Turing Machines and Universes

Written by Sam Vaknin

In 1936 an American (Alonzo Church) and a Briton (Alan M. Turing) published independently (as is oftenrepparttar coincidence in science)repparttar 133585 basics of a new branch in Mathematics (and logic): computability or recursive functions (later to be developed into Automata Theory).

The authors confined themselves to dealing with computations which involved "effective" or "mechanical" methods for finding results (which could also be expressed as solutions (values) to formulae). These methods were so called because they could, in principle, be performed by simple machines (or human-computers or human-calculators, to use Turing's unfortunate phrases). The emphasis was on finiteness: a finite number of instructions, a finite number of symbols in each instruction, a finite number of steps torepparttar 133586 result. This is why these methods were usable by humans withoutrepparttar 133587 aid of an apparatus (withrepparttar 133588 exception of pencil and paper as memory aids). Moreover: no insight or ingenuity were allowed to "interfere" or to be part ofrepparttar 133589 solution seeking process.

What Church and Turing did was to construct a set of allrepparttar 133590 functions whose values could be obtained by applying effective or mechanical calculation methods. Turing went further down Church's road and designedrepparttar 133591 "Turing Machine" a machine which can calculaterepparttar 133592 values of allrepparttar 133593 functions whose values can be found using effective or mechanical methods. Thus,repparttar 133594 program runningrepparttar 133595 TM (=Turing Machine inrepparttar 133596 rest of this text) was really an effective or mechanical method. Forrepparttar 133597 initiated readers: Church solvedrepparttar 133598 decision-problem for propositional calculus and Turing proved that there is no solution torepparttar 133599 decision problem relating torepparttar 133600 predicate calculus. Put more simply, it is possible to "prove"repparttar 133601 truth value (orrepparttar 133602 theorem status) of an expression inrepparttar 133603 propositional calculus but not inrepparttar 133604 predicate calculus. Later it was shown that many functions (even in number theory itself) were not recursive, meaning that they could not be solved by a Turing Machine.

No one succeeded to prove that a function must be recursive in order to be effectively calculable. This is (as Post noted) a "working hypothesis" supported by overwhelming evidence. We don't know of any effectively calculable function which is not recursive, by designing new TMs from existing ones we can obtain new effectively calculable functions from existing ones and TM computability stars in every attempt to understand effective calculability (or these attempts are reducible or equivalent to TM computable functions).

The Turing Machine itself, though abstract, has many "real world" features. It is a blueprint for a computing device with one "ideal" exception: its unbounded memory (the tape is infinite). Despite its hardware appearance (a read/write head which scans a two-dimensional tape inscribed with ones and zeroes, etc.) it is really a software application, in today's terminology. It carries out instructions, reads and writes, counts and so on. It is an automaton designed to implement an effective or mechanical method of solving functions (determiningrepparttar 133605 truth value of propositions). Ifrepparttar 133606 transition from input to output is deterministic we have a classical automaton if it is determined by a table of probabilities we have a probabilistic automaton.

With time and hype,repparttar 133607 limitations of TMs were forgotten. No one can say thatrepparttar 133608 Mind is a TM because no one can prove that it is engaged in solving only recursive functions. We can say that TMs can do whatever digital computers are doing but not that digital computers are TMs by definition. Maybe they are maybe they are not. We do not know enough about them and about their future.

Moreover,repparttar 133609 demand that recursive functions be computable by an UNAIDED human seems to restrict possible equivalents. Inasmuch as computers emulate human computation (Turing did believe so when he helped constructrepparttar 133610 ACE, atrepparttar 133611 timerepparttar 133612 fastest computer inrepparttar 133613 world) they are TMs. Functions whose values are calculated by AIDED humans withrepparttar 133614 contribution of a computer are still recursive. It is when humans are aided by other kinds of instruments that we have a problem. If we use measuring devices to determinerepparttar 133615 values of a function it does not seem to conform torepparttar 133616 definition of a recursive function. So, we can generalize and say that functions whose values are calculated by an AIDED human could be recursive, depending onrepparttar 133617 apparatus used and onrepparttar 133618 lack of ingenuity or insight (the latter being, anyhow, a weak, non-rigorous requirement which cannot be formalized).

Quantum mechanics isrepparttar 133619 branch of physics which describesrepparttar 133620 microcosm. It is governed byrepparttar 133621 Schrodinger Equation (SE). This SE is an amalgamation of smaller equations, each with its own space coordinates as variables, each describing a separate physical system. The SE has numerous possible solutions, each pertaining to a possible state ofrepparttar 133622 atom in question. These solutions are inrepparttar 133623 form of wavefunctions (which depend, again, onrepparttar 133624 coordinates ofrepparttar 133625 systems and on their associated energies). The wavefunction describesrepparttar 133626 probability of a particle (originally,repparttar 133627 electron) to be inside a small volume of space defined byrepparttar 133628 aforementioned coordinates. This probability is proportional torepparttar 133629 square ofrepparttar 133630 wavefunction. This is a way of saying: "we cannot really predict what will exactly happen to every single particle. However, we can foresee (with a great measure of accuracy) what will happen if to a large population of particles (where will they be found, for instance)."

