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We start from axioms, use rules of logic, and derive theorems. These theorems establish what is the case in relation to the context. In all disciplines employing mathematics, we reason by saying 'because A, therefore B'. We can model it in computer. Now suppose theory evolves, and we add more variables or find more factors. Still we can model in computer (and so on). Clearly, human action can be modeled in computer.

Alternatively think of it as follows: Every new theorem (which asserts something) must be logical, and therefore we must be able to show its logical path -the computation (or provide a sound reasoning). So it must be computable, and therefore a computer can do it. It seems that in realm of rigorous reasoning, a computer, when constructed, is as powerful as human mind.

So my question is: what is it that human mind can do which a computer (Universal TM) can not?

  • Mathematics is not only deriving theorem from axioms; first of all is discovering new concepts and new axioms. – Mauro ALLEGRANZA Feb 17 at 12:50
  • @MauroALLEGRANZA So keeping discovering new axioms/concepts aside, can we then say computer is as powerful as mind? – Ajax Feb 17 at 12:53
  • Keeping aside what is relevant for human mind... YES. Electronic computers are physical implementation of the abstract model of Turing machine that formalize all "computing processes" that we can perform. – Mauro ALLEGRANZA Feb 17 at 12:56
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    Please, note that human mind (embodied into Alan Turing) discovered the abstract theory of computing before the existence of artificial computers: only reasoning about human processes and abstracting from them a formal model: THIS IS MATHEMATICS. – Mauro ALLEGRANZA Feb 17 at 12:57
  • What computer can do is verify a proof given to it. Coming up with a proof given a theorem, not that well. Coming up with new conjectures to be proved, even worse. Coming up with new systems of axioms to model something, not at this time. – Conifold Feb 17 at 12:59
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So my question is: what is it that human mind can do which a computer (Universal TM) can not?

INTRODUCTION

Let us presume that you set aside the obvious retort: human brains are embodied and have control mechanisms like the endocrine system which regulate behavior based on emotion. Also, let us set aside the difference in performance characteristics between biological-based computation (think professor with pencil) and a supercomputer. Clearly the rate of computation and the lack of errors a computer makes clearly differentiates it from a professor. As currently constructed most computers are built around a high-speed ALU. Almost the entire architecture of a computer or network is meant to serve the purpose of shuffling around data and instructions to feed the ALU which transforms those data according to a set of instructions delimited by the op codes of the processor; often these days they have multiple cores allowing parallel threads to be executed at frequencies which are staggering incomprehensible compared to human minds.

The difference comes to the act of how a computer solves problems, and how a brain does; and to be forthright, there is no exact understanding of what the limits of a Turing machine are in simulating the performance of the brain, and part of the reason is the brain is not entirely understood. With more than more than 200 neurotransmitters and approximately 86,000,000,000 neurons, the complexity of the brain eclipses most supercomputers in ways hard to describe. Remember, unlike a silicon wafer which is designed and etched, the brain accumulates matter and differentiates itself through proteomic expression beginning with the genes of a single cell: the zygote. While logical circuits like the FPGA have an impressive ability to differentiate themselves, no electronic product on the market remotely resembles the brain, it's growth from a neural tube, and it's plasticity.

PHILOSOPHY AND ARTIFICIAL INTELLIGENCE

One aspect of the human brain is that it does have the capacity to function like a Turing machine, although to be more accurate, the Turing machine is merely a description of one ability of the human brain. Automata theory is a fascinating formalism that captures aspects of the behavior of brains, including its use of language, as evidenced by generative grammars and the models that the Chomskian hierarchy provides. The philosopher Daniel Dennett made a great effort in his Consciousness Explained to make accessible an analysis of the origin and nature of the conscious mind and it's relation to the brain. Dennett attacks the Cartesian duality as an Oxfordian, proposes heterphenomenology, and pushes his views as an eliminative materialist including his "disqualification of qualia".

