Information is the new Aristotelianism (and Dawkins is a hylomorphist)

UniverseMath_m_0131by John Wilkins

“In seeking tales and informations.” [Henry VIII, Act V, scene 3]

For some time now [1] I have had problems with the notion of information. Not, please note, with this or that piece of information, but with the notion itself, especially in the natural sciences. In this age of computers and internets, we have taken to mistaking the thing described for the thing itself, and treat information as a property out there in the world, not a representation in our heads and language.

Let me set the scene. Back when Dawkins wrote about biology, he proposed the idea that genes were a special case of what he called the Replicator:

“A replicator may be defined as any entity in the universe of which copies are made.” [2]

Notice the word “copy.” I can copy things in a number of ways, from imitation to tracing, but Dawkins has a particular sense in mind, which he explored in an especially purple prose passage in The Blind Watchmaker (1986):

“It is raining DNA outside. … [downy seeds from willow trees] The cotton wool is mostly made of cellulose, and it dwarfs the tiny capsule that contains the DNA, the genetic information. The DNA content must be a small proportion of the total, so why did I say that it was raining DNA rather than cellulose? The answer is that it is the DNA that matters… whose coded characters spell out specific instructions for building willow trees… It is raining instructions out there, it’s raining programs; it’s raining tree-growing, fluff spreading, algorithms. That is not a metaphor, it is the plain truth. It couldn’t be any plainer if it were raining floppy disks.” (Chapter 5, p 111)

DNA, and the replicators they are a special case of, are information. This is not a metaphor. Similarly, physicists will occasionally assert the same claim about physical things. “The physical world is just a mathematical construct, and things like electrons have only mathematical properties,” says Max Tegmark, a physicist at MIT [3]:

“… all the properties that electrons have are purely mathematical. It’s just a list of numbers. So in that sense, an electron is a purely mathematical object. In fact, there’s no evidence right now that there’s anything at all in our universe that is not mathematical.”

We get the “it” from “bit” [4]. Some mischievous philosophers [5] have even suggested that we do, actually, live in the Matrix, although what the Matrix lives in is unclear.

So, why am I unhappy? Is this wrong? I think it is.

To get at this I need to hit you with a little bit of natural philosophy from the Greeks, in particular from Plato and Aristotle. Plato famously proposed that the real world was the world of Forms, or ideas (the Greek word he used was ideai, from the root eidos, meaning appearance, something seen). Forms were more real than what you see around you. A physical circle is at best an imperfect instantiation of the real circle, which exists nowhere in physical form.

Aristotle, in contrast, explained the physical things in the world by supposing that they had matter, which filled space and gave weight (made from several admixtures of the four elements, two light and two heavy) which the scholastics called substance (substantia, meaning that which stands under), and form, the structure and mathematical properties of a thing. This matter/form dualism is called hylomorphism, from the two Greek words hule, meaning stuff (it originally meant “wood”) and morphe, or form. Hylomorphism was intended to be an alternative view to atomistic materialism, which had become a widely held (and generally atheistical) view in his day. Epicurus had an entire philosophical school based upon the older Democritan atomism [6].

Now hylomorphism was roundly demolished as a scientific hypothesis when Daltonian elements were named and investigated in the nineteenth century. By 1900, terms like “substance” (for matter that is propertyless apart from mass and extension in space) and “form” had taken on a largely philosophical sense that differed extensively from Aristotle’s own views. Instead, an increasingly elaborate atomism had won the day, far beyond anything Epicurus or Democritus had posited. The properties of things, including their mass and filling of space, were the result of fields in space-time.

And yet, a kind of hylomorphism remained, even in science. Biologists argued that form determined many properties of organisms in ways that could not be reduced to their parts, and this kind of thinking was co-opted by the molecular biologists and geneticists of the 1950s, especially since around that time, computers were getting going and information was a hot topic (it had not been much prior to that period). Thus, we get the “Central Dogma” in genetics:

“The central dogma of molecular biology deals with the detailed residue-by-residue transfer of sequential information. It states that such information cannot be transferred back from protein to either protein or nucleic acid.” [7]

Read physically, this means only that the structure of the DNA molecule is not reproduced from the structure of proteins, a perfectly reasonable account of the molecular processes. But because Crick used the word “information,” some scientists, including Dawkins, took this to mean genes are informational entities that “code” for organismic traits from the molecular level up to the entire organism and even beyond.

Likewise, physicists like Tegmark, Wheeler and so on, who say that the physical world is “just” information can be read as saying that there is physical structure in the world. This is harmless.

But this is not how “information” is interpreted usually. Instead, we get the idea that information is itself a kind of universal property that underlies all physical things. Information, which is the modern equivalent of Aristotle’s morphe, has become the equivalent also of Aristotle’s hule. And this is where I part company.

When scientists talk about the information content or the informational entropy of something, they can mean several things. They can mean the entropy of the string of characters that are used to measure or describe that thing, like a mathematical description of a process, or a sequence of symbols like the G, T, A, and C, of DNA. But DNA is not composed of G, T, A, or C. It is composed of molecules, nucleotides, that bear the symbols as names, and they have properties that mean that occasionally they do not follow the mathematical or semantic descriptions of these names. For example, there is a “fifth nucleotide,” 5-methyldeoxycytidine (5-mC), which can pair up in 5′-CG-3′ dinucleotide positions. 5-mC is a methylated molecule, a class of chemicals that modify the expression of the DNA. The informational entropy (or information content) of a sequence is therefore just a measure of how the DNA is represented. 5-mC can even breech the Central Dogma.

The point here is that the representation abstracts away from the physical properties of the molecules. Measures of the informational entropy are therefore actually measures of the abstract representations, not the things themselves. But suppose we had a simulation or representation of the things right down to the level of quarks (if that were physically possible): would the informational entropy of the objects be identical to the physical properties? Would we have the physical informational entropy of the objects? I’ll get back to that. First I’d like to consider some of the other meanings of “information” in science.

