, thought is just a part of the human experience. We are all so much more. And when we go into discovering what we truly are, we get into a whole realm undescribable by thought, and therefore by science - this is where we also find true happiness and this is where religions started.

      I wish science would be powerful enough to acknowledge that which it cannot describe.

      • Dina Strange

        What "so much more" are we?

        • orthorim

          A true answer to that cannot be expressed in words, and a second-hand answer will sound meaningless.
          It's easier to define the negative, what you are not: You are not your thoughts; you are not your emotions; you are not your body; you are not your beliefs; you are not the roles that you play in your life - even if these roles are important.
          Given that - who are you?

          • Dina Strange

            I am my thoughts, my emotions, and my body. Even my roles are me.

    • epistememe

      It seems to me that any question science can’t answer doesn’t have an answer, only opinions.

  • M Collings

    Isn't this argument the same argument that gets repeated in every nuance of our Societys history since the Greeks?

    Plato vs Aristotle
    Heaven vs Earth
    Mind vs Body
    Mysticism vs Reason
    Subject vs Object

    The fact is we're stuck because Science in its Aristolean form has been so successful for us these last 300 years. Its served us very very well. Perhaps this impasse means we're ready to even up the balance sheet.

  • Derek Roche

    Is it we who impose our logic on the world or the world which imposes its logic on us? When we take a really close look at it, the world seems to be telling us we can have it both ways: neither particles exclusively nor exclusively waves - and both, a thought anathema to dogmatists and bigots of every stripe. But before we throw up our hands and rush to the sanctuary of either absolute certainty or absolute relativism, we should pause and consider the possibility that what the world is telling us is that its logic is, after all, not exclusively 2-valued but inclusively 4-valued: neither/nor; both/and.

  • WendyKroy1983

    " understanding of the electromagnetic spectrum will help me to
    understand why certain shades of yellow make me nauseous, while electric
    orange fills me with joy."


  • APhysicist

    Mostly, it seems to me that this article argues against a position that very few, if any, physicist really take: it is a composite of extreme sounding ideas from very different sources. It paints the community of physicists, even theoretical physicists, with too broad a brush, by talking for example about «the fashion» in theoretical physics as if all theoretical physics was strings. And whichever their metaphysics, an overwhelmingly majority of physicist accept the confrontation of predictions with experiment as the ultimate arbiter of scientific models. When people calculated the electron self-energy and found a divergence they didn't claim it was actually infinite; they searched for a way to measure it, and for a theory better theory to predict it.

    There were some interesting points on taking equations as reality. But I think in fact, the reification of the mathematical structures of Hilbert spaces, state vectors, and hermitian operators occurs precisely when we ask things like «what in the wavefunction is waving?». Confronted with a concrete proposal for a model (some kind of aether, perhaps?) that can generate testable predictions, physicists will be happy to test them. But when done in such a way that there is no consequence to the answer, physicists will mostly don't care. If I pledge myself to a many-worlds, or a Copenhagen interpretation, the transition probabilities or expectation values I compute will remain the same. How can we, even in principle, tell the difference?

    Lastly, the two-slits experiments are not ambiguous pangolins that we struggle to accommodate; we understand when an electron will be a wave, and when it will be a particle. Both come from the same mathematical structure; it is not so much a matter of mystery but of counter-intuitiveness, of shattering of expectations. We believe a thing has to be one of the other; but experiments show that is not true, so we accept that's the way things are. Theoretical physicists may ask: «what would it be like it they *had* to be one or the other?», and the answer is, not at all like it actually is, in very specific ways, like atoms would not be stable, and so on. So we conclude that, even if at human scales things seem to be either particles or waves, in truth they can be both. That's not a neurotic, ever-refining categorization. Rather, it is the merging of categories when they are shown not to be different after all. What produces a crisis is the rigidity of arbitrary categories, when new facts cannot be fitted in then and are therefore put in a special bin. A pangolin threatens your world view until you understand what makes it a mammal and why it belongs, unambiguously, to that category, even if you have to change your category a bit because you realize that it is not scales that make lizards, but some other characteristic, like a quadrate bone in the skull.. Science successfully proceeds in this way. (Why don't we care so much about renormalizability as we do about predictability? Because we transformed our categories.)

    • margaret wertheim

      Thanks for this very thoughtful comment on my article. I agree that not all physicists are Platonists and some have very sophisticated alternative philosophical views. But the public face of theoretical physics is very much a Platonic one - as represented by Stephen Hawking, Brian Greene, Lawrence Krauss and so many others. I did actually write in the draft of my article that this was an issue regarding the public representation of physics but that got edited out by the magazine. One of the issues here is that the public representation of physics is very narrow yet physicists don't make a fuss about this or try to present more nuanced views. I have participated in many panels with physicists in public arenas when precisely the attitudes I describe were expressed, and any challenge to hard-core Platonism from myself or others was dismissed. I would love to see a broader range of philosophical perspectives presented to the public by physicists, but on the whole that's not happening. Lee Smolin's books are interesting in part because he does try to show other views. It would be wonderful if more physicists like you were willing to challenge the representation of your field as it is promulgated by its current public proponents. It would be especially interesting to hear concrete challenges to Platonism from within the physics community. My characterization is, I think, a fair representation of how physicists are representing themselves. If the article can help to spark more nuanced presentations of physics, I'd be delighted. I hope that indeed, more physicists like yourself, will come foreword.

      • Arnold Trehub

        Doesn't physics have to come to terms with the fact that all of it is a product of human biology? If this is the case, shouldn't we expect that the concepts and the laws of physics are likely to change over time. In particular see Smolin's essay on Edge and my response here:

        • Al_de_Baran

          I strongly recommend that others here who are interested in this topic read Arnold Trehub's linked response to Lee Smolin. It is far more pertinent than the long-winded reply by "APhysicist", for instance, and far more worthy of serving as a focus of discussion.

        • orathaic

          No. From computer science/cognitive theories we can show that certain types of computing machines are capable of solving any type of problem - humans are not capable of coming up with changing kind of physics without changing the tools they use, but they are capable of solving different kinds of problems (maybe not every type of solvable problem, but many)

          We imagine that the physics exists independent of human biology, this is a claim and it is not clear how testable it is. However i consider reality real, independent of me and that we share this common reality.

          Physics may need to come to terms with the limitations of human cognition and learn how to build machines without these limitations in order to uncover better theories, but were we to do so we would likely find it difficult to comprehend those theories.

          • Arnold Trehub

            Orathaic, I too believe that a real universe has always existed, independent of conscious brains. But physics is not reality. Physics is a complex body of human-made propositions and images about what human brains imagine reality to be like. Do you really claim that the propositional canon of physics came into being spontaneously without a source in the human brain? Physics, like all sciences, is a pragmatic enterprise, critically dependent on empirical tests, and it is always open to revision.

            You say "From computer science/cognitive theories we can show that certain types of computing machines are capable of solving any type of problem ...". If this is so, show us how physics can solve the problem of subjectivity/consciousness.

          • Dave Wats

            Of all the sciences Physics is one of the least pragmatic, and is often advanced not by new observations, but by a shift in the way people view the system as they deal with problems I think that one way to approach this dilemma is to view physics as a combination of both empirical observations and rational mathematics to give us a stable enough method for practicing science and technology.

          • brmckay

            I'm curious, what would make (a?) universe more real if consciousness is removed from it's manifestation?

            (Or is it just consciousness as manifested by brains that you are referring to?)

      • Ian McNeal Laue

        Might I suggest "Pythagoras" as a better metaphor for this position than plato. It seems pythagoras put far more focus on mathematics as "real" and "describing reality" while Plato certainly also emphasized math, his use of "the good, the true, the beautiful" however abstract is still human and psychological at the end of the day. Though he certainly was the first to emphasize categorization, then again its that categorization that made science possible. In this context I cant help but think "pythagorean" might be a more apt metaphor.

      • Overleaf

        What is this "nuanced view" that you keep on harking about? I know that "nuance" is a word in fashion today by a certain discredited political faction. But why do you want to force something into it that may not belong there? You are taking a literary-theoretic game and want to impose it on physics, and then you think you have arrived or will arrive at something sublime. Like someone saying if only we could get the internal combustion engine to work with water instead of gasoline, what a wonderful world we would have. Unfortunately it is people like you who discredit physics (and science) by trying to impose a new-agey framework on it, attracting an army of humanities types who think they now have something to add to science. Read the Sokal hoax.

    • MatthewJamesGoodwin

      Nail hit right on the head.

      • Al_de_Baran

        As a sage once observed, when the only tool you have is a hammer, you treat everything as if it were a nail.

        • MatthewJamesGoodwin

          Drilled it flush.
          Placed it square.
          Straight as a die.

          • Al_de_Baran

            That's still a pretty limited toolbox.

  • ordaj

    Maybe Occam's Razor applies. It's an electric universe and there is no such thing as time.

  • Charles Zigmund

    Leaving aside the issue of ultimate truth, physics and the other physical sciences have led to incredible technology which has transformed our lives. Notwithstanding this technology is both good and bad and we may destroy ourselves, in any case the achievement, the mastery and penetrating understanding of natural processes is substantial. The evidence from this is science does move toward closer approximations of reality even if ultimate reality is always out of reach. The author argues for a more inclusive and nuanced view of the world, rejecting Platonic certainty. Yet she is the one demanding a comprehensive reality. Many scientists are satisfied with what passes through the gates of experiment.

  • kage

    The critics of Platonic physicists point to current mysteries in physics and say "there, you can't explain that" or "you're having an awfully difficult time explaining that, huh?" and take this to mean that physics has finally met it's match. But there have always been head-scratching mysteries in physics (and any hard science for that matter), and there always will be. Wave-particle duality is certainly one of these, but it's absolutely false to say that physics has slowed down in any sense of the word in grappling with this. Hard science continues to advance at a rapid pace, an does not need a complete re-work from the axioms on up.

    • David

      well put. Synthetic field theories arose years ago (with string theory being one of the outputs) out of a need to explain experiments better than previous attempts via either first principles, or phenomenological based approaches were doing. There are new, creative approaches being taken every day in science - such work is just not accessible, and certainly not appreciated, by most people, including most writers, :)

  • philipparees

    Following Lester. Perhaps the irreconcilability of contradictory hypothesis is a product of science's embedded requirements for both predictability and observation. The first anticipates the future ( a small gulf in space time), the second divorces mind from event ( another gulf in spacetime). The gulf created between concept and time, and between mind and matter ( however infinitely small) is perhaps the creation of the irreconcilability. Our conceit lies in imagining our intellect is separated from what it observes. What consciousness posits creates, what intellect posits divides. The two fields, mind and matter are perhaps really mattermind but like duck rabbit are a matter of perception because the human brain ( and its though processes) has been shaped by this division. Science cannot escape it, nullius in verba is non-negotiable.

