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It from Bit

July 8, 2013

There's a saying, apparently originating with the psychologist, Abraham Maslow, that "if all you have is a hammer, everything looks like a nail." This was one criticism of Stephen Wolfram's 2002 book, "A New Kind of Science."[1] I wrote about Wolfram's book in a previous article (Peer Review, October 8, 2012).

Wolfram is a mathematical physicist, and he's also a computer scientist known for creating the Mathematica scientific computation program. It's no wonder that he thinks that the universe is a computer; or, at least, it can be analyzed as one. Each subsequent state of the universal computer is computed from the previous state, which sounds a lot like an idea called Laplace's demon.

This idea by mathematician and astronomer, Pierre-Simon Laplace, is a logical consequence of Isaac Newton's preceding work. Laplace reasoned that you could predict the future state of the universe if you knew the precise location and momentum of every one of its atoms. Of course, our present conception of quantum mechanics, as summarized in Heisenberg's uncertainty principle, is that it's impossible to know the location and momentum at the same time, so Laplace's demon can't do his calculation.

Isaac Newton and Pierre-Simon Laplace

Isaac Newton ((1642-1727, left) and Pierre-Simon Laplace (1749-1827, right). (Source images, left, Sir Godfrey Kneller's 1689 Portrait of Isaac Newton; and, right, Sophie Feytaud's 1842 Portrait of Pierre-Simon Laplace, via Wikimedia Commons)

According to Wolfram, the evolution of his universal computer is not fundamentally unknowable; but, rather, it's too complicated to figure out. Whether or not the universe functions as a digital computer, or by some other mechanism, all its elementary particles still "know" at time τ how to behave at time (τ + 1). We might not have predictability in the Laplace sense, but the universe evolves according to a set of rules which we call the laws of physics.

The idea that the universe calculates its existence from moment to moment has been around since the earliest computers. Konrad Zuse, who is often credited as the inventor of the digital computer, was the first to write about this idea in his 1969 book, "Rechnender Raum" ("Space that is Computing"). This idea was also pursued by entrepreneur and inventor of the Fredkin gate, Edward Fredkin.[2]

Just as Laplace extrapolated the consequences of the laws of classical physics, theoretical physicist, John Archibald Wheeler, mathematically extended the concept of the universal computer. Wheeler's idea, called "it from bit," is that physics at a fundamental level is based on answers to "yes-no" questions. This idea was qualitatively expressed in 1977 by Columbia University physicist, Frederick W. Kantor, but Wheeler gave it a mathematical framework in 1989. Luigi Foschini of the Istituto Nazionale di Astrofisica (INAF), the Osservatorio Astronomico di Brera, has posted an article on John Wheeler and "it from bit" on arXiv.[3]

As Wheeler wrote in his 1989 paper,
"Every physical quantity, every it, derives its ultimate significance from bits, binary yes-or-no indications"[4].
Wheeler's had a strong interpretation of "it from bit." In his 1998 autobiography,[5] "Geons, Black Holes, & Quantum Foam (W.W. Norton & Co., New York, 1998), co-authored with Kenneth W. Ford, he imagined such bits to be "quanta of reality,"
"I suggest that we may never understand this strange thing, the quantum, until we understand how information may underlie reality. Information may not be just what we 'learn' about the world. It may be what 'makes' the world.[5] (My emphasis)
Wheeler continues with an example of photon absorption. Until the photon is measured by absorption, it has no reality for us. By that measurement, we get another bit of information about the universe; but, also, "...that bit of information determines the structure of one small part of the world. It ‘creates’ the reality of the time and place of that photon's interaction."[5]

John Archibald Wheeler at Copenhagen, 1963

John Archibald Wheeler at a conference in Copenhagen, 1963.

Wheeler autographed his 1998 autobiography, "Geons, Black Holes, & Quantum Foam," for me at a conference in New York City in 2000.

It can be seen that Wheeler, like all of us, had trouble switching from one millennium to the next, first writing "19" as the year.

(Photograph of Wheeler by Gerhard Hund, via Wikimedia Commons. Signature scanned from author's book.)

As pointed out by Foschini, binary encoding of information is robust against corruption and misinterpretation. Placing information into "0" and "1" bins allows a sharp demarcation of data with little chance of misinterpretation; or, no chance of misinterpretation at the quantum level. Waxing philosophical, Foschini adds the following,
"It is the human being that, by assigning a meaning and creating a tongue with the signs so obtained, creates the it from bit... One can be satisfied for thinking that it is a gift (e.g. Wigner) or can try to understand how this happen."
The gift about which Foschini writes is the one in Eugene Wigner's May 11, 1959, Richard Courant lecture in mathematical sciences at New York University, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences."[6] As the title indicates, it seems so easy to express the laws of physics using mathematical equations.

Physicist, Max Tegmark, argues that this is true because the physical world is structured mathematically, and we discover this bit by bit. At times, our mathematics will only approximate the real mathematics of the universe, but it's interesting how we always find a better mathematical way when our first approximations are found to be insufficient.


  1. Stephen Wolfram, "A New Kind of Science," Wolfram Media, Inc., May 14, 2002. ISBN 1-57955-008-8.
  2. Ah, the joys of computer entrepreneurship. As documented in the article, Did the Universe Just Happen? by Robert Wright in the April, 1988, Atlantic Monthly, Fredkin once owned his own island. This 125 acre island, known as Moskito Island, is now owned by Sir Richard Branson. The sale price in 2007 was about $20 million.
  3. Luigi Foschini, "Where the "it from bit" come from?" arXiv Preprint Server, June 3, 2013.
  4. J. A. Wheeler, "Information, physics, quantum: the search for links," Proceedings III International Symposium on Foundations of Quantum Mechanics, Tokyo, 1989, p. 354-368.
  5. John Archibald Wheeler and Kenneth W. Ford, "Geons, Black Holes, & Quantum Foam," W.W. Norton & Co., New York, 1998.
  6. Eugene P. Wigner, "The unreasonable effectiveness of mathematics in the natural sciences," Communications on Pure and Applied Mathematics, vol. 13, no. 1 (February 1960), doi:10.1002/cpa.3160130102, pp. 1-14. PDF file available, here.

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