The proof that 1+1=2 is nontrivial despite it being clear and obvious. It does not rely on physicality nor experience to prove.

There are areas of utility here. Things need not be able to do all actions to be useful.

There isn't a serious proof that 1+1=2, because it's near enough axiomatic. In the last 150 years or so, we've been trying to find very general logical systems in which we can encode "1", "2" and "+" and for which 1+1=2 is a theorem, and the derivations are sometimes non-trivial, but they are ultimately mere sanity checks that the logical system can capture basic arithmetic.

If this is new, then you're one of today's luck 10,000![2] Serious logical foundations take a lot of time and exposition to start from fundamentals. Dismissing them as non-serious because GP's argument failed to consider them is misguided, IMHO.

[0] The classic reference: https://en.wikipedia.org/wiki/Principia_Mathematica -- over 1,000 pages, Betrand Russell

[1] https://cmartinez.web.wesleyan.edu/documents/FP.pdf -- a bit more modern, relying on other mathematics under the hood (like DRY reduces the base count), 11 pages

[2] https://xkcd.com/1053/

[3] Some reasonable review https://blog.plover.com/math/PM.html

Am I the only one that always felt like that xkcd post came from a place of insane intellectual elitism?

I teach multiple things online and in person... language like that seems like a great to lose a student. I'd quit as a student, it's so condescending sounding. It's only lucky because you get to flex ur knowledge!(jk, pushing it I know lol but i can def see it being taken that way)

Keep in mind I know you're just having fun.

I can't be too condescending with the number of typos I have to edit :D

I actually really like the message for 1 in 10,000. As a social outsider for much of my life, it helped me to learn that the way people dismissed my questions about common (to them) topics was more about their empathy and less about me.

But, these sorts of things are difficult to communicate via text media, so we thus persist.

Yeah I guess I've had only a few people be the other person that treated me right as the 1 - I feel ya on being an outsider having things dismissed. Does make sense. Another person gave me a good alternate view as well.

On a side note my couple of times I thought I was treating someone to some great knowledge they should already know I'm pretty sure I came across as condescending. Not bc they didn't know it - i always aim to be super polite - just being young, stupid, and bad at communicating, heh.

The key thing to focus on with XKCD 1053, is that the alternative before that comic was to make fun of the person who didn't know there's a proof for, eg 1 + 1 = 2. "Oh, you didn't know there's a proof for that? are you an idiot? who doesn't know the proof for 1 + 1 = 2 by Alfred North Whitehead and Bertrand Russell?", to which I think you could agree would put possible students off more by that than being told they're in luck today.

Ah okay that's a good read. I'm just always on edge about my language and sometimes view the worst possible interpretation rather than what most would read. I'm not a negative person... just goes back to some "protecting myself" instincts I unfortunately had to develop. Thanks for that view.

Yes, as I said: systems such as Russell's encoded "1", "2" and "+" in such a way that the theorem "1 + 1 = 2" is non-trivial to prove. This doesn't say anything about the difficulty of proving that 1 + 1 = 2, but merely the difficulty of proving it in a particular logical encoding. Poincare ridiculed the Principia on this point almost immediately.

And had Russell failed to prove that 1 + 1 = 2 in his system, it would not have cast one jot of doubt on the fact that 1 + 1 = 2. It would only have pointed to the inadequacy of the Principia.

There's no way you get to 1+1=2 without experience. There would be no one to even make that statement.

See the work I posted in sibling comment in this chain.

The subject has been debated ad nauseam by everyone like Descartes, Hume, Kant, and so on. If there were no one around to state 1 + 1 = 2, there would be no such statement. Hence, it does rely on at least 1 person's experience. Yours in fact, since everyone else could be an illusion.

So are you saying people who have CIPA are less intelligent for never having experienced a hot shower? By that same logic, does its ability to experience more colors increase the intelligence of a mantis shrimp?

Perhaps your own internal definition of intelligence simply deviates significantly from the common, "median" definition.

It's the totality of experiences that make an individual. Most humans that I'm aware of have a greater totality of experiences that make them far smarter than any modern AI system.

