Talk:Antikythera mechanism/Archive 2

Archive 1

Archive 2

Archive 3

Archive 4

Archive 5

Greek origin?

May I ask why this mechanism is considered to be of Greek origin? I understand it was found on a Roman vessel, and is only DESCRIBED in Greek sources, but it's construction is neither described, nor applied in Greece. According to this article http://users.otenet.gr/~garof/hoc.html Ancient Greek city states did not use the calendar as depicted by the mechanism. It seems to me that to find the place of manufacture, one needs to look for a culture that used all possible calculations which can be achieved by the mechanism. The fact that the mechanism has Greek inscriptions does not make it Greek either. If I purchase a laptop made in France, I don't expect to have to learn French to operate it, or to even read instructions on its use! It seem there is an important clue to the origin of the mechanism in its calculation of the Metonic cycle. Which cultuure around the Eastern Mediterranean used this cycle c.300 BCE? --Mrg3105 21:56, 2 December 2006 (UTC)

Well, the Metonic cycle is named after the Athenian Greek astronomer Meton. Therefore, Greek influence on some level may be assumed. SunSw0rd 19:30, 4 December 2006 (UTC)

Yes, this is obvious, but it was not named Metonic because Meton invented the cycle. Did Greeks use the 'metonic' cycle? Did anyone else use/continue to use this cycle?--Mrg3105 21:17, 26 December 2006 (UTC)

The Greeks DID use the Metonic Cycle and it was probably known even to the ages that Homer lived, see http://en.wikipedia.org/wiki/Metonic_cycle Similar devices like the Antikythera mechanism have been made from the time of Archimedes and generally the ancient greeks had a tradition in technology. They even had made different kinds of automata ("ancestors" of modern robots), first steam engines (though they were not used for practical purposes), cannons that worked with steam, flamethrowers and many other inventions ,see also http://www.mlahanas.de/Greeks/Greeks.htm —The preceding unsigned comment was added by 88.218.37.170 (talk) 23:48, 24 February 2007 (UTC).

Pronunciation?

How is "Antikythera" pronounced? -- StAkAr Karnak 02:59, 15 November 2006 (UTC)

According to a 22 November, 2006 preview of current research results to be announced at the Athens conference beginning 30 November, 2006, it is pronounced antih-KITH-ehra. Athænara ✉ 09:15, 26 November 2006 (UTC)

Yes, that's how it would be pronounced by English speakers. A more traditional English spelling is Anticythera, with the same pronunciation except that c is pronounced "s." Wareh 20:53, 30 November 2006 (UTC)

[wrongly.] There's no freaken "h" or "k" or "s" anywhere! This is not a muttish (what ye fakely call English) word; this is Hellènic! Spell the word in Latin if not English: Anticute'èra (Hellènic) or Anticyte'ira (Còinè), or Antecuthera or Antecith'eera. There is also onely one "a"—don't mung im. -lysdexia 20:57, 25 October 2007 (UTC) —Preceding unsigned comment added by 69.110.107.167 (talk)

News coverage, Nov 2006

• Australian: Ancient calculator ahead of its time
• BBC News: Ancient Moon 'computer' revisited
• Nature: Decoding the ancient Greek astronomical calculator known as the Antikythera Mechanism
• NetworkWorld: High tech helps solve mystery of ancient calculator
• New York Times: An ancient computer surprises scientists
• Telegraph: Ancient Greek computer reveals its secrets

--Rob C (Alarob) 19:32, 29 November 2006 (UTC)

What exactly do these new discoveries tell us about the 150-100 BC world?Elatanatari 21:54, 2 December 2006 (UTC)

