William M. Briggs

Statistician to the Stars!

It from bit: What about God? Guest Post by Bob Kurland


Editor’s note: See Kurland’s page for an extended version of this article, with references.

‘It from bit’ symbolizes the idea that every item of the physical world has at bottom—at a very deep bottom, in most instances—an immaterial source and explanation; that what we call reality arises in the last analysis from the posing of yes-no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and this is a participatory universe. —John Wheeler, Information, Physics, the Quantum: the Search for Links


These are the three questions:

  1. How come existence?
  2. How come the quantum?
  3. How come “one world” out of many observer-participants?

Wheeler’s answer to the first question is: “…every it—every particle, every field of force, even the spacetime continuum itself—derives its function, its meaning, its very existence entirely—even if in some contexts indirectly—from the apparatus-elicited answers to yes or no questions, binary choices…bits.”

That statement seems to be implicitly based on a a physicalist view of reality; that only those things measured or tied to a physical picture of the world are real. What about all those important things that can never be quantified as a binary choice? I’ll mention just three in which degree, rather than “yes” or “no” enter as qualifiers: love, faith, happiness.

Wheeler gives three examples to support the claim that information theory—“it from bit”—is a foundation for quantum theory: (1) The Wootters-Zurek demonstration that the photon can not be split, can not be cloned; (2) The Aharanov-Bohm experiment in which a magnetic field, negligible in the neighborhood of an electron, nevertheless affects its trajectory; (3) The Beckenstein entropy of dark holes, in which the entropy of a black hole is proportional to the area encircled by its horizon, and thus contains (lost?) information.

Information theory as foundational for quantum theory is very much in vogue these days. The most thorough and intelligible discussion of information theory/quantum mechanics that I’ve found is Christopher Timpson’s Ph.D. Thesis, “Quantum Information Theory and the Foundations of Quantum Mechanics“. I’ll not attempt to summarize that work, but only remark that Timpson shoots holes in several attempts to establish information theory as the grounding for quantum mechanics, but does endorse one proposal, which lays a quantum mechanics foundation not only on information theory but on the mathematics of C-algebras.

As did Wheeler, I’ll leave the answer to the third question until the “four no’s” and “five clues” are discussed.


  1. No “tower of turtles”;
  2. No laws;
  3. No continuum;
  4. No space, no time.

The “no tower of turtles” statement asserts that infinite regress in a causal chain is not possible. In this Wheeler, St. Thomas Aquinas, and other philosophers are in agreement.

The “no laws” assertion denies that the universe is a machine built on law, a machine that would entail a multiverse, “universes in infinite variety and infinite number”. Rather, Wheeler envisions a “world self-synthesized”: “…the notes struck out on a piano by the observer-participants of all places and all times, bits though they are, in and by themselves constitute the great wide world of space and time and things.”

The “world self-synthesized” by “observer-participants of all places and all times” is, presumably, the answer or part of the answer to the third question above. But more questions are raised than answered here. Would an annelid worm, an eagle, and a human synthesize the same world, or is it only “intelligent beings”? If the last, what about the world synthesized by a Cro-Magnon man, an Australian aborigine, and Helen Keller? I don’t see a coherent scheme here.

By stating there is “no continuum”, Wheeler denies the reality of transcendental and irrational numbers. He uses quotes from the mathematician Hermann Weyl and the philosopher Willard Quine. to support that claim. One should also note that the “no continuum” condition requires that space and time must be discrete (but see below).

Wheeler’s “no space, no time” condition is perhaps the most unappealing intuitively. He claims that space and time are man-made inventions, and that at the beginning of the universe, “The Big Bang”, quantum behavior would override General Relativity—there would be no connectivity in space and before and after would have no meaning.


The five clues are listed below, but I’ll not go into a detailed discussion of them, because (frankly) I find them confusing.

  1. The boundary of a boundary is zero;
  2. No question, no answer;
  3. The super-Copernican principle;
  4. Consciousness;
  5. More is different.