Another one is the semantic meaning: what one thing (e.g., a gene) represents (e.g., the phenotype). This is the “information as signal” view, based loosely or strictly on Shannon’s Communication Theory account. One thing “refers” to another (in Shannon’s theory, the received message “refers” to the sent message). This, as Shannon noted, is not a theory of the content of a signal. After all, a gene sequence does not represent the phenotype by describing it. A similar view is Wiener’s notion of information as control, the cybernetic account. It is very hard to think of these kinds of information underpinning the physicists’ view above. Here, the properties are just informational, or as they put it, mathematical. Program-style accounts of genes are in this class.

A third kind of information is the information, or rather the accuracy, of measurements. This is called “Fisher information” after its originator. It is roughly the point on a curve of measurements where the second derivative is zero, or where the error curve is flat. This cannot apply to either physical or biological information, as it is a measure of how well and closely we can measure a physical system. Ironically, it is in my view the only actual physical sense of information, since it requires a physical state to be measured, and a physical system to do the measuring.

So let us get back to the physicists’ claim that the universe is just information. I have argued before [see note 1] that if an electron has mathematical properties, this is not the same thing as saying that the electron is just a mathematical object. An analogy might make this clear. Suppose I program my computer as an orrery, a simulation of the solar system. If I do this, the computer represents the mass and physical constants as numbers, and processes them according to the mathematical equations of physics. But that solar system in my computer doesn’t have the mass of a real solar system (luckily for me, and everyone else on earth). Instead it has an abstract mass, and the ways the abstract sun and planets interact is, well, abstract. A mathematical description of a system like the solar system is abstract. Apart from instances of that description in physical objects like heads, paper or computers, it exists nowhere in space or time. Consequently, abstract properties do not cause anything in the physical world.

Moreover, the abstractions must leave something out. As the genetic A, C, G, and T leave out the actual physical properties of adenine, cytosine, guanine, and thymine, which can occasionally do things the symbols cannot, even the most well specified and detailed representation of a thing will leave out properties and capacities we are not interested in representing, and so they will sometimes deviate in their representation from the actual things. And if we have the fundamental objects (quantum fields?) of the universe, we could not compute the system without first constructing a computer capable of dealing with the whole system, and for a universe, that would have to be a universe-as-computer.

When physicists or philosophers say that we are living in the Matrix, or equivalent statements like the properties of atomic and subatomic objects are merely mathematical, they make a classical mistake: they are mistaking the representation of a thing for the thing. The late medieval scholastics like Lombard knew this error and named it long before Saussure: the sign is not the thing signified. The word is not the world. If we are living in the Matrix, what does the Matrix live in? We know of no information processing system that is not, itself, physical.

This is the New Hylomorphism. Information is, as a commentator on Antievolution.org said [8], seen by Intelligent Design proponents as a kind of caloric or phlogiston. But it isn’t. It causes nothing at all. An abstraction cannot cause a physical process, and to think otherwise is a category error, unfortunately common among theoreticians as well as Intelligent Designists.

The notion of “information” in genetics is an honorary one. It can only mean causal specificity, not anything involving “real” information (on this, see Griffiths and Stotz’ Genetics and Philosophy [9]). And since we have no real reason to adopt hylomorphist views of the real world any more (atomism, or its linear descendants, won the battle), one has to wonder why some scientists and some philosophers think it necessary to reintroduce form as information. Replicators are not informational objects; they are molecules and systems of molecules [10, 11]. For this reason I much prefer the notion of a “reproducer” [12], which is a physical entity (or class of entities).

It is time that we stopped making this mistake in science. It is time to give up on hylomorphisms, old or new. In the end, these metaphors (and they are metaphors) only mislead us. I think that is enough about information from me [too much information].

_____

John Wilkins is a Melbourne-based, University of Sydney and University of Melb affiliated historian and philosopher of science, especially biology. He blogs at Evolving Thoughts. He wrote Species: A History of the Idea, University of California Press, 2009. Most recently, he is the co-author of The Nature of Classification.

[1] See: Is information essential for life? No.Why not information?Mechanism, informationism and OckhamismMore of me in Spanish, and information againInformation and metaphysicsInformational caloric; and Descartes before the horse — does information exist?

[2] Replicators and Vehicles, by R. Dawkins, 1982.

[3] Do We Live Inside a Mathematical Equation?, Science, 16 February 2013.

[4] Digital physics, Wikipedia.

[5] The Matrix as Metaphysics, by D.J Chalmers.

[6] Epicurus, by D. Konstan, Stanford Encyclopedia of Philosophy.

[7] Crick, Francis H.C. 1958. On Protein Synthesis. Symp. Soc. Exp. Biol. XII, 139-163.

[8] See here.

[9] Griffiths, Paul, and Karola Stotz. 2013. Genetics and Philosophy: An Introduction. Cambridge University Press.

[10] Griesemer, J.R. (2005) “The informational gene and the substantial body: on the generalization of evolutionary theory by abstraction.” In Idealization XII: Correcting the Model. Idealization and Abstraction in the Sciences, edited by Martin R. Jones and Nancy Cartwright, 59-115. Rodopi Publishers.

[11] Waters, K. (2000) “Molecules Made Biological.” Revue Internationale de Philosophie 54:539-564.

[12] Replication and Reproduction, by J.S. Wilkins, Stanford Encyclopedia of Philosophy.

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61 replies

  1. The metaphor of the brain, or anything biological, as like a computer is as flawed by current cultural language uses as the notion of biological systems as clockworks or steam mechanisms.
    Pop metaphors seek to simplify complex experiences regardless of loss of usefulness and accuracy.

    Same to the discussion of biological and medical-brain matters using everyday language and philosophical ideas. It adds no value and likely just further obscures already technical topics.

    The notion that armchair philosophizing and intuitive language use add to knowledge.

    • The metaphor of the brain, or anything biological, as like a computer is as flawed by current cultural language uses as the notion of biological systems as clockworks or steam mechanisms.

      No. Can you add 1069 to 299? Yes, of course you can. The brain is literally a computer – ie something that can compute. Whether the brain is only a computer is another matter.

      • You’re using ‘computer’ purely based on it’s meaning, the article is using it as the label of a specific type of machine, one which doens’t operate in the same way as biological entities do.

