Robert Marks on the math paradox challenging physics
|December 15, 2015||Posted by News under Information|
Anything algorithmic can be done by a computer. Give me a recipe for doing something, and I can whip it up in the kitchen. There are things which are not algorithmic the most celebrated of which is Turing’s halting problem: there exists no algorithm able tell whether or not a computer program runs forever or halts. (The halting algorithm must work for any and all computer programs.)
But a computer program will halt or won’t halt. But since there is no algorithm to figure this out, the halting problem is undecidable. We don’t know before running the program whether or not it will halt. It could run trillions of years and then halt long after we’re dead. If it doesn’t halt, we may never know (unless we know the so-called busy beaver numbers which is the same as knowing Chaitin’s number which is unknowable. But I digress.)
I’ve always thought this is a strong statement about determinism. A computer program that doesn’t use randomness is deterministic. There it is. All 12,465 lines of code. Yet we don’t know whether or not this deterministic program will halt or not. Rice’s Theorem extends undecidability to any “non-trivial” property of the computer program. We can’t even write an algorithm to tell us whether or not the number 3 will be printed by a computer program! So undecidability is much greater than only the problem of halting.
Chaitin wrote a book called The Unknowable that addressed this view of undecidability. (His other books are better.) Chaitin’s number is a single number between 0 and 1 that, if known, would allow solution of ALL the unsolved problems in math that can be resolved with a single counterexample (assuming we had gobs of time and computer memory.) Its construction uses the halting problem. So the C++ on your computer has a deterministic Chaitin’s number. But it is unknowable. Bummer.
Lastly, Roger Penrose in Shadows of the Mind and The Emperor’s New Mind makes the case the human mind, through creativity and the creation of information, does nonalgorithmic things (and is therefore not merely a computer).
I am starting to believe creation of information requires a nonalgorithmic process, hence intelligent design.
Creation of information as a nonalgorithmic process? Most writers you’d ever want to read would understand that. See also: How DOES creativity happen? Have we found the answer via neuroscience?
The creation of new information is not incomprehensible. But it often cannot be understood in the way many insist on trying to understand it. On the other hand, their attempts do often generate suitable subjects of fun.
See also: Math problems unanswerable due to physics paradox? Or versa vice? Early overheard comments say that the issue turns on undecidability and could have big implications for naturalism.
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