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A superintelligence is a machine that can surpass all intellectual activities by any human, and such a machine is often portrayed in science fiction as a machine that brings mankind to an end.

Any machine is executed using an algorithm. By the Church-Turing thesis, any algorithm that can be executed by a modern computer can be executed by a Turing Machine. However, a human can easily simulate a Turing Machine. Doesn't this mean that a machine can't surpass all intellectual activities, since we can also execute the algorithm?

This argument is most likely flawed, since my intuition tells me that superintelligence is possible. However, it is not clear to me where the flaw is. Note that this is my own argument.

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    $\begingroup$ A Turing Machine can execute any algorithm given infinite time. But a human has finite time. So they cannot execute every algorithm with pen and paper. There is nothing stopping an agent from executing its own algorithm (and that algorithm executing another instance of the agent) although at a slower speed for each as it uses up its computational resources. $\endgroup$
    – Conor Cosnett
    Commented Aug 2, 2016 at 20:57
  • $\begingroup$ How about 'surpassing' the human by simulation their execution of the algorithm? I'm not just complicating things deliberately here - your notion of 'surpass' seems to be quite closely tied to the notion of simulation. A clearer definition of what you mean by 'surpass' would probably help people to better answer the question. $\endgroup$
    – NietzscheanAI
    Commented Aug 5, 2016 at 13:52

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I believe this argument is based on the fact that intelligence is a single dimension when it really isn't. Are machines and humans really on the same level if a machine can solve a complex problem in a millionth of the time a human can?

It also assumes that the Turing machine is still the best computational model for the time period that you are in, which is not necessarily true for the future, it is just true until this point in time.

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  • $\begingroup$ What do you mean by "single dimension"? $\endgroup$
    – nbro
    Commented Jun 25, 2019 at 21:22
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A quantum computer has a huge amount of internal state that even the machine can't get at directly. (You can only sample the matrix state.) The amount of that state goes up exponentially with each quantum bit involved in the system. Some operations get insane speedups from quantum computing: you just put the quantum wire through a quantum gate and you've updated the entire matrix at once.

Simulating a quantum computer with a classical one would take exponentially longer for each qubit. With several dozen qubits, the machine's computing power for some tasks couldn't even be approached by a normal computer, much less a human mind.

Relevant: my answer on To what extent can quantum computers help to develop Artificial Intelligence?

Note that with quantum computers, you've gone beyond the normal zeroes and ones. You then need a quantum Turing machine, which is a generalization of the classical one.

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    $\begingroup$ The quantum Turing Machine that you link is no more computationally expressive than a traditional TM - it is simply (for some algorithms) exponentially faster in operation. Hence, it's not clear what relevance this has to the OP's question. $\endgroup$
    – NietzscheanAI
    Commented Aug 5, 2016 at 13:42
  • $\begingroup$ @user217281728 Like the accepted answer, I'm showing that a human can't actually "easily simulate a Turing machine"; a quantum computer would absolutely whoop a human for these algorithms. $\endgroup$
    – Ben N
    Commented Aug 5, 2016 at 16:15
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    $\begingroup$ Well, the question could certainly use a lot of clarification, but the whole point of the concept of simulation in CS is that it doesn't much matter how long the simulation takes, merely that something functionally equivalent is produced. $\endgroup$
    – NietzscheanAI
    Commented Aug 5, 2016 at 16:18
  • $\begingroup$ It really depends on whether 'surpass' is defined as 'can do more intellectually' AND 'do it faster' or just the former. $\endgroup$
    – NietzscheanAI
    Commented Aug 5, 2016 at 16:25
  • $\begingroup$ What do "exponential speedups" have to do with super-intelligence, which is a general intelligence? You can be super fast at doing certain calculations and still be quite specific. $\endgroup$
    – nbro
    Commented Jun 25, 2019 at 21:21
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The flaw in your argument is that "surpass" doesn't just mean that you should be able to run all algorithms, it includes a notion of complexity, i.e. how many time steps you will take to simulate an algorithm.

How do you simulate an algorithm with a Turing machine? A Turing machine consists of a finite state machine and an infinite tape. A Turing Machine does run an algorithm, determined by its initial state and the state transition matrix, but what I think you are talking about is Universal Turing Machines (UTM) that can read "code" (which is usually a description of another Turing machine) written on a "code segment" of the tape and then simulate that machine on input data written on the "data segment" of the tape.

Turing machines can differ in the number of states in their finite state machines (and also in the alphabet they write on the tape but any finite alphabet is easily encoded in binary so this should not be the big reason for differences among Turing machines). So, you can have UTMs with bigger state machines and UTMs with smaller state machines. The bigger UTM could possibly surpass the smaller one if they use the same encoding for the "code" part of the tape.

You can also play around with the code used to describe the TM being simulated. This code could be C++, for example, or could be a Neural network with the synapse strength written down as a matrix. Which description is better for computation depends on the problem.

An example comparison among UTMs with different state machines: consider different compilers for the same language, say C++. Both of them will first compile C++ to assembly and then run another UTM which reads and executes assembly (your physical CPU). So, a better compiler will run the same code faster.

Back to humans vs computers, humans are neural networks that run algorithms like those you would write in C++. This involves a costly and inefficient conversion of the algorithm into hand movements. A computer uses a compiler to convert C++ to assembly that it can run natively, so it's able to do a much more efficient implementation of C++ code. Alternately, humans have a ton of neurons, and the neural code, i.e. synapse strength, is hard to read, so current computers cannot run that code yet.

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  • $\begingroup$ We don't really know how close a model an ANN is to the operation of the human brain. For all we know, it could require Penrose's quantum microtubules... $\endgroup$
    – NietzscheanAI
    Commented Aug 5, 2016 at 13:46
  • $\begingroup$ @user217281728 While what you say is true, I think you are underselling neuroscience research. The McCullogh-Pitts neuron is a relatively good model for neurons, and we do understand a fair bit (at different scales) about how neurons work, how nerve bundles function, how information flows in some brain regions. In any case, my answer is an attempt to explaining to a non-expert the differences among various models of computation $\endgroup$
    – Harsh
    Commented Aug 5, 2016 at 14:20
  • $\begingroup$ OK, I now appreciate that you wanted to paint a simplified picture. $\endgroup$
    – NietzscheanAI
    Commented Aug 5, 2016 at 14:32

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