  2. I see it in the opposite way from the Tegmarkians:

    It’s not the case that there are first things called information, mathematics, abstractions, computations, and then there is matter or the physical world. It’s the case that first there is matter or the physical world, and then things called information, mathematics, abstractions, computations are all composed of matter.

    The code in my MacBook Pro is not literally a collection of 0s and 1s, but some sort of array of electrical charge directions in spacetime. Soon there may be a 3-D printer that can print out strands of DNA from programs of AGTCs in my computer. But then these strands of DNA may become computers themselves (called DNA computers).

    • It’s not the case that there are first things called information, mathematics, abstractions, computations, and then there is matter or the physical world. It’s the case that first there is matter or the physical world, and then things called information, mathematics, abstractions, computations are all composed of matter.

      If this were true then it would be the case that a reality where physics was completely different would have different mathematics. So a right angled triangle defined on a cross product of reals might have the sum of the squares of the sides adjacent to the right angle not equal to the square of the remaining sides?

      No, clearly not possible even in principle.

      You would have, in principle, a reality in which there was an algorithm which enumerated the digits of a Chaitin constant?

      Again, not possible. We know for a fact that these are constraints on the types of realities which are even possible.

      So mathematics clearly comes before the physical – it constrains what kinds of things are, in principle, physically possible.

      • We know for a fact that these are constraints on the types of realities which are even possible.

        How do we know that?

      • It’s the physical world that constrains the mathematics within it. Real numbers are not “natural” things but are things that are constructed in computer systems likes Coq [ coq.inria.fr ] so that theorems (like Pythagoras Theorem) can be proved. In universes (perhaps bot ours) with Malament-Hogarth spacetimes [ arxiv.org/abs/gr-qc/0609035 ] one could build computers that “can compute far beyond the arithmetic.” Chaiten [ arxiv.org/abs/math/0306042 ] advocates accepting hypotheses (like the Riemann Hypothesis) based on computational evidence.

      • Hi Philip,

        I am struggling to understand why you think any of that contradicts what I said. I never said that real numbers were natural things and I never said that there cannot be any hypercomputers.

        I think those things are more problems for you than they are for me. For example if you are saying that mathematics is a product of the natural world, shouldn’t you be .saying that real numbers are natural things?

        But if you are saying that the physical constrains the mathematical then you must be saying that it is in principle for there to be a reality in which a right angled triangle defined on a cross product of reals might have the sum of the squares of the sides adjacent to the right angle not equal to the square of the remaining sides? Yes or no?

        You must be saying that in principle that there was an algorithm which enumerated the digits of a Chaitin constant. Yes or no?

      • How do we know that?

        So, how do we know, for example, that there cannot be, even in principle, a reality in which there is an algorithm to enumerate the digits of a Chaitin constant?

        Well suppose there was such a reality and such an algorithm in it. In order for there to be such an algorithm it would have to be expressible in some alphabet. An alphabet is a set of distinct values and the nature of the medium encoding these values is not important and so an exactly equivalent sequence of values could be in our universe.

        If there was such a sequence then we could also enumerate the digits of a Chaitin constant and the Halting Theorem would be false. But it has been proved to be true. So that reality cannot exist,

      • An alphabet is a set of distinct values and the nature of the medium encoding these values is not important and so an exactly equivalent sequence of values could be in our universe.

        This part of your argument presumes that there could be a one-to-one mapping between our reality and an alternative reality. If that alternative reality worked on very different logic to our own then that mapping may not be possible.

      • Hi Coel,

        My argument makes no such assumption. If another reality worked by a different kind of logic to ours then obviously a Chaitin constant would make no sense in that reality in the first place and then we still would not have an algorithm to enumerate it. So my statement still stands.

        There is no possible reality in which there can be an algorithm to enumerate the digits of a Chaitin constant.

    • This is all biology and medical physiology, don’t see why analogies or physics, etc. is useful at all.
      How is there information with the brain?

    • Hi Philip,

      Just to point out that there isn’t actually an argument in your comment, just assertions.

      I would say the code in your MacBook Pro is literally a collection of 0s and 1s, at least at some level. My argument is that this code is the same code that runs in my MacBook Pro, but we don’t have the same atoms with precisely the same electrical charges.

    • Phil,

      What exactly is “physical”? You keep mentioning that word but we can’t even define what it really means (which is why I define myself more as a naturalist instead of a physicalist/materialist, and without resorting to any crackpot supernaturalism). When you start to think about physical objects it should start to disturb you a little bit. Atoms are actually something like 99.999% empty space, and the subatomic particles that make up the protons/neutrons/electrons are known to have no physical substructure down a radius of about 10^-22 meters, meaning they look to be literal point particles in the strict mathematical sense. Even if they are composed of something like “vibrating strings of energy” or “loops of spacetime,” what does that even mean? A vibrating band of energy sounds like something pretty abstract and ephemeral to me.

      We need to stop pretending that physical objects are really rigid at their fundamental level; they’re actually not. The only reason you think they are is because they are held together by the interactions of countless electromagnetic fields (which also seem to be unphysical), and these fields happen to reflect light, making objects look opaque and “solid.” The physical seems to actually boil down to mathematical relations between these fundamental “objects” that we describe as physical.

      This fact is one of several reasons (though I think the strongest) for embracing abstract objects and mathematical realism. Not only are they incredibly useful to our theories and incapable of being divorced from them, but you just can’t seem to escape them at the deep levels of existence.

      • If the physical “seems to actually boil down to mathematical relations” and if a simulation program running on a computer boils down to the same mathematical relations, then what’s the difference between the physical and the program? I’m not an expert on the definition of “physical” (in the SEP entry on Physicalism: “everything supervenes on, or is necessitated by, the physical” and the “Wittgensteinian family resemblance” definition seems as good as any) but it makes more sense to me that there is just the physical world and mathematical relations are constructions made by sentient beings and their computers within it.

  3. Reblogged this on thomaswischer and commented:
    “the sign is not the thng signified”

  4. “abstract properties do not cause anything in the physical world”

    Agreed. Nice addition to the footnotes on Plato…

    • Hi Ed,

      If abstract properties do not cause anything in the physical world then they cannot have been any part in the cause of the sentence: “abstract properties do not cause anything in the physical world” since that sentence exists in the real world.

