Turing Machines and Universes

Written by Sam Vaknin


Continued from page 1

This is whererepparttar first of two major difficulties arose:

To determine what will happen in a specific experiment involving a specific particle and experimental setting an observation must be made. This means that, inrepparttar 133585 absence of an observing and measuring human, flanked by allrepparttar 133586 necessary measurement instrumentation repparttar 133587 outcome ofrepparttar 133588 wavefunction cannot be settled. It just continues to evolve in time, describing a dizzyingly growing repertoire of options. Only a measurement (=the involvement of a human or, at least, a measuring device which can be read by a human) reducesrepparttar 133589 wavefunction to a single solution, collapses it.

A wavefunction is a function. Its REAL result (the selection in reality of one of its values) is determined by a human, equipped with an apparatus. Is it recursive (TM computable and compatible)? In a way, it is. Its values can be effectively and mechanically computed. The value selected by measurement (thus terminatingrepparttar 133590 propagation ofrepparttar 133591 function and its evolution in time by zeroing itsrepparttar 133592 other terms, barrepparttar 133593 one selected) is one ofrepparttar 133594 values which can be determined by an effective-mechanical method. So, how should we treatrepparttar 133595 measurement? No interpretation of quantum mechanics gives us a satisfactory answer. It seems that a probabilistic automaton which will deal with semi recursive functions will tacklerepparttar 133596 wavefunction without any discernible difficulties but a new element must be introduced to account forrepparttar 133597 measurement andrepparttar 133598 resulting collapse. Perhaps a "boundary" or a "catastrophic" automaton will dorepparttar 133599 trick.

The view thatrepparttar 133600 quantum process is computable seems to be further supported byrepparttar 133601 mathematical techniques which were developed to deal withrepparttar 133602 application ofrepparttar 133603 Schrodinger equation to a multi-electron system (atoms more complex than hydrogen and helium). The Hartree-Fok method assumes that electrons move independent of each other and ofrepparttar 133604 nucleus. They are allowed to interact only throughrepparttar 133605 average electrical field (which isrepparttar 133606 charge ofrepparttar 133607 nucleus andrepparttar 133608 charge distribution ofrepparttar 133609 other electrons). Each electron has its own wavefunction (known as: "orbital") which is a rendition ofrepparttar 133610 Pauli Exclusion Principle.

The problem starts withrepparttar 133611 fact thatrepparttar 133612 electric field is unknown. It depends onrepparttar 133613 charge distribution ofrepparttar 133614 electrons which, in turn, can be learnt fromrepparttar 133615 wavefunctions. Butrepparttar 133616 solutions ofrepparttar 133617 wavefunctions require a proper knowledge ofrepparttar 133618 field itself!

Thus,repparttar 133619 SE is solved by successive approximations. First, a field is guessed,repparttar 133620 wavefunctions are calculated,repparttar 133621 charge distribution is derived and fed intorepparttar 133622 same equation in an ITERATIVE process to yield a better approximation ofrepparttar 133623 field. This process is repeated untilrepparttar 133624 final charge andrepparttar 133625 electrical field distribution agree withrepparttar 133626 input torepparttar 133627 SE.

Recursion and iteration are close cousins. The Hartree-Fok method demonstratesrepparttar 133628 recursive nature ofrepparttar 133629 functions involved. We can sayrepparttar 133630 SE is a partial differential equation which is solvable (asymptotically) by iterations which can be run on a computer. Whatever computers can do TMs can do. Therefore,repparttar 133631 Hartree-Fok method is effective and mechanical. There is no reason, in principle, why a Quantum Turing Machine could not be constructed to solve SEs orrepparttar 133632 resulting wavefunctions. Its special nature will set it apart from a classical TM: it will be a probabilistic automaton with catastrophic behaviour or very strong boundary conditions (akin, perhaps, torepparttar 133633 mathematics of phase transitions).

Classical TMs (CTMs, Turing called them Logical Computing Machines) are macroscopic, Quantum TMs (QTMs) will be microscopic. Perhaps, while CTMs will deal exclusively with recursive functions (effective or mechanical methods of calculation) QTMs could deal with half-effective, semi-recursive, probabilistic, catastrophic and other methods of calculations (other types of functions).

The third level isrepparttar 133634 Universe itself, where allrepparttar 133635 functions have their values. Fromrepparttar 133636 point of view ofrepparttar 133637 Universe (the equivalent of an infinite TM), allrepparttar 133638 functions are recursive, for all of them there are effective-mechanical methods of solution. The Universe isrepparttar 133639 domain or set of allrepparttar 133640 values of allrepparttar 133641 functions and its very existence guarantees that there are effective and mechanical methods to solve them all. No decision problem can exist on this scale (or all decision problems are positively solved). The Universe is made up only of proven, provable propositions and of theorems. This is a reminder of our finiteness and to say otherwise would, surely, be intellectual vanity.



Sam Vaknin is the author of Malignant Self Love - Narcissism Revisited and After the Rain - How the West Lost the East. He is a columnist for Central Europe Review, United Press International (UPI) and eBookWeb and the editor of mental health and Central East Europe categories in The Open Directory, Suite101 and searcheurope.com.

