Monday, June 28, 2004
On the nature of logic and computing, is there a difference?
(new beads are edited for a few days until the grammar is correct)
Sent: Monday, June 28, 2004 7:54 PM
Subject: RE: Foundations to Knowledge Science
Wojtek and John:
To have an executable process does not require logic, throwing dice is a mechanical process. The rules of logic do not judge whether the method of throwing is right or wrong. The question is instead -- whether you choose to play a game the whole world plays -- that simply is what it is.
If instead of using a cpu, I use a gated counter attached to a radio active source and use it to generate a seemingly random number reflecting perhaps the consequences of some "natural law". We might call that the experimental measurement of a quantum event. The criteria for judging the acceptability of this finding of consequence -- deals only with the global capability to reproduce and verify the result with independent observations, not that logic played any causative, descriptive, or epistemological role in its modeling or acceptance.
By my definition "computing" is any use of a predictable (not deterministic) "physical process" to divine (map) the rational outcomes of theory. It is the reverse process of proving a theory by experiment. Any mapping may be judged representative, if it is variously isomorphic, homomorphic, suggestive, etc, of the theory espoused. So absolutely any theory -- logical, stochastic, economic, political, ethical, esthetic, etc. -- that makes useful predictions and establishes thereby a mapping process (one to one, many to one, many to many, etc.) creates a computer -- made of electronics, paper, table, nomogram, operational amplifier, analog, digital, beads, gears, ... -- medium or mechanics play no role.
For a paper semantic network or a map of California to become a declarative computer, requires only an understanding of the meaning of the lines (relationships) connecting one point (entity to another), i.e. what influence or theory establishes the meaning of seeing a connection between two or more things on the map, but not the existence of an identical relationship with other places or entities on that same map.
A declarative semantic map "computes" the outcomes of all theories used in its construction. It has no need for a cpu whose only function is to reaffirm that 3+3 still equals 6, and 2 is still greater than 1. Truly we only need a cpu, when there might be plausible, conditional situations in our computations, when 3+3 = 5 and 2 < 1.
The problems that John points out with quantum devices is that they do not return true/false answers reliably, they always say "maybe". Quantum computing is not about making flip-flops and AND gates smaller and cheaper. That is what makes today's nanocomputing such a joke to a physicist. Quantum computing is about modeling natural law with quantum uncertainty, not logical truth.
Sent: Sunday, June 27, 2004 10:11 PM
Subject: RE: Foundations to Knowledge Science
I was just trying to avoid questions about unknown developments at some unforeseeable time in the future:
JFS Perhaps. But if the software runs on current digital
computers, it can be formalized in first-order logic.
Any claim to the contrary is self deception."
WMJ Is it correct to say: "software" - non run-able "on current
digital computers" - could be in a no "first-order logic"
At present, nobody knows. In the 1930s, there were three independent developments that all turned out to be computationally equivalent, in the sense that anything that could be computed by one could also be computed by the other two: Goedel's recursive functions, Church's lambda calculus, and Turing's automata. Furthermore, no computing device since then -- either imagined or implemented -- has been shown to compute anything that could not be computed by any or all of the three methods defined by Goedel, Church, and Turing. And all three of those methods as well as every computing device invented since then can be defined in first-order logic.
Some people, such as Penrose (as in _The Emperor's New Mind_), have claimed that perhaps quantum mechanical mechanisms might be able to compute things that cannot be computed by current digital computers. However, that claim is still unproven. The quantum mechanical mechanisms promise to be able to compute certain kinds of things many times faster than current machines, but nobody has shown that they can compute anything that cannot be computed by the mechanisms of Goedel, Church, and Turing (or by any ordinary digital computer). Right now, the current Q-M devices are still extremely unreliable, and it is very hard to get them to do things that are trivially simple with ordinary digital computers (although certain problems might be solved much more quickly if and when the technology is improved).
So the short answer to your question is that nobody knows.