  • DrPhysics

    Although well-written, this article seems to heavily mischaracterize the state of modern physics. Quantum mechanics doesn't present mysteries in the sense of actually generating logical paradox, it's just that the outcomes of the equations are counterintuitive to us. Much as children think Aristotelian physics is intuitive, and talking about Minkwoski space was absurd until relativity came along, we don't have an intuition for quantum mechanical realties like wave-particle duality or entanglement. So instead we talk about state vectors and resolve an entangled state as the sum of some vectors. But just because we can't explain these concepts without abstracting them mathematically doesn't make them not real. Entangled states have been demonstrated in the lab, and they behave exactly like we expect.

    And more of a quibble, but entanglement really isn't controversial, SR just prohibits information transfer faster than the speed of light, but entangled particles just have predefined correlations or anticorrelations dependent on the basis state. So the EPR state mentioned 1/sqrt(2) * ( |0>|1> + |1>|0>) resolves to either |0>|1> or |1>|0> when measured since the vectors are orthogonal, each with 50% probability. So if the first particle has state |0> the other one is |1> and vice versa. This unique determination just means the particles had their relationship encoded a priori, not that we're violating SR.

    It's always good to read an introductory QM textbook with some solid math before writing about QM.

    • margaret wertheim

      I acknowledge in my article that entanglement is real. Zeilinger's work is quoted. Thanks for clarifying about the EPR state of the particles. The experiments that are currently being planned to perform in space with entangled photons are being done precisely because we don't know what will happen. Modern physics has made extraordinary achievements, as my article acknowledges, but there are still large areas of unknown science and QM is one arena in which there continues to be heated debate. Its important for the public to understand that science is a continuing process - which is what makes it so exciting.

  • neal

    I "suffer" from what could be termed mathematical synthesia. Modern physics is a lot like a zookeeper explaining what is observed about the wolves to one that has been raised by such, of course, the irony is broadcast by the results. Even very small things are alive, and play the game of life, maybe the one thing the part with rules and the part that is no rules play together. Now, that is math, but one needs to play along in order to understand, and try to make sense of it. Now, if that sense is grounded in spin, that is Life, maybe, in some nutshell.

  • intempore

    There is no direct way to prevent the "quantification project" from infecting humanity with a mass neurosis. Apart from its material successes, the notion that we must develop a Theory of Everything is a feeling, something ungrounded. It can't be stopped, since there is no way to discern the difference between conquerable uncertainty and radical doubt/ambiguity, no rational means for distinguishing a temporary dilemma from "intended" dilemma.

    It's logical that reason and science cannot see, let alone accept, their own limits. But it's a logic easily overwhelmed by the emotion of going All The Way. Another CERN will only provide a better statistical distribution on the likely existence of the H-B particle. We can never nail it down. It will be too late by the time we realise the misbegotten nature of our reductionist frenzy.

    On this basis, the only way to address the "problem" is to pose and answer the indirect question: why does humanity possess the special attributes of reason and language, yet is, in the end, unable to use them to full effect? Reason can't, by definition, resolve the dilemmas you speak of, but it may be able to resolve why such dilemmas are our lot.

    • Charlie Foxtrot

      What other tools exist that are better suited to elucidating reality than reason and science? Reason and science and mathematics have been the best tools so far at pinning down their own limits--logic has paradoxes it is unable to resolve, but they are all phrased in the language of logic. Mathematics has proofs of its own inadequacy--Godel's incompleteness theorems, Turing's proof that the halting problem was insoluble, Gregory Chaitin's work on incalculable numbers. Science can tell us that electron spins will be up or down with a certain frequency in a known field, but it also tells us that it cannot tell us which--up or down--a particular electron will be, except as a statistical trend.

      Science can be seen as the act of taking data and 'compressing' it down into a core theory which generates it, and so it obviously only works on data sets which are compressible. Surely there are numerous data sets which aren't compressible, and are thus forever outside of the reach of science.

      Ironically, mathematics gives us information theory, which is partially the study of which data sets are or aren't compressible. Information entropy, which is the measure of the predictability of a message, is also THE measure of the compressibility of a message. Data sets for which a very accurate theory can be developed are very compressible--reams and reams of paper can be boiled down to (for example) Boltzmann's entropy formula (s = k log W) plus some small deviancy caused by uncertainty--but this equation takes up much less space than the collected data from which it is derived.

      So what about those incompressible things, the things without patterns which science can't probe?

      Well, those things are random. The fact that compressibility is determined by predictability (as is amenability to scientific theory) means that anything uncompressible (and thus out of reach of science) is by necessity unpredictable. And that means that there are no tools we can use to deal with them.

      You could say "human experience and consciousness" and so forth are forever out of reach of science, but unless they are completely random they're not. The fact that something is comprehensible as a thing and not noise means that your mind detects a pattern in it; and if your mind can do that then so can science.

      In that way, I think you ought to think of science not as a new-fangled materialist worldview but rather as an extension of mankind's inborn ability to recognize patterns. In the end the ONLY things that exist in the universe are patterns and noise, and science is the ONLY way of differentiating the two.

      • Charlie Foxtrot

        What I mean to say by this is that science (in the broad sense of detecting and decoding patterns) is the only method that we have or have ever had of attaining knowledge. The fact that we can put limits on science shows that there are fundamental limits on our knowledge--not that there is some post-science way of learning about the world. Short of a verifiable spontaneous revelation (which is a patently nonsensical notion) such a thing cannot exist. We can never have any measure of certainty about knowledge without the benefit of science.

        • intempore

          There are ways of knowing other than through science and reason. Love is a subjective internal experience, irreducible to a theory or a law, yet it is "real". Woody Allen was not
          being flippant when said the heart simply wants what the heart wants. The gut feel, the mythos, utterly trumps
          logos, regardless of quality facts, regardless of well-honed forensics. Indeed, assenting to an ineradicable unknowingness, the je na sais quoi, is how we ratify the emotional truth of our deepest beliefs.

          Thanks to abuse of this fact by religion for the last couple of millennia, modern secularists can't come at this. What science doesn't know is, by definition, self-evident. You can't apply the scientific method to a rabbit hole - well you can, which is what we are now doing. My point was: once tumbling, you can't resort to reason to slow the descent. We must
          ask less direct questions, ironic questions.

          Yes, science and reason uses patterns. Thus they cannot identify the meta-pattern of their obsession with patterns. For science to produce a Theory of Everything it would need observations from a vantage point beyond the universe. Preoccupied with deliverance from error, the Western mind remains blind to the prospect our lusty quest for certainty is the very error it longs to escape. As the Jewish saying goes: "God laughs. Man thinks"

          • Brian M

            But I think you miss one point, that "the gut" is that very pattern recognition process which science takes and rationalizes and formalizes. "The mythos" again, is generall y pattern recognition, explanation, etc. If the underlying reality is random/incomprehensible, than the mythos will not provide a real answer.
            That is not to claim that everything is true or can be reduced to patterns. You are correct that there are emotional states, feelings, preferences, etc. which may not be easily reducible.

          • intempore

            No, I don't miss the point at all. We may use logos to inform mythos, but they are entirely separate. Just as a great poker player must know probability, Woody Allen will have a view on the pattern-based attributes of his perfect woman. But in the end, the decision totally disregards such limiting information. You go with your gut.
            A random/incomprehensible underlying reality is "evidence" (the only possible evidence one could expect) of this relationship writ large. Reality itself is a "combination" of logos and mythos, physical and spiritual, real and beyond real. We are in a moment of History where society lacks the capacity to acknowledge the ironic, non-overlapping relationship between such matters. And it wont because it implies reason is "useless" - which it is, but only if not admitted.

          • Overleaf

            With a workable theory of consciousness, you will be able to reduce 'love'. To say it is irreducible, is a pre-judgement.

        • Arnold Trehub

          Charlie, science does not detect and decode patterns, people do. For details about pattern processing, see The Cognitive Brain (MIT Press 1991). For more about the biological basis of our phenomenal world, see the following:

      • margaret wertheim

        Hi Charlie: I am a great believer in the value of science as a great exercise in recognizing and describing patterns in the world. I hold with your argument that science - especially physics - is fundamentally a great and powerful pattern-recognition scheme. If I'd had 10,000 words, I'd have talked at length about just that. Part of the purpose of my article was to highlight and celebrate that very power. Many commenters on the story have focused on my idea that there may be limits to that power, but for me a big reason to write the story was to point out the humanities folks how unique and important physicists pattern-recognition technologies actually are.

        You write that the only things that exist in the universe are "patterns and noise." But the issue here is what do we recognize as a "pattern." Newton's law of gravity is clearly a pattern, but what about "love", "empathy", "beauty" and "fear". Are these things, patterns, or noise? Science has many strengths, but there are other domains of representation that also have great power and value - such as literature and sociology. I would argue that The Divine Comedy remains - after 600 years - a remarkable font of "truth" about the foibles of human nature. It is in no way diminishing to physics - or to science as a whole - to suggest that we can find wisdom and epistemological validity elsewhere as well.

        • Al_de_Baran

          As someone wisely observed, "We see not what order there is, but order what there is by how we see".

          There are no preexisting Platonic patterns sitting out there waiting to be found. Patterns are effectively created by different observers, whose sensoria, language, and concepts determine and delimit the patterns they are able to "recognize".

          Therefore, it is the height of human arrogance to assume that our patterns are the "right" ones, and that they represent objective. absolute truth--or even that their patterns exist in any sort of objective or transpersonal way.

          Believe it or not, we poor, benighted Humanities types seem to be the ones who best understand this. For that reason, among others, we don't need sops of praise thrown our way, nor do we need the glories of science and technology's pattern recognition demonstrated or explained to us. In fact, the advocates of Scientism should come to learn from us, and not us from them.

  • Dirac

    I agree with the spirit of the article but I don't think we're dominated by explicit Platonism. Explicit Platonism would be like a Max Tegmark, who's recently said that the universe (in its purest form) exists as mathematical objects. It's a fascinating thought at least to consider. Perhaps the extreme end of the spectrum?

    I'd make the armchair philosophical contention that "red" is still not the same as a wavelength but *correlated* with that electromagnetic wavelength. A lot of mystery still exists in how exactly we categorize qualia. I am reluctant to rule out a more fundamental biophysical explanation that neuroscientists are resistant to pursue as those explanations could indeed be counterintuitive and not conform to the literalist orthodoxies in that domain.

    • ArchiesBoy

      What most of us forget about is the fact of our inherent limitations. We evolved to survive the conditions of this planet, to stay alive and procreate. Everything else is gravy. We weren't designed specifically to understand the universe, and our limitations will probably prevent us even sensing, let alone understanding aspects of Reality that are forever beyond our limits. We are "doomed" to a set of *renditions* of reality, created well within our human physical and mental limits. We can never climb outside the box of our nature.

  • Mark

    Dr Land invented Polaroid film around 1947. He invented a polarizing filter (not the same thing) around 1932.

  • witheo

    I guess we are genetically bound to treat language as a means to describe an alleged extra-linguistic 'reality'. As a dominant paradigm, this persuades us to keep trying to explain to each other what we mean by the things we say and hear, read and write.

    I confess, I've posted this comment on this website only a few days ago, but I think the present discussion can accommodate my central thesis: Words cannot convey meaning.