As near as I can understand the first clue, it rests on topology: for example, the boundary of a line are end-points—zero length; the boundary of a plane area is a circumference, zero area; etc. The second clue I don’t understand in full, other than it says that probabilistic analyses in physics are misleading and that physics should be built on bit-theoretic principles. The third clue extends the Copernican spatial principle to time (we are not the center of the universe; any location is equally suitable as a reference): “now” is a misleading characterization of reality. By “consciousness”, Wheeler does not refer to any of the issues that engage philosophers of mind, connecting quantum theory with an observer directly.

Rather (as near as I can understand it) he refers to shared communication, as per his quote of Fellesdal: “Meaning is the joint product of all the evidence that is available to those who communicate.” D. Fel1esdal: “Meaning and experience,” in Mind and Language, p. 25-44.

“More is different” states what many philosophers and scientists propose: there are “emergent” properties of a group of elements that are not best analyzed by reduction to the properties of the individual elements; for example, superconductivity is not best treated as a problem involving individual electrons in a metal.


Missing from Wheeler’s thesis is any notion of the Divine as Creator and Sustainer of the universe, and to me, this lack renders the enterprise without value, however interesting it might be. I believe that quantum mechanics does provide an insight into Divine intervention.

In an article posted two years ago (almost to this day!) I wrote about the theological and philosophical implications of the quantum delayed choice experiment. The experiment was originally proposed by Wheeler, and has been successfully implemented by several physicists, What are the philosophical/theological implications of the delayed choice experiment? I believe this has been best expressed by the American physicist Raymond Chiao, in his article “Quantum Non-Localities: Experimental Evidence” in Quantum Mechanics—Scientific Perspectives on Divine Action.

Although it’s a long quote, it expresses better than I can the link between quantum mechanics and neo-Berkeleyan vision of Divine intervention.

I shall assume as a basic principle that the universe we live in bears witness to the Creator who created it [emphasis added]…let us generalize Berkeley’s philosophical principle to a ‘neo-Berkeleyan point of view’ in which God is the Observer of the universe, in the quantum sense of ‘observer’. This generalization starts from small systems…in which an observer created reality is seen to occur upon every elementary act of observation, and ends up with large systems—in particular with the entire universe.

In this viewpoint, every elementary, individual quantum event…is a result of a creative act of the universal Observer, in which all properties of all particles come into existence on their observation, in continual acts of creatio ex nihilo, which constitutes a kind of creatio continua occurring everywhere at once. Thus the existence of the universe itself is contingent upon the continual observations of the Creator. The idea of contingency of existence, in the sense of the utter dependency of the universe for its properties and existence at each moment upon its Creator, is thereby introduced via quantum physics into philosophy and theology…

…Furthermore, this viewpoint suggests a new meaning of the immanence of the Creator with respect to creation, since God is acting everywhere at once in the universe. Thus God is omnipresent, omniscient, and omnipotent…The neo-Berkeleyan viewpoint introduced here suggests not only a continual creatio ex nihilo qua creatio continua by an immanent Creator, but also a singular creatio ex nihilo by a transcendent Creator.

Moreover, the above Einstein-Podolsky-Rosen effects imply a quantum non-separability, which ties together the universe non-locally as a whole. This reminds one of the words of the Apostle John, ‘All things come into being through him, and without him not one thing came into being that has being.’ (John I:3) and of the words of the Apostle Paul, ‘All things have been created through him and for him…and to him all things hold together.’ (Colossians I:16,17)…We infer that ‘all things’ refers to the universe. Not only are all distant parts the universe woven together throughout space, but also its future and its past are entangled throughout time, as if the universe were one seamless garment

The Anglican theologian Bishop George Berkeley gave us the dictum, “esse est percipi“—to be is to be perceived, which we can invert: percipi est esse. In this Wheeler’s Participatory Universe stands, but it is God who is the participating observer. And to reinforce this point, what could be better than Monsignor Ronald Knox’s limerick about Berkeleyan idealism:

There was a young man who said, ‘God
Must think it exceedingly odd
If he finds that this tree
Continues to be
When there’s no one about in the Quad.’


