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I don't consider this an example of discovering multiplication. The set theory rules were given to the computer. Can a computer be built to start only with se

I don't consider this an example of discovering multiplication. The set theory rules were given to the computer. Can a computer be built to start only with sensory input and then discover the rules of set theory? Would it ever be able recognize why the patterns and rules for operating with sets are important and worth further study? I'm skeptical. Would a program flag the discovery of multiplication as important because it understood that this discovery is interesting or would it flag its discovery as important because the programmer encoded it to have this understanding? That is can a program discover something new and alert to humans to this discovery and for it to be truly interesting and new?

maaku 11y ago
Absolutely. Look at Pat Langley's BACON program back in the 80's. He didn't work on multiplication per se, but given nothing but "sensory input" it discovered laws of planetary motion, rules of physical chemistry, conservation laws, etc.
- yequalsx 11y ago
  I looked at a summary of his work. I've never heard of him or of the BACON program so my knowledge is essentially zero in this. Looking at summary of his work it doesn't seem to me to qualify either. I'm not sure how to convey the idea in my head to English in such a way to make it clear why I think BACON doesn't qualify as discovering new ideas. I'll try though. From the write up, by Langely, of the program he wrote the program to detect regularity in data and if it found such regularity it would "leap out" to the program so that "it could take appropriate" action. As I understand the program it picks up on any sort of regularity. The program doesn't understand which forms of regularity are important and which are not. The programming system and data it looks at are geared to finding regularity that are meaningful. If the data inputs are vastly widened then it seems to me it would find regularity that wouldn't be considered meaningful. I can imagine the program fixating on a regularity pattern that is meaningless. I hope what I'm writing makes sense. The work he did is interesting and I wonder what advances have been made since then. Let me ask this question. Would a program that looks for regularity discover that in finite probability spaces probability zero events never occur? I think this is something a computer could discover. Could it end up concluding that probability zero events can occur if one looks at uncountable probability measure spaces? It seems to mean that programs will never be able to think or discover things at a meta level. Would a program be able to discover Godel's incompleteness theorem? Of course I don't know the answer. I just suspect that the answer is no. However, humans took thousands of years to discover these things. So perhaps an AI that ran for that long could as well. Thank you for pointing me to the BACON program. I'd never heard of it before.
  - maaku 11y ago
    I'm not the one giving you downvotes. I believe you are incorrect, but you have taken the effort to explain your thinking and have the courage to admit that you could be wrong, so I wouldn't down-vote that. In any case, let me flip the question around at you: how did Goedel come up with his incompleteness theorem? Surely it didn't just magically appear in his head? Most likely he followed some standard procedures of mathematical practice: manipulate symbols according to learned rules, look for 'surprising' features in the result, build a sample demonstration of a surprising result, and use intuition regarding its outcome to drive further thinking, etc. You can look at any intellectual behavior and find processes underlying it, unless you want to argue that we don't live in a materialist universe and people have souls. Unless you go down that route, there must be mechanisms to thought, and indeed applied psychology agrees. So if there are mechanism to thought, why can't those run on a computer instead of biology?
DonaldFisk 11y ago
Eurisko, AM's successor, did that: AM and Eurisko used a measure of interestingness to direct their searches. Here is one of Eurisko's inventions: From EURISKO: A program that learns new heuristics and domain concepts: "Almost immediately, symmetry heuristics produced a very powerful yet simple device, one which simultaneously computes NAND and OR, using only two small metal regions, two n-doped regions, two p-doped regions, and one intrinsic channel region."
eli_gottlieb 11y ago
> Can a computer be built to start only with sensory input and then discover the rules of set theory? Yes. Abstract knowledge is learnable, and the brain is an inference machine.
- danielam 11y ago
  Non sequitur. In fact, what appears to be your stated premise actually argues against the conclusion, not for it. Besides, the mechanistic characterization of mind (you say brain, but for all intents and purposes here it makes no difference) is highly problematic.

maaku 11y ago

Absolutely. Look at Pat Langley's BACON program back in the 80's. He didn't work on multiplication per se, but given nothing but "sensory input" it discovered laws of planetary motion, rules of physical chemistry, conservation laws, etc.

yequalsx 11y ago
I looked at a summary of his work. I've never heard of him or of the BACON program so my knowledge is essentially zero in this. Looking at summary of his work it doesn't seem to me to qualify either. I'm not sure how to convey the idea in my head to English in such a way to make it clear why I think BACON doesn't qualify as discovering new ideas. I'll try though. From the write up, by Langely, of the program he wrote the program to detect regularity in data and if it found such regularity it would "leap out" to the program so that "it could take appropriate" action. As I understand the program it picks up on any sort of regularity. The program doesn't understand which forms of regularity are important and which are not. The programming system and data it looks at are geared to finding regularity that are meaningful. If the data inputs are vastly widened then it seems to me it would find regularity that wouldn't be considered meaningful. I can imagine the program fixating on a regularity pattern that is meaningless. I hope what I'm writing makes sense. The work he did is interesting and I wonder what advances have been made since then. Let me ask this question. Would a program that looks for regularity discover that in finite probability spaces probability zero events never occur? I think this is something a computer could discover. Could it end up concluding that probability zero events can occur if one looks at uncountable probability measure spaces? It seems to mean that programs will never be able to think or discover things at a meta level. Would a program be able to discover Godel's incompleteness theorem? Of course I don't know the answer. I just suspect that the answer is no. However, humans took thousands of years to discover these things. So perhaps an AI that ran for that long could as well. Thank you for pointing me to the BACON program. I'd never heard of it before.
- maaku 11y ago
  I'm not the one giving you downvotes. I believe you are incorrect, but you have taken the effort to explain your thinking and have the courage to admit that you could be wrong, so I wouldn't down-vote that. In any case, let me flip the question around at you: how did Goedel come up with his incompleteness theorem? Surely it didn't just magically appear in his head? Most likely he followed some standard procedures of mathematical practice: manipulate symbols according to learned rules, look for 'surprising' features in the result, build a sample demonstration of a surprising result, and use intuition regarding its outcome to drive further thinking, etc. You can look at any intellectual behavior and find processes underlying it, unless you want to argue that we don't live in a materialist universe and people have souls. Unless you go down that route, there must be mechanisms to thought, and indeed applied psychology agrees. So if there are mechanism to thought, why can't those run on a computer instead of biology?

DonaldFisk 11y ago

Eurisko, AM's successor, did that: AM and Eurisko used a measure of interestingness to direct their searches. Here is one of Eurisko's inventions: From EURISKO: A program that learns new heuristics and domain concepts: "Almost immediately, symmetry heuristics produced a very powerful yet simple device, one which simultaneously computes NAND and OR, using only two small metal regions, two n-doped regions, two p-doped regions, and one intrinsic channel region."

eli_gottlieb 11y ago

> Can a computer be built to start only with sensory input and then discover the rules of set theory? Yes. Abstract knowledge is learnable, and the brain is an inference machine.

danielam 11y ago
Non sequitur. In fact, what appears to be your stated premise actually argues against the conclusion, not for it. Besides, the mechanistic characterization of mind (you say brain, but for all intents and purposes here it makes no difference) is highly problematic.