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September 14 - September 23, 2018
The idea is that mental activity is simply the carrying out of some well-defined sequence of operations, frequently referred to as an algorithm.
according to strong AI, the difference between the essential functioning of a human brain (including all its conscious manifestations) and that of a thermostat lies only in this much greater complication (or perhaps ‘higher-order structure’ or ‘self-referential properties’, or some other attribute that one might assign to an algorithm) in the case of a brain.
As far as I can make out, one of the most important factors underlying the strong-AI philosophy is this equivalence between physical computing devices. The hardware is seen as being relatively unimportant (perhaps even totally unimportant) and the software, i.e. the program, or the algorithm, is taken to be the one vital ingredient.
What distinguishes the person from his house is the pattern of how his constituents are arranged, not the individuality of the constituents themselves.
Let us accept that a person’s individuality has nothing to do with any individuality that one might try to assign to his material constituents. Instead, it must have to do with the configuration,
If we accept the operational viewpoint, then the question rests on the equivalence of universal Turing machines, and on the fact that any algorithm can, indeed, be effected by such a machine – together with the presumption that the brain acts according to some kind of algorithmic action.
There is perhaps some irony in the fact that this aspect of Turing’s own work may now indirectly provide us with a possible loophole to his own viewpoint concerning the nature of mental phenomena.
All we need to know, beyond this finiteness is that the behaviour of the device is completely determined by its internal state and by the input.
One could fairly say that a putative algorithm is not much use when it runs forever without stopping.
We have said nothing whatever about the insolubility of single problems, but only about the algorithmic insolubility of families of problems.
some well-defined operations in mathematics are actually not computable (like
It can be an intriguing puzzle for them to decide, of some mathematical operation, whether or not it is computable. It is especially intriguing because the general solution of that puzzle is itself non-computable!
if mental phenomena can indeed find a home of this general kind, I do not believe that it can be with the concept of an algorithm. What would be needed would be something very much more subtle. The fact that algorithmic things constitute a very narrow and limited part of mathematics will be an important aspect of the discussions to follow.
What Gödel showed was that any such precise (‘formal’) mathematical system of axioms and rules of procedure whatever, provided that it is broad enough to contain descriptions of simple arithmetical propositions (such as ‘Fermat’s last theorem’, considered in Chapter 2) and provided that it is free from contradiction, must contain some statements which are neither provable nor disprovable by the means allowed within the system.
Gödel’s argument enables us, by the use of insight, to go beyond the limitations of any particular formalized mathematical system under consideration.
The point of view that one can dispense with the meanings of mathematical statements, regarding them as nothing but strings of symbols in some formal mathematical system, is the mathematical standpoint of formalism. Some people like this idea, whereby mathematics becomes a kind of ‘meaningless game’. It is not an idea that appeals to me, however. It is indeed ‘meaning’ – not blind algorithmic computation – that gives mathematics its substance
The strict mathematical formalists should indeed be worried, because by this very reasoning we have established that the formalist’s notion of ‘truth’ must be necessarily incomplete.
The formalist’s professed lack of interest in ‘mathematical truth’ seems to me to be a very strange point of view to adopt for a philosophy of mathematics. Furthermore, it is not really all that pragmatic. When mathematicians carry out their forms of reasoning, they do not want to have to be continually checking to see whether or not their arguments can be formulated in terms of the axioms and rules of procedure of some complicated formal system.
without Gödel’s theorem it might have been possible to imagine that the intuitive notions of ‘self-evidence’ and ‘meaning’ could have been employed just once and for all, merely to set up the formal system in the first place, and thereafter dispensed with as part of clear mathematical argument for determining truth.
An essential property of a formal mathematical system is that it should be a computable matter to decide whether or not a given string of symbols constitutes a proof, within the system, of a given mathematical assertion.
The most common problems that one is likely to come across in some specific area can often be handled by simple algorithmic procedures – procedures which may have been known for centuries. But some will escape the net, and more sophisticated procedures are needed to handle them.
Complexity theory is concerned not so much with the difficulty of solving single problems algorithmically, but with infinite families of problems where there would be a general algorithm for finding answers to all the problems of one single family.
Can it be that a human brain, which I am taking for this discussion to be a ‘physical device’, albeit one of amazing subtlety and delicacy of design, as well as of complication, is itself taking advantage of the magic of quantum theory? Do we yet understand the ways in which quantum effects might be used beneficially in the solving of problems or the forming of judgements?
Perhaps, on the other hand, there is more to our feelings of awareness than mere algorithms.
The issue of determinism in physical theory is important, but I believe that it is only part of the story. The world might, for example, be deterministic but non-computable.
The kind of issue that I am trying to raise is whether it is conceivable that a human brain can, by the harnessing of appropriate ‘non-computable’ physical laws, do ‘better’, in some sense, than a Turing machine.