      If so then how can that sentence be about abstract properties?

  5. Likewise, physicists like Tegmark, Wheeler and so on, who say that the physical world is “just” information can be read as saying that there is physical structure in the world. This is harmless.

    Harmless and trivial, however this is clearly not what Tegmark is saying. I wonder if you have read his original paper, in particular where he argues that any object is exhausted by its mathematical properties? Here is a link: http://arxiv.org/pdf/0704.0646.pdf

    The trouble is that the paper argues in terms of the Plato and Aristotle, but a lot of water has flowed under the bridge since then and these are not the arguments to be addressed.

    For example when Mach spoke of the “superfluity of the thing in itself” it had a huge influence on the philosophy of science for more than a century. Although the philosophy of the Vienna Circle has been superceded, there has never really been a case made for the “thing in itself”.

    What mistake are people making, exactly, when they speak of things as being information? What exactly has been left out? What exactly is “real” mass?

    Also, is it really true that abstract concepts don’t have any effect on things. The algorithms that run a computer are abstract things. Ideas like “freedom of speech” are abstract and yet they have an effect on things. Money is an abstract thing. Property is an abstract thing. All of these things are having real effects.

    • To be a little more specific, Tegmark’s argument I mentioned in in section II “The Mathematical Universe Hypothesis” of the paper linked above.

    • Also, is it really true that abstract concepts don’t have any effect on things. The algorithms that run a computer are abstract things. Ideas like “freedom of speech” are abstract and yet they have an effect on things. Money is an abstract thing. Property is an abstract thing. All of these things are having real effects.

      The examples of abstractions you gave don’t seem to have real effects, in and of themselves. Their “instantiations” certainly do, though. If a speech recognition algorithm existed before 1900 it would have no effect because the notion of a self-modifying computing system that could run it hadn’t been conceived yet (as far as we know). The concept of money would have no practical effect without some kind economy where it could find use. And so on…

      I suppose I’m claiming that the abstraction alone is not enough. You also need a (concrete) realization of it, or at least the possibility of a realization.

      • The same thing goes for physical objects. A telescope would have no effect if it was pitch black. A computer could not compute if it had no power. The fact that there are circumstances in which abstract objects can’t have an effect is not sufficient reason that they can’t have an effect at all. I would say that the concrete realisation is, in itself, the abstraction having an effect. You can’t have a concrete realisation of an abstract thing unless you have that abstract thing.

        Other examples are Turing Machines, which were never even intended for concrete realisation but nonetheless have had an immense effect. The biggie is of course Calculus which has had probably more effect than any other abstraction.

  6. I have found it interesting that many people find the whole metaphor of information or even mathematical reality as so intriguing, especially among physicist as it seems like more philosophical musings (and bad ones at that). It seems to me, speaking from a natural science perspective, math is a part of the linguistic repertoire of human beings that is very effective at describing and explaining functions in our world but it does not therefore follow that math is our world.

    To say that math is somehow the universe itself is to me some what a mystical view and essentialist view of human beings, where math is not just a linguistic tool used by an organism on earth but the very nature of the universe itself and our species just happens to know it.

    • Hi imzasirf,

      I disagree with you on all counts.

      There’s nothing mystical about the MUH. The MUH is the very antithesis of mysticism. In fact, I would say that denial of the MUH is mystical. Even though mathematics can perfectly describe and account for the physical world, you suppose there is this extra property somehow breathing life into it and making it real.

      Math is not a language, at all. Mathematical notation is a language. Mathematics itself is the concepts expressed by that language.

      Math is independent of human being.

      • DM,

        >>>There’s nothing mystical about the MUH. The MUH is the very antithesis of mysticism. In fact, I would say that denial of the MUH is mystical. Even though mathematics can perfectly describe and account for the physical world, you suppose there is this extra property somehow breathing life into it and making it real.<<>>Math is not a language, at all. Mathematical notation is a language. Mathematics itself is the concepts expressed by that language…Math is independent of human being.<<<
        I honestly don’t even know what that means. I am a realist so I agree that there is a real world independent of human beings. However, there is no “math” to be found in the universe outside of humans using it. I’m tempted to say we are not going to run into the number 2 when we explore other solar systems but I know that’s probably a horrible caricature of MUH so I’ll let you explain this one further as I don’t see how we get math beyond linguistic notations.

      • DM, Sorry, the post is messing up again. Here it is in chunks:

        You wrote:
        There’s nothing mystical about the MUH. The MUH is the very antithesis of mysticism. In fact, I would say that denial of the MUH is mystical. Even though mathematics can perfectly describe and account for the physical world, you suppose there is this extra property somehow breathing life into it and making it real)

        I made no such claim of some extra property breathing life into the physical world. Only that math is a great but limited linguistic tool used by Homo sapiens to better interact and understand their world. Nothing mystical about saying math is limited and cannot describe everything.

      • You wrote:
        Math is not a language, at all. Mathematical notation is a language. Mathematics itself is the concepts expressed by that language…Math is independent of human being.

        I honestly don’t even know what that means. I am a realist so I agree that there is a real world independent of human beings. However, there is no “math” to be found in the universe outside of humans using it. I’m tempted to say we are not going to run into the number 2 when we explore other solar systems but I know that’s probably a horrible caricature of MUH so I’ll let you explain this one further as I don’t see how we get math beyond linguistic notations.

      • Hi imzasirf,

        I acknowledge you made no claim of some mystical thing breathing life into the world. However that is how your views look to me. I claim that math can completely account for the physical properties of the world. You didn’t directly challenge me on that, so let’s take it as a given.

        If that is true, and if everything that happens in the world is at some level driven by physical events, then mathematics is all that is needed to provide a foundation for our existence. The denial of the MUH is the idea that there is something missing from this picture, something to breathe life into these equations and make them real. The electron has not only charge, spin, mass, etc, but “realness” which is needed to distinguish it from its mathematical model. This property of “realness” seems mystical to me. You may not think of it in these terms but that’s how it looks from where I’m standing.

