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Multiplying 3842 by 543 is very hard for humans. They're slow and inaccurate. Computers do it perfectly at incredible speeds. Inventing multiplication is somet

by beat 11y ago

Multiplying 3842 by 543 is very hard for humans. They're slow and inaccurate. Computers do it perfectly at incredible speeds. Inventing multiplication is something no computer (as we currently understand them) would ever be able to do. For another analogy, moving ten tons of rock a thousand feet is something humans can do, and have done for millennia. It's very slow and difficult. A bulldozer can do the same thing in minutes. But a bulldozer would never, ever have a reason to move ten tons of rock.

arethuza 11y ago
Doug Lenat's Automated Mathematician (AM) apparently did "discover" multiplication by itself: http://web.onetel.net.uk/~hibou/ai-course/lenat.txt http://web.onetel.net.uk/~hibou/ai-course/lenat.txt https://en.wikipedia.org/wiki/Automated_Mathematician https://en.wikipedia.org/wiki/Automated_Mathematician Of course, you could argue that multiplication was implicitly there in the rules and facts it was programmed with.
- adamsea 11y ago
  Write me program that could write Doug Lenat's Automated Mathematician. ;) I think the OP's point was until humans invent true strong AI there is a qualitative difference between human and computer intelligence. And even if/when a true "thinking machine" is invented, the intelligence which was able to create said machine would be nothing to sneeze at!
  - lyle_nel 11y ago
    Write me a programs that could write me a program that could write Doug Lenat's Automated Mathematician ... and so on and so forth.
    - beat 11y ago
      I wonder how many people in this thread have read Hofstadter's Gödel, Escher, Bach?
- progressive_dad 11y ago
  Let me know when humans invent something not governed by the rules the universe was programmed with ;-)
  - maaku 11y ago
    Theoretical physicists do that every day. It's only noteworthy when they find one that actually corresponds to the real world...
  - beat 11y ago
    Poetry.
    - progressive_dad 11y ago
      I wouldn't go that far. Maybe, "witty", but I wouldn't call it Shakespeare.
  - camelNotation 11y ago
    Literature, Art, Music, Philosophy, Religion... Basically everything that isn't a science.
  - kazinator 11y ago
    A lot of mathematics doesn't correspond to anything happening in the known universe. Mathematics describes infinities, infinitesimals and uncomputable numbers that are only hinted at using symbols which are not to be confused with those numbers themselves.
- deleted 11y ago
  [deleted]
- varjag 11y ago
  That's what Lenat himself argues in his follow-up paper. But I generally agree, there's nothing preventing computers "as we know it" to exhibit human level general intelligence. Humans weren't just smart enough so far to program it yet.
DonaldFisk 11y ago
> Inventing multiplication is something no computer (as we currently understand them) would ever be able to do. AM, the discovery learning program developed by Doug Lenat, discovered multiplication, beginning with a few basic facts about set theory, and using about 200 heuristics.
- yequalsx 11y ago
  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.
ta_donk_gt 11y ago
Small nit, but as hinted at by the other responses, humans didn't "invent" multiplication, they discovered it. In the same way we didn't "invent" the fact that the earth revolves around the sun, we discovered it.
- beat 11y ago
  I'd argue that we discovered the earth goes around the sun, but we invented multiplication. It's a philosophical argument, however.
  - Retric 11y ago
    Generally invention applies to the first discovers. I would suggest in the entire universe both observable or not we are unlikely to be the first species to discover multiplication. Languages like English, French etc on the other hand have much better odds even if language as a concept is really old. PS: I have even seen 'rediscovery' used for the same situations when a math idea was lost etc.
- simondedalus 11y ago
  that's debatable, once you appreciate the point about having a reason to do something. calculation itself really only exists with purpose. it's a thing to do if you have a reason to do it. of course, these kinds of things too seem more "discovered" than "invented", but it's a very different kind of discovery than "the earth revolves around the sun". the earth revolves around the son, as far as we can figure these days, whether any agent/subjectivity/etc intends anything or not. however, no full-blooded calculation will ever occur anywhere in the universe unless someone needs to figure something out. in other words, intention is implicit with calculation (and truth-functional representation, by the by). as such, you could make a case for an argument for "inventing" strategies in mathematics. and of course, a lot depends on your ontology of mathematics in the first place. if you're a wittgensteinian about numbers, and you think any of what i said above is at all compelling, you may be inclined to believe that mathematics itself is an invention. you may admit of some more nuanced way that entities like "number" still exist without mathematics as a tool, you may not, but you'd probably see all mathematics existing as active work, not pre-existing objective Truth. of course, most people think of math as an always-there abstract object (roughly). maybe they're right. even so, there must be some force in the "i use it as a tool" and "it just revolves around the sun no matter what anyone--god or man or beast--wants" distinction.
baddox 11y ago
Does that really matter though? It seems a bit like not giving humans credit for their accomplishments since, after all, sexual reproduction evolved a billion years before humans even existed.
klipt 11y ago
The average human couldn't invent multiplication either - it took humanity as a whole thousands of years to get to that point. Even writing was only independently invented a handful of times in history.
dota_fanatic 11y ago
How many people work jobs today that are akin in nature / level of fulfillment to inventing multiplication? How many people work jobs that are best done by a machine? How much energy does it take for a human intelligence to do these jobs vs a machine? How many people are furthermore stunted in their growth due to forced submission to their middle managers, a power differential that hardly need exist but feels great for the manager (king in their little castle)? I'm pretty sure computers, as we currently understand them, are entirely capable of inventing multiplication, provided sufficient source code and input. Evolution is unique in being able to "create" a thing that can formalize multiplication? Human intelligence is not magic.
- beat 11y ago
  Human intelligence is not magic, but it is categorically different from machine intelligence. What's amazing isn't that Deep Blue could beat Kasparov, given the depth of analysis it could do. What's amazing is that Kasparov could beat Deep Blue, despite not being able to analyze thousands of possible moves a second in his head.
  - fossuser 11y ago
    I think Alpha Go is more in the category of human intelligence. My probably oversimplified understanding is that the neural network training on a massive amount of games develops something like intuition. It can't explain why a certain move it makes is the best, but only that it is the most likely to win. This seems similar to advanced human play.
    - ArkyBeagle 11y ago
      One heuristic is that anything that is AI that actually works gets reclassified as something else. Are Kalman filters machine intelligence? It sort of doesn't matter, really.
deleted 11y ago
[deleted]
jhayward 11y ago
In this thread we rediscover the truism that "AI is everything that hasn't been done yet." [1] [1] https://en.wikipedia.org/wiki/AI_effect https://en.wikipedia.org/wiki/AI_effect
- danielam 11y ago
  It is no truism. It is merely dismissive and does not constitute a legitimate argument. There are numerous philosophers who have made arguments that challenge the notion of AI in the strong sense and who have no such interest in "preserving" feelings of human specialness that are allegedly being threatened. To lump all arguments against strong AI and computationalism in with "AI effect" is ignorant.