Astrology

There is a "See also" link to Horoscopic astrology, and I see above that this page is included in an astrology WikiProject. This seems appropriate, even though the Nature article, and the Wikipedia article so far, don't mention possible astrological uses. While discussion of the actual use of the mechanism is speculative by nature, and there may be issues with what can be cited on this, I thought I'd point to the informal discussion on an email list for classicists as evidence that there is speculation among informed scholars that the primary use may have been astrological. I agree with the discussants there that it's an odd bias on the part of the Nature writers not to consider this possibility at all (is the idea that advanced technology can be developed in the service of superstition unstomachable?). Wareh 21:16, 30 November 2006 (UTC)

It was not unusual for scientific mathematical and observational astronomy to be used by astrologers, even in the Roman Catholic Church. Copernicus dedicated his De revolutionibus orbium coelestium to Pope Paul III, a devoted astrologer—see (pp. 8-9) J.L. Heilbron ,The Sun in the Church: Cathedrals as Solar Observatories, a fascinating history of this research and the Church's simultaneous support and opposition in the medieval period. (A review by D. Graham Burnett, "What Time Is It in the Transcept?", The New York Times, October 24, 1999, serves also as an excellent external introduction to Heilbron's book.)

For the Church, the determination of the correct date of Easter was a complex mathematical astronomy problem, one which Giandomenico Cassini (who was not only an astronomer and engineer but, however strange it may seem now, an astrologer as well) did much to solve.

The journal is not Society or History but Nature—its focus is scientific research. It's not actually odd when Nature doesn't mention that support for observational and mathematical astronomy historically often came from those who intended to use the results for astrology. Athænara ✉ 02:30, 1 December 2006 (UTC)

Many people have been asking about whether this device could have been used for astrology. One of the researchers answered 'no' in an interview on the grounds that astrology had not yet caught on at the time of its dating (early 1st century BC). It depends on who owned the instrument - technical astrology certain was flourishing in the Greek language in the 1st century, and likely a little earlier if we accept accounts of Berossus bringing Babylonian astrology to Greece and the dating of other works to 2nd century BC. The interviewee may have been thinking of astrology specifically in Rome. So I don't think it can be dismissed as having an astrological purpose. Maybe they are slightly off with the dating and it is really late 1st century BC. Zeusnoos 14:32, 1 December 2006 (UTC)

Indeed. A better question would be whether the individual or individuals who created it, or commissioned it's creation, intended for it to be used for astrology. Because clearly a device that can calculate astrological phenomena has astrological uses. But it also has use as a calendar, not to mention being a technical marvel for its complexity and the ingenuity of its creators. Unfortunately, barring new archaelogical finds it's unlikely we'll ever know the actual intent of the creators, even if we know the function it was capable of performing.

With all our means of timekeeping today, I suppose it is hard to fathom exactly how many applications might have been interested in such devices; we know the obvious applications (astrology, astronomy), but also agriculture (predicting moon phases), seafaring (tides and star positions), cartography (shape of the world), and even rudimentary (though ultimately flawed) attempts at weather prediction (remember, it was the weather that prompted the resurgence of computation devices in more recent history). 12.104.195.112 22:24, 18 January 2007 (UTC)

I think trying to decide whether this device was (or could be) used for astrological purposes is futile, because the distinction between astrology and astronomy is a fairly recent one and the dividing line between them tends to be to some extent culturally defined. Advances in what we now call astronomy have always been used in astrology because both seek to enable prediction through the observation and calculation of cycles (though their interpretations of what the data actually allows you to predict have little in common). 67.170.148.111 04:03, 11 March 2007 (UTC)

What does Avalon mean in this context?

"In 1971 Price, by then the first Avalon professor of science history at Yale University" (paragraph about Function and purpose)? It seems to me like random word in this context? Can you explain it to me, please? —Preceding unsigned comment added by Paxik (talk • contribs) 19:51, 1 December 2006 (UTC)

Evocative name, Avalon, isn't it? Avalon Professorships are endowed by the Andrew W. Mellon Foundation; for more information, see the Avalon disambiguation page in the organizations section. Athænara ✉ 00:07, 2 December 2006 (UTC)

Error in the article - Differential gear

"Differential gear" theory by Derek Price has been falsified by Wright. There was nothing like that in the mechanism. See [1], section "Study, speculation, theories". Olaf —The preceding unsigned comment was added by 83.5.214.22 (talk • contribs) 15:27, 3 December 2006 (UTC).