Visit Sam's Web site at http://samvak.tripod.com




The Fourth Law of Robotics - Part I

Written by Sam Vaknin


Continued from page 1

Let us assume that by some miraculous wayrepparttar problem is overcome and robots unfailingly identify humans. The next question pertains torepparttar 133584 notion of "injury" (still inrepparttar 133585 First Law). Is it limited only to physical injury (the elimination ofrepparttar 133586 physical continuity of human tissues or ofrepparttar 133587 normal functioning ofrepparttar 133588 human body)?

Should "injury" inrepparttar 133589 First Law encompassrepparttar 133590 no less serious mental, verbal and social injuries (after all, they are all known to have physical side effects which are, at times, no less severe than direct physical "injuries")? Is an insult an "injury"? What about being grossly impolite, or psychologically abusive? Or offending religious sensitivities, being politically incorrect - are these injuries? The bulk of human (and, therefore, inhuman) actions actually offend one human being or another, haverepparttar 133591 potential to do so, or seem to be doing so.

Consider surgery, driving a car, or investing money inrepparttar 133592 stock exchange. These "innocuous" acts may end in a coma, an accident, or ruinous financial losses, respectively. Should a robot refuse to obey human instructions which may result in injury torepparttar 133593 instruction-givers?

Consider a mountain climber should a robot refuse to hand him his equipment lest he falls off a cliff in an unsuccessful bid to reachrepparttar 133594 peak? Should a robot refuse to obey human commands pertaining torepparttar 133595 crossing of busy roads or to driving (dangerous) sports cars?

Which level of risk should trigger robotic refusal and even prophylactic intervention? At which stage ofrepparttar 133596 interactive man-machine collaboration should it be activated? Should a robot refuse to fetch a ladder or a rope to someone who intends to commit suicide by hanging himself (that's an easy one)?

Should he ignore an instruction to push his master off a cliff (definitely), help him climbrepparttar 133597 cliff (less assuredly so), drive him torepparttar 133598 cliff (maybe so), help him get into his car in order to drive him torepparttar 133599 cliff... Where dorepparttar 133600 responsibility and obeisance bucks stop?

Whateverrepparttar 133601 answer, one thing is clear: such a robot must be equipped with more than a rudimentary sense of judgment, withrepparttar 133602 ability to appraise and analyse complex situations, to predictrepparttar 133603 future and to base his decisions on very fuzzy algorithms (no programmer can foresee all possible circumstances). To me, such a "robot" sounds much more dangerous (and humanoid) than any recursive automaton which does NOT includerepparttar 133604 famous Three Laws.

Moreover, what, exactly, constitutes "inaction"? How can we set apart inaction from failed action or, worse, from an action which failed by design, intentionally? If a human is in danger andrepparttar 133605 robot tries to save him and fails how could we determine to what extent it exerted itself and did everything it could?

How much ofrepparttar 133606 responsibility for a robot's inaction or partial action or failed action should be imputed torepparttar 133607 manufacturer and how much torepparttar 133608 robot itself? When a robot decides finally to ignore its own programming how are we to gain information regarding this momentous event? Outside appearances can hardly be expected to help us distinguish a rebellious robot from a lackadaisical one.

The situation gets much more complicated when we consider states of conflict.

Imagine that a robot is obliged to harm one human in order to prevent him from hurting another. The Laws are absolutely inadequate in this case. The robot should either establish an empirical hierarchy of injuries or an empirical hierarchy of humans. Should we, as humans, rely on robots or on their manufacturers (however wise, moral and compassionate) to make this selection for us? Should we abide by their judgment which injury isrepparttar 133609 more serious and warrants an intervention?

A summary ofrepparttar 133610 Asimov Laws would give usrepparttar 133611 following "truth table":

A robot must obey human commands except if:

Obeying them is likely to cause injury to a human, or Obeying them will let a human be injured. A robot must protect its own existence with three exceptions:

That such self-protection is injurious to a human; That such self-protection entails inaction inrepparttar 133612 face of potential injury to a human; That such self-protection results in robot insubordination (failing to obey human instructions). Trying to create a truth table based on these conditions isrepparttar 133613 best way to demonstraterepparttar 133614 problematic nature of Asimov's idealized yet highly impractical world.

Here is an exercise:

Imagine a situation (considerrepparttar 133615 example below or one you make up) and then create a truth table based onrepparttar 133616 above five conditions. In such a truth table, "T" would stand for "compliance" and "F" for non-compliance.

Example:

A radioactivity monitoring robot malfunctions. If it self-destructs, its human operator might be injured. If it does not, its malfunction will equally seriously injure a patient dependent on his performance.

One ofrepparttar 133617 possible solutions is, of course, to introduce gradations, a probability calculus, or a utility calculus. As they are phrased by Asimov,repparttar 133618 rules and conditions are of a threshold, yes or no, take it or leave it nature. But if robots were to be instructed to maximize overall utility, many borderline cases would be resolved.

Still, evenrepparttar 133619 introduction of heuristics, probability, and utility does not help us resolverepparttar 133620 dilemma inrepparttar 133621 example above. Life is about inventing new rules onrepparttar 133622 fly, as we go, and as we encounter new challenges in a kaleidoscopically metamorphosing world. Robots with rigid instruction sets are ill suited to cope with that.

Sam Vaknin is the author of Malignant Self Love - Narcissism Revisited and After the Rain - How the West Lost the East. He is a columnist for Central Europe Review, United Press International (UPI) and eBookWeb and the editor of mental health and Central East Europe categories in The Open Directory, Suite101 and searcheurope.com.

Visit Sam's Web site at http://samvak.tripod.com




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