    Every speaker relies on a competent listener to make sense. Language cannot create meaning. Each brain is called upon, consciously and unconsciously, to invest language with meaning, each and every time afresh. Each iteration will always be slightly different and unique, just so long as the “I am” of consciousness is present to make the observation. When we read or listen, we see marks on a page and hear the sound of speech, raw sensory stimuli (bearing no logical relationship to words, sentences or books) of which the brain "makes sense".

    However, if we did all see and hear the same things, we would all make the same sense of one “real world”. Of such assumptions is “common sense” made. It is our eminently convenient and indispensable assumptions that are offended by 'metaphysics', 'figments of the imagination' and 'optical illusions'. But we forget, illusions are no bad thing. To the extent that we are rarely aware of the requisite evidence, most of what we know is fiction. All language is ambiguous, wide open to translation, interpretation, reiteration. All meaning is determined by the particular pretext, context and sub-text.

    Human knowledge is based on elaborate narratives, essential for a sense of “reality”, just to get out of bed, to get along. We must believe there’s only one dominant narrative. We send our children to school, drive a car at speed, believe a green light means it's safe to proceed. And we expect to arrive safely when we board a plane. But we know it’s not true. I cannot see the world through your eyes. We cannot get into each other's head.

    If we all saw the same world, there would be no need for language, religion, lawyers. But the “real world” is not made of cold, hard facts. We are obliged to take each paradigm as we find it, from our own point of view, derived from the unique circumstances of each birth, upbringing, education and life experience. We each construct a different narrative, we have no choice. But much of each of these narratives seem to overlap, like so many holiday snapshots – only the faces look different – producing the pervasive illusion of "one universal reality".

    The world, as we each see it, is not governed by dictionary definitions and the laws of physics and math. Rather, we are obliged to all make our very own, unique sense of an immensely complex, constantly changing and ephemeral web of interconnected relationships.

    We talk about objects, people, events, invoking the usual specific definitions; ‘The United States’, ‘The Second World War’, ‘my house’, ‘God’, ‘our wedding day’, ‘democracy’, ‘happiness’. But no two people can ever hope to agree in detail – and there's the rub – on what each label should mean. Every parent, teacher, doctor, politician and preacher knows, there's many a devil in the detail.

    Meaning cannot fly through the air. “Communication” is not exchanging information, but irritating each other’s brain to make sense of what we see and hear.

    • Frank Knarf

      Discuss the global telecommunications network and the processor in your computer in this context. How did these things come into existence and why do they function predictably.

      • witheo

        Yo, Frank. How’s it hanging in Boise? 90 in the shade today, I believe. Thank you for that delightfully illuminating provocation. I appreciate it. I’ll take it as a compliment, confirmation that I’m worth the effort. I hope you will take this likewise and with equal equanimity.

        But I don’t think I can do your question justice. At least, not to your complete satisfaction. Absent a question mark, I am obliged to interpret your post as rhetorical rather than interrogative. The questions are ever legion. And ubiquitous. Rhetorically mute, like the telephone. But, once fitted with that impertinent question mark, the confounded literary device is ringing, imperiously demanding an immediate response.

        Your (deficient?) punctuation rather beautifully illustrates my problem with language. Other than the words you chose to use, I have no way of knowing what you might have had in mind, or thought you meant, when you wrote them. So I have to guess. As you do, when you read this.

        However, for what it’s worth. In the context of my text, I shall treat your “global telecommunications network and the processor in [our] computers”, as mere cold, hard facts. When I’m speaking, the “real world” is not made of these. Any more than my left foot, the Milky Way, or Napoleon are part of my real world, until they enter the current narrative. Not before. (The possessive pronoun is central to my thesis.)

        By conjuring with such ‘common knowledge’ terminology, crudely excised from any discernible narrative, we conveniently avoid the detail. That is how we arrive at a resolution, a consensus, if you will. Climate Change, gun control, whatever. To make peace and sign the contract, we avoid the detail. After all, that is how we managed to get a dozen men on the Moon: Stick With The Program. (Never mind that your Mom is sick in hospital. Don’t let your own real world narrative intrude in the job at hand.) That is the only way to survive a tour in Iraq. Without losing your marbles.

        It’s whatever narrative each of us happens to attach to the cold, hard artefacts from time to time that makes them real. And, because of where I’ve been and what I’ve seen and heard, my narratives can never be your narratives. That is why I say, the “real world” is not made of cold hard facts.

        I will not claim that is what Lee Smolin meant to say in his ‘Time Reborn’. But that is what I read into the text (past tense). Tomorrow, or whenever I read a book a second time, I know I will read very different perceptions into the same text. Which the author may very well vehemently disown. Because, inasmuch as this computer was different last week, I am not the same person I was yesterday or will be tomorrow. I don’t even know when or where I was born. I wasn’t there. All I have for evidence is this here piece of paper. And hearsay. I gotta believe something.

        As I was saying. The meaning we put into a text is derived from the pretext, context and sub-text.

        The pretext is our ‘hidden agenda’. Yes you do, we all have hidden agendas. Our very own a priori knowledge, on which we all depend to make sense of any “breaking news”, the things we had never heard of until that moment. That, and all our reassuring assumptions.

        The context, within which we make sense of any text, written and spoken, is vast. It includes not only time and place, but mood, background and ambient sounds, blood chemistry, last time you ate, air quality, everything you plan to do that day, things you have to remember not to forget, as well as such vital banalities as your inner ear, by which your brain keeps tabs on the centre of the Earth – without which, you could not sit, stand or walk, let alone run, or read these words. It’s our sixth sense, as vital as the (more) famous five.

        Sub-text. Yes, Virginia. There is always a sub-text. I know, we say “the Bible says …”, or “I see where Obama said …”, or “It says right here on the label …”. But that’s because we want to believe that we know, and we have no choice but to believe that we know, that the “I” that I am knows, not only what I’m talking about, but also what s/he’s talking about. All the stuff that’s stuck between the lines. That is, my private interpretation of the text. And that is all that matters to me.

        Two weeks ago, the following comment was posted, under your tag, on a Chronicle of Higher Education discussion about “Where Thomas Nagel Went Wrong”:

        Frank Knarf (25 May 13) “This is not about what science is doing, it is about what the world is doing. Some hold the view that there is no world outside our skulls, or the weaker version, that there may be a world but it does not matter. Stupid indeed.”

        But then, in March last year, on about “Fink: God is not so easily explained”

        Frank Knarf wrote (March 2013):

        “Dawkins makes a convenient foil for this sort of thing, but Dan does not mention that Dawkins is right about evolution and the southern evangelist is wrong, a distinction that ought to count for something. Most atheists don't deny that goddesses are real in the same sense that other products of the human imagination are real, and many atheists admit that imaginary beings are worth contemplating. Both Moses and Captain Ahab have things to tell us.”

        Assuming there is only one Frank Knarf on Earth at any one time, we must acknowledge that the real FK can never stand up. I don’t even know who I am really supposed to be, or when and where I’m really at home. We play roles. Some more convincingly than others.

        Nevertheless, last month this FK dismissed the view that “there is no world outside our skulls” as “stupid indeed”. Two months earlier the same FK claimed to know that “most atheists don’t deny that … products of the human imagination are real …”.

        Memory and imagination. It’s what we all depend on, to make our very own sense of everything we see and hear. It’s just that, by definition, my memory and imagination (that possessive case again) cannot, by any stretch, match yours.

  • Albert Nahnimmus

    i get the idea, but here's what's so contradictory about wave-particle duality: a particle is 0-dimensional, whereas a wave is multidimensional. it's fundamentally unequal: literally, the definition of waves and particles (and lines, 1-dimensional objects, if they exist in nature) can be said this way: particle =/= line =/= wave =/= particle. anything that can possibly exist, by definition, must be in one, and only one, category. and that's the paradox: quabjects (the name i give to quantum objects) are counter-definitionarily both particles and waves.
    i know i put a lot of emphasis on the word "definition", which this article's whole point is that that's the problem, but what i mean by something being by definition something else is that the limits of our minds can only comprehend the first something being a member of the second something's category.

  • Bruce W.

    All very nice theories but because we fit a mathematical description as far as can be seen doesn't mean it is true.
    The song writer might have been right with "it ain't necessarily so."
    Actually, the further the physicists and mathematicians go the more a quite like the idea of God.

  • ArchiesBoy

    Actually, I suspect Reality is not simply "two things," the big and the small, but an indivisible sliding scale of various atomic and subatomic behaviors based on levels of complexity. I suspect it's more like the division of colors in the rainbow. Where does one color leave off and another begin? The whole thing is an illusion, and arbitrary at best. This bifurcation of reality also seems to me arbitrary, and will only be in vogue until more knowledge is collected. And let's not forget that human knowledge goes from cutting-edge to obsolete extremely rapidly.

    Reality is what it is. It operates perfectly according to its nature, and human beings will, because of our inherent limitations of mind and body, never be able to get more than a narrow rendition of it, no matter how bright the brightest minds of the day, no matter, how sophisticated our technology, how much we discover. However much our machines can detect, it still must be boiled down and translated to a version that the human body can sense. I suspect there are aspects to it that will be forever beyond our ability to even sense, aspects that are beyond our ability to even conceive.

    For the same reasons that your cat will never be able to read the sports page, I posit we will never be able to discover the entire story of the nature of Reality or even come close.

  • CE Lathrop

    Instead of "nauseous," you mean "nauseated." If you're nauseous, you make others ill. Unless you're both, like a wave-particle.

    • barry

      British and American usage diverges here. All Americans would understand the writer without flinching.

  • Ashish Dalela

    Niels Bohr was not a positivist. But he introduced the idea of complementarity in quantum theory stating that we have hit a limit in language where our language can only describe things in complementary ways and not simultaneously. He also insisted that we cannot use any other language except the language of classical physics, because only that language maps the reality to our sense perceptions. And for science to be empirical we had to continue to use sense perceptions.

    I believe that we haven't understood language yet. We think that language is a physical set of signs to which we give meanings (a la Descartes who separated mind from matter). Can language itself carry meanings, such that there are two things in nature - a physical token and a meaning? We commonly see a complementarity between tokens and meanings. For instance, the color red can denote ideas of "stop", "danger", "passion", "war", etc. If you looked at red you can interpret it in many ways. Science lacks this property of "interpretation" or meaning, which exists in ordinary language, but not in mathematics.

    In this regard, Semoticians (e.g. Ferdinand Saussure) talked about the relation between signifier and signified and as the above example illustrates, you can think of signs exhibiting complementary properties.

    So, there can be a deeper relation between physics and language, but in a different sense than you have pointed out. The language of mathematics has reached a limit in describing nature, because this language only represents syntax and not semantics. If linguistic signs represented meaning as well, then you could see that each sign had two aspects, which are complementary.

    The interesting question is - what would it take for mathematics to be like ordinary language? Such that we can use that mathematics to describe nature as both a token and meaning, which do not violate our intuitions?

    • margaret wertheim

      If mathematics were like a natural language, then in Douglas' view, the semantic limits she describes would certainly apply. The more challenging question is do those limits apply to a non-natural language, such as mathematics is now? Many commentators since the seventeenth century have tried to ague that, effectively, math can escape the "confusions" of natural language and thus give us a category system that is more pure and direct and totalizing. I believe that Douglas is correct and that math itself is subject to limits as a language for categorizing "reality."