One outstanding question which is related to Searle's controversial Chinese room (to which whole books have been devoted) is whether or not Turing machines can give rise to minds and intentionality. (I made a brief argument for it on SE here). Searle's position is that Turing machines cannot. Many philosophers of AI rely on the fact that there is nothing inherently special about the nature of matter in systems and that the same properties should arise from systems if they are functionally equivalent. Of course, any progress towards having Turing machines function as human minds has been slow going. Nils Nilsson covers the dream of creating minds from matter in his The Quest for Artificial Intelligence. One of the most famous critics is Hubert Dreyfus's What Computers Still Can't Do: A Critique of Artificial Reason.

STRENGTHS OF THE MIND

It does behoove us to take a look at the current state of technology, and some skills human brains have over their artificial counterparts. One of the most obvious was recognized by Pascal:

We must see the matter at once, at one glance, and not by a process of reasoning, at least to a certain degree... Mathematicians wish to treat matters of perception mathematically, and make themselves ridiculous... the mind... does it tacitly, naturally, and without technical rules. (Pensees)

Human brains take in a tremendous amount of data through transduction of their physical embodiments. The number of cells devoted to sight, sound, taste, smell, touch, proprioception, and so on is staggering from a design perspective. Part of the reason the human brain has so many cells is that vast areas are devoted to encoding experience from sensation, the visual cortex being a terrific example. Perhaps best studied, the visual system dwarfs any camera system manufactured. In principle, parallel Turing machines can be constructed, but until we know how and why to construct them, for the moment, the brain has a tremendous advantage in parallelism. In fact, some have claimed that the complexity goes beyond the ability of the human mind to comprehend and that evolutionary algorithms and artificial neural networks (ANN) are the only technique that might get us there. ANNs for instance have been constructed that are content-accessible instead of address accessible. These constructs have the property of association, much like our brains work, built into their input-output performance.

From that complexity and parallelism, it's not clear how Turing machines can be constructed or evolved to exhibit dispositions that brains excel at. One of the most promising areas of research, however, is that of machine learning which can be divided into strategies such as reinforcement, supervised, and unsupervised learning techniques, many of which mimic how the brain learns in some regard.

CONCLUSION

So, the philosophical implications of the Church-Turing thesis are still an area of active research and conjecture, and no one can speak with any authority on the limits of the von Neumann architecture to emulate the human brain. Few serious analytical philosophical thinkers reject the notion that the brain is a biological computation device. John Searle of Chinese room fame in his The Mystery of Consciousness even accepts the fact that at least part of the brain functions as a Turing Machine. What is not clear is the exact nature of how the mind arises from the brain with all of it's ontological and epistemological implications. In principle, there is nothing that excludes a powerful computer becoming sentient, but in practice, it certainly hasn't been achieved. The brain has the capacity to create a flexible representation of external reality, use it in to solve problems intuitionally (without self-knowledge), and create and share language to communicate about it ways that computers just can't pass muster. For all of its many flaws, the Turing Test still demonstrates how little comprehension computers have in the simplest of conversations, although projects like IBM Watson continue to chip away at humanity's claim to a monopoly on knowledge-how and knowledge-that.

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    On the question of whether a Turing machine can in principle simulate a human brain (or any other physical system) to an arbitrarily high degree of accuracy, there was also a theorem proved by physicist David Deutsch in this paper showing that according to the current understanding of quantum physics, "every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means". – Hypnosifl Feb 17 at 23:12
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Usually computers hardly have power of imagination. In other words its power of imagination is very low. So it cannot compose beautiful poems, dramas or other similar creations in which very great imagination is required.

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Qeuestion: So my question is: what is it that human mind can do which a computer (Universal TM) can not?

Answer: The answer is “to have qualia and consicousness” it its system.

Physically, our mind functions from a very complex group of biological circuits made up of carbon-based elements, but these circuits operate solely on physical laws (i.e., no magics have been found to be involved in their functions). So, if they operate solely on physical laws, theoretically, we should be able to replicate whatever functions our mind has with appropriate circuits made up of other elements, like silicon.