Greater totality of experiences than having read the whole internet? Obviously they are very different kind of experiences, but a greater totality? I'm not so sure.

Here is what we know: The Pile web scrape is 800GB. 20 years of human experience at 1kB/sec is 600GB. Maybe 1kB/sec is bad estimate. Maybe sensory input is more valuable than written text. You can convince me. But next challenge, some 10^15 seconds of currently existing youtube video, that's 2 million years of audiovisual experience, or 10^9GB at the same 1kB/sec.

I feel the jump from "reading the internet" to experience has a gap in reasoning. I'm not experienced in philosophy or* logic enough(no matter how much I read, heh) to articulate it, but seems to get at the person's idea of lacking street smarts, common sense. An adult with basic common sense could probably filter out false information quicker since I can get Claude to tell me false info regularly(I still like em, pretty entertaining) which has not only factual but contradictory flaws any person wouldn't make. Like recently I had two pieces of data, then when comparing them it was blatently incorrectly(they were very close, but claude said one was 8x bigger for... idk why.)

Another commenter also mentioned sensory input when talking about the brown rat. As someone who is constantly fascinated at the brains ability to reason/process stuff before I'm even conscious of it, I feel this Stat is Underrated. I'm taking in and monitoring like 15 sensations of touch at all time. Something entering my visual field coming towards me can be deflected in half a second all while still understanding the rest of my surroundings, and where it might be safe to deflect an object. The brain is constantly calculating depth perception and stereo location on every image and sound we hear - also with the ability to screen out the junk or alter our perception accurately(knowing the correct color of items regardless of diff in color temp).

I do concede that's a heck of a lot of video data. It does have similar issues to what I said(lacks touch, often no real stereo location, good greenscreen might convince an AI of something a person intuitively knows is impossible) but the scale alone certainly adds a lot. That could potentially make up for what I see as a hugely overlooked thing as far as stimulus. I am monitoring and adjusting like, hundreds of parameters a second subconsciously. Like everything in my visual field. I don't think it can be quantified accurately how many things we consciously and subconsciously process, but I have the feeling it's a staggering amount.

The people that have have barely used the internet are often far better conversation (and often more useful in the economy) than people who are addicted to the internet.

See the responses section https://en.wikipedia.org/wiki/Knowledge_argument This idea certainly has been long considered but I personally reject it.

While interesting, this is a separate thought experiment with its own quirks. Sort of a strawman, since my argument is formulated differently and simply argues that AIs need to be more than brains in jars for them to be considered generally intelligent.

And that the only reason we think AIs can just be brains in jars is because many of the people developing them consider themselves as simply brains in jars.

Not really. The point of it is considering whether physical experience creates knowledge that is impossible to get otherwise. Thats the argument you are making no? If Mary learns nothing new when seeing red for the first time an AI would also learn nothing new when seeing red for the first time.

> Do they know what a hot shower feels like? They can describe it. But do they actually know? Have they experienced it

Is directly a knowledge argument

Mary in that thought experiment is not an LLM that has learned via text. She's acquired "all the physical information there is to obtain about what goes on when we see ripe tomatoes". This does not actually describe modern LLMs. It actually better describes a robot that has transcribed the location, temperature, and velocity of water drops from a hot shower to its memory. Again, this thought experiment has its own quirks.

Also, it is an argument against physicalism, which I have no interest in debating. While it's tangentially related, my point is not for/against physicalism.

My argument is about modern AI and it's ability to learn. If we put touch sensors, eyes, nose, a mechanism to collect physical data (legs) and even sex organs on an AI system, then it is more generally intelligent than before. It will have learned in a better fashion what a hot shower feels like and will be smarter for it.

> While it's tangentially related, my point is not for/against physicalism.

I really disagree. Your entire point is about physicalism. If physicalism is true than an AI does not necessarily learn in a better fashion what a hot shower feels like by being embodied. In a physicalist world it is conceivable to experience that synthetically.

I love hearing someone else tell me I'm not saying what I'm saying.