  • Mathgradstudent

    First a qualification: I know very little Physics. Growing up I used to devour popular physics books, but I found them more confusing than illuminating. At the time, I really had no explanation for it. Now, however, after having struggled through a few years as a math grad student, I've a theory for what was happening. I also think, perhaps stupidly, that many philosophical problems in physics stem largely from a similar source, which is that a great many people still believe that physics, like anthropology, can be spoken and thought about using languages like english. Mary Douglas' analysis is itself bound by the concepts made available to it by the language she uses, for example, the notion of 'categories'. She has assumed that English is sufficiently equipped to deal with her subject matter.

    But, why is it plausible that language and the concepts it makes available to us - something that evolved during a period radically different from now, with different challenges none of which involved understanding what happens at planck scale - is even remotely suitable for grasping the world?

    In grad school, one learns many mathematical concepts which have no analogue in english and ideas which cannot be explained in english. But, some of these ideas and concepts are exquisitely well-suited to understanding the world.

    By this I don't mean that mathematics is a language. I think this metaphor (as beautifuly captured in Galileo's quote) is itself a big part of the problem. In truth, mathematics is nothing like any of the languages that I know.

    At this point, I just want to point out the unfortunate fact that high school does not really convey any idea of what mathematics actually is. Numbers, though are things of joy forever, are not the only mathematical objects out there. And, math can go beyond just 'quantification.'

    The trouble begins when we try to explain the world using language instead of mathematics. To be honest, I found Stephen Hawking's A Brief History of Time quite baffling. And, it was precisely because he decided to eschew the math. I have no problem understanding a fact about the universe such as 'the Poincare group has no cohomology'. However, english sentences can't both talk about what that fact says and at the same time not be baffling.

    Perhaps the way out of the fly bottle in the case of most philosophical problems in physics (for ex: how can something be both a wave and particle?) is to simply realise that languages are ill-equipped to talk and deal with nature at every level of discourse. And that the problems modern theoretical physicts face are not really philosophical issues but mathematical ones.

  • John Merryman

    I think the problem with time is that we experience it as a sequence of events and so treat it as a vector from past to future, which physics re-enforces by treating it as a measure of duration, but the underlaying cause is that it is change, due to action, which turns future into past. Tomorrow becomes yesterday because the earth rotates, rather than the earth traveling some fourth dimension from yesterday to tomorrow. Duration is not some vector transcending the point of the present, but is the state of the present between events.

    The reason clocks run at different rates is because change happens at different rates. If time were a vector from past to future, one would think the faster clock moved into the future more rapidly, but the opposite it true. It ages more rapidly and thus moves into the past quicker. Ref; the twin in the faster frame dies before the other returns.

    This make time an effect of activity, much like temperature. Time is to temperature, what frequency is to amplitude. Temperature gets short shrift because we think of it as just a statistical measure, but those particles, molecules, whatever, exchange energy, so it is a localized entropic state. The most elemental states of matter, such as vacuum fluctuation, or cosmic background radiation are better described in thermal terms, rather than temporal terms. We could even use ideal gas laws to construct a "temperaturespace." Which is to say "spacetime" is correlation, not causation. No "fabric of spacetime," any more than there are giant cosmic gearwheels. So no expanding universe. Redshift is probably due to not fully understanding the wave properties of light and thinking photons travel as point particles for billions of lightyears, when a wave action would be much more logical, as well as distribute the energy.

    • John Merryman

      Also it is probability collapsing into actuality which causes events. The probability is the cat is either dead or alive in the future, but the actual sequence of events will decide its fate.

  • lukelea

    For questions of this kind I trust Lubos Motl. He discusses them in his inimitable style here:

  • annou

    This fine article echoes somewhat the recent small book of Thomas Nagel, "Mind and Cosmos". He points out that there are kinds of data (e.g., consciousness) and patterns of data that are not empirical and and not describable by math. He has caught hell from some scientists for daring to say so
    out loud, especially since he also suggests that a (non-theist) teleology might help clear up the mess at the foundations of science.

  • Luigi Foschini

    Great essay! I too am in favor of the linguistic view of mathematics, but not as Platonist. You might find interesting my recent essay on a similar topic:

  • beachcomber

    Wonderful essay and some very erudite comments, but as a complete non-mathematician, isn't the hard problem really that we as sentient beings (and perhaps even artificial intelligence) can never be entirely objective, and so the glimpses of perfection in mathematics and physics will forever remain that as a consequence of our subjective state of being?

  • Granite Sentry

    Been saying for years that the problem is with the ineffective measuring tools we're trying to work with. Like any other language, mathematics has its limits. For example, how can there be an infinite number of points in a limited space between any two points on a line?

    • Bacon Pancakes

      Step 1: Define a and x0 (a < b) as 2 real numbers (any line can be modeled as the real number line)
      Step 2: Average a and x0, yielding x1 ([a+x0]/2 = x1)
      Step 3: Go to Step 1, inputting x(n-1) in the place of x0 for the nth iteration and yielding xn which is used in place of x0 in the n+1th iteration. (i.e. the first iteration yields x1, the next x2 etc.). This produces an infinite loop giving an (in this case countable) infinity of numbers (points) between a and b.
      The problem in this case is not the limitation of maths but that it exceeds some people's capability to be intuitively familiar with it (that's not to say maths doesn't have its limits, see Kurt Gödel's incompleteness theorems). The most straightforward problem I see with your actual argument is that maths has been made in order to overcome the limits of the old maths, especially if the limits are in modeling reality with it. This is why Newton developed his calculus.

      There are some problems I see in the discussion itself about the limits of science. One is that it covers a plethora of subjects, historical cases and philosophies so the discussion tends to get confused, misinformed and "all over the place" by leaving crucial bits of opinion or information vague. In a discourse about it clarifying each others opinions on determinism and such might be forgotten leading to irritation for both parties because of a failure to communicate certainty about the meanings, at face value and underlying, of each others words.

      Another is that in order to talk science one has to actually know (some) science and be familiar with how science and scientists work and what philosophies they are mostly going by. This would help people avoid basing their central arguments on a big misunderstanding.

      Lastly, at least in my experience, the debate has mostly centered on physics and it seems many don't realize how meta the discussion is (the point, made somewhere in the comments, about physics being based on biology is quite true, but as is biology). (Also, I'm more interested in other things than this debate at the moment so if you reply don't expect a reply back from me.)

      • Bacon Pancakes

        *x0 not b

  • David

    Came to this article via link from the BBC site when i was reading my mid-morning news.. Perhaps the author is related to Michael Wertheim, an icon in statistical physics? So I read a bit ...

    Like 'APhysicist,' I have the impression the author is addressing issues of little interest to physicists. I am not as kind as 'APhysicist' in going beyond that statement, as I have seen this sort of confusion all too many times before. So in spite of her (extensive?) contact with theoretical physicists, I posit that Ms. Wertheim lacks an understanding of the scientific method(SM), and the lens that it gives scientific investigators.

    Here the SM in a nutshell: Reality is what we measure. Theorists piece together heuristics, hypotheses, theories, and finally physical laws in a time honored process. Theories have validity only when they can predict the results of independent experimentation/measurement. Physical laws are scientific theories which have withstood the test of time. Interpretations of the equations that underpin theories are an essential part of the theorists work. HOWEVER: Explanation about why things are the way they are, and other deeper truths are left to philosophy, including religion.

    This is the view of every true scientist (as opposed to zealots) I have ever met, whether in Academia, Bell Laboratories, Government etc. And those who call themselves scientists and who go beyond the framework of the scientific method lose credibility very quickly if them attempt to bring philosophy into scientific discussions. This is why most scientists tread very lightly when they speculate, and usually say so very clearly - eg Freeman Dyson's old Rev Mod Phys piece. This is also why true scientists generally stay away from political issues, in public anyway.

    btw, for what it's worth, my PhD was with another icon in Statistical Physics, a Boltzmann Medal winner. But this just means that I was well trained, not that my conclusions mean anything. Judge for yourself!!

    • witheo

      Excuse me? You dare surmise “Ms. Wertheim lacks an understanding of the scientific method"? That she would rise in your estimation if only she were “related to Michael Wertheim, an icon in statistical physics?” Perhaps you're right; you really ought to “read a bit …”

      “Margaret Wertheim is the writer and host of Faith and Reason. She is an internationally noted science writer and commentator, originally from Australia and now living in Los Angeles. She has written extensively about science and society for magazines, television, and radio. She is the author of two books: Pythagoras' Trousers, a history of the relationship between physics, religion, and women, [W.W.Norton]; and The Pearly Gates of Cyberspace, a cultural history of space from Dante to the Internet, [W.W. Norton, Feb. 1999].

      Margaret has two science degrees: a Bachelor of Science majoring in pure and applied physics, and a Bachelor of Arts majoring in pure mathematics and computing. For fifteen years she has worked as a science writer, first in her native Australia and now in the USA. Her articles have appeared in many magazines and newspapers including The New York Times, The Sciences, New Scientist, Omni, Science Digest, The Australian Review of Books, 21C: Magazine of Science, Technology and Culture, The Daily Telegraph (London), Die Zeit (Germany), Australian Geographic, Vogue, Elle, and Glamour.

      Margaret has written ten television documentaries, including the award winning series Catalyst which she conceived and co-directed. Catalyst is a six-part series about science and technology aimed at teenagers. Margaret has also written and directed three interactive video programs, including the Canadian public health program What About AIDS; and she has produced several short films. Margaret has appeared frequently on television and radio in the USA, Australia, and Europe talking about science in a social context. She is a regular guest on the Canadian Broadcasting Corporations weekly TV current affairs program Sunday Morning Live, and has been a contributing reporter on the PBS program Religion and Ethics News Weekly.

      Margaret lectures regularly about science and society, and about science and religion, at universities and colleges across America - and also abroad. In 1998 she was the Australian Broadcasting Corporations official spokeswoman for Science Week. She has recently been on a lecture tour of South Africa, speaking about the interaction between physics and religion both historically and today.”

      And in the read corner:

      Dr. Michael Wertheim retired as Professor of Physics at the end of Spring Semester 2003. He joined the Physics Department [Michigan Tech] in 1990 as a Professor. He received his PhD in Physics in 1957 from Yale. Before coming to MT he held faculty positions at Rutgers and University of Guelph. Dr. Wertheim specializes in the theory of liquids, using statistical mechanics to calculate the thermodynamic and dielectric properties of fluids. He has advanced basic theory, computed results for chemical engineering, investigated bulk fluids, studied polymerization and inductive forces, and contributed to the modern theory of the gas- liquid interface."

      You “have seen this sort of confusion all too many times before”? Really?

      The problem with science, as even Einstein could appreciate, is how to communicate intelligibly with your audience. As you are trying so admirably and patiently to do here, with your “SM in a nutshell”. But are you connecting? Is the language we use reliable? What of the inherent ambiguity?

      “Reality is what we measure.” Define reality.

