theotherquantumjim t1_je8ysa1 wrote on March 30, 2023 at 8:00 AM

Reply to comment by Andriyo in The argument that a computer can't really "understand" things is stupid and completely irrelevant. by hey__bert

This is largely semantic trickery though. Using apples is just an easy way for children to learn the fundament that 1+1=2. Your example doesn’t really hold up since a pile of sand is not really a mathematical concept. What you are actually talking about is 1 billion grains of sand + 1 billion grains of sand. Put them together and you will definitely find 2 billion grains of sand. The fundamental mathematical principles hidden behind the language hold true

Andriyo t1_jeam834 wrote on March 30, 2023 at 4:59 PM

There is nothing fundamental behind 1+1=2. It's just the language that we use to describe reality as we observe it as humans. And even beyond that, it's cultural: some tribes have "1", "2", "3", "many" math and to them it is as "fundamental" as Integer number system to us. The particular algebra of 1+1=2 was invented by humans (and some other species) because we evolutionary optimized to work with discrete objects to detect threats and such.
I know Plato believed in the existence of numbers or "Ideas" in a realm that transcended the physical world but it's not verifiable so it's just that - a belief.

So children just learn the language of numbers and arithmetic as any other language by training on examples - statistically. There might be some innate training that happened on DNA level so we're predisposition to learn about integers easier but it doesn't make "1+1=2" as something to discover that exists on its own like, say, gravity or fire.

theotherquantumjim t1_jearid2 wrote on March 30, 2023 at 5:33 PM

That is one school of thought certainly. There are plenty in academia who argue that maths is fundamental

Andriyo t1_jedirnp wrote on March 31, 2023 at 5:55 AM

It is certainly fundamental to our understanding of the world, but if we all forget tomorrow that 1+1 =2 and all math altogether, the world won't stop existing :)

theotherquantumjim t1_jednh7n wrote on March 31, 2023 at 6:56 AM

Whilst this is correct, 1+1=2 will still be true whether there is someone to observe it or not.

Andriyo t1_jeds606 wrote on March 31, 2023 at 8:03 AM

maybe it's my background in software engineering but truthiness to me is just a property that could be assigned to anything :)

say, statement 60 + 2 = 1 is also true in for people who are familiar with how we measure time.

anyway, most children do rote memorize 1+1=2, 1+2 = 3 - they even have posters with tables in school. they also show examples of "car is one","apple is one" etc. so basically what LLMs is doing. anyway, long story short LLMs is capable of doing long arithmetic if you ask it to do it step by step. The only limitation so far is the context length.

theotherquantumjim t1_jedspfh wrote on March 31, 2023 at 8:11 AM

The language and the symbols are simply the tools to learn the inherent truths. You can change the symbols but the rules beneath will be the same. Doesn’t matter if one is called “one” or “zarg” or “egg”. It still means one. With regards LLMs I am very interested to see how far they can extend the context windows and if there are possibilities for long-term memory.