Newtonian billiard-ball world can be computed as closely as desired (ignoring multiple collisions) – and, in this sense we can say that the Newtonian world is indeed computable. There is a sense, however, in which this world is ‘non-computable’ in practice.
This arises from the fact that the accuracy with which the initial data can be known is always limited. In fact there is a very considerable ‘instability’ inherent in this kind of problem. A very tiny change in the initial data may rapidly give rise to an absolutely enormous change in the resulting behaviour.
Suppose we have a physical device that, for known theoretical reasons, imitates some interesting non-algorithmic mathematical process. The exact behaviour of the device, if this behaviour could always be ascertained precisely, would then yield the correct answers to a succession of mathematically interesting yes/no questions for which there can be no algorithm (like those considered in Chapter 4).
Any given algorithm would fail at some stage, and at that stage, the device would give us something new.
I have tried to keep one eye on the issue of computability, as distinct from that of determinism, and I have tried to indicate that computability issues may be at least as important as those of determinism when it comes to the questions of ‘free will’ and mental phenomena.
In other descriptions one learns that the uncertainty is a property of the particle itself, and its motion has an inherent randomness about it which means that its behaviour is intrinsically unpredictable on the quantum level.
Such a picture was abhorrent to Einstein, who believed that there must indeed be an objective physical world, even at the minutest scale of quantum phenomena. In his numerous arguments with Bohr he attempted (but failed) to show that there were inherent contradictions in the quantum picture of things, and that there must be a yet deeper structure beneath quantum theory, probably more akin to the pictures that classical physics had presented us with. Perhaps underlying the probabilistic behaviour of quantum systems would be the statistical action of smaller ingredients or ‘parts’ to the system,
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It begins to seem that if anything is definite at all, then the entire space-time must indeed be definite!
It seems to me that there are severe discrepancies between what we consciously feel, concerning the flow of time, and what our (marvellously accurate) theories assert about the reality of the physical world. These discrepancies must surely be telling us something deep about the physics that presumably must actually underlie our conscious perceptions – assuming (as I believe) that what underlies these perceptions can indeed be understood in relation to some appropriate kind of physics. At least it seems to be clearly the case that whatever physics is operating, it must have an essentially
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The laws of mechanics are time-reversible; yet the time-ordering of such a scene from the right frame to the left is something that is never experienced, whereas that from the left frame to the right would be commonplace.
The deterministic equations of classical physics (or the operation of U in quantum physics, for that matter) have no preference for evolving in the future direction. They can be used equally well to evolve into the past. The future determines the past in just the same way that the past determines the future. We can specify some state of a system in some arbitrary way in the future and then use this state to compute what it would have had to be like in the past.
hinted above, the cerebellum seems to be much more of an ‘automaton’ than the cerebrum. Actions under cerebellar control seem almost to take place ‘by themselves’ without one having to ‘think about’ them.
If ‘awareness’ is merely a feature of the complexity of an algorithm – or perhaps of its ‘depth’ or some ‘level of subtlety’ – then, according to the strong-AI view, the complicated algorithms being carried out by the cerebral cortex would give that region the strongest claim to be that capable of manifesting consciousness.
it has been suggested that geometrical thinking (particularly in three dimensions), and also music, may normally be carried out mainly within the right hemisphere, to give balance to the verbal and analytical abilities of the left.
Let us see how it would be possible in principle to build logic gates from neuron connections. We need to have some new way of coding the digits, since the absence of a signal does not trigger off anything.
It is easy to see that a computer could simulate any such model of neuron interconnections; whereas the detailed constructions above give an indication of the fact that, conversely, systems of neurons are capable of simulating a computer – and so could act as a (universal) Turing machine.
we should consider various differences between brain action and present-day computer action that might possibly be of significance.
In the first place, I have oversimplified somewhat in my description of the firing of a neuron as an all-or-nothing phenomenon. That refers to a single pulse travelling along the axon, but in fact when a neuron ‘fires’ it emits a whole sequence of such pulses in quick succession. Even when a neuron is not activated, it emits pulses, but only at a slow rate.
When it fires, it is the frequency of these successive pulses which increases enormously. There is also a probabilistic aspect of neuron firing. The same stimu...
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brain plasticity. It is actually not legitimate to regard the brain as simply a fixed collection of wired-up neurons. The interconnections between neurons are not in fact fixed, as they would be in the above computer model, but are changing all the time.
if we think of the connections of neurons in the brain as constituting, in effect, a computer, then it is a computer which is capable of changing all the time!
there is another aspect of the release of neurotransmitters by synaptic knobs. Sometimes these do not occur in synaptic clefts at all, but enter the general intercellular fluid, perhaps to influence other neurons a long way away.
Certainly the state of the brain can be influenced in a general way by the presence of chemicals that are produced by other parts of the brain
The whole question of neurochemistry is complicated, and it is difficult to see how to provide a reliable detailed computer simulation of everything that might be relevant.