See also [2] page 4 Silthor 17:48, 3 December 2006 (UTC)

The article in The American Mathematical Society about the differential gear of the Antikythera mechanism [3] was written in 2000. Later Wright found out that this is wrong assumption. The newest research papers published in Nature doesn't mention differential gear. 83.144.77.10 13:20, 4 December 2006 (UTC)

In fact, the 2006 Nature article explicitly states: We find no evidence in the CT for an idler wheel carried on e3 and between e5 and k1 or between k2 and e6, as has been previously proposed. --Diomidis Spinellis 10:27, 21 February 2007 (UTC)

Need to redo "Function and Purpose"

In light of previous comments and breaking news, I think the "Function and purpose" section should be rewritten. Much of what is in there now really belongs under the history of study. —Długosz

Your article contains a suggestion that the wreck of the Roman ship in which this device was found may have been plunder being sent to Rome by Iulius Caesar. That appeared to me to be incorrect. In the first place, your article states that the wreck was believed to have occurred in the period 150-100 BCE. Iulius Caesar was either not yet born then, or was an infant. Later, however, contradicting the earlier, imprecise dating, it dates the wreck to 80 BCE. My understanding is that Caesar could not have been sending plunder to Rome at that time, either. To check my recollection, i consulted your page on Iulius Caesar. In 80 BCE, Caesar was a minor military commander, without independent military command, and was seconded to the King of Bythinia. He did not return to Rome until after the death of Sulla in 78 BCE. Therefore, your article on Caesar (and my understanding of ancient history) contradicts the contention that the Roman ship in the wreck of which the Antikythera Mechanism was found could have been plunder being sent to Rome by Iulius Caesar.

John Kelly

209.197.129.19 16:27, 5 December 2006 (UTC)

References cleaned up.

The references were a mess - so I cleaned house a bit. To avoid making such a horrible mess again, would contributors please note that:

1. We use the <ref>{{cite...|nested=yes}}</ref> format for references embedded in the text.
2. Things that make interesting reading but which are not explicitly referred to in the text are Further Reading (if they are books, magazines, etc) or External Links (if they are web sites). You should still use the {{cite...|nested=yes}} format for these things so they have a nice uniform formatting.
3. For web sites, we NEED an 'accessdate' field so that should the link 'die' because the owner removed or renamed it, somone stands a chance of finding it using the Internet archive (aka The Wayback Machine).

SteveBaker 16:40, 23 March 2007 (UTC)

Thanks for that - however, I have to disagree with the further reading part. I've fixed it per MOS, and have explaine dmy rationale in the edit summary (references are books, books are to read & therefore are "further reading"). Simple explaination, but basically they are one in the same. All other similar FA's I've taken part in have a similar style, so I'm sure you won't mind the change. Thanks Steve... :) Spawn Man 07:40, 24 March 2007 (UTC)

Yes, I do mind - I'm reverting that change for the reasons described below... SteveBaker 04:56, 28 March 2007 (UTC)

References or Footnotes?

As a part of major referencing cleanup, I renamed the section containing the <references/> tag to be ==References== (rather than 'Footnotes') in accordance with the example in the MOS section that specifically covers this part of the document and the referencing style this article now uses (post-cleanup): Wikipedia:Citing_sources#Footnotes - whilst the MOS sometimes uses the word 'footnotes' and elsewhere 'references' to describe these things, it is clear from the example that what they expect to see in the article itself is the section heading 'References' and then the references tag. This change was reverted - and I'm now re-reverting it on the basis of what the most applicable part of the MOS actually says. I have gotten two articles through FA to the front page (one just a couple of weeks ago) by doing it this way - I think I know the rules!