by beat 11y ago

arethuza 11y ago

Doug Lenat's Automated Mathematician (AM) apparently did "discover" multiplication by itself: http://web.onetel.net.uk/~hibou/ai-course/lenat.txt http://web.onetel.net.uk/~hibou/ai-course/lenat.txt https://en.wikipedia.org/wiki/Automated_Mathematician https://en.wikipedia.org/wiki/Automated_Mathematician Of course, you could argue that multiplication was implicitly there in the rules and facts it was programmed with.

adamsea 11y ago
Write me program that could write Doug Lenat's Automated Mathematician. ;) I think the OP's point was until humans invent true strong AI there is a qualitative difference between human and computer intelligence. And even if/when a true "thinking machine" is invented, the intelligence which was able to create said machine would be nothing to sneeze at!
- lyle_nel 11y ago
  Write me a programs that could write me a program that could write Doug Lenat's Automated Mathematician ... and so on and so forth.
  - beat 11y ago
    I wonder how many people in this thread have read Hofstadter's Gödel, Escher, Bach?
progressive_dad 11y ago
Let me know when humans invent something not governed by the rules the universe was programmed with ;-)
- maaku 11y ago
  Theoretical physicists do that every day. It's only noteworthy when they find one that actually corresponds to the real world...
- beat 11y ago
  Poetry.
  - progressive_dad 11y ago
    I wouldn't go that far. Maybe, "witty", but I wouldn't call it Shakespeare.
- camelNotation 11y ago
  Literature, Art, Music, Philosophy, Religion... Basically everything that isn't a science.
- kazinator 11y ago
  A lot of mathematics doesn't correspond to anything happening in the known universe. Mathematics describes infinities, infinitesimals and uncomputable numbers that are only hinted at using symbols which are not to be confused with those numbers themselves.
deleted 11y ago
[deleted]
varjag 11y ago
That's what Lenat himself argues in his follow-up paper. But I generally agree, there's nothing preventing computers "as we know it" to exhibit human level general intelligence. Humans weren't just smart enough so far to program it yet.

