In seeking tales and informations [Henry VIII, Act V, scene 3]
For some time now* 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. [“Replicators and Vehicles” 1982]
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:
… 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”. Some mischievous philosophers 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, his contemporary, had an entire philosophical school based upon the older Democritan atomism [see this excellent review just revised in the Stanford Encyclopedia].
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 remained and was co-opted by the molecular biologists and geneticists in 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 time). 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. [Crick in 1958]
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 molecule in methylation molecules, which themselves 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 meaning of “information” 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] 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 leaves out the actual physical properties of adenine, cytosine, guanine, and thymine, which can do things occasionally the symbols cannot, even the most well specified and detailed representation of a thing, at least above the fundamental building blocks of the universe if we ever can say we have them, will leave out properties and capacities we are not interested in representing, and so they will, sometimes but inevitably, 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, even worse than getting involved in a land war in Asia. 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, 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). And since we have no real reason to adopt hylomorphist views on 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 (Griesemer 2005, Waters 2000). For this reason I much prefer the notion of a “reproducer”, 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].
Crick, Francis H.C. 1958. On Protein Synthesis. Symp. Soc. Exp. Biol. XII, 139-163.
Dawkins, Richard. 1982. “Replicators and vehicles.” In Current problems in sociobiology, 45-64. Cambridge UK: Cambridge University Press.
Dawkins, Richard. 1986. The blind watchmaker. Harlow: Longman Scientific and Technical.
Griesemer, James 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. Amsterdam: Rodopi Publishers.
Griffiths, Paul, and Karola Stotz. 2013. Genetics and philosophy: an introduction. Cambridge: Cambridge University Press.
Tegmark, Max. 2008. “The mathematical universe.” Foundations of Physics 38 (2):101-150.
Waters, Kenneth. 2000. “Molecules Made Biological.” Revue Internationale de Philosophie 54 (4):539-564.