        However, there is no “math” to be found in the universe outside of humans using it

        That’s because you think of mathematics as a set of tools and notations rather than the concepts those tools and notations have been developed to work with. Wherever in the universe there is one pebble and another pebble forming a set of two pebbles there is mathematics. The fact that one plus one equals two is independent of humans or any notation used to describe it.

        If mathematics is language, then “two” is completely different from “2″. If they have anything in common, it is that they refer to the same thing, which is some concept which is independent of the language or symbols used to describe it. In the same way that “rock” means pretty much the same thing as “boulder” despite being a completely different word, the meanings of the terms and sentences for language should not be confused with linguistic constructs.

        So I say again, mathematics is most categorically not a language. Languages have to be about something, and mathematics is what mathematical notation is about. I think what you may want to say instead is that mathematical entities are useful fictions which help us to model the real world in some way.

      • Hi DM,
        I admit it escapes me why you think if you can’t explain physical properties mathematically that it must be mystical. Not all of science even relies on math, is science mystical as well then?

        As for your claim that all physical properties can be explained mathematically, I would have to unpack that considerably. First, we would have to get clear about what you mean by physical, as I think that you also consider something non-physical. I am a neutral monists as I don’t think “physical” is well defined enough and implies non-physical. Now if by physical you mean everything that we can study empirically, than I think there are plenty of things math cannot explain. My writing this post for one is an easy example but we can think of everything from love, poetry, dancing to more things like qualia or values.

        However, I will grant you the premise that mathematics can explain everything, all things that need explaining. Even then, I don’t see your argument for MUH working as it’s still very much a human linguistic phenomena. I can give a perfect description of something I see but my words describing the object I see don’t become the object themselves. Similarly, math may track well with the world (even perfectly) but that doesn’t mean math magically becomes the world itself. This is what I believe John meant by “they are mistaking the representation of a thing for the thing… the sign is not the thing signified…The word is not the world.”

        Stepping back, it seems like we may have very fundamental differences in terms of how we look at the world even though reading your reply, at times I can’t tell how our views are different outside of you wanting to call properties of the world math. I agree those properties are there and math describes them well but they are distinct from math as I consider math a linguistic tool and a cognitive ability of humans just like other languages.

        However, I did want to address your specific challenges you brought up. For your pebble example, I agree that the pebbles would exist without humans but the concept of two is not in the universe but rather in the human mind. In fact, I can’t see how you would square conceptual difficulties of level of analysis with MUH. Are there two pebbles or is just one big rock (planet) or is it millions of little molecules or is it trillions of atoms, etc. All of these are constructs we use to better interact with our world from my perspective. The concepts that work well are talking about real properties of the world so if your saying you want to call those properties math, I have no problem with that but I think that’s very misleading. I also thought MUH to be saying more than that but I maybe mistaken.

        For your other challenge of math not being a language because “two” is different from “2”, I don’t see how this makes the point your trying to get across. My abbreviation of your online name “Disagreeable Me” into “DM” does not mean two completely different things even though visually they are two very different stimuli. They both refer to you, a “real” organism in the world. This is stimulus equivalence, which explains both why 2 = two and DM = disagreeable me.

        Finally, in terms of math not being language, perhaps that would take us too far aside into what language is from a cognitive perspective but even though there are some important differences, they are to me fundamentally the same thing at the core. Both are functions of cognition, and more specifically relational frames. They differ in terms of what they refer to and to what degree of accuracy but I don’t see anything fundamentally different about them.

      • “However, there is no “math” to be found in the universe outside of humans using it. “

        Hi imzasirf,

        The above is obviously wrong because if SETI started receiving signals that encoded strings of prime numbers we would obviously not conclude that humans had somehow made there way out there.

        Maybe you mean intelligent beings.

    • Hi imzasirf,

      I admit it escapes me why you think if you can’t explain physical properties mathematically that it must be mystical. Not all of science even relies on math, is science mystical as well then?

      By mystical, I mean a view which makes ontological or metaphysical claims that relies on notions which resist any attempt to define. I think this concept of ‘realness’, which distinguishes ‘real’ objects from their mathematical models, is such a concept. Even notions in the soft sciences such as sociology can be given an approximate definition that makes some kind of sense. All definitions of “reality” I have ever seen are circular in some way.

      In what way do you regard the MUH as mystical? What do you take ‘mystical’ to mean?

      My writing this post for one is an easy example but we can think of everything from love, poetry, dancing to more things like qualia or values.

      I don’t think love, poetry, dancing, qualia or values are physical. I think the presence of love-correlated hormones in the bloodstream, the putting of ink to paper, the movement of limbs, the neural correlates of qualia and the behaviour of social organisms are physical. By physical, I’m talking exclusively about stuff like the movement of atoms. I’m not talking about what significance or meaning we might attribute to such movements. With this clarified, naturalism is in my opinion the view that all physical events can be modelled mathematically.

      I can give a perfect description of something I see but my words describing the object I see don’t become the object themselves.

      But, again, mathematics is not a language for describing the world. Mathematical notation is a language for describing mathematical objects. If I say 1+1=2, I am not saying one apple plus one apple equals two apples. I am making a more general claim that is not about specific physical objects in the world but about numbers.

      Are there two pebbles or is just one big rock (planet) or is it millions of little molecules or is it trillions of atoms, etc.

      All of the above. Mathematics is general. It is not about specific physical objects. Two pebbles instantiate all of the above at the same time.

      My abbreviation of your online name “Disagreeable Me” into “DM” does not mean two completely different things even though visually they are two very different stimuli. They both refer to you, a “real” organism in the world. This is stimulus equivalence, which explains both why 2 = two and DM = disagreeable me.

      Exactly. Read what you wrote again and please see how it makes my point perfectly. “DM” and “Disagreeable Me” both refer to a real thing, so though the terms are different, it is clear that the terms are not the thing itself so there is no problem. Similarly, “2″ and “two” both refer to a real thing, and that is a mathematical object, not a linguistic term.

  7. And as I often say, physics does not require the hypothesis that there is something that the hypothesis is about.

    Planck and Schrodinger would have disagreed about what the theories were about, Planck would have said a theory in physics was about physical reality, Schrodinger would have said it was about consciousness. Bohr would have said that the question was meaningless.