DonaldFisk 11y ago

> Inventing multiplication is something no computer (as we currently understand them) would ever be able to do. AM, the discovery learning program developed by Doug Lenat, discovered multiplication, beginning with a few basic facts about set theory, and using about 200 heuristics.

yequalsx 11y ago
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.

ta_donk_gt 11y ago

Small nit, but as hinted at by the other responses, humans didn't "invent" multiplication, they discovered it. In the same way we didn't "invent" the fact that the earth revolves around the sun, we discovered it.

beat 11y ago
I'd argue that we discovered the earth goes around the sun, but we invented multiplication. It's a philosophical argument, however.
- Retric 11y ago
  Generally invention applies to the first discovers. I would suggest in the entire universe both observable or not we are unlikely to be the first species to discover multiplication. Languages like English, French etc on the other hand have much better odds even if language as a concept is really old. PS: I have even seen 'rediscovery' used for the same situations when a math idea was lost etc.
simondedalus 11y ago
that's debatable, once you appreciate the point about having a reason to do something. calculation itself really only exists with purpose. it's a thing to do if you have a reason to do it. of course, these kinds of things too seem more "discovered" than "invented", but it's a very different kind of discovery than "the earth revolves around the sun". the earth revolves around the son, as far as we can figure these days, whether any agent/subjectivity/etc intends anything or not. however, no full-blooded calculation will ever occur anywhere in the universe unless someone needs to figure something out. in other words, intention is implicit with calculation (and truth-functional representation, by the by). as such, you could make a case for an argument for "inventing" strategies in mathematics. and of course, a lot depends on your ontology of mathematics in the first place. if you're a wittgensteinian about numbers, and you think any of what i said above is at all compelling, you may be inclined to believe that mathematics itself is an invention. you may admit of some more nuanced way that entities like "number" still exist without mathematics as a tool, you may not, but you'd probably see all mathematics existing as active work, not pre-existing objective Truth. of course, most people think of math as an always-there abstract object (roughly). maybe they're right. even so, there must be some force in the "i use it as a tool" and "it just revolves around the sun no matter what anyone--god or man or beast--wants" distinction.

baddox 11y ago

Does that really matter though? It seems a bit like not giving humans credit for their accomplishments since, after all, sexual reproduction evolved a billion years before humans even existed.

klipt 11y ago

The average human couldn't invent multiplication either - it took humanity as a whole thousands of years to get to that point. Even writing was only independently invented a handful of times in history.

dota_fanatic 11y ago

How many people work jobs today that are akin in nature / level of fulfillment to inventing multiplication? How many people work jobs that are best done by a machine? How much energy does it take for a human intelligence to do these jobs vs a machine? How many people are furthermore stunted in their growth due to forced submission to their middle managers, a power differential that hardly need exist but feels great for the manager (king in their little castle)? I'm pretty sure computers, as we currently understand them, are entirely capable of inventing multiplication, provided sufficient source code and input. Evolution is unique in being able to "create" a thing that can formalize multiplication? Human intelligence is not magic.

beat 11y ago
Human intelligence is not magic, but it is categorically different from machine intelligence. What's amazing isn't that Deep Blue could beat Kasparov, given the depth of analysis it could do. What's amazing is that Kasparov could beat Deep Blue, despite not being able to analyze thousands of possible moves a second in his head.
- fossuser 11y ago
  I think Alpha Go is more in the category of human intelligence. My probably oversimplified understanding is that the neural network training on a massive amount of games develops something like intuition. It can't explain why a certain move it makes is the best, but only that it is the most likely to win. This seems similar to advanced human play.
  - ArkyBeagle 11y ago
    One heuristic is that anything that is AI that actually works gets reclassified as something else. Are Kalman filters machine intelligence? It sort of doesn't matter, really.

deleted 11y ago

[deleted]

jhayward 11y ago

In this thread we rediscover the truism that "AI is everything that hasn't been done yet." [1] [1] https://en.wikipedia.org/wiki/AI_effect https://en.wikipedia.org/wiki/AI_effect

danielam 11y ago
It is no truism. It is merely dismissive and does not constitute a legitimate argument. There are numerous philosophers who have made arguments that challenge the notion of AI in the strong sense and who have no such interest in "preserving" feelings of human specialness that are allegedly being threatened. To lump all arguments against strong AI and computationalism in with "AI effect" is ignorant.