3 ms·

I find a simple thought experiment answers this question. Imagine we trained an LLM using modern methods, and gave it infinite compute, on the entirety of human

I find a simple thought experiment answers this question. Imagine we trained an LLM using modern methods, and gave it infinite compute, on the entirety of human knowledge from 200,000 years ago. Would that AI then be able to create calculus, even if by another name obviously? I offer that as an example, because there's 0 need for knowledge of the physical world to derive calculus. All of mathematics is entirely an invention of the human mind. I think the answer is quite obviously no. LLMs can recite their training, and recombine it in ways that correlates strongly to how a human might do so. But creating entirely new knowledge, that goes above and beyond recombinations of what is already known, remains entirely outside the domain of LLMs. An LLM trained on slow classical music is not going to create rap. And an LLM trained on rap is not going to create classical music. And those are trivial examples since it's not entirely new, but just taking a concept and using it a slightly different way than 'normal.' Math, by contrast, is literally creating something from nothing. And this ability to create something from nothing is probably the most key indicator of intelligence. And we've yet to even step foot on the path towards creating software with this ability.

keiferski 3y ago
Another way of saying this point is that intelligence requires interaction with the world, or embodiment. Hip hop can’t be derived from European classical music without the context of 70s-80s NYC.
- somenameforme 3y ago
  We could debate that, but I think it's easier to just refer to the primary example of math. I offered that as an issue that requires absolutely no external interaction required there, whatsoever. It's entirely a mental creation. Like a child might say we somehow just 'thought it up.'
  - keiferski 3y ago
    I might be talking past you here, but: The idea that mathematics is entirely mental is a contentious statement and not one a lot of mathematicians would necessarily agree with. https://plato.stanford.edu/entries/philosophy-mathematics/ https://plato.stanford.edu/entries/philosophy-mathematics/ I think your intuition is right but I think it’s more because of the embodiment of humans in the world. The machine wouldn’t invent calculus because it wouldn’t be in a physical world that needed to.
    - akasakahakada 3y ago
      Again nonsensical body-experience argument. Do you need to see 11 dimensional world in order to invent math to deal with string theory? Do physicist see those extra dimensions in their eyes?
      - exe34 3y ago
        No they were trained in 4 dimensions, and had equations that seemed to make more sense in 11 dimensions.
      - necovek 3y ago
        Discussion here seems to be about "invention" of mathematics. I am pretty sure math does not happen without human bodies in the physical world as it is. Eg. imagine a life happening on a small gravity object travelling through space at speed approaching speed of light: how does space exploration look like and with what math? 11 dimensional vector calculus is a pretty clear example of recogniting generality between 1, 2 and 3 dimensions we can experience, and extending it to an arbitrary number. While humans, in their mind, do construct things they did not experience, we develop tools to do that based on what we do (even things like axiom of parallelism: we experience "intersections" or lack of them, so we can ask ourselves "what if two parallel lines do intersect?"). Mathematics has really become abstract in the last 2 centuries, and was pretty tied to physical reality up to that point.
        akasakahakada 3y ago
        What you mean is just a dataset of records of interaction around gravity as input to a system, and math as the output. There is no necessity for a "boby" to be included in here. And you are required to see 11 dimension to stand for your body experienceism. You are not allowed to extend linear algebra from 3D to arbitrary dimensions.
        necovek 3y ago
        I have no idea what you are talking about, sorry — what do you mean with "not allowed"?
akasakahakada 3y ago
Your logical loophole is that you forgot to include "process of creating thing" into the subset of human activity and this can be trained. Back in the days AlphaGo make some magical novel move in the game that shocked every Go experts. People study how AI play games to improve themselves nowadays. LLM nowadays solve insane hard science problem, invent new algorithms that you don't see.
- somenameforme 3y ago
  A game move, no matter how remarkable, is just a recombination within a strictly defined domain. And LLMs can do some awesome things in these very tight and well defined domains, especially when there is a way for them to determine victory or score. But stepping outside of well defined domains and creating knowledge that does not directly derive from what is already known is where intelligence shines. We somehow created mathematics out of absolutely nothing. We looked at the world around us and simply 'though it up' as a child might say.
  - exe34 3y ago
    No we didn't. We are very good at parallel construction, to come up with the clean implementation of what the maths can be, but most of the examples given here were extensions of thinking about physical problems. Remixing Jazz tokens might never generate classical music, but an evolutionary algorithm using musical notes and basing its cost function on what humans seem to enjoy might still discover something similar or better. A transformer could then generate infinite versions of that discovery.
    - somenameforme 3y ago
      I think this is provably false by looking at the various semi-isolated primitive tribes. They think about the world endlessly, yet many have yet to invent even basic mathematics. Many lack even the concept of numbers. For instance one tribe [1] only has concepts a few, more, and a lot. And in reality that's all you would ever really need for real world usage, pre mathematics. Mathematics largely creates the problems that it's used to solve. More interesting is that these tribes also tend to lack the ability to recall even basic quantities of things if it's more than 2. You can give them 5 balls, but they will have extremely poor recollection of the number after just a few moments. There's these countless things humans need to simply invent, from nothing, over and over to advance to the next technological era. It only seems like a natural application of logic in hindsight, because it actually works! [1] - https://www.sciencedaily.com/releases/2012/02/120221104037.htm https://www.sciencedaily.com/releases/2012/02/120221104037.h...
episteme 3y ago
I think also interesting if you ask, what if the model consumed all information up to the point that a great discovery was made? If a model has all the information that Einstein had, could it determine that E = mc2?