      “Theorists piece together heuristics, hypotheses, theories, and finally physical laws in a time honored process.” As do theologians, shaman, astrologers, economists, political commentators …

      “Theories have validity only when they can predict the results of independent experimentation/measurement.” According to whom, possessed of whose qualifications, with whose money?

      “Physical laws are scientific theories which have withstood the test of time.” So have Zionism, Capitalism, Racism, Eugenics, Mysticism …

      “Interpretations of the equations that underpin theories are an essential part of the theorists work.” Not unlike common Scriptural Hermeneutics, is it?

      “HOWEVER: Explanation about why things are the way they are, and other deeper truths are left to philosophy, including religion.” Translation: “We just say how it is. What you make of it is not in our brief.” Pilate washing his hands.

      “This is the view of every true scientist you have ever met”? You must have privileged access to an awful lot of private mail. I’m not even sure of my own “views”, from one day to the next. Are you?

      “Those who call themselves scientists and who go beyond the framework of the scientific method lose credibility very quickly …” Define credibility, according to whose criteria.

      “… if them [sic] attempt to bring philosophy into scientific discussions.” Doesn’t that rather depend on what you mean by “philosophy”? Can you really breathe, in a world made entirely of cold hard facts, devoid of esoteric contemplation, poetry, music?

      “This is why most scientists tread very lightly when they speculate, and usually say so very clearly.” Most? You must have to keep in intimate touch with an awful lot of people. Who has the time?

      “This is also why true scientists generally stay away from political issues, in public anyway.” Oh dear. “True scientists”? Can you really sit there and seriously claim that what you are doing when you post a comment on the Internet is not in any sense political? If you're in any sense human, you cannot practically, intellectually, physically or morally "stay away from political issues".

      “For what it's worth”, don’t you see, 'David'? Your anonymously post-scripted qualifications really do genuinely lack the slightest credibility, as they cannot be independently verified. “Judge for yourself!!” Indeed.

      In the end, it’s not even a question of what to believe, nor what you can or indeed ought to believe. In the final analysis, it comes down to what you must believe and what you want to believe. It takes a special kind of wisdom, peculiar to none, to appreciate the difference.

  • margaret wertheim

    I'd like to respond to some of the comments posted here by physicists. One of the purposes of this piece was to show how physics, with its mathematical formalisms, is a very special way of knowing, uniquely capable or revealing certain kinds of truths. The project of quantification and its success is something my article seeks to celebrate. Part of my intention was to explain to folks in the humanities why and how the language of mathematics is not "just another" language, like Chinese or Italian, but a very different form of language that has especially powerful pattern-describing powers. As I say, it would not be possible to express in any other language the relationship between electron spin and electric fields, and other such quantum qualities, that have enabled us to build microchips and other technological marvels. Math as a non-natural language has powers of expression we don't find elsewhere.

    That said, I believe Mary Douglas is correct that all linguistic systems have limits in their ability to categorize reality, including math-based systems. We are up against the age-old dilemma of what the medievals called the debate between "realism" and "nominalism": Are our categories "in the world" or "in our minds"?

    The Platonist position is one of realism that sees mathematical categories as having a kind of super-real status. Most of what is presented about physics in the public arena presents a highly realist philosophy - Stephen Hawking, Stephen Weinberg, Lawrence Krauss, Brian Green, Max Tegmark are just a few of the current realist superstars. Some commentators have objected that not all physicists are Platonists and that is so; but these are not the positions we hear publicly. If one of the consequences of this article is to encourage non-realists to step forward, I would be delighted. Part of what we face here is public relations issue: Why does realism dominate public representations of this science? One answer is that realism sells. Books, science magazines, and TV programs like NOVA, constantly support a realist metaphysics. I agree with "Aphysicist" below - we need to hear more nuanced views from physicists themselves.

    Regarding wave-particle duality: Physicists have of course made tremendous advances in understanding this duality over the past century. Yet mysteries remain. Work over the past decade has shown that quantum entanglement is a genuine feature of our world. Einstein was wrong. John Bell was right. But to suggest, as some commentators have, that our current understanding of this phenomenon transcends the tension between a quantum understanding (which is now well articulated) and special relativity, is disingenuous. Either something happens here between the 2 particles that is outside the collapse of the wave function - in which case, as Einstein believed, there is potentially some sort of classical relationship going on. Or there is only quantum correlations, and in that case, as the Wikipedia entry on the subject states "part of the transfer happens instantaneously." Wiki is of course not the final word on any subject, but the reference is from Nature magazine. Physicists continue to disagree about how to interpret and understand entanglement, which is precisely why it is such a fruitful area of research.

    • witheo

      If I may say so, Ma’am, I am much relieved, to see you quoting from Wikipedia. Your laconic ice-breaker, “I'd like to respond to some of the comments posted here by physicists”, could engender the (unintentional?) impression that even here, on a publicly accessible website (wohlbemerkt), comments from the “great (non-physicist) unwashed” shall be studiously judged unqualified, read: patently unhelpful.

      But, with respect, how do you recognise a physicist on-line? As you may recall, the Biblical injunction reads, “By their fruits ye shall know them” (Matt. 7:20). Not by their words. Wasn’t it Einstein who intoned, “If you can’t explain it to a six year-old, you don’t understand it yourself”? But what did he know. What’s it like to be six anyhow? Anyone? People used to listen to their elders.

      I’ve been toying nightly for more years than I care … with this idea.

      (The only problem with the loneliness of growing old, disgracefully remembering to forget about having fun, is that you’re not dead yet. And the really funny thing about not being allowed to die, when you’re too old to remember what it was like to have fun, is that you’re expected to die laughing. In a pleasantly situated last resort.)

      In my experience, if you don’t want to upset anyone, don’t say anything. Oh, you can talk, by all means. A lot of people talk without saying anything for that reason. Not that they don’t have anything to say. They prefer not to say anything for fear of upsetting somebody.

      That said: Rather than accept Descartes’ “(self) consciousness” as irrefutable evidence of one’s being-there-ness, perhaps we ought to admit that it’s not our alleged “thinking”, but, rather, the very conscious act of saying “I am”, the actual and very deliberate mobilisation of the words, that serves as the only requisite, axiomatic proof.

      If the pursuit of science (both its quarry and method) is nothing if not utterly dependent upon “our” socio-culturally defined linguistic “discursive practices”, all “knowledge” will always hang utterly and abjectly by the gossamer thread (threat?) of the universal position of speech, “I am”, the only locus from which it is possible to articulate language, strictly confined by rules of syntax and grammar, to make known (comprehensible) what is (but temporarily) knowable.

      I’m sure it wasn’t Wittgenstein who first bemoaned the “tyranny of language”. Here is Thomas S. Kuhn (The Structure of Scientific Revolutions, 1962, 169-70):

      “We may... have to relinquish the notion, explicit or implicit, that changes of paradigm carry scientists and those who learn from them closer and closer to the truth... The developmental process described in this essay has been a process of evolution from primitive beginnings—a process whose successive stages are characterized by an increasingly detailed and refined understanding of nature. But nothing that has been or will be said makes it a process of evolution toward anything.“

      Also from Wikipedia:

      “Competing paradigms group concepts in different ways, with different similarity relations. According to Kuhn, this causes fundamental problems in communication between proponents of different paradigms. It is difficult to change such categories in one's mind, because the groups have been learned by means of exemplars instead of definitions. This problem cannot be resolved by using a neutral language for communication, according to Kuhn, since the difference occurs prior to the application of language.

      Kuhn’s perspective was replaced in the 1970s by a localist and semanticist vision in which incommensurability is now defined as the relationship between two theories that are articulated in two languages that are not completely interchangeable, as Kuhn states in the following extract:

      “The phrase "without common measure" is converted into "without common language". To state that two theories are incommensurable means that there is no neutral language, or other type of language, into which both theories, conceived as sets of statements, can be translated without remainder or loss... [Although] the majority of the terms shared by the two theories function in the same way in both…”

      Or take as another example of linguistic mystification this Wiki discussion on algorithms:

      “Algorithms can be expressed in many kinds of notation, including natural languages, pseudo-code, flowcharts, programming languages or control tables (processed by interpreters). Natural language expressions of algorithms tend to be verbose and ambiguous, and are rarely used for complex or technical algorithms. Pseudo-code, flowcharts and control tables are structured ways to express algorithms that avoid many of the ambiguities common in natural language statements.”

      It turns out that, while an algorithm has something to do with the attempt to write a precise list of precise instructions for the calculation of mathematical problems, the term ‘algorithm’ defies precise definition.

      “While there is no generally accepted formal definition of "algorithm," an informal definition could be "a set of rules that precisely defines a sequence of operations." Which would include all computer programs, including programs that do not perform numeric calculations. For some people, a program is only an algorithm if it stops eventually. For others, a program is only an algorithm if it performs a number of calculation steps.”

      And further:

      “The concept of algorithm is also used to define the notion of decidability. That notion is central for explaining how formal systems come into being starting from a small set of axioms and rules. In logic, the time that an algorithm requires to complete cannot be measured, as it is not apparently related with our customary physical dimension. From such uncertainties, that characterize ongoing work, stems the unavailability of a definition of algorithm that suits both concrete (in some sense) and abstract usage of the term.”

      I rest my case.

      • margaret wertheim

        Hi Witheo: Thanks for you Kuhnian response here. I enjoyed your thoughts on the incommensurability of differing explanatory systems. My opening line was not in any way intended to ignore or dismiss "the great unwashed" (my father used to adore that phrase when I was a child) - I just need to respond to some of the physics comments because they have been rather consistently critical in certain ways that I feel need to be addressed. But of course your point stands - as a great New Yorker cartoon once opined: "On the internet nobody knows you're a dog", or anything else for that matter.

        • Al_de_Baran

          "Math as a non-natural language has powers of expression we don't find elsewhere."

          So does poetry. In fact, I think that your next project should be to explain poetry and poetic thinking to "non-humanities folks". They seem to be much more in need of instruction on that subject than we do on science and math.

          • witheo

            When the lamp is shattered
            The light in the dust lies dead—
            When the cloud is scattered
            The rainbow's glory is shed.
            When the lute is broken,
            Sweet tones are remembered not;
            When the lips have spoken,
            Loved accents are soon forgot.

            Explain Shelley?
            No matter how expressive, if the cadence falls on deaf ears …

          • Al_de_Baran

            "Explain" was a poor word choice, but I wasn't referring to an explication de texte. In any event, "describe" would be a better choice.

            Either way, though, the incommensurability would be illustrated, the Great Scientific Unwashed would be illuminated, or at least educated, and that would complete the reciprocal good deed.

          • witheo

            Describe poetry and poetic thinking? Good Lord. In any event?

            I’m not sure. To even attempt to describe the internal combustion engine is surely to explain how it works, n’est ce pas? And that, of necessity, by taking it quite apart. Then, when the workshop is fairly littered with nuts and bolts and what not, we go to lunch, rejoicing in the knowledge that now we know how the infernal what’s it would have worked, had we left the thing alone, beneath its shiny bonnet, intact.

