# It from Bit, Information as Fundamental

The main problem that leads Wheeler to propose his ‘it-from-bit’ doctrine is the mysterious nature of the fifth axiom of quantum mechanics, viz. the collapse postulate, which we will discuss later.  ‘It-from-bit’ is an antimetaphysical thesis.  The motivation for holding an antimetaphysical thesis is that it provides a clearer notion of truth and a definite, methodical path to getting there.

Wheeler’s central distinction is between ‘its’ and ‘bits.’  An it is a thing (that is, something that we ascribe existence to).  This class includes particles, forcefields, the spacetime ‘continuum,’ and your mother’s rosebush.  A ‘bit,’ is an apparatus-elicited answer to a yes-or-no question (that is, a binary choice); e.g. the counter registers a click in a specified second, indicated ‘yes’ for ‘photon.’1   Every ‘it’ derives its function, meaning, and existence from ‘bits.’  The reality of every ‘it’ is derived and established from the affirmative answer to a binary/digital question.  I establish the reality of my coffee mug by asking ‘is there a coffee mug on the table?’, looking to it and registering the familiar shape of the cup and handle, and the characteristic deep blue color, in my visual experience (resulting in an affirmative answer), and then I can say, ‘there is a coffee mug on the table.’

Wheeler says that ‘It from bit symbolizes the idea that every item of the physical world has at [very] deep bottom…an immaterial source and explanation;…reality arises in the last analysis from the pose of yes-no questions and the registering of equipment evoked response.’  This amounts to: all things physical are information-theoretic in origin — that is, information is in some sense ‘prior to’ the physical world.  We can break most things down and explain them in terms of their component parts — and take those component parts and do the same.  But eventually we will bottom out somewhere (binary).  Suppose we reach the most fundamental physical particle — some physical point — call it $\omega$.  At that point, the only question we can ask is the brute question, ‘is an $\omega$ there?’ as we cannot explain it in terms of other things (or anything else more fundamental).  If we can measure its presence, and in the affirmative, then that is the brute bottom of our explanation of $\omega$.  But the reality of $\omega$ comes from being able to measure its presence.  The information precedes the ascription of existence to the physical object.

Wheeler shows how this comes out in a number of ways.  Take a putative physical object, like a forcefield.  We measure the strength of a forcefield by using a device which measures shifts in interference patterns by representing the number of ‘fringes’ in the pattern.  But all the fringes can possibly stand for is a statistical pattern of yes-no registrations.  Or consider how we determine the existence of a photon.  We ask a question like, ‘did a counter register a click during a specified second?’  If so, we say, ‘a photon did it,’ thus ascribing existence to the putative physical object on the basis of binary information.  Blackholes furnish a particularly interesting example.  Consider the following discovery by Bekenstein.  The surface area of the horizon of a blackhole measures the entropy of the blackhole.  Thorne and Zurek explain that, in performing an operation on the value of the surface area we get $N$, the number of binary digits (‘bits’) required to specify in all detail the constituents of the blackhole.  Entropy is a measure of lost information.  No outside observer can determine which of the $2^N$ configurations of bits compose the blackhole.  So the size of a blackhole (an ‘it’) is defined by the number of ‘bits’ lost within it.  Finally, a more ordinary example.  You wish to determine whether or not your tea is too hot to drink.  If you taste it and burn your mouth then ‘yes’ it is too hot to drink.  If you taste it and do not burn your mouth, then ‘no’ it is not too hot to drink.  In this way, the evaluation of a putatively physical property like temperature is reduced to a binary choice, and so the information precedes the ascription of the property.

What this means is that physics can be cast in terms of information.  Wheeler calls (physical) reality a ‘theory.’  We can make each physical item a (metaphysically neutral) element (in some arbitrary state — either 0 or 1) in an information space, and characterize the relations (and their similarities and differences) between elements without ever being committed to a metaphysical claim about what those elements actually are.  Physics does not require a commitment to physicalist metaphysics.

