Electronic Disconnects! – Which way are YOU leaning?

Written by Ib Hagsten, Ph.D., CAC, Dpl. ACAN

“Every second, worldwide, a PC (personal computer) is connected forrepparttar first time, and every half second a cellular telephone is activated,” Frank Feather, futurist from Canada. Contrast such dramatic electronic explosion withrepparttar 133586 comment from a business exceutive a few weeks ago, “You don’t have to be there” (onrepparttar 133587 web viarepparttar 133588 computer).

We are at a cross-roads between “the way we do it” andrepparttar 133589 new web-evolution. This new “webolution” will trigger a greater 30- to 50-year change thanrepparttar 133590 Industrial Revolution. Most people then (Industrial Revolution) did not understand what was happening around them and to them – neither will many understand what is already happening viarepparttar 133591 web.

Do we want to stick our head inrepparttar 133592 sand aboutrepparttar 133593 changes that are affecting our clients and us? Or will we become informed aboutrepparttar 133594 changes? (regardless of how little we personally feel like participating). Alexander Graham Bell discoveredrepparttar 133595 telephone. 4,000 phone companies started, yet most did not survive. The recent “high mortality rate” among dot.com companies just proves that history has a way of repeating itself.

A new computer being connected every second, somewhere inrepparttar 133596 world, and a new cell phone every half second is not “stuff out of “ Star Wars” or Popular Mechanics – it is what is happening, right now. Today halfrepparttar 133597 world’s population has never made a phone call; yet it is highly probable that they will all have cell phones and computers within one generation.

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)."

Cont'd on page 2 ==>
ImproveHomeLife.com © 2005
Terms of Use