            Likewise, describing “poetry and poetic thinking” may be not unlike the peeling of an ordinary white onion. It behoves one to know, eyes watering, when to stop.

            But I’m not quite sure how, precisely, that would illustrate (demonstrate?) the alleged incommensurability between ‘Science/Math’ and ‘The Humanities’.

            I must say, I do like your unabashed double entendre, “the Great Scientific Unwashed would be illuminated” – neatly implying the coincident exposure and enlightenment of said uncouth, rational, evidence-based technophile, once suitably constrained to read poetry.

            However, while ’tis said, “in spring a young man’s fancy turns to love”, I’m not sure that brute exposure to raw romance would necessarily turn an inveterate nerd’s head, any more than pure calculus a dreamer.

            In any event, I’m not as sure, as perhaps once I was, about this whole left brain/right brain dichotomy. After all, Alice’s father, Charles Lutwidge Dodgson (aka Lewis Carroll), of Wonderland fame, was, it must be said, among many other delightful things, a mathematician, logician, Anglican Deacon and photographer, all of a piece. It turns out, as luck will have it and it would appear, language and math actually do exercise pretty much the same regions of the brain.

            It simply will not do then, are we agreed, to dismiss out of hand those of scientific bent as poetically illiterate?

          • Al_de_Baran

            I hoped that the ironic tone of my reference to Margaret's noble attempt to explain to Humanities types what physics actually does was apparent. It seems not.

            At any rate, if "whereof one cannot speak, thereof one must be silent" applies to describing the poetic mind, then it certainly should apply to the scientific mind, as well. I look forward, therefore, to your chiding and nitpicking at Margaret on this point.

            "It simply will not do then, are we agreed, to dismiss out of hand those of scientific bent as poetically illiterate?"

            This statement demonstrates a rather spectacular missing of my point.

            Also, I never raised the subject of brain lateralization. The entire left-right brain thinker dichotomy has been long refuted, and has nothing to do with my point.

            Roger Cardinal's Figures of Reality: A Perspective of the Poetic Imagination does a fine job of exposing the workings under the hood without leaving lots of messy nuts and bolts about.

            And no, to describe is not to explain.

            Signing off, now.

          • witheo

            The judge's decision is final and no correspondence will be entered into.

          • Al_de_Baran

            "and no correspondence will be entered into."

            Thank Alastor for small favors!

        • witheo

          Thanks Margaret, I appreciate it. You thank, therefore I am. Bit like, you drive, I’ll follow you on the map. The symbiotic relationship of two personal pronouns; you scratch my back … Could a feral child, bereft of the intuitively nurtured I/you dichotomy, even perceive the other?

          On that note, I do wonder, now, what it was about the unwashed your father adored so much. Perhaps it really isn’t just the roar of the grease paint, after all, that keeps us coming back for more. But why add, “when I was a child”? You mean, like Einstein, he could only appreciate the term by invoking it when you were six? Lovely analogy. Who is instructing whom? Recalls the Wordsworth-inspired Blood, Sweat & Tears debut album, The Child is Father of the Man.

          Finally, on being a dog. You’re referring of course to Peter Steiner’s classic cartoon, published 20 years ago next month. The point being that not even my dog knows he’s a dog. His being a dog is what I make of him. And only when I say so. Not before. The subtle distinction between whether it’s “the physicists” or “the physics comments” that are consistently critical, serves as a beautiful case in point: Is it I under investigation, or, “was it something I said?”

    • physics student

      The only reason you'd think that there's tension between quantum mechanics and special relativity is that you're trying to force a metaphysics onto quantum mechanics that doesn't fit. You're either unjustly assuming hidden variables, or unjustly reifying the 'state' and assuming it's some physical property attached to the system.

      Correlation is not causation. For a simple classical analogy, suppose you had two packages, one with chocolate in it and the other with some vanilla candy. You know beforehand that each box has only one of the two, and the other box has the other sort of candy. One box is sent to you, the other to Alice. If you open the box and find chocolate, you know with 100% certainty that Alice got vanilla candy. This is just correlation; your opening the box did not cause Alice to get the vanilla candy. It merely caused you to change your assessment of the odds that she would.

      It's still the case with entangled particles in QM. The difference is that QM allows for a greater amount of correlation than classical physics does. And this difference comes about because QM is not realist. But you're still just calculating correlations, and when you measure the polarization state of an entangled photon, you don't cause the measurement outcome of the other photon; you merely change your assessment of the odds. QM tells you how to do this, and QM gets it right every time (so there's certainly no mystery about it).

      One mistake you may be making is reifying the state. The state is a tool for calculating the odds of measurement outcomes, not a property of the system. A lot of people make this mistake because they're only familiar with Schrodinger's picture of QM, and even then mostly think about the wave function as a function of space and time (as a real wave would be) rather than configuration space and time (as it is).

      Try thinking about QM using the Heisenberg picture instead, and use the density matrix to signify the state instead of a state vector or wave function. This picture is better for relativity anyway since your field operators are actually functions of spacetime in it. The state is now just an operator with no space or time dependence, which is used to calculate probabilities and expected values, and which only ever changes in response to a measurement. It's clearly a generalization of probability in this picture, and probability is a function of available information about the system, rather than a physical property of the system itself. Accordingly, different observers can ascribe different states to a system, if they have different information available to them; but when they reconcile this information, of course they'll find consistent results.

      So, in an EPR/Bell experiment, you'd think that some sort of 'transfer' would occur between the entangled particles if you thought the state was something that inhered in the system. Alice measures her photon before Bob measures his, so it changes the state of Bob's. (Or the other way around? Depends on your frame of reference. Maybe they measure simultaneously.) You'll end up with that tension you were talking about.

      If you don't think this, and consider the state just a means of calculating odds, then the state Bob ascribes to his particle would not change when Alice makes her measurement, since Bob does not have access to Alice's result. He'll then make his measurement, and then can use his result to calculate the odds that Alice will have gotten various results from her measurement, using QM. And when the experiment is repeated many times, he'll find that the experiment verifies his calculation. No tension with relativity appears.

      All the more reason to avoid metaphysics (and realism in particular).

      • node

        I get the impression that the author wants to paint all physicists as platonists and so we must all believe in a realistic QM, i.e. an ontic wavefunction.

        Admitting to the epistemic interpretation doesn't fit in at all with the article, which is a shame as it is a common viewpoint that solves several conceptual issues raised in the article.

    • PD

      No, you are misrepresenting entanglement here.

      "Either something happens here between the 2 particles that is outside the collapse of the wave function" -- what on Earth does this mean? I assume you are thinking of hidden variables here because you mention Einstein. In which case, yes, Bell's theorem shows that hidden variables must be nonlocal and therefore in conflict with special relativity.

      However, one can choose not to believe in hidden variables, following Niels Bohr. You don't really describe this option except to quote something vastly unhelpful from Wikiedia. But this option rejects realism; a quantum particle has no particular property before we measure it. In fact the act of measuring brings the property into the world (e.g. we force a particle to have spin in a certain direction by measuring it). This is a popular position and not at all in conflict with special relativity.

  • James Hayes

    My theory below provides a far more rational explanation
    of the universe than any I’ve seen from physicists. If you are going to do
    reductionism, as scientists do – go the whole hog.

    Time is actually the only "real" thing that does exist.


    It is the only thing that could possibly qualify as being infinite.

    Space could be thought of as infinite, but it is actually a coincidental by product
    of time.

    Why is Time the only possibly for the term infinite?

    It is that which logically must have always existed, it is without beginning and without end - thus is outside of the idea of a first cause.

    To be infinite means to be endless, not bounded by anything else.

    In other words the definition of the word infinite itself requires that which
    is infinite to be "all there is".

    As there is something, then by default the universe (or I prefer The Totality)
    must be infinite. The universe in its totality did not pop into existence from
    a timeless state.

    What does time do?

    Time is self-expanding pre-dimensional "space-energy". It is essentially a "plane of nothingness" that expands on an omni-directional basis. It is not really nothingness, but it only has 1 property - it expands - so in an observational sense it will always appear as if it were nothingness (we can only observe things that can be divided as it is by division into multiple parts that we sense things).

    How Does Time become Things

    The very act of Expansion creates differentiation. As Time expands on an
    omni-directional basis, that means it is expanding everywhere both outwards and
    inwards at the same time. This is where is at its most fundamental, where it
    stems from. That portion of Time that is expanding inwards we call Gravity.

    What is "internal" is always lesser in expansionary power as the "newer" time expanding outside of it is limiting the speed of the outwards expansion. This creates a pressure imbalance, where almost instantly the internal pressure overcomes the inward power of times expansion and the perfect expanding Time circle bursts like a balloon (little big bangs and big big bangs happen everywhere at some point). There is only one true law of nature – The Path of Least Resistance.

    This process happening everywhere, forever, causes an eternal time "soup" where time of varying ages reforms with different mixtures of time than before. The first level of the differentiation heirarchy is Space, which is pushed around by everything already existing - it curves and overlaps across all size scales. Then via evolution (the path of least resistance), this overlapping eventually gives us the spectrum of properties of things we can observe.

    This process is all that is needed to create the immensity of the universe. But you require the continuous expansion/structural fracture/contraction to get any size whatsoever. Contraction is the overlapping of time planes that appears as if it were contraction, it is not true contraction. That is why atoms contain so much expansionary energy - why an atom converted to energy by fracturing
    will take up so much space (as per E=MC2 where C2 represents the post
    conversion space required for that mass).

    The so-called first cause is always the current cause. It is Time's expansion that creates the power behind forces. Continuous expansion is the universes infinite battery. Times arrow is caused by this continual expansion - it is always pushing outward (creating more thingness) and inwards causing change within.

    If you begin view Time as The Cause rather than as everyone seems to view it,
    namely, as a non-existent effect, as just a measurement relating to observed
    change, then you can get a very good grasp of how the universe works without
    needing the very much overly complex science. This theory does not reject
    anything science has observed, it just rejects false conclusions such as time
    commencing when The Big Bang occurred.

  • Al_de_Baran

    One last word on the subject (not that anyone's likely to read it).

    Just as believers in simple-minded faiths cried like babies when scientists yanked the pacifier of religious certainty from their mouths, so in turn the religious believers in Science will cry like babies when the pacifier of scientific objectivity and "objective truth" is yanked from their mouths. We've seen some of that in this very comments thread, in fact.

    Such a result shouldn't surprise anyone, since the emotional needs that both Religion and Science cater to--the need for order, stability, and certainty--are essentially identical, although the means of satisfying them are radically different. So far as humans go, plus ça change, plus c'est la même chose.

    More radical forms of thinking are needed, and they certainly aren't going to come from scientists, or likely from anywhere within Homo sapiens sapiens, as it is currently constituted. As the fictional mutation "Odd John" Wainwright states in Olaf Stapledon's remarkable novel, "And we know, you must remember, that
    Homo sapiens has little more to contribute to the music of this planet, nothing in fact but vain repetition. It is time for finer instruments to take up the theme." Those "finer instruments" are not, to put the matter mildly, our current epistemic categories, still less our "pattern recognition".