For Wheeler, the notions of ‘meaning’ and ‘existence’ are intertwined.  Meaning is ‘the joint product of all the evidence that is available to those who communicate.’  So for something to be meaningful it must be (1) communicable and (2) empirical.  Let’s explain 1 first.  It’s plausible to say that anything expressible is communicable (and vice versa). If something that is meaningful were not expressible, then it could not mean anything, for that which expresses nothing clearly means nothing.  So for something to be meaningful it is necessary that it be expressible. Now let’s explain 2.  Something that is meaningful must make an empirical difference — that is, there must be some item in possible perceptual experience, which is logically possible to access, that corresponds to the thing’s truth-value.  This notion of meaning is not as impoverished as you might expect, for there is quite a bit of evidence available to communicators.  Even with regard to the past, an intrepid crew of investigators, armed with the right equipment, will be able to establish that such-and-such happened so-and-so long ago in the past, based on some chain or network of physical evidence.  Their findings will contribute to the establishment of that past event’s meaning.  Here’s how this importantly ties into existence.  If a $\phi$ is not meaningful, then it is meaningless to assert something like, ‘$\phi$ exists.’  (Attach any other predicate you choose, and it will nevertheless presuppose the existence of $\phi$.)  For suppose I do assert that ‘$\phi$ exists.’  That entails there must be some possible item in my perceptual experience which ‘verifies,’ so to speak, the existence of $\phi$.  If there isn’t anything that I could see, or smell, or taste, or hear as some result of $\phi$‘s existence, then it means nothing to say that $\phi$ exists.  What would it mean to ascribe existence to something which could never impinge upon our perceptual experience?  Its existence or lackthereof will never affect the truth-value of any proposition of this world.  So if something is not meaningful, any assertion of its existence is meaningless; therefore we can only grant existential status to those things which are meaningful.

Chalmers’ observes that this sits nicely with the idea of Shannon information.  In Shannon information, where there is information, there are information states embedded in an information space — where an information space is a structure of (difference) relations between its components.  Differences may be transmitted down some causal pathway.  Notice how this sits nicely with how Wheeler thinks that past events are meaningful.  Consider the infamous tree that fell in the forest with no one to hear it.  Nevertheless, its fall will leave some kind of evidence (like a depression in the ground, scattered needles, etc…) which some investigators may happen to stumble across (and so make the fall meaningful).  On this picture, the tree in the forest, prior to its fall, is an information state (to be defined in terms of its relations to other trees, perhaps).  The information space evolves, differences are transmitted, and some information relates to the tree in such a way that it falls (its fall constituting continuous differences down a causal pathway).  When the information corresponding to the falling tree is related to the ground, there are changed information states corresponding to the depression it leaves and the needles which scatter.  The information is finally communicated when our intrepid explorers see the depression and so receive the information of the tree having fallen.

Physical ‘its’ must come from ‘bits,’ which are discrete, for there is no continuum in physics.  There is no continuum in physics because there can be no continuum in mathematics.   Of the number continuum, Weyl says ‘belief in this transcendental world taxes the strength of our faith hardly less than the doctrines of the early Father of the Church.’  Likewise there can be no continuum of/for physical objects; they must be discrete.  Quine articles this point quite well, ‘Just as the introduction of the irrational numbers… is a convenient myth [which] simplifies the laws of arithmetic… so physical objects are postulated entities which round out and simplify our account of the flux of existence…  The conceptual scheme of physical objects is a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part.’  (1) That physics is discrete in this way means that it must yield to digital questions and consequently physics will be information-theoretic.  (2) I think that the phrase, ‘conceptual scheme of physical objects’ is particularly telling.  We interpret empirical evidence through a particular theory or conceptual lens — to call an object ‘physical’ is just to conceptualize a feature of our perceptual experience in a certain way.  We reserve the word ‘physical’ just for those meaningful, empirical items in our perceptual experience.

So on Wheeler’s account, ‘reality’ has the status of theory.  Reality is constructed out of the kinds of questions we ask about the world, and the ways in which we interpret those binary answers.  To press the point, consider how we measure the spin-properties of electrons.  Suppose I have an electron.  I cannot ascribe either ‘black’ or ‘white’ or both (or neither) until I shoot the electron through a color-box.  If the color-box does its job right, the outcome of the measurement will be with ‘black’ or ‘white’ (each with exactly $1/2$ probability).  But my choice to measure color disrupts the electron’s hardness value — that is, I can never predicate a definite hardness property and a definitely color property to the same electron at the same time.  The moral is that the choice of question (e.g. what is the hardness? vs. what is the color?) and the choice of when the question is actually asked play (some [but not the whole]) part in deciding what we can justifiably assert about reality or ‘the World.’  So to say that reality is a theory isn’t as unintuitive as it may first appear.

So if information is primary to physical objects — and, indeed, the status of physical objects is merely theoretical — then it seems like something which must be fundamental is perceptual experience.  This is the notion which led Chalmers to suggest something like Wheeler information as the fundamental constituent of reality.  Our conscious perception of ‘the World,’ or of things underlies all other empirical (and even metaphysical) knowledge.  Without it, reality wouldn’t even speakable.  So on this picture, physics has a distinct theoretical quality, whereas perceptual experience is non-theoretical and most fundamental.

1. Here’s the reason why I put scarequotes around ”photon.”  We ascribe existence to the thing we think caused the counter to register a click.  But a photon is a theoretical entity (you can never actually see a photon — only its causal influence).  If we conducted the experiment within a different theoretical/conceptual framework, we may attribute the registering of a click to some other theoretical entity.