But it makes sense my way - 'References' are (by definition) things to which we referred. In your version of things, everything in the 'References' section were books to which we absolutely DID NOT REFER. In that regard, they are like 'External Links' - they are things we think people might like to read - but they are definitely not 'references'. So - your "References" must become something else "Further reading" is a common heading used in lots of articles. The "Footnotes" section is a long-obsolete Wiki convention that is superceded in almost every FA you look at over the last six months by the section heading "Reference".

I've reverted those changes accordingly. SteveBaker 04:55, 28 March 2007 (UTC)

Computer or not?

If I have understood the articles referred to in the external links section and footnotes, the "device" did accept input from its operator, and was able to vary its operation. If I did not misunderstand, the decipherment of the operationg instructions engraved on the machine itself, indicate that to vary the results, the operator is to keep some points fixed, while letting others slide freely, and by such "switching" provide input affecting which planetary motions he will obtain. Do correct me if I have it wrong, but to me that clearly makes the "device" a computer. -- Cimon Avaro; on a pogostick. 04:30, 5 April 2007 (UTC)

The word computer has changed meanings at least twice over the past 100 years. In the 1940's and earlier it meant "A person who makes a living performing calculations" - later, when mechanical calculators started to appear it meant "A gadget that can do arithmetic" - but by the 1960's we began to reserve the term for machines that are programmable. Hence we once called the Atanasoff–Berry Computer a "computer" - but nowadays we'd describe it as a calculator...it could do only about what a modern (non-programmable) pocket calculator could do. In these terms, the Antikythera mechanism cannot remotely be described as a computer in modern terms. It also cannot be described as a computer in terms of the earliest use of the English word because back then it referred to a human being who calculated things. So, no - I don't think the Antikythera mechanism should ever be described as "a computer". It's a calculator at best. "Mechanical Calendar" might be the most accurate term. SteveBaker 12:53, 5 April 2007 (UTC)

SteveBaker is right, the article computer makes a cogent (if implicit) argument that the word no longer means anything other than a 'stored program digital computing machine'. OTH, this beauty certainly deserves to be called an "Analog Computer", of which it may be the finest example I know of in history. Predicting eclipses in Ancient Greece for land's sake! Astonishing, ain't it? Eaglizard 17:42, 25 June 2007 (UTC)

I think the term analog computer is the best way to describe this device, as it does follow a set of instructions in the form of it's geartrains. The calculations nessessary for accuratly mapping any type of harmonic motion such as the paths of the stars and planets across the sky are complex, involving many of the discoveries of the Pathagorians. So while it is not a modern computer (ie digital programable) it is a type of computation device which follows instructions, aka computer. Just my opinion.--Scorpion451 01:14, 1 July 2007 (UTC)

I'm sorry - but "Analog Computer" is a terrible way to describe it - firstly, it's not analog and secondly, it's not a computer. I explained before why it can't be called a computer using the modern (ie post-1960's) meaning of the word - it does follow hard-wired instructions - but it's absolutely not programmable and that's the touch-stone of the modern definition of the word. You wouldn't describe the engine of your car as a 'computer' - although it does use cams and gears to precisely time injection of fuel and air and emission of exhaust. Old fashioned carburettors "calculated" the fuel/air mixture using the engine vacuum and carefully shaped needles to effectively do arithmetic.

It's not "analog" either - an exact number of turns of the crank will produce an exact corresponding change in the dials because each tooth in each gear wheel interlocks with corresponding teeth in the next wheel. There is a precise digital correspondance between their motions. A fixed number of turns of this gear produces an utterly exact number of turns in the gear it meshes with. Strictly, each wheel counts the number of teeth in the wheel that's driving it. In an analog computer, the voltages (or whatever) that are approximate in nature are multiplied, added, subtracted, etc - with error building up in variable increments as the calculation proceeds. If the wheels in Antikythera had little rubber tyres on them that gripped each other - or were pulleys with drive bands connecting them - then it would have been an analog device.