‘Dear Sir:
Your astonishment’s odd:
I am always about in the Quad.
And that’s why the tree
Will continue to be,
Since observed by
Yours faithfully,


  1. Thanks, Bob.

    However, there is, if not an active contradiction, a massive disjuncture at the least, in Raymond Chiao’s argument, since He from Whom “All things come into being” is said by the Evangelist to be the Word, the Son; and similarly with the quote from Colossians. And there is nothing in the ‘observer God’ argument that demands, or even implies, the Son of God.

    In short, the ‘observer God’ argument is at best an Imagination Pump; it’s not a real argument — if your intention is to illuminate anything at all about actual Catholic doctrine.

    As I keep telling Matt (and you, I guess, by implication): the ‘Deus Unus’ just will not cut it as Catholic theology. And the gigantic holes in the concept, papered-over but never really addressed, are now so time-worn, so inbred, that neither you, nor Dr. Chiao, nor, I presume, your editor Matt, even noticed that those Scriptures are talking about the Son, and therefore that Dr. Chiao’s whole train of thought fails as an argument before it even begins.

    You guys are so fixated on the ‘Deus Unus’ that you could not see this, even though it was staring you in the face. This ‘Deus Unus’ thingie is actively clouding your thinking.

    But I’m talking to a wall. So it goes.

  2. I’ve studied topology a bit and I understand what he means by “the boundary of a boundary is zero” — but only in the mathematical sense. More technically, “is the empty set” would be more accurate. The iteration of the boundary operator is the key there. With much handwaving, the boundary operator takes a manifold and finds what is necessary to “complete” it, to add in the boundary. But a boundary is necessarily “complete” itself. An attempt to complete it finds that nothing whatsoever needs to be done — after all, if the boundary were incomplete then it wouldn’t have really completed the manifold in the first place, contradicting its definition — and thus the boundary of a manifold’s boundary must be 0.

    See https://en.wikipedia.org/wiki/Homology_(mathematics) for a more rigorous (and competent) description of the concept.

    What relevance any of that has to anything in physics or philosophy, I haven’t a clue. All that stuff just goes right over my head, frankly. That doesn’t stop me from trying to comprehend it, but I’m quite aware my brain and abilities were engineered quite specifically for mathematics.

  3. @ARB:

    “But a boundary is necessarily “complete” itself. An attempt to complete it finds that nothing whatsoever needs to be done — after all, if the boundary were incomplete then it wouldn’t have really completed the manifold in the first place, contradicting its definition — and thus the boundary of a manifold’s boundary must be 0.”

    There are different concepts of boundary. If for example, you are talking about topological boundary, then it is easy to find examples where the boundary of a boundary is not empty. But since you spoke of manifolds, presumably you are talking about the boundary of a manifold. But then (1) the boundary, while it can be interpreted in several cases as a sort of “completion” (e.g. “complete” the manifold with the “points at infinity”), it has a fairly straightforward definition that has nothing to do with that and (2) under the standard definitions, the boundary of a boundary can be non-empty, e.g. if the manifold has corners.

    The boundary operator in homology is a related, but different beast. In that context you *want* the boundary of a boundary to be zero — zero, not the empty set — so you rig your definitions to accomplish precisely that (e.g. define the boundary of a simplex as an alternating sum of its faces), that is, it is not a purely geometrical fact, and it has little or nothing to do with any “completions” whatsoever.

  4. @G. Rodrigues
    I was mostly trying to dismantle the complexity and strike at the heart of the concept for those who aren’t topologists or students of topology. (I am only the latter; and for all positive integers n not (1/2^n) as proficient as I strive to be, as you may have noticed.) I’ve mostly interacted with the idea through the simplicial complex (and yes, in that context it is “0”, not empty). My hummingbird-esque attempt at handwaving away an entire field’s complexity assumes a well-behaved n-manifold (call it A) embedded in R^n with the boundary definition one would obtain from Wikipedia or an undergrad introductory analysis course, bd(A):=clos(A)\Int(A), about which it would be more accurate to say bd(bd(A))=bd(A). (Also “completion” was certainly a poor choice of vague descriptive language; I cringed reading my post as it awaited moderation with nary an “edit” link in sight.)