    • Mark Robert

      I read what you wrote. Also liked it. Where do you think these radical forms of thinking will come from?

      • Al_de_Baran

        It's obviously very early days, but I think that if better and more radical ways of conceptualizing what we call "reality" do arise, then they may do so from areas as diverse as non-classical logic (see the work of Stephane Lupasco, for instance), certain ideas in the Gurdjieff system of development and "harmonizing the Centers" (but mutatis mutandis!), mythopoeic/analogical thinking, complexity theory, Schwaller de Lubicz's concept of Symbolique, and explorations of "in-between" forms of awareness, such as hypnagogic states, among others. All this will proceed from the bedrock notion that we create patterns, we do not perceive or "recognize" them.

        In any case, the problem is that we have a very long way to go, and human stupidity seems a long way ahead in the race. To refer to Stapledon's Odd John once again, the title character rightly observes that leaving humans in their current state of development in charge of an advanced technological society is about as wise as putting a stag behind the wheel of an automobile.

        Intellectually, Homo sapiens sapiens remains in its infancy, and I am also not convinced that the current line has a bright future, or any future at all. As I mention above, progress may come only through mutation or speciation--assuming that the elements out of which mutations or a branching species may arise exist long enough for either process to occur. And that, to me, is a questionable assumption.

        • witheo

          Who mourns for Adonais?

          I think it’s only fair, don’t you, for the benefit of the unwashed multitude hereabouts, rushing as one does, lemmings all, for the exits, to reveal the following, “not that anyone's likely to read it”, of course.

          Adonaïs: An Elegy on the Death of John Keats, a pastoral elegy written by Percy Bysshe Shelley in 1821 and widely regarded as one of Shelley's best and most well-known works, was composed in the spring of 1821, when Shelley heard of Keats' death. The title may be a merging of the Greek "Adonis", god of fertility, and Hebrew "Adonai" ("Lord").

          Shelley mistakenly believed Keats had died from a rupture of the lung induced by rage at the harsh reviews of his verse in the Quarterly Review and elsewhere. Shelley's admiration of Keats was not entirely reciprocated. Keats had reservations about Shelley's dissolute behaviour, and found some of Shelley's advice patronising (the suggestion, for example, that Keats should not publish his early work).

          Shelley's affection for Keats remained undimmed until his death in 1822 when a copy of Keats' works was found in a pocket on his drowned body. Shelley said of Keats, "I am aware indeed that I am nourishing a rival who will far surpass me and this is an additional motive & will be an added pleasure." He regarded Adonais as the "least imperfect" of his works.

          Mick Jagger of the Rolling Stones read a part of Adonais on the Brian Jones memorial concert at London's Hyde Park on July 5, 1969. Jones, founder and guitarist of the Stones, had drowned July 3, 1969 in his swimming pool. Before an audience estimated at 250,000 to 300,000, Jagger read the following verses from Adonais:

          Peace, peace! he is not dead, he doth not sleep
          He hath awakened from the dream of life
          'Tis we, who lost in stormy visions, keep
          With phantoms an unprofitable strife,
          And in mad trance, strike with our spirit's knife
          Invulnerable nothings. — We decay
          Like corpses in a charnel; fear and grief
          Convulse us and consume us day by day,
          And cold hopes swarm like worms within our living clay.
          The One remains, the many change and pass;
          Heaven's light forever shines, Earth's shadows fly;
          Life, like a dome of many-coloured glass,
          Stains the white radiance of Eternity,
          Until Death tramples it to fragments. — Die,
          If thou wouldst be with that which thou dost seek!
          Follow where all is fled!

          The English rock band The Cure recorded a song entitled "Adonais" as a B-side single and on the collection Join The Dots: B Sides and Rarities, 1978–2001 (2004). "Adonais" was originally the B-side to "The 13th", released in 1996.

          Episode 31 of the original Star Trek series was titled, ‘Who Mourns for Adonais?’, first aired on September 22, 1967 on NBC. It was written by Gilbert Ralston and Gene L. Coon, and directed by Marc Daniels.

          Where would we be, as mere mortals, without Wikipedia?

          The take-away for me, from all of this is that the late great, poor old Shelley wrote his magnum opus on a mistaken belief. There, but for the grace of [insert name of favourite idol here] go we all, what?

          • Mark Robert

            Thanks for the explication, though I still make no sense of it:

            I'll shed far more tears for Adonais than I will for humanity as it is currently constituted.

            Is it that most people are a bunch o' dopes and only poets are worthy of tears?

          • Al_de_Baran

            Of course, I had Keats in mind, too, but the reference was really more to the Star Trek episode, to be honest. Can't be highbrow all the time, after all. ;-)

        • Mark Robert

          Your references fly almost entirely over my head -- nice! a kind of cool breeze up there stimulating some study hours on this infernal machine rather than sitting out in the garden, but what can I say, I like it -- anyway regarding non-classical logic, it seems to me that Aristotle's three laws of thought pretty much sum up the problem in the basis of common scientific thinking. The fact that these are unthinkingly taken to be LAWS -- just because our minds habitually think that way -- blinding us to conceptual possibilities (the logic of Nagarjuna's tetralemma, being at least one promising alternative), I think is part of the emotional fervor one encounters in debate with (some) scientists.

          Intellectually I don't have much depth (though I have at least an undergraduate degree in physics and a fair amount of graduate work in areas of psychology and philosophy), but it seems most of the fresh air I can bring to these types of discussions comes from many years study of Buddhist philosophy, and especially many years practice of meditation, with some familiarity with the types of clarity possible from such investigation.

          I say this because at some point in many people's meditative career, as has occurred in mine, one has experiences that clarify what is "mind-made" and what is not. Without such experience, EVERYTHING is experienced as mind made, or alternatively, projected outward as the REAL, out there.

          So, you say:

          All this will proceed from the bedrock notion that we create patterns; we do not merely perceive or "recognize" them.

          And I would absolutely agree, with the caveat being that ultimately there is no "we" creating any patterns. There is most assuredly the human brain doing what it does, which is pattern-creation-and-subsequent-recognition. There is no "outer pattern" being recognized. At the same time, fundamentally there is no distinction between inner and outer -- this is a mind-made distinction, or you could even say, this is a reality-made distinction, it's simply how things tend to display -- but it is not the basic situation, as it is. The basic situation is non-dual awareness with no separation between subject and object, and all forms appearing as dream-like apparitions, their appearance limited only by the perceptual and conceptual apparatus of seemingly separate but ultimately not separate individual organisms, with not a wisp of unchanging reality anywhere to be found, yet still, everything appearing, just as it is, due to the inexorable nature of dream-like yet functioning interdependent cause and effect. That's basically how it's taught in the tradition I come from anyway, and it's experimentally verifiable simply by close introspection.

          So I would not go looking for in-between states of awareness or special states of awareness for clear insight into what's going on here. Rather, one simply needs to become convinced that one's habitual perception may well contain a radical error -- one needs that doubt -- and then see if it's possible to correct it, to find the actual normal state of awareness. I think (as many have pointed out), that what we culturally take for normal perception is a highly altered, habituated state that is not seeing things as they are, the biggest problem being the imposition of a seemingly obvious but illusory split between subject and object -- and with training, it can be mended. With luck too. With grace also, I'd say.

          • Nat Scientist

            Mark, all these words and you missed the first lie we are told, that we are not always there. This is poignantly revisited in the cliche of the family vacation ride, "Mommy,Daddy, Daddy,Mommy, Mommies, Daddies, Mommy, Daddy (PC-ized), are we there yet?", when the truth is that we are always there. In a similar vein, the proper answer to "What do you want to be when you grow up?", is "I want to be alert." But that's before all the billions of words that lead to war sooner than to peace.

          • Mark Robert

            Yes of course, we're always there. Or is it here? But who realizes it, Nat Scientist friend? And not realizing it, we're in a pickle. And so i gotta use words when I talk to you, and to myself too...

          • Nat Scientist

            Of course, but I have not your pickle, since I happen to realize it. And those and these are the words I use to school you. I am not we, nor do I care to join who you think that we are what ever.

          • Al_de_Baran

            I am glad to read that you were able to make at least somewhat better sense of my answer in between responses.

            I personally differ with the Eastern traditions that claim we can "awaken". My view, and my own experience supports it, is that "lucid dreaming" within a perspectival system is the best we can hope for. No one is or will ever be fully "awake". Relative awakening, which remains constantly entangled with dreams, is the reality of the situation.

            I don't have a problem with that, myself, though. As someone whose youth was spent in the company of works by the English and German Romantics and the Surrealists, the Eastern/Gurjieffian/et al. hatred of dreams never made the least sense to me, and it still does not, today.

            As to non-duality and the illusion of separation, well, of course the latter is not absolute. Still, separation may only be relatively true, but it is true, nonetheless. Quantum entanglement or no, if someone punches me in the face, the person standing next to me doesn't feel it. Our habitual notions of "I" and "ego" may be faulty, naive, and incomplete, but that does not mean that what they refer to, however clumsily, does not exist, at all.

            As for the in-between states, you might find Jurij Moskvitin's brilliantEssay on the Origin of Thought interesting, if you can unearth a copy of it,

  • orthorim

    Very nice and balanced article. I think my main issue with science is the idea of it as presented in the media - as something that is truth. When in reality it is as you say, an attempt, often successful, to quantify certain things.
    We can find the truth, but not through science.

  • Mark Robert

    I first encountered the duck-rabbit illusion many years ago in the wonderful book "Patterns of Discovery," by Norbert Russell Hanson, a brilliant contemporary of Kuhn. Hanson wrote about the distinction between "seeing" and "seeing as," and, if I remember correctly, argued that all seeing is seeing as. In other words, all objects whatsoever are constructions.

    Years later in the writing of the Tibetan Buddhist meditation master Chogyam Trungpa, I encountered that idea that Westerners tend to look, and then see. Whereas there is another possibility: to see, and then look. The view of reality insinuated by Trungpa is that there is something that can be "seen" even before an object is seen.

    For me, the brightest spark in the article was here:

    Douglas notes that all category systems contain liminal confusions, and she proposes that such ambiguity is the essence of what is seen to be impure or unclean.

    Whatever doesn’t parse neatly in a given linguistic system can become a source of anxiety to the culture that speaks this language, calling forth special ritual acts whose function, Douglas argues, is actually to acknowledge the limits of language itself. In the Lele culture of the Congo, for example, this epistemological confrontation takes place around a special cult of the pangolin, whose initiates ritualistically eat the abominable animal, thereby sacralising it and processing its ‘dirt’ for the entire society.

    In the highest expression of the Tibetan Buddhist worldview, contained in the Mahamudra or Dzogchen teachings, depending on the lineage of instruction, reality is taught to be fundamentally pure. This teaching is nearly always difficult for people to accept. How could dirt be pure? War be pure? Good might be pure, sure, but bad too?

