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If or when we reach singularity, is there a law that limits the intelligence of the machines? If yes what is it and how can we be so sure (taking into account our own intelligence is rather limited)?

Basically my question is; is there an upper limit to to artificial intelligence that we know about?

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    $\begingroup$ If artificial wormholes or FTL communication exists in your universe and is feasible, then there is no direct limit. However if not, the speed of light will place an upper limit on computational speed, which will affect artificial consciousness, and subsequently, perceived intelligence. $\endgroup$ – Scott Downey Apr 6 '16 at 11:00
  • $\begingroup$ @ScottDowney neuron speed limits are well-known, however, we know nothing about how it limits our consciousness $\endgroup$ – enkryptor Apr 6 '16 at 11:51
  • $\begingroup$ In our world? Yes, but they are very high (thanks @armatita). In your world? That's up to you. $\endgroup$ – Devsman Apr 6 '16 at 13:02
  • $\begingroup$ Important consideration in this regard is, do you have a definition of intelligence that is quantifiable. I have answered the question with one important theoretical result that can help with that, below $\endgroup$ – Brad Thomas Apr 6 '16 at 13:27
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    $\begingroup$ Since this is tagged singularity, anything goes. If you reached the technological singularity in your world, most of the issues raised in the comments above have vanished. The AI can and probably will be undistinguishable from god. The too broad arises from this problem. You should probably move away from the singularity to get good answers. The fact none of the answers addressed the stated tech level show this need. $\endgroup$ – Mindwin Apr 6 '16 at 14:45
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We can only makes "laws" — which are statements of the sort "this is how this thing seems to work, as far as we can make out" — about things that we have an understanding of. We do not have an understanding of intelligence, nor artificial intelligence.

So: no, there is no such law, or more exactly — as demonstrated by the comment by @AlexandreTHOUVENIN — there is a law that says that presently there can be no such law. :)

It is rather as if humans tried to make laws about how radio works before Maxwell set up his equations on electromagnetism.

The furthest we can get is an understanding of how much information it is physically possible to store in a given space. But intelligence is not information; it is the ability to process information and make something useful of it.

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    $\begingroup$ Gödel's incompleteness theorems : en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems this theorem is about the inherent limit of logic and mathematics. There are laws about thing we don't understand and this one is a perfect example. We don't understand math perfectly but we already now that certain things are impossible $\endgroup$ – Nyashes Apr 6 '16 at 10:26
  • $\begingroup$ @AlexandreTHOUVENIN Thank you. Edited answer to reference this. :) $\endgroup$ – MichaelK Apr 6 '16 at 10:29
  • $\begingroup$ Not exactly my point. Gödel's incompletness theorems are "laws" mathematically proving that math are limited. So there are laws about things we don't have a complete understanding of. Even if I don't have any knowledge of any law limiting AI. The fact that we don't have a full understanding of intelligence is not enough to say that a law like this can't exist. $\endgroup$ – Nyashes Apr 6 '16 at 10:39
  • $\begingroup$ @AlexandreTHOUVENIN Point well taken. Answer adjusted accordingly. $\endgroup$ – MichaelK Apr 6 '16 at 10:41
  • $\begingroup$ It is not true to say "we do not have an understanding of intelligence, nor artificial intelligence". We have some understanding of both, that understanding is non-trivial and that understanding is growing all the time. There are also some rigorous mathematical definitions for intelligence e.g. AIXI that make upper limits on intelligence eminently quantifiable. $\endgroup$ – Brad Thomas Apr 7 '16 at 0:56
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There are speculated limits for computation, notably the Bekenstein bound for information storage and Bremermann's limit for maximum computational speed of a self contained system. The latter assumes:

$ 1.36*10^{50} $ bits per second per kilogram. For example, a computer with the mass of the entire Earth operating at the Bremermann's limit could perform approximately $ 10^{75} $ mathematical computations per second.

Also more recently the Margolus-Levitin theorem states a limit dependent on energy (relevant for quantum computation):

The processing rate cannot be higher than $ 6 × 10^{33} $ operations per second per joule of energy.

None of the above state anything about the nature of "intelligence" because this is concept without any conclusive and definitive explanation. We are unable to reproduce a brain by design.

In any case studies in neuroscience seem to show that:

Overall, larger brain size and volume is associated with better cognitive functioning and higher intelligence. The correlations range from 0.0 to as high as 0.6, and are predominantly positive.

, also:

The specific regions that show the most robust correlation between volume and intelligence are the frontal, temporal and parietal lobes of the brain. Therefore it can be safely concluded that larger brains predict greater intelligence.

, notice, however, that all of this is still speculation and vague (and certainly not without exception). As so it's taken more as an argument and less as a fact. In any case we can speculate that if:

  • The frontal lobe contains most of the dopamine-sensitive neurons in the cerebral cortex. The dopamine system is associated with reward, attention, short-term memory tasks, planning, and motivation.
  • The parietal lobe integrates sensory information among various modalities, including spatial sense and navigation.
  • The temporal lobe is involved in processing sensory input into derived meanings for the appropriate retention of visual memories, language comprehension, and emotion association.

, are the most relevant sectors in this notion of dependence (and by the way those three sectors are actually most of the human brain) than we could hypothesize that both information retention and emotional stimulus are significant for the concept of intelligence.

So potentially the Bekenstein bound could be a physical limit to intelligence. As a final comment notice that most of the resources linked in the text above are mostly of philosophical nature. I think we are far away from having (from the science point of view) a reasonable answer for your question.

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I would refer you to Hutter's AIXI theory. In particular this talks about intelligence as simply a manifestation of the ability to compress data. As such there are very well quantified limits.

AIXI on Wikipedia

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There comes a time in every scientific society when you finally manage set up a real AI to do work for you. Everything is glorious, chores are automatically done for you, everyone is wealthy. To make further scientific progress you tell AIs to do more science and it works great, until the AI invents an AI to do the work for it. That AI invents an AI which invents an AI and so on and while things keep moving, no progress is made. This is the limit of intelligence, you cannot get past the "make an AI to do the work for me"-phase like that.
To solve this issue an AI was made that lives in a simulation that has slightly different rules than reality. It is missing a key component to make an AI, so no matter how hard the original AI tries or how smart it gets, it can never create an AI, so it has to do its own work.
We will see in the next decades if this trick lets us help our masters to get past the limit.

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The No Free Lunch Theorem states that no search algorithm is optimal over all possible worlds. This defines a limit on AI because no matter what strategy the AI uses for thinking, there is the possibility for domains in which the way it goes about finding answers is non-optimal or even is the worst-case strategy for solving the problem.

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