    And yet they all three collaborated on the same theory, the most successful physics theory we have.

    Even Stephen Hawking says that it is meaningless to ask if a theory is about reality, only if it matches and can make predictions about observations.

    So it is far from clear to me that any mistake has been made by calling things “information”.

  8. So philosophers and theologians as saying that the self-referential and unempirical nature of their claims are made legitimate because they are like advanced physics!?

    • Brain Molecule Marketing wrote: “So philosophers and theologians as saying that the self-referential and unempirical nature of their claims are made legitimate because they are like advanced physics!?”

      Goodness me, where did you get an idea like that??? Has anyone even mentioned theologians here?

  9. Hi John Wilkins,

    This post is well written and researched, and obviously you have thought about it a great deal. However your position is one I vehemently oppose.

    I think you are perhaps too quick to assume that holders of contrary positions have simply not thought their ideas through.

    Now hylomorphism was roundly demolished as a scientific hypothesis when Daltonian elements were named and investigated in the nineteenth century.

    I am very suspicious of this claim. If hylomorphism is belief in both substance and in form, then physical discoveries may have expanded our understanding of substance, but it did not do away with form. Even if matter is composed of stuff with only mathematical properties such as quarks or fields or what have you, those quarks/fields are arranged in particular ways. These patterns of arrangement correspond to form and it is not the same as the substance itself.

    some scientists, including Dawkins, took this to mean genes are informational entities that “code” for organismic traits from the molecular level up to the entire organism and even beyond.

    You may have raised interesting points with regard to how our view of the genetic code is sometimes too simple, but there can be no doubt that code exists and influences physical processes. However apt the analogy may or may not be to genetics, real code influences real physical process all the time when running in electronics. There’s no particular need to discuss genetics when you can discuss the metaphysics of real computer code instead.

    However, there are a few points I would make regarding genes. If there is a ‘fifth nucleotide’, that doesn’t undermine the idea that genes are code at all, it just means that the code has another previously unknown symbol. Much of your discussion of genes is confused that genes code for phenotypes directly. They do not. They code for all kinds of things, including logical operations such as control of replication. Most simply, they sometimes code for particular proteins. In this case, they can indeed be said to ‘refer’ to the proteins by ‘describing’ them in terms of their sequence of amino acids.

    Your analogy to the virtual orrery reveals the same mistakes usually made by people who don’t understand the Mathematical Universe Hypothesis and also echoes the confusion of John Searle denying that a simulation of a conscious brain would be conscious, saying that a simulation of a rainstorm doesn’t flood the computer lab.

    But that solar system in my computer doesn’t have the mass of a real solar system (luckily for me, and everyone else on earth).

    But it would have mass from the perspective of a virtual person living within the simulation. If the real world were a mathematical object, then we would be abstract mathematical people, and from our perspective the abstract mathematical mass of the sun would be just as real as we perceive it to be. Your argument simply doesn’t work.

    And if we have the fundamental objects (quantum fields?) of the universe, we could not compute the system without first constructing a computer capable of dealing with the whole system, and for a universe, that would have to be a universe-as-computer….If we are living in the Matrix, what does the Matrix live in? We know of no information processing system that is not, itself, physical.

    This makes the mistake of assuming that a mathematical object needs a computational process to sustain it. It does not. On Platonism, mathematical objects exist even if there is nothing to think about them or compute them. We need computational processes to explore and learn about mathematical objects, not to cause them to exist. If we exist within a mathematical object, there need be no computer to compute it. It simply is.

    they are mistaking the representation of a thing for the thing… the sign is not the thing signified…The word is not the world.

    Or “the map is not the territory”. This is generally true but it is not always true. When dealing with mathematical objects, the map can indeed be the territory.

    Consider a black box function. You pass values into it and it spits values out. By looking at the values, you produce a model of what it is doing. Your model may be reasonably accurate or very accurate. In the special case that the model you have produced is precisely the same as the mathematics implemented by the black box, then your assumption fails. You have a mathematical function in mind (the map), and the black box implements a mathematical function (the territory), and it is possible for those functions to be the same.

    Our universe is such a black box. We describe its behaviour with laws of physics that are not quite accurate but pretty close. But there may be a completely accurate description of the laws of physics, and if such a description exists, and if the universe really is a mathematical object, then the universe really is simply that true model of the laws of physics. To claim that the map is never the territory is only to admit your preconception that the universe cannot be a mathematical object.

    • Thanks for the comments, Disagreeable. I never said Platonism is not coherent. I said that it is not relevant to us. As Norbert Weiner, one of the “fathers” of information theory, once said, “Information is information, not matter or energy. No materialism that does not admit this can survive at the present day.” If we accept the reality of physical objects and processes, then we have no reason to objectify information. We do not live in a simulation of the solar system; we live in the solar system. Maps are not territories unless the maps become territories.

      I don’t expect this argument to be a knockdown rebuttal to Platonisms, but I do expect it to undermine the motivation for being a Platonist.

      • We do not live in a simulation of the solar system; we live in the solar system.

        How do you know?

        • Robin, that’s not going to get you anywhere, I’m afraid. Yes, you can always mount the radical skeptical challenge, but it is sterile, with nowhere to go. Do you seriously think you are living in a simulation of a solar system, or are you playing devil’s advocate just for the hell of it (which is fine, of course)?

      • Hi John,

        Thanks for responding.

        If we accept the reality of physical objects and processes, then we have no reason to objectify information.

        I disagree. I think that like energy and momentum, it sometimes makes sense to think of information as a physical quantity in order to make sense of some physical systems, especially those regarding entropy. The black hole information paradox is an example of a real physical problem where information needs to be taken seriously to understand the issues.

        There are independent reasons for Platonism, such as making sense of the independent discovery of the same mathematical objects by different people, and to understand what it is that mathematical notation refers to.

        We do not live in a simulation of the solar system; we live in the solar system

        To be clear, Tegmark does not believe we live in a simulation, he believes we live in a universe which is an abstract mathematical object (and so do I), however I agree that the simulation is a suitable analogy so that’s OK. Unless I’m interpreting you incorrectly, the point of your virtual orrery was to illustrate the difference between our “real” world and an abstract world. However, clearly it cannot be legitimate to assume that our world is “real” in order to prove that it is “real” (whatever that means), so your virtual orrery does not even begin to address Tegmark’s view.