    But the teaching is adamant: It's all pure, everything is pure. Within the discourse of teachings on enlightenment, this is a fact about reality that can readily be experienced, but cannot be known by the mind. Here one needs to tread carefully. Why not "known"? Because the mind makes distinctions. You could say, the mind IS distinctions. It's what it does, what it's like. Therefore it cannot know the purity being talked about. In Buddhist discourse -- different from scientific discourse -- a distinction is made between knowing and experiencing. Something can be experienced, but not "known." Hard for the mind to accept? Of course. That's exactly how the mind is.

    In the famous Aspiration Prayer of Mahamudra by the Third Karmapa, Rangjung Dorje, this hidden purity it written about this way:

    It is not existent -- even the Victorious Ones do not see it.
    It is not nonexistent -- it is the basis of all samsara and nirvana.

    This is not a contradiction, but the middle path of unity.
    May the ultimate nature of phenomena, limitless mind beyond extremes, he realised.

    If one says, "This is it," there is nothing to show.
    If one says, "This is not it," there is nothing to deny.
    The true nature of phenomena,
    which transcends conceptual understanding, is unconditioned.
    May conviction he gained in the ultimate, perfect truth.

    According to this view, it is, as you wrote, "childishly naive" to believe that all the distinctions made by mind are true. Just because the mind can mathematically construe existing universes exceeding the number of particles in our universe by more than 400 orders of magnitude, simply does not mean that it is true.

    The mind can see a rabbit, then a duck. Then a rabbit again. A duck. What's "true"? It's just the mind doing what it does. Or....reality doing what it does. The problem is precisely in trying to say what is "really" there. Because, according to the enlightenment teachings, there is no thing "really" there.

    According to the well-known formulation in the Heart Sutra:

    Form is emptiness. Emptiness is form. Emptiness is no other than form. Form is no other than emptiness.

    One could say that the wave nature of matter relates to its empty nature, while the particle nature of matter relates to its form nature. But the whole thing cannot be nailed down precisely: that's the point here. It's part of the nature of the beast that it cannot be nailed down AS something exactly, because reality as something is always in union with it's empty, ineffable, undefinable nature.

    According to this point of view, when this empty nature is realized ("seen" in Trungpa's words, even though it cannot actually be seen), then one experiences liberation. From what? From the ignorance of how things actually are, which leads one to endlessly reify every duck and rabbit one comes across, with the all the consequences that follow from that.

  • Nat Scientist

    No scientific breakthrough of paradigm disruption ever came out of an experiment or a blackboard set of equations. Albert confided to Dmitri Marianoff, a Russian reporter, that after years of futile calculations, general relativity came to him one night in a total package. Nature is that package, and it is our opportunity to observe and unpack its testable facts if we choose to trust our original brain that truly feels. It comes in a wave or a particle and only nature cannot lie. Narratives are on the other hand, are nothing but politics manufactured for a synthetic environment bounded only by all competing reality. Lies you can believe in.

    Albert learned he was awarded the Nobel Prize on his return from Japan in October, 1922. The fifth rejection, in 1916, was in a tie with Brownian motion; both it and general relativity were passed over and the physics prize was not awarded. In 1921, he was long due leaving Berlin since his life was in danger and newspapers were reporting threats on his life. He did it his way and was extremely lucky to have survived with his truth. Past performance is no guarantee that it won't reoccur in the future since it's gone viral and most just leave it alone.

  • Howard Treesong

    Don't call it 'CERN' Mark II. The LHC has been a great instrument at negligible cost. I'll happily chip in to build a new generation device if so required.

  • Jeffrey Eldred

    As a physicist, I find this article more than a little frustrating. For all the author seems to know about physics and physicists, there is just a lot that just mixes the mark. Wave-particle duality is a descriptive paradox but not a mathematical one. The double-slit experiment is slightly different, and most physicists are open-minded about things like Many Worlds or String Theory but not beholden to it. Quantum entanglement is not a violation of relativity, because particles, forces, matter, information, and energy all still can't beat the speed of light. It is absurd to suggest that the universe fundamentally coexists with mathematical contradiction, what is perhaps too bold about physicists behavior is to suggest that the fundamental nature of the universe might be accessible. However, they might be forgiven, as it is their job.

    • PD

      Exactly! There are several opinions given to physicists here, but I am a physicist and I hold none of them!

  • Jonathan_Briggs

    Science, like many other aspects of life, has bandwagons onto which people jump, as a popular theory gets more funding than one which is derided, even though, in the fullness of time, the derided one may turn out to be correct. Even scientists occasionally try to force the wrong part of the jigsaw puzzle into what they think is the right place.

  • MJA

    The solution is much more simple than thought.
    Once the problem of measure is removed, the truth becomes crystal clear. There is no certainty in the differences that measure and divide us, but there is truth, the absolute in what unites us. Empirically or mathematically the definition or equation for unity, for truth is equal, is =. Remove the flaw of uncertain measure and the Universe comes clear.
    Can you see is too? =

  • Veronica

    Only 1 other comment here on the 'Electric Universe' theory below - all else is mathematical constructs, and now that it is realized that these cannot provide any final answers, maybe it is time NOW to rethink, and change from these fancy mental gymnastics that are taking everything in the wrong direction - get back to the basics that are NOT being considered - try Hans Alfven and Plasma Cosmology ideas before you tie yourselves in any more mathematical knots !!!

  • Felix Erwin

    Since consciousness is significant in QM it seems clear to me that the theory is incomplete. If Darwin and Dawkins are to be believed, the sole purpose of our consciousness is to serve the genome.

    I believe the question should be: What role does consciousness play in QM?

    • Jonathan Dunn

      is there experimental evidence of consciousness? by definition,no. then there is the problem of other minds. whatever hard science comes up with to describe and define human brains and actions, it will be apart from the model of "conscious agency" rather than somehow including or explaining it.

  • oomas

    Honestly speaking, the time has come to abandon old, anachronic paradigms indeed, but this is solely the case of shitty postmodernism. Science is doing great, thank you, and none of the so-called "problems" in this article is any deterrement to it.

  • Jonathan Dunn

    "Entanglement suggests that either quantum theory or special relativity, or both, will have to be rethought." - perhaps this rethinking need only extend so far as "Superdeterminism" - i.e. both our action of measurement at A and the measurement of the entangled particle at B are "fated" by their common deterministic roots. Any entanglement experiment takes place inside some light cone or other, and thus local determinism ala relativity cannot be categorically ruled out, however spookily FTL the measurements appear to correlate.

  • B K

    Numbers don't lie simply because they cannot tell the truth.

  • Felix Erwin

    If we can design an experiment, and write down the theory and expected results, then perform the experiment, we are not only confirming a theory, we are communicating that theorem; consciousness performs this act, even if only a thought experiment; cogito ergo sum. That theory becomes law when there is lack of contradictory evidence from other consciousness. In the case of QM, the theory is itself contradictory and subject to multiple interpretations. Consiousness does not agree on what is even being observed.

    The act of measurement is creative input balanced by an entropic output; observation correlated to the passage of time. Whether matter exhibits duality, may not be the issue. It may be that consciousness can only accomodate the act in one of two ways. That is, conciousness is deterministic, and there is no phantom element.

  • PD

    "Entanglement suggests that either quantum theory or special relativity, or both, will have to be rethought." -- No, it doesn't. If one wants to believe in realism (often via hidden variables), then nonlocality is introduced. Otherwise quantum theory and special relativity are perfectly fine together.

  • SmilingAhab

    The Universe is, and it seems to behave consistently. To say that physicists' axioms may have to be rethought because they don't solve paradoxes is understandable, but no matter who thinks what, or if there are no humans to think, the Universe still is, and still seems to behave consistently. What Douglas seems to be reaching for is the opposite end of Platonism, wherein consciousness and perception are actively, physically shaping and changing reality. They're both mad.

    We need a new vocabulary and way of approaching physics, not more New Age perceptionalism or outright mysticism and ignorance worship.

  • Felix Erwin

    I am not sure we can say that the Universe exists independently, though it seems to make logical sense. Look into the heavens and you will see something that no longer exists. Take the question of a tree falling in the woods. It is a pressure wave that is created. It takes an observer to hear sound, which is a dependent creation of consciousness, and at that time, no longer dependent on the existence of the tree. We think in causal terms, but QM theory is based on probability, which means that either there are hidden variables, or the Universe only appears to be.

  • Jamie Lee

    My god. A comment thread where I can't spot a single person out of the blue proclaiming the Obama or Fox news put nanobot spiders in their oatmeal. Terrific.

    Also, really enjoyed the article. It deals with a number of things I've been musing with lately, though I've not come to any particular conclusion on them. It seems no one has, really.

  • JackForster

    One specific comment on entanglement --it is my understanding that entanglement does not, in fact, violate special relativity as it cannot be used to transmit information. Rather, it violates the principle of locality (which was Einstein's issue with it) however the non-local nature of entanglement was put on a solid mathematical footing by Bell, and demonstrated experimentally (again, if I'm remembering correctly) by Alain Aspect et al.

  • Felix Erwin

    There is not believed to be any information transfer, it is simply an entangled state. When we measure one we instantaneously know the other has a correlated value, no matter how far away. Since the value is indeterminate until measured, the causal history in support of the measurement is also created; an apparent time dilation. One possible explanation is that we got the the arrow of time wrong, just like we did electricity originally, and the measurement is made a priori.

  • Overleaf

    OMG - I occasionally run into articles that make serious category mistakes. But not so frequently one that is unstructured bullshit artistry pretending to be deep thought. This is such an article. Imagine how disappointed serious readers are when they waste a half an hour going through such nonsense, simply because of the catchy title and byline to this article. Does Aeon have any standards of publication?

  • EmpiricalWarrior

    "This mathematically based science, he said, was just ‘another kind of storytelling’."

    This is the crux of all the problems of modern science being grappled with in this article. All we have anymore is a mathematically based science and mathematically based science is to real science as science fiction is to science.

    Certain misperceptions plague the modern scientific endeavor. One is the idea that mathematics is the language of science. This is false as fact and as metaphor. Swahili, Russian, English, etc are languages, mathematics is not. The proper metaphor for the role of math in science is this: Mathematics is a tool of science - a useful and essential tool but it is only a tool. It is not science itself and doing math is not the same thing as doing science.

    The idea that mathematics is in some way the basis of science has become commonplace in the community of academically trained scientists. The real basis of science however is empiricism. It is empiricism not quantification, as stated here, that distinguishes science from other modes of inquiry such as philosophy, theology, metaphysics , etc.

    The role of empiricism in science is to restrict science's range of inquiry to that which can be observed and measured. That which cannot be observed and measured lies beyond the purview of science. Unfortunately, the mathematically based physics of of our modern world is chockablock with empirically baseless particles, forces, entities, and events. A partial list includes the various quarks, the Higgs boson, gravitational waves, gravitons, gluons, dark matter, dark energy, expanding space, curved space, the big bang and inflation.

    It is because we have mistaken mathematics for science that the modern scientific endeavor is an incoherent jumble of rarified mathematical concepts that, individually and collectively, present a picture of reality that bears no resemblance whatsoever to the physical reality we actually observe. The last 100 years of mathematically based physics has deteriorated into a vast intellectual wasteland. The sooner it is scrapped the sooner we human beings can return to an empirically based scientific study of the real world we actually live in.