The Fourth Law of Robotics - Part II

Written by Sam Vaknin

Note - Godel's Theorems

The work of an important, though eccentric, Czech-Austrian mathematical logician, Kurt Gödel (1906-1978) dealt withrepparttar completeness and consistency of logical systems. A passing acquaintance with his two theorems would have savedrepparttar 133432 architect a lot of time.

Gödel's First Incompleteness Theorem states that every consistent axiomatic logical system, sufficient to express arithmetic, contains true but unprovable ("not decidable") sentences. In certain cases (whenrepparttar 133433 system is omega-consistent), both said sentences and their negation are unprovable. The system is consistent and true - but not "complete" because not all its sentences can be decided as true or false by either being proved or by being refuted.

The Second Incompleteness Theorem is even more earth-shattering. It says that no consistent formal logical system can prove its own consistency. The system may be complete - but then we are unable to show, using its axioms and inference laws, that it is consistent

In other words, a computational system can either be complete and inconsistent - or consistent and incomplete. By trying to construct a system both complete and consistent, a robotics engineer would run afoul of Gödel's theorem.

Note - Turing Machines

In 1936 an American (Alonzo Church) and a Briton (Alan M. Turing) published independently (as is oftenrepparttar 133434 case in science)repparttar 133435 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 133436 result. This is why these methods were usable by humans withoutrepparttar 133437 aid of an apparatus (withrepparttar 133438 exception of pencil and paper as memory aids). Moreover: no insight or ingenuity were allowed to "interfere" or to be part ofrepparttar 133439 solution seeking process.

What Church and Turing did was to construct a set of allrepparttar 133440 functions whose values could be obtained by applying effective or mechanical calculation methods. Turing went further down Church's road and designedrepparttar 133441 "Turing Machine" – a machine which can calculaterepparttar 133442 values of allrepparttar 133443 functions whose values can be found using effective or mechanical methods. Thus,repparttar 133444 program runningrepparttar 133445 TM (=Turing Machine inrepparttar 133446 rest of this text) was really an effective or mechanical method. Forrepparttar 133447 initiated readers: Church solvedrepparttar 133448 decision-problem for propositional calculus and Turing proved that there is no solution torepparttar 133449 decision problem relating torepparttar 133450 predicate calculus. Put more simply, it is possible to "prove"repparttar 133451 truth value (orrepparttar 133452 theorem status) of an expression inrepparttar 133453 propositional calculus – but not inrepparttar 133454 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.

Ringtones Explained - Monophonic, Polyphonic or Whatever Phonic Rings Your Bell

Written by Lillian Fuller

Downloadable Ring tones - The Latest Trend

What can you say about ring tones? NOTHING…except that cell phones capable of downloading ringtones arerepparttar newest “must have” item today! One ofrepparttar 133431 fastest growing features today is ringtones, especially downloadable ones! There are other downloadable items available onrepparttar 133432 Internet too like Java Games. Various wallpapers and screen savers are hot too but by farrepparttar 133433 most popular feature requested is downloadable ringtones.

The cell phone and their various ringtones have become status symbols. Ringtones show that you’re up to date and happening. You can even take a test that defines which ringtone best suits your personality. You can truly display your lifestyle and certainly your musical taste on your sleeve.

This article will describe briefly what ring tones are, what’s currently available and whatrepparttar 133434 future holds. It will also suggest a caveat to consider prior to downloadingrepparttar 133435 multitude of formats of available onrepparttar 133436 market. Prices are low andrepparttar 133437 sky’srepparttar 133438 limit, so read on.

  • Just What Are Downloadable Ringtones?
  • A Caveat Before You Buy!
  • What’s Available?
  • A Brief Glimpse At Ancient History.
  • Ringtones – Where Do We Go From Here?
  • Other Products Available On Ringtone Websites
  • What Can You Say About Ringtones
Just What Are Downloadable Ringtones?

Ringtones arerepparttar 133439 sound that a regular or cell phone makes when it’s rings. Early ring tones were simple chimes and on later models, a combination of chimes. Limited numbers of ringtones were available and mostly consisted of different patterns of tones or chirps. An example of one ofrepparttar 133440 most infamous ringtones wasrepparttar 133441 ominous” ring ring…ring ring” that is reminiscent of Todd Beamer’s last telephone call on 9/11. You can hear that ringtone featured as an intro to Neil Young’s famous song “Let’s Roll.”

Ringtone technology developed quickly and has progressed a lot since that song was recorded. Originally, you purchased a cell phone and had a choice of monophonic ring tones that produced a one note song. The number of songs was extremely limited and downloadable ring tones were simply an Engineering student’s good idea.

Because of lightning speed technology and numerous service providers, one ofrepparttar 133442 latest and greatest features available today is downloadable ringtones. When you’re surfingrepparttar 133443 ‘Net you’ll find plenty of sites offering tones by today’s hottest musicians; you can pick monophonic, polyphonic or true tone formats. More on that later.

A Caveat Before You Buy!

The first thing you need to know before you select, buy and download a suitable ring tone is if your cell phone is up to date enough to utilize this feature. Like everything else in technology, cell phones have evolved very quickly. As a resultrepparttar 133444 cell phone that you purchased just a year ago may not haverepparttar 133445 ability to fully accessrepparttar 133446 type of ring tone currently available. So make sure you check. Re-read your manual or call your service provider to find out. It’s possible that you can upgrade your phone for a reasonably low fee.

What’s Available?

Ringtones are divided into three formats.

  1. Monophonic
  2. Polyphonic
  3. True Tone or Real Tone
To understand this type of technology, a person needs to have a physics/mathematics background and understand musical composition. Luckily, all that is needed to know is what types of ringtones are available and what they sound like. The following is a description of three types of ringtones, monophonic, polyphonic and true tone. Most websites offer samples of each and once you hear an example, you’ll know what type you’ll want to use on your cell phone.

A) Monophonic Ringtones Some ofrepparttar 133447 first cell phones came equipped withrepparttar 133448 capability of having a one tone ringer. “Monophonic” isrepparttar 133449 simplest of ring tone technology that uses a midi format. This “one note wonder” changed ringtones. Gone wererepparttar 133450 chirps and chimes; now you could play a song. A monophonic ringtone is single notes playing a song. You can recognize your favorite song but it sounds a little lame. Most monophonic tones are offered free of charge because of more full bodied tones now available, but if you’re trying to make a statement, however, read on.

B) Polyphonic Ringtones Polyphonic ring tones also use midi technology butrepparttar 133451 tonal quality is richer and has more depth. This is because polyphonic ringtones can play up to 40 notes or more. A quick example isrepparttar 133452 sound produced when Windows XP® starts up. It reproducesrepparttar 133453 sound of an orchestra playing a note rather than one instrument playingrepparttar 133454 same note.

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