No - it's a fixed-function mechanical calculator - and that's what we must call it. It's not a matter of what it "deserves" to be - it's a matter of what it actually is. I don't want to detract from how clever it is or how beautiful the design was or how intricate the construction may have been...nor even how useful it may have been - it was certainly all of those things. But we just can't call it a "computer" as some kind of honorary title without grossly misleading the people who read this article. The computer (as we currently know it) was invented by Charles Babbage in the form of his Analytical Engine - Antikythera was at most, a very clever, complex, beautiful, fixed function mechanical calculator - period. SteveBaker 06:04, 1 July 2007 (UTC)

Actually, the real issue is not what we perceive it as being but what the experts describe it as. What are our sources for saying it's either an analog computer or a fixed-function calendar? -- ChrisO 09:23, 1 July 2007 (UTC)

And answering my own question, it turns out that the Antikythera Mechanism Research Project itself describes the Mechanism as a "complex mechanical computer". [4] -- ChrisO 09:28, 1 July 2007 (UTC)

SteveBaker, did you not read my refutation of your position above? It is definitely *not* hardwired, but rather clearly programmable. The programming is done by holding some parts of the mechanism fixed while allowing others to move freely, and the programming consists of which parts to hold fixed for a given computation; quite analogical to flipping switches on the early electronic computers. -- Cimon Avaro; on a pogostick. 11:17, 1 July 2007 (UTC)

1. User:Cimon Avaro: Yes, I did read what you wrote - but it doesn't refute my point. To see why not, let's get properly technical about what this term "programmable" means. Fortunately, we don't have to rely on any fuzzy dictionary definition - there is a very formal mathematical definition that we should use here. Please read Church–Turing thesis and tell me whether the Antikythera device is equivelent under its terms to a Turing machine. IMHO, its quite clear that it doesn't come within a million miles of reaching that basic definition of programmability. Assuming you carefully read those definitions and understand what they mean - you will then agree with me that Antikythera's controls are simply the selection of alternative 'hard wired' calculations (in much the way that pressing the '+' key on a pocket calculator makes it do something different than holding down the 'x' key). This means that the device is NOT a computer.
2. User:ChrisO: You may have a point about references for this fact and we might risk violating WP:NOR if we don't carefully elaborate on why we don't accept the Antikythera Mechanism Research Project's (AMRP) description. However, there are plenty of sources for the definition of programmability in the Church–Turing thesis and Turing machine articles that we can refer to. We can say something along the lines of "the device is a mechanical calculator (although the AMRP erroneously describes it as a complex mechanical computer)" - referencing some suitable Church-Turing document for the first part of that statement - and the AMRP's description in the second part. WP:NPOV#Undue weight says that we shouldn't give undue weight to the AMRP's definition of "computer" if we can provide suitable weight for the standard definition...which we easily can. To quote from WP:NPOV:

From Jimbo Wales, paraphrased from this post from September 2003 on the mailing list:

• If a viewpoint is in the majority, then it should be easy to substantiate it with reference to commonly accepted reference texts;
• If a viewpoint is held by a significant minority, then it should be easy to name prominent adherents;
• If a viewpoint is held by an extremely small (or vastly limited) minority, it does not belong in Wikipedia (except perhaps in some ancillary article) regardless of whether it is true or not; and regardless of whether you can prove it or not.

What I think we have here is that the AMRP's implied definition of what constitutes a computer falls into the second of these categories - and the mainstream definition of what it means to be 'programmable' (and hence a 'computer') falls into the first category. That the definition of a "computer" includes devices such as this is a view held by a tiny minority (eg no computer scientist of any standing would agree with them) - but it's a significant minority since they are the supposed authority on the device - so we should say that they hold this view - but we must also explain that this is not the view of established computer science since the 1930's. I hate to accuse the AMRP of promoting a fringe theory - but this situation is analogous to the argument in Wikipedia:Fringe theories about 'flat earth' theories being explained in the Earth article. They are notable enough to gain a mention - but we must not take the stance that they are true because they are in the minority of scientific views.