The Fourth Law of Robotics - Part I

Written by Sam Vaknin

The movie "I, Robot" is a muddled affair. It relies on shoddy pseudo-science and a general sense of unease that artificial (non-carbon based) intelligent life forms seem to provoke in us. But it goes no deeper than a comic book treatment ofrepparttar important themes that it broaches. I, Robot is just another - and relatively inferior - entry is a long line of far better movies, such as "Blade Runner" and "Artificial Intelligence".

Sigmund Freud said that we have an uncanny reaction torepparttar 133584 inanimate. This is probably because we know that pretensions and layers of philosophizing aside we are nothing but recursive, self aware, introspective, conscious machines. Special machines, no doubt, but machines allrepparttar 133585 same.

Considerrepparttar 133586 James bond movies. They constitute a decades-spanning gallery of human paranoia. Villains change: communists, neo-Nazis, media moguls. But one kind of villain is a fixture in this psychodrama, in this parade of human phobias:repparttar 133587 machine. James Bond always finds himself confronted with hideous, vicious, malicious machines and automata.

It was precisely to counter this wave of unease, even terror, irrational but all-pervasive, that Isaac Asimov,repparttar 133588 late Sci-fi writer (and scientist) inventedrepparttar 133589 Three Laws of Robotics:

A robot may not injure a human being or, through inaction, allow a human being to come to harm. A robot must obeyrepparttar 133590 orders given it by human beings, except where such orders would conflict withrepparttar 133591 First Law. A robot must protect its own existence as long as such protection does not conflict withrepparttar 133592 First or Second Laws. Many have noticedrepparttar 133593 lack of consistency and, therefore,repparttar 133594 inapplicability of these laws when considered together.

First, they are not derived from any coherent worldview or background. To be properly implemented and to avoid their interpretation in a potentially dangerous manner,repparttar 133595 robots in which they are embedded must be equipped with reasonably comprehensive models ofrepparttar 133596 physical universe and of human society.

Without such contexts, these laws soon lead to intractable paradoxes (experienced as a nervous breakdown by one of Asimov's robots). Conflicts are ruinous in automata based on recursive functions (Turing machines), as all robots are. Godel pointed at one such self destructive paradox inrepparttar 133597 "Principia Mathematica", ostensibly a comprehensive and self consistent logical system. It was enough to discreditrepparttar 133598 whole magnificent edifice constructed by Russel and Whitehead over a decade.

Some argue against this and say that robots need not be automata inrepparttar 133599 classical, Church-Turing, sense. That they could act according to heuristic, probabilistic rules of decision making. There are many other types of functions (non-recursive) that can be incorporated in a robot, they remind us.

True, but then, how can one guarantee thatrepparttar 133600 robot's behavior is fully predictable ? How can one be certain that robots will fully and always implementrepparttar 133601 three laws? Only recursive systems are predictable in principle, though, at times, their complexity makes it impossible.

This article deals with some commonsense, basic problems raised byrepparttar 133602 Laws. The next article in this series analysesrepparttar 133603 Laws from a few vantage points: philosophy, artificial intelligence and some systems theories.

An immediate question springs to mind: HOW will a robot identify a human being? Surely, in a future of perfect androids, constructed of organic materials, no superficial, outer scanning will suffice. Structure and composition will not be sufficient differentiating factors.

There are two ways to settle this very practical issue: one is to endowrepparttar 133604 robot withrepparttar 133605 ability to conduct a Converse Turing Test (to separate humans from other life forms) -repparttar 133606 other is to somehow "barcode" allrepparttar 133607 robots by implanting some remotely readable signaling device inside them (such as a RFID - Radio Frequency ID chip). Both present additional difficulties.

The second solution will preventrepparttar 133608 robot from positively identifying humans. He will be able identify with any certainty robots and only robots (or humans with such implants). This is ignoring, for discussion's sake, defects in manufacturing or loss ofrepparttar 133609 implanted identification tags. And what if a robot were to get rid of its tag? Will this also be classified as a "defect in manufacturing"?

In any case, robots will be forced to make a binary choice. They will be compelled to classify one type of physical entities as robots and allrepparttar 133610 others as "non-robots". Will non-robots include monkeys and parrots? Yes, unlessrepparttar 133611 manufacturers equiprepparttar 133612 robots with digital or optical or molecular representations ofrepparttar 133613 human figure (masculine and feminine) in varying positions (standing, sitting, lying down). Or unless all humans are somehow tagged from birth.

These are cumbersome and repulsive solutions and not very effective ones. No dictionary of human forms and positions is likely to be complete. There will always berepparttar 133614 odd physical posture whichrepparttar 133615 robot would find impossible to match to its library. A human disk thrower or swimmer may easily be classified as "non-human" by a robot - and so might amputated invalids.

What about administering a converse Turing Test?

This is even more seriously flawed. It is possible to design a test, which robots will apply to distinguish artificial life forms from humans. But it will have to be non-intrusive and not involve overt and prolonged communication. The alternative is a protracted teletype session, withrepparttar 133616 human concealed behind a curtain, after whichrepparttar 133617 robot will issue its verdict:repparttar 133618 respondent is a human or a robot. This is unthinkable.

Moreover,repparttar 133619 application of such a test will "humanize"repparttar 133620 robot in many important respects. Human identify other humans because they are human, too. This is called empathy. A robot will have to be somewhat human to recognize another human being, it takes one to know one,repparttar 133621 saying (rightly) goes.

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