Thus, theoretically, with current knowledge, we can can construct a computer or robot to do almost everything the human mind can: receiving information from environment (vision, sound, mechanical impact, taste, smell, and even other information that humans can’t have like electroreception, magnetoreception, and echolocation); analyzing information; calculating; planning; making choices; storing information (remembering); recalling stored information; behaving like human (speaking, talking, walking, working, playing games, etc.); controlling its various functions (such as its rate of energy consumption – equivalent to human metabolism, its rate of heat dispersion – equivalent to human perspiration, skin vasodilatation, mouth gasping, etc., and its rate of waste excretion – if they have some).

The only thing we cannot construct a computer or robot to do nowadays is “to have qualia and conscicousness” it its system. Currently, we do not know how qualia (like the redness of the color red in your mind) and consciousness (like the conscious awareness and conscious experience of that redness in your mind – or what it is like to be aware of and experience that redness in your mind) occur from our biological circuits. So, nowadays we cannot construct a computer or robot to have qualia and consciousness. Everything that is going on in the present-day computers and robots goes on “in the dark” – no qualia and no conscious awareness and experience of the qualia – computers and robots nowadays do not have the feeling of what it is like to experience the redness of the red color in their systems.

The problem of not knowing how qualia and consciousness occur in us is called “the hard problem of consciousness”.

References.

  1. Qualia. Standford Encyclopedia of Philosophy Archive.

  2. Qualia Internet Encycopedia of Philosophy.

  3. Chalmers DJ. Facing up to te problem of consciousness Conscious Stud. 1995;2(3):200-219.

  4. Chalmers DJ. Moving forward on the problem of consciousness J Conscious Stud. 1997;4(1):3-46.

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  • There is an argument that qualia - consciousness - would arise in a sufficiently intelligent computer. In particular, Integrated Information Theory links consciousness to the level of sophistication of the information being processed, the physical substrate (be it natural or artificial, carbon or silicon based) is wholly irrelevant. The lack of qualia in today's computers thus closely parallels the lack of qualia in a comatose brain. – Guy Inchbald Feb 18 at 13:04
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    @Guy Inchbald I agree with you. The problem is, currently, we don’t know the exact details of the circuits and their exact ways of functioning that can create qualia and consciousness. Theoretically, if they are known and if the possibility of having qualia and consciousness is not restricted to only biological processes by some basic factors, then computers and robots that have qulia and consciousness can be built. This is in accordance with the principle of organizational invariance of Chalmers [ref 3, 4] and section 6.6.2, Chapter 6 of this article. – user287279 Feb 18 at 16:55
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"So my question is: what is it that human mind can do which a computer (Universal TM) can not?" For a start, UTMs once set in motion have no inputs so can't perceive anything. You might say, well we'll simply make an extension to Turings 1936 definition of a UTM that allows real-time inputs, but (a) that's not a UTM and (b) allowing real-time inputs opens up issues that might turn out to be a can of worms. But computers are not UTMs so to answer the question the nature of the computer needs first to be adequately understood.

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  • They are Turing Complete, they can be modeled as Turing Machines. It is common to say they are Turing Machines, when what is really meant is they are equivalent to a more complex and impractical but still functional Turing Machine. – CriglCragl Feb 20 at 14:23
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what is it that human mind can do which a computer (Universal TM) can not?

What about thinking? Its a fact, that Turing himself, in his papers on the Turing Machine, side-stepped the question on the nature of what thought is.

This is rather like a physicist who doesn't marvel at a rainbow, but marvels at the equation that represents the rainbow.

Somehow, one thinks, that this is the wrong way around. You begin by

We start from axioms, use rules of logic, and derive theorems.

Actually its well-known in logic, that its the theory that counts, and not the axioms; its quite possible to take certain theorems as axioms and begin from there instead; why we don't always do so, makes an interesting exercise in why certain axiom schemas are more sucessful than others. Here, I'd say its a question of organic growth (and hence of human thinking) and of aesthetics (likewise).

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