The current text of the article is even worse than it was before - contrasting the term "mechanical computer" against "digital computer" - when mechanical computers are almost always digital, so no contrast there exists. What's worse, someone linked "mechanical computer" to the article: Analog computer - which exhibits a deep lack of understanding of either term! If we were to fully qualify the description of Antikythera according to modern computing practices, we'd have to say it was a "digital, mechanical, fixed-function, astromical calculator". I don't have the time to write a better text with references to Church-Turing that will fit within a tight paragraph in the introduction to the article - so for now, I have to simply revert to 'mechanical calculator' in order to avoid stating a total un-truth in the article header.

SteveBaker 13:25, 1 July 2007 (UTC)

You stated in an earlier post here that the gears do not represent a form of mutiplying and dividing magnitudes and error. This is not true. While I will not change the article, I will say that any geartrain system is by definition both of these things. Any imprecision or wear in the gears will by necessitybe multiplied by a factor of the ratio of the gears. A gear with a circumferance of 1cm with a flaw in a single tooth, turning a gear with a circumferance of 10cm, will result in the one-tooth flaw being magnified by a factor of ten, because for each rotation the small gear make the larger gera turn one tenth of a rotation. You also mentioned that a car engine could be considered a type of computer by the definition I gave for analog computer. Yes, it can. Data in the form of fuel, the driver's actions over the rate of fuel, the gearing in the engine and transmision, not to mention the differential gears used in the axels in four wheel drive veihicles. All of these factors of input come into play to calculate and provide the exact amount of force needed to maintain the car's motion. It is one of the best examples of an analog computer immaginable. And finally, the lack of programability of the device is not at issue. However, there are numerous examples of completely hardwired devices that are, in fact, computers. The regulating computers on factory lines are frequently simple hardwired devices monitoring and processing the data they take in from the sensors on the manufacturing line. They then report back to the central server, itself a fairly hardwired device with a degree of adaptivity between hardwired modes. The graphics card in a any computer is also hardwired. It takes in simple data describing the shape of the object to be rendered and the texture to be laid over it and runs this electrically represented data through a series of hard wired circuits and outputs the picture in the form of electrical pulses. The device is completely hardwired, the only way to accomplish such a task at a high rate of speed.--Scorpion451 19:47, 1 July 2007 (UTC)

Imprecision in geartrains: As you say - if a tooth breaks off of a gearwheel, there will be an accumulating error - this is just like any digital system that is so seriously degraded that entire bits are dropped. But just like other digital systems, gear wheels perform well for small amounts of wear - there is no accumulation of error. What you describe is the very essence of a digital system. You're doing a great job of backing up my position!

Car engines are never described as 'analog computers' - never. My point is that systems that behave like this are not ever called 'computers' - and neither should Antikythera.

The lack of programmability is absolutely at issue. The very definition of a computer is that it is programmable. Your examples are of non-programmable systems that make use of a fully programmable computer as a part of their workings. So, for example, my dishwasher is not programmable - it could have been made with clockwork timers - or it might contain a general-purpose computer that has been programmed to act as a dishwasher controller. We aren't attempting to define the entire dishwasher as "A Computer" - it's not because it's not programmable. It has a handful of fixed settings - it cannot behave as a Turing machine - and is therefore not a computer. The computer it contains as a small component is indeed a computer in every sense - it can be programmed flexibly - it is equivelent to a Turing machine. Antikythera simply doesn't meet that definition.

From the introduction of our article Computer:

The ability to store and execute programs makes computers extremely versatile and distinguishes them from calculators. The Church–Turing thesis is a mathematical statement of this versatility: Any computer with a certain minimum capability is, in principle, capable of performing the same tasks that any other computer can perform. Therefore, computers with capability and complexity ranging from that of a personal digital assistant to a supercomputer are all able to perform the same computational tasks as long as time and storage capacity are not considerations.