        Maps are not territories unless the maps become territories.

        This statement is reasonably compatible with my views. Our mathematical understanding of the world is our map. The world is the territory. But if the two are the same thing, which is the view expressed by Tegmark, then the map is indeed the territory. (I would not say “become” because mathematical objects do not “become” anything, they are changeless).

        • Some accounts of physical causation rely upon a “conserved quantity” account. One can recast “preserved information” as a “conserved [physical] quantity” without loss. I prefer that account, as you may gather.

          As to maps becoming, I have in mind Lewis Carroll’s Sylvie and Bruno Concluded:

          “Mein Herr looked so thoroughly bewildered that I thought it best to change the subject. “What a useful thing a pocket-map is!” I remarked.

          “That’s another thing we’ve learned from your Nation,” said Mein Herr, “map-making. But we’ve carried it much further than you. What do you consider the largest map that would be really useful?”

          “About six inches to the mile.”

          ” Only six inches ! ” exclaimed Mein Herr. “We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all ! We actually made a map of the country, on the scale of a mile to the mile !”

          “Have you used it much?” I enquired.

          “It has never been spread out, yet,” said Mein Herr: “the farmers objected: they said it would cover the whole country, and shut out the sunlight ! So we now use the country itself, as its own map, and I assure you it does
          nearly as well.”

      • Hi Massimo,

        Robin, that’s not going to get you anywhere, I’m afraid.

        I really think that your criticism of Robin is misplaced. In context, we are discussing whether John was right to conclude that the real world is not a mathematical object by comparing it to a simulated world which from our perspective has no mass. Whether the physical world is abstract is precisely what is at stake, so Robin is quite right to point out that John is simply assuming that it is not.

        In any case, Robin is not putting forth a radical skeptical position. This is not solipsism, or a denial that the universe exists. Instead, Robin is questioning John’s unexamined assumptions about what physical reality is, and quite rightly too. The MUH and the Simulation Hypothesis are both ideas in worth taking seriously but dismissed out of hand by John’s preconceptions about reality.

      • Robin, that’s not going to get you anywhere, I’m afraid. Yes, you can always mount the radical skeptical challenge, but it is sterile, with nowhere to go.

        I am not aware of having mounted any radical skeptical challenge.

        But what I said makes my point exactly.

        If this were a simulation then the observable objects would be information and there would be nothing that the information was about.

        Since we cannot tell whether or not we are in such a simulation then it makes not empirical difference, adds no explanatory power, to assume that there is something that the information is about.

        Even if we were not a simulation, it still would not follow that there is something that the information is about. We can only see as far as we can see.

      • Do you seriously think you are living in a simulation of a solar system, or are you playing devil’s advocate just for the hell of it (which is fine, of course)?

        Neither – I just don’t know one way or the other.

        Given that our superstar theoretical physicists are lining up to go on the telly and trumpet the possibility, I don’t think it is that radical a proposition.

      • Hi John,

        I fail to see how casting information as a conserved physical quantity makes it less real. Energy and momentum are also conserved physical quantities which some would regard as real.

        Thanks for reminding me of Sylvie and Bruno’s map. I had read that many years ago. Lewis Carroll is insightful and thought-provoking as always.

        I remain confused as to whether you think the point about maps and territories has been settled or not. Again, my view is that maps can be identical to the territories if both are mathematical objects, and as such it is wrong to claim that people who suspect the universe may be a mathematical object are simply confusing the map for the territory.

        Whether they are right or wrong, it seems clear to me that there is more than simple muddled thinking going on and it doesn’t do them justice to dismiss them so easily with aphorisms such as “the sign is not the thing signified”.

        (The sign is the signified if what you are trying to signify is the sign itself, e.g. the symbol ‘+’ in this example both signifies and is the symbol ‘+’.)

      • Disagreeable, I do not think making information (as structure in the world) a conserved quantity makes it less real, but it does tend to undercut the semantic and syntactic elements of physical information. Given that there is structure in the mind-independent world, call it information if you like, but do nto import the semantic and syntactic connotations, which is what I am objecting to. This is a form of reification fallacy.

  10. In the end it comes down to personal preference. If someone wants to assume the reality of physical objects and processes, what ever it might mean to do so, then they can.

    It makes no difference one way or another, science would be done the same either way.

    Sometimes assuming the existence of physical objects might serve as a useful intuition pump and sometimes it is better to simply shut up and do the maths.

    As I said eariler, our most successful physical theories were developed by a collaboration of physicists who had widely disparate views on ontology.

    Einstein said, in a letter to Schlick, that to call something “real” was as meaningful as calling it “cock-a-doodle-do” but that nevertheless reality was a very useful concept.

    • Robin, no, it doesn’t just come down to preference. You Have To assume the reality of physical processes, or you won’t be able to navigate the world successfully. Plus, you wouldn’t be able to make sense of the difference between what we feel is real and what we know is simulated.

      • Robin, no, it doesn’t just come down to preference. You Have To assume the reality of physical processes, or you won’t be able to navigate the world successfully.

        It is the information that helps me navigate the world successfully. I have managed to navigate the world more or less successfully without making any assumptions about its reality for at least 20 years now. How would any assumption about reality increase my ability to do so?

        Plus, you wouldn’t be able to make sense of the difference between what we feel is real and what we know is simulated.

        Since I cannot know that I am not a simulation I can’t do that whether physical objects are real or not,

      • I have managed to navigate the world more or less successfully without making any assumptions about its reality for at least 20 years now. How would any assumption about reality increase my ability to do so?

        That I find hard to believe. No assumptions? I think you are making assumptions about not making assumptions that are unwarranted.

      • Hi Michael,

        Please re-read, I didn’t say I made no assumptions.

        I said I made no assumptions about the world’s reality.

  11. This is a physical scenario of how we could be living in a type of Matrix: Some super being in his part of the universe/multiverse had a super 3D-4D printer that printed out our observable universe in the form of programmable matter. (See selfassemblylab.net @ MIT.)

