JB

I just finished reading a paper that is both fantastically interesting, and a little disheartening. It is disheartening only because I thought that my senior paper for seminary was going to be freshly novel, but it turns out that someone else already made 90% of my arguments 11 years ago, and actually made most of them better than I could. The paper is "Algorithmic Information Theory, Free Will, and the Turing Test" by Douglas Robertson (*Complexity* 4(3): 25-34).

Here are some quotes from the paper (note that AIT is "Algorithmic Information Theory"):

"...free will appears to create new information in precisely the manner that is forbidden to mathematics and to computers by AIT" (26)

"There would be no reason to prosecute a criminal, discipline a child, or applaud a work of genius if free will did not exist. As Kant put it: "There is no 'ought' without a 'can'" (26)

"A 'free will' whose decisions are determined by a random coin toss is just as illusory as one that may appear to exist in a deterministic universe" (26)

"AIT appears to forbid free will not just in a Newtonian universe, or in a quantum mechanical universe, but in every universe that can be modeled with any mathematical theory whatsoever. AIT forbids free will to mathematics itself, and to any process that is accurately modeled by mathematics, because AIT shows that formal mathematics lacks the ability to create new information." (26)

"The fundamental secret of inspired mathematical practice lies in knowing what information should be destroyed or discarded, and what rearrangement of available information will prove to be most useful." (30)

"The very phrase "to make a decision" strongly suggests that the information is created on the spot." (31)

"If...we do accept this definition of free will, then an immediate corollary from AIT is that no combination of computer hardware and sofware can exercise free will, because no computer can create information." (31)

"There is perhaps no clearer demonstration of the ability of free will to create new information than the fact that mathematicians are able to devise/invent/discover new axioms for mathematics. This is the one thing that a computer cannot do. The new axioms produced by mathematicians contain new information, and they cannot be derived from other axioms. If they could, they would be theorems rather than axioms." (31)

"it has long been accepted that free will is impossible in a Newtonian deterministic universe. But now the impossibility is seen to carry over into all possible physical theories, not just Newtonian theories, because it is inherent in mathematics itself. According to AIT, no physical model (i.e. no mathematical model for a physical process) can allow the creation of information. In other words, free will is impossible in any physical universe whose behavior can be accurately modeled by a computer simulation." (33)

"All theory is against the freedom of the will; all experience for it" (33 citing Samuel Johnson)

"The idea that all physical processes can be modeled is an assumption that is so deeply ingrained in physics that it is seldom questioned, seldom even noticed." (33)

"It may be that physicists since the time of Newton have been exercising a careful (but generally unconscious) selection proess. Physicists may have studied only those physical processes that happen to be susceptible of mathematical modeling. This would immediately explain the reason behind Eugene Wigner's famous remark about the "unreasonable effectiveness of mathematics." But if it should turn out that many physical processes are not susceptible to mathematical modeling, just as nearly all numbers cannot be expressed with any mathematical formula, this would represent as deep a shock to physics as Godel's theorem was to mathematics, and one that is far greater than the shock that resulted from the loss of Newtonian determinism when quantum mechanics was developed or the loss of Euclidean geometry when general relativity was discovered." (34)

"The possibility that phenomena exist that cannot be modeled with mathematics may throw an interesting light on Weinberg's famous comment: "The more the universe seems comprehensible, the more it seems pointless." It might turn out that only that portion of the universe that happens to be comprehensible is also pointless" (34)

"The existence of free will and the associated ability of mathematicians to devise new axioms strongly suggest that the ability of both physics and mathematics to model the physical universe may be more sharply limited than anyone has believed since the time of Newton." (34)

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