  5. “this viewpoint suggests a new meaning of the immanence of the Creator with respect to creation, since God is acting everywhere at once in the universe.”

    A massive confusion of categories. God is the First Cause while quantum mechanics studies Secondary Causes of things.

  6. “God is the Observer of the universe, in the quantum sense of ‘observer”

    Reducing all events to miracles, strictly speaking and denying to God an ability to create a world in which things consistently interact with other things.
    That is, a denial that things have natures –a stable pattern of behavior and interaction.
    Philosophically, you have Occasonalism, the bane of Islamic science.

  7. Bob,
    I have been a bit reluctant to comment on this thread for personal reasons, but one additional aspect seems worth noting. I think the study of John Wheeler’s thoughts alone would be a completely satisfying use of a person’s life except for one thing: I believe he would not want you to spend as much time studying his thoughts as thinking your own. In the talk discussed here, Wheeler very painstakingly tried to see to the marrow of the concepts that comprise physics and explain them in a way that would stimulate thought in others. His fundamental theme throughout is not, I think, choices of formalisms or axioms but the key role of what he calls the “observer.” But I think he meant observer in a larger sense than has been used traditionally in relativity and quantum mechanics. Often an observer is viewed as something like a machine that operates a device and records the results of the device interaction with a physical system, almost like an idealized Turing model of a computer examining the next item of memory and acting accordingly (or halting if that ever gets proven). Such an observer would then interpret the past based on the outcome of that measurement and communicate (or output) the results. I think his view of an observer was much more active, more participatory in the unfolding of the universe. In that view, the will, or desire, even the pleasure derived from choosing to observe is as important as the subsequent phenomena. In a certain sense, the universe (at least according to physics) exists because we want to know it. But I think he would not want one to crease the brow and hunker down to solve the most complicated equations one could find in morose frenzy– unless it gave you the pleasure of knowing the universe. A key point I think he was trying to make is that the reason we don’t understand aspects of the universe is not the universe’s fault, in fact the universe is doing us a tremendous favour by playing the game with us. Wheeler would urge us to play the game.

    He was confident that many of the unanswered questions of his day (and still our current day) would be answered and that we will be chagrined at how simple the answers turn out to be. But I am not sure he believed that the game would ever be over. I suspect we will simply have more questions to answer. Part of the game that is so wonderful is that the active participant observer can choose the questions he or she wants to ask of the universe. I have grown fond of number theory and prime numbers of late but I can’t say why. Some people just like to study them. Hilbert famously said, “If I were to awaken after having slept for a thousand years, my first question would be: has the Riemann hypothesis been proven?” I suspect different participants in the conversation with the universe would want to see different questions answered after sleeping 1000 years. But in Wheeler’s view that would be fine, it is the act of playing the game with honesty, humility, and humor that “causes” the universe.

    I was very lucky to study under Wheeler (he would have said “with” him, but it wasn’t truly). I never heard him mention God or religion or metaphysics. It was all just physics. I was told he was a Unitarian but I am not sure it is true. At times it was almost scary because you never quite knew what he would say next. Often he would challenge you with an apparently off the wall idea, all the while smiling impishly. Some of the more conservative minded physicists said he was getting crazy as he got older. One of Wheeler’s famous students, Richard Feynman said that “Some people think Wheeler’s gotten crazy in his later years, but he’s always been crazy.” But he meant crazy like a fox, an impish, but humble, and ever so industrious fox. Once Wheeler asked me “Do you know why students come to the University?” I don’t remember what oafish answer I mumbled. His was “So the professors can learn from them,” followed by that impish smile. That is the approach to the universe I think he meant to instill.

  8. “…every it—every particle, every field of force, even the spacetime continuum itself—derives its function, its meaning, its very existence entirely—even if in some contexts indirectly—from the apparatus-elicited answers to yes or no questions, binary choices…bits.”

    Does every “It” includes the “its” of the measuring apparatus and the observer?

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