    • Indeed, but I always wonder about the assumption that, if we were a simulation, the simulation would be carried out in a reality similar to ours.

      If we were a simulation then all our laws of physics, spacetime, gravity, particles quantum fields etc might just be a fiction invented by the designer of the simulation.

      The real world might have radically different physical laws to our own in ways we couldn’t possibly imagine. So the number of ways we could be a simulation are beyond number.

      • My point was to contrast a simulation with an assembly. For example, we can run a model of a human heart in a computer (a simulation), but apparently we are close to having a 3D printer that can print out that model as a working heart (an assembly).

        Maybe someday we could print out the model of a new universe with a different physics that comes out on the other side of a black hole. The sentient beings (they would not be living in a simulation, but an assembly) that may come about may not ever know.

  12. John Wilkins: “Consequently, abstract properties do not cause anything in the physical world. …
    Suppose I program my computer as an orrery, a simulation of the solar system. If I do this, the computer represents the mass and physical constants as numbers, and processes them according to the mathematical equations of physics. But that solar system in my computer doesn’t have the mass of a real solar system (luckily for me, and everyone else on earth). Instead it has an abstract mass, and the ways the abstract sun and planets interact is, well, abstract. A mathematical description of a system like the solar system is abstract. Apart from instances of that description in physical objects like heads, paper or computers, it exists nowhere in space or time. Consequently, abstract properties do not cause anything in the physical world. …
    An abstraction cannot cause a physical process, and to think otherwise is a category error, unfortunately …”.

    Amen!

    If I am the one who completes the ‘Final’ physics theory which describes the Nature to its last detail, I will immediately realize two facts when the last period is dotted on that paper.
    a. All mysteries of this universe are documented as ‘information’ in my model.
    b. The details of this information ‘were’ implemented for creating a something (which we call it as ‘this’ universe today) about 15 billion years ago by, by, by, …, not by me.

    Science has done a great job for mankind. But, the scientism is not good by all means. When someone mistaken the science information on paper as the reality itself, there is something terribly wrong on this. But, those kind of nonsense will not truly hurt the advancement of science, at best, just nuisance. The greatest killer on the advancement of science is the ‘box’ demarcated by scientists themselves. A short dialog with Nigel Lockyer (Fermilab director) on this ‘box’ issue at (http://www.quantumdiaries.org/2014/04/24/massive-thoughts/#comment-191676 ) highlights it.

  13. I was going to comment merely that I think the Central Dogma is not that all information flows from DNA to, ultimately, proteins. I think that it says that there is no process that the amino acid order of any given protein is instantiated in a novel DNA strand. And I think the distinction makes a great deal of difference in research in abiogenesis and also in understanding tRNAs.

    However, it seems that a recurring controversy over the ambiguity of skeptical epistemology has, well, recurred. So far as living in a simulation goes, I’m pretty sure that there are multiple issues regarding computability, computation time, decidability of algorithms budgeting processing time, problems with chaotic determinism. Just one example: How does the simulation program input a value for the effect of a butterfly flapping its wings in Brazil? How do you round off and where does the hurricane blow after that? Oh, I admit it, I liked, here’s a second example: How do you simulate interstellar photons that might be detected by a Hanbury Twiss Brown interferometer?

    I don’t think there’s any sensible way to say that the universe can be simulated. All this chatter about Chaitin restraints seem to me to make it perfectly clear that talk about computing a simulation is nonsense. Again, given the foundational issues in mathematics, I don’t know how mathematical Platonism can hope to claim to be mathematical knowledge. Mathematical Platonism seems to be self-refuting, relying solely upon a fixed determination that only the unchanging logically necessary a priori counts as knowledge. Undecidability and incompleteness would leave blank spots in the simulation. I am amenable to trying to understand a brief sketch of how they don’t? The thing is, i don’t think the most unregenerate mathematical Platonist has even made the slightest effort to do that.

    And further, doesn’t Occam’s Razor, which if I understand correctly was always meant to apply to Forms, which means that any Platonism needs to explain which abstract objects are relevant in any given instantiation? Which is to say, we need some rule to determine which Forms are the minimum needed to “explain” whatever it is the philosopher is trying to explain about the real world. The thing there is, is that among other implications of Turing’s work, is the conclusion that all the Platonic forms can be abstracted as programs. That brings back all those pesky problems with decidability and computing time, meaning that the Platonic Forms can’t calculate the world either. But there erupts a kind of War in (Platonic) Heaven, in which the mathematical Forms of Whiteness and Horseness and Hoofiness and Animal Metabolism struggle eternally to “explain” the white horse.

    (If I have offended anyone by treating Occam’s Razor as a critique of Forms instead of a heuristic guide for empirical investigation and thereby desecrated his spirit, my apologies.)

  14. It’s a bit from an it and the rest is useless shit,
    in terms of what can be described by bits for its.
    But all that useless shit,
    that’s not described by bits,
    nonetheless
    exists.

  15. There once was a physicist who thought it
    Was formed from a collation of bit
    When his computer crashed
    He went and got smashed
    And admitted he was full of excrement.

  16. John, thanks for this article. Your writing is clear and confident – exactly what I’d like to read more of.

    DisagreeableMe, it seems to me you have two main points in favor of your view – first, that mathematics is sufficient to account for reality, and so positing some other stuff on top of it is unreasonable. This begs the question, I *think*: maths is sufficient to account for our best description of reality, but there’s no way to know that it can account for reality itself. Better to say “I don’t know”? And second, that math is independent of minds (2 is 2 no matter where it shows up, even if there are no minds to think about it; a^2 + b^2 = c^2; etc.). Is it the same with logic, e.g., A = A? I think A = A is dependent on minds, even though I also think that any mind worthy of the name would have to formulate and use A = A. So, to me, it’s not inconsistent to say the same about math (that math is dependent on minds, and that all minds would create the same math).

    Robin Herbert, you wrote “I would say that the concrete realisation is, in itself, the abstraction having an effect. You can’t have a concrete realisation of an abstract thing unless you have that abstract thing.” I think this is directly begging the question. One might as easily contend that you can’t abstract from something without first having the concrete referent, and that abstractions supervene on their representations, not vice versa.

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