I suppose I should help clarify the subject by disambiguating terms.
Calculation in the broadest sense consists of the transformation of inputs into outputs. This is a process of deduction. (top down) Mathematics is Calculation.
Computation in the broadest sense is the performance of operations. (bottom up) in the absence of deduction, induction, or inference. Arithimetic is computation.
Probability, in now-popular AI, this difference is now re-conflated and restored to ambiguity because our computers, perform computations, using human-derived calculations, to produce bayesian accounting probabilities, as if they were inferences, because the number of dimensions of measurement and number paramaters exceed the human ability to calculate, in the category we call artificial intelligence. And since all langauge is reducible to measurements, where the measurement consists of a dimension that is subjectively testable by human experience, while still retaining it’s reducability to mathematical expression by substitution of arbitrary numbers as names and values as weights instead of natural naming (vs cardinal or ordinal).
Machines cannot perform mathematics however, they may perform computations, and therefore may perform arithmetic. Even though, as painful as it is, division is still a matter of tabular trial and error. Just as so much of mathematics is a matter of ‘fitting’.
I find math boring but I find the foundations of math, logic, and all the grammars (rules of continuous recursive disambiguation) fascinating. 😉
Reply addressees: @Zamicol @cryptogeni
Source date (UTC): 2024-01-08 13:40:22 UTC
Original post: https://twitter.com/i/web/status/1744353353725816832
Replying to: https://twitter.com/i/web/status/1744169409831145592
IN REPLY TO:
Unknown author
THE GODEL NONSENSE IS AN INTERGENERATIONAL INFECTION. 😉
–“There’s no proof that everything is computable. Information theory is in agreement with Gödel.”– Replying to @Zamicol and @cryptogeni
That is a naive statement. You are confusing the limits of mathematics with the limits of computation and not grasping computation as a sequence of possible operations. The fact is if the universe can construct anything at all – if ANYTHING can exist, then it is computable because there is no difference between computation and construction by permutation.
The difference is that mathematics is universally statistical (categorical) so that we can predict what is mathematically reducible, and that is only a subset of what is computable. The problem with computability is that there is no means of prediction – there is only a means of trial and error.
You also misunderstand Godel. The point is that not everything is provable because there is no closure to computability, and provability is a statement about logic given a set of fixed premises and not about existential possibility. Furthermore, the proof appears to be limited to arithmetical operations and nothing more complicated.
It appears you also misunderstand information theory given that the purpose of the theory is to explain the problem of entropy and noice precisely because of the information loss in mathematical (verbal, ideal) reduction vs computational (operational,real) procedures is due precisely to the fact that mathematics loses information and computation doesn’t (at least down to -35 decimal places).
I did not realize until the early nineties that this false understanding of Godel was spreading like a virus with each new generation of students learning programming – but who have no basic comprehension of its narrowness. However, there are authors who have written books, one in particular that I can’t recall off the top of my head, that I felt was largely accessible to the STEM degree-educated population.
I hope this helps you at least head in the right direction.
Let me know if you require further explanation.
Cheers
Original post: https://x.com/i/web/status/1744169409831145592
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