Suggested New Year Resolution: Learn !

Resolve to get a better education for yourself, your children or grandchildren (dependant on your age).

Educational levels - and, sadly, educational standards - have fallen even during my lifetime (I'm 62). Let me quote some official findings supporting my impression :-

"The UK Department for Education and Skills says 14.9m people lack the numeracy skills expected of an 11-year-old child." Probably the number is higher 'cos the civil servants there added up the columns wrongly ;-) Look too at the appalling spelling on the local authority address plate quoted above.

The number of ASBOs ( Anti-Social Behaviour Orders) in an area correlates negatively with the educational levels in those areas. The less well educated children/teenagers are, the less chance of them getting a decent job and so the more chance of them living off social security and becoming criminal pains-in-the-neck for their local area. This continues into adulthood off-course of coarse (sic!). The sheer scope of the drunken, vomiting, Blair-ingly loud and violent clubbing going on when I visited Bristol(UK) recently this year shocked me; England has gone seriously downhill :-(

Frank Chalk - my favourite blogging teacher - often states in his excellent blog that a major problem is the lack of discipline and respect in ASBO-class schools. As parents, you cannot just leave education to the teachers. Even if your own education level is not sufficient to help your children with their homework, you should teach them discipline and respect. That way teachers like Frank - and there are many - would be able to concentrate on teaching rather than merely maintaining a semblence of discipline. And every child needs this; after all, just one disruptive element slows down the whole class :-( Local teacher friends confirm Frank's point, it's not just the UK.

But it is not just the ASBO-classes who have a problem. Even those lucky enough to go to university are studying stupidly soft combinations (e.g. 'underwater basketweaving' and sociology) which offer no subsequent job prospects. In fact, with the wisdom of hindsight - a third of graduates believe they studied the wrong course at university, a survey suggests. More business- or science-oriented degrees wanted.

However some rethinking is going on. For example, The UK schools minister has called for a debate on whether state schools should be allowed to offer International GCSEs. Also A-level exams are to be made harder again (after having being made really easy over the past two decades); A-levels get an A^* grade and all young people in England will be able to study for the International Baccalaureate getting them back up to e.g. the standards we have here in Germany. It is encouraging too that more money is being assigned to the UK's brightest pupils. I'm sure this will pay back in the longer term (sic).

Even as adults we should continue to educate ourselves. Praise here to Liz Hinds who has gotten a copy of Amo, amas, amat in order to learn Latin. Way to go, Liz!

But what can we seniors do to alleviate the (mis-)education situation? Well, we can resolve to teach more. We can provide snippets of knowledge on a daily basis (see this blog's Mission Statement over in the right side-bar). Or provide collections of useful and interesting trivia. Or anthologies of poetry we like. Whatever we can do.

Personally I have resolved to try some teaching of schoolchildren in 2007. I have arranged with a friend who is the head-master at a local grammar school to go there and teach some voluntary classes for the more advanced (A-level) pupils. I'll kick off by teaching some history of science, maths and particularly cryptography, motivating the kids with James Bond anecdotes etc. etc. Hopefully they'll learn some geography, history, politics, foreign languages, maths and statistics too in the process :-)

Now what will your contribution be in the education battle? Make a resolution now!

Now playing on the iPod : Jethro Tull's Thick as a Brick ;-)

Copyright ^© Stu Savory on 31st December 2006 at 06:31 CET permalink Email

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A Babylonian Wedgie ;-)

Back in the time of Hammurabi - about 1800 BC - the Babylonians were already keeping written records. They trimmed sticks to wedge-shapes and pressed them into drying blocks of clay, several of which still exist today. As number symbols they used for One and for Ten. Thus was Twelve and was Thirtyone. Surprisingly (for 1800 B.C.), positional notation was also used, and since the Babylonians counted to base 60, the number is 12*60 + 31 = 751. A particularly interesting cuneiform ( Cuneus is Latin for 'wedge' ) tablet is the one shown below, known to historians as Plimpton 322, and kept at Columbia University.

Archeologists being archeologists (and not mathematicians), they thought this was a set of accounting records for some commercial transaction or other. But then the one and only Otto Neugebauer - with more insight in his little finger than many have between their ears - pointed out that this is (an almost perfect) three-column table of

of a set of pythagorean right-angled triangles!

OK, OK, as you can see (if you care to translate the numbers) there are 4 minor mistakes on lines 8,9,13 and 15. But otherwise here we have a table of Pythagorean right-angled triangles cast in stone (well, clay) about 1800 B.C.! That's about 1250 years BEFORE Pythagoras (540 B.C.)! How's that for a Babylonian wedgie ? :-)

Copyright ^© Stu Savory on 29th December 2006 at 06:29 CET permalink Email

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Photo taken by Birgit Braum; thanks, Birgit.

Copyright ^© Stu Savory on 26th December 2006 at 06:26 CET permalink Email

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We demand Equal Rites!

European Union legislation demands equal rites(sic!) for all religions. So, in the spirit of this excessive, obsessive-to-punitive, Political Correctness, I protest today at the monopoly being claimed on this day by the youngest of the Gods. According to airline captains' hallowed seniority rules, the older Gods are demanding at least Equal Rites today. Rather than trying to cover all of them, I'll just outline the three in the photo, L2R, OK?

Anubis (left) is the Greek name for the ancient jackal-headed god of the dead, as worshipped in ancient Egypt. He is still around, cropping up in popular SF novels; for example Anubis appears as the scheming antagonist in Roger Zelazny's Creatures of Light and Darkness. He also crops up as 'Mister Jacquel', who co-owns a funeral parlor in Cairo, Illinois with Thoth (as 'Mister Ibis') in Neil Gaiman's American Gods :-)

Jupiter (centre) was the father of the Gods for the Romans, just like Zeus in the Greek pantheon. He is the chief god of the Capitoline Triad (with Juno and Minerva). In ancient Rome, people swore to Jove in their courts of law