keiferski 3y ago

Another way of saying this point is that intelligence requires interaction with the world, or embodiment. Hip hop can’t be derived from European classical music without the context of 70s-80s NYC.

somenameforme 3y ago
We could debate that, but I think it's easier to just refer to the primary example of math. I offered that as an issue that requires absolutely no external interaction required there, whatsoever. It's entirely a mental creation. Like a child might say we somehow just 'thought it up.'
- keiferski 3y ago
  I might be talking past you here, but: The idea that mathematics is entirely mental is a contentious statement and not one a lot of mathematicians would necessarily agree with. https://plato.stanford.edu/entries/philosophy-mathematics/ https://plato.stanford.edu/entries/philosophy-mathematics/ I think your intuition is right but I think it’s more because of the embodiment of humans in the world. The machine wouldn’t invent calculus because it wouldn’t be in a physical world that needed to.
  - akasakahakada 3y ago
    Again nonsensical body-experience argument. Do you need to see 11 dimensional world in order to invent math to deal with string theory? Do physicist see those extra dimensions in their eyes?
    - exe34 3y ago
      No they were trained in 4 dimensions, and had equations that seemed to make more sense in 11 dimensions.
    - necovek 3y ago
      Discussion here seems to be about "invention" of mathematics. I am pretty sure math does not happen without human bodies in the physical world as it is. Eg. imagine a life happening on a small gravity object travelling through space at speed approaching speed of light: how does space exploration look like and with what math? 11 dimensional vector calculus is a pretty clear example of recogniting generality between 1, 2 and 3 dimensions we can experience, and extending it to an arbitrary number. While humans, in their mind, do construct things they did not experience, we develop tools to do that based on what we do (even things like axiom of parallelism: we experience "intersections" or lack of them, so we can ask ourselves "what if two parallel lines do intersect?"). Mathematics has really become abstract in the last 2 centuries, and was pretty tied to physical reality up to that point.
      - akasakahakada 3y ago
        What you mean is just a dataset of records of interaction around gravity as input to a system, and math as the output. There is no necessity for a "boby" to be included in here. And you are required to see 11 dimension to stand for your body experienceism. You are not allowed to extend linear algebra from 3D to arbitrary dimensions.
        necovek 3y ago
        I have no idea what you are talking about, sorry — what do you mean with "not allowed"?

akasakahakada 3y ago

Your logical loophole is that you forgot to include "process of creating thing" into the subset of human activity and this can be trained. Back in the days AlphaGo make some magical novel move in the game that shocked every Go experts. People study how AI play games to improve themselves nowadays. LLM nowadays solve insane hard science problem, invent new algorithms that you don't see.

somenameforme 3y ago
A game move, no matter how remarkable, is just a recombination within a strictly defined domain. And LLMs can do some awesome things in these very tight and well defined domains, especially when there is a way for them to determine victory or score. But stepping outside of well defined domains and creating knowledge that does not directly derive from what is already known is where intelligence shines. We somehow created mathematics out of absolutely nothing. We looked at the world around us and simply 'though it up' as a child might say.
- exe34 3y ago
  No we didn't. We are very good at parallel construction, to come up with the clean implementation of what the maths can be, but most of the examples given here were extensions of thinking about physical problems. Remixing Jazz tokens might never generate classical music, but an evolutionary algorithm using musical notes and basing its cost function on what humans seem to enjoy might still discover something similar or better. A transformer could then generate infinite versions of that discovery.
  - somenameforme 3y ago
    I think this is provably false by looking at the various semi-isolated primitive tribes. They think about the world endlessly, yet many have yet to invent even basic mathematics. Many lack even the concept of numbers. For instance one tribe [1] only has concepts a few, more, and a lot. And in reality that's all you would ever really need for real world usage, pre mathematics. Mathematics largely creates the problems that it's used to solve. More interesting is that these tribes also tend to lack the ability to recall even basic quantities of things if it's more than 2. You can give them 5 balls, but they will have extremely poor recollection of the number after just a few moments. There's these countless things humans need to simply invent, from nothing, over and over to advance to the next technological era. It only seems like a natural application of logic in hindsight, because it actually works! [1] - https://www.sciencedaily.com/releases/2012/02/120221104037.htm https://www.sciencedaily.com/releases/2012/02/120221104037.h...

episteme 3y ago

I think also interesting if you ask, what if the model consumed all information up to the point that a great discovery was made? If a model has all the information that Einstein had, could it determine that E = mc2?