Computers Can't Do Math

https://www.plough.com/en/topics/life/technology/computers-cant-do-math

by danielam • 2 years ago

3 11 2 years ago

rini173• 2 years ago

Getting the sad vibes of "philosophy dept. hopelessly trapped in bubble with microsoft and wolfram products, nevermind ever speaking to CS dept."

The argument may be valid, but could have been lightyears advanced if author had any inkling there already were attempts for computers to "think" symbolically and they underdelivered and there was an "AI winter". The reason was NOT that infinite precision arithmetic was not possible.

danielam3• 2 years ago

The author could have perhaps made this clearer, but charitably read, the argument isn't really about numerical precision. Precision only functions as an instrument to demonstrate the point, which is that human beings possess the concept of number, while computers do not. And because we possess the concept of number, not only do we not suffer from such representational limitations per se, but we know or can know when they hold in certain representations. The essential distinction is between concept and representation. In computers, there are only representations of a conventional sort, whose meaning is entirely dependent on the interpreter (us). Human beings form concepts, and these concepts are the normative basis for producing and judging representations. Without concepts, computers cannot even in principle make such judgements.

rini173• 2 years ago

Why cannot computer possess concepts or meaning? Because they can't possess consciousness? And why is that, what is consciousness? Because <<... boils down to some kind of magical thinking...>>

joegibbs• 2 years ago

It’s a very interesting article that’s based entirely on a flawed premise, that floating point is the only way to represent numbers in a computer. It’s true that there are numbers that can’t be represented by a computer using any system, but they are so huge that you probably couldn’t represent them any other way either (say a random number with a quadrillion digits, since a billion digits is totally possible and a trillion is pushing it on consumer hardware. Even then, it could probably be done with a million bucks of hardware).

defrost• 2 years ago

It all hinges about the mentioned tract “Dangers of Computer Arithmetic”.

FWiW many of the mathematicians I knew that worked on the early iterations of the CAYLEY|Magma symbolic algebra system were equally ill suited to multiplying large numbers and bookkeeping - if not by numerical manipulation talent then certainly by temperament.

None the less they managed to cobble together a computer math system that could generate a headline:

Quantum encryption algorithm cracked in minutes by computer running Magma

but of course that was not arithmetic.

danielam3• 2 years ago

See my reply: https://news.ycombinator.com/item?id=40633347

gus_massa• 2 years ago

Computers can't play Chess

Computers can't play Go

Computers can't do Math

aidenn02• 2 years ago

The precision argument is so amazingly bogus that I won't refute it except with a link[1], so here are refutations of some other parts:

My kids sometimes ask me how high I can count. I’ve noticed that they stop asking this question once they reach a certain age, usually around six or seven. This is because the question does not make sense once you understand what a number is. If there’s a single highest number you can count to, you don’t really grok numbers. The difference between computers and humans doing math is a bit like the difference between the younger kids who think that “how high you can count” is a real thing and the older kids who have successfully understood how numbers work.

There actually is an answer to this; most people's short term memory for digits is less than a dozen, so the author likely can't count higher than 1e12, as they won't be able to go from e.g. 374841483741 to 374841483742 without getting one of the digits in the middle wrong.

The representation of the numbers that occurs only in the mind of the human is conflated with the execution of a particular program that takes place in the computer

This merely argues that computer math can be different than human math, which even that I'm not quite going to concede, since it would imply e.g. that the mathematicians behind the IEEE 754 standard were unaware of the implications of floating point arithmetic.

To us the transition between the theoretical and the actual happens almost instantly and unnoticeably.

Indeed it is happening almost instantly and (being generous to the author) without the author noticing throughout this paper, conflating concepts to the point where one could demonstrate almost anything is beyond the reach of computers, even things that are clearly well within the reach of them!

1: https://github.com/stylewarning/computable-reals

Computers Can't Do Math

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