This truly isn't a matter of opinion. Computers are (since the 1960's) defined as programmable devices - and the definition of programmability has been defined in a solid mathematical sense in the Church-Turing thesis. I repeat my earlier question: Can Antikythera come within a million miles of being able to emulate a Turing engine? If not, it cannot, must not, be described as a computer in an encyclopedia. This isn't some kind of wishy-washy debateable matter - it's absolutely cut and dried. If you cannot or do not understand Church Turing and it's implications for programmability and computability - then please back out of the argument and accept the word of an expert. SteveBaker 21:15, 1 July 2007 (UTC)

Quite the contrary, that paragraph makes quite implicit that Church-Turing does not *define* programmability, but does present a significant threshold in the level of it. "Any computer with a certain minimum capability is, in principle, capable of performing the same tasks that any other computer can perform." That bit about "minimum capability" clearly suggests that while computers that lack that minimum capability *will not* be able to perform *all* tasks that other computers are able to, for all that they are computers. Limited computers, but computers nevertheless. I know it takes close reading, and ability to parse precisely formulated statements, but that is what the article says, and no amount of wrangling can extract from that language that Church-Turing defines what programmability is. It only defines what _universal_ programmability is. There is _limited_ programmability below that threshold, which despite being limited, is still programmability. -- Cimon Avaro; on a pogostick. 06:22, 2 July 2007 (UTC)

Church-Turing complete != programmable

To quote from Colossus computer: "Colossus was the first of the electronic digital machines to feature limited programmability. However, it was not a fully general purpose computer, not being Turing-complete, even though Alan Turing on whose research this definition was based, worked at Bletchley Park where Colossus was put into operation. ". The Antikythera is clearly programmable. It accepts variable instructions, not just variable values, but essentially varying what it does with those values. That this programmability is not universal in the Church-Turing sense, doesn not detract from the fact that it is programmable in a *limited* sense, quite like the Colossus computer. I hasten to add, that it is not even a case of one instruction, one operation, but the instructions combine, multiplying the number of operations possible, like programs in fact do. It is not like a garden variety calculator where pressing the multiply sign will get the multiplication operation and nothing else, no matter what you do. with an analogy to calculators, the thing that the antikythera does that qualifies it as programmable is like the pocket calculator being able to do something weird and wonderful apart from multiplication, if you follow pressing the multiplication key in the correct order with the plus key, the equals key, the minus key, and then after entering the correct sequence of these operator keys only enter the values to be operated on. -- Cimon Avaro; on a pogostick. 06:12, 2 July 2007 (UTC)

Furthermore; from Turing completeness (emphasis mine): "Turing completeness is significant in that every plausible design for a computing device so far advanced can be emulated by a universal Turing machine - an observation (it is not and cannot be mathematically proven) that has become known as the Church-Turing thesis."

The phrase that I emphasized in that statement, I think clearly indicates that Turing completeness is the logical end-point for complexity of normal computers, not its beginning. -- Cimon Avaro; on a pogostick. 06:43, 2 July 2007 (UTC)

ISPANIA

We say "The name of ISPANIA (Spain) in these texts is the oldest reference to this country", and that the texts are dated "150 to 100 BC", yet the Hispania article says that "Hispania" was "first mentioned [in] 200 BC by the poet Quintus Ennius". It is also curious that Hispania was the Roman name, but the Greeks called it Iberia. --Heron 12:12, 24 June 2007 (UTC)

I think that Ispania is the name of the country Spain, and Hispainia is the name of the peninsula Ispainia is on. The country might be named after the land it was on, like like the US of America. So the poet could have been referencing the land, and the texts the country founded there.--Scorpion451 20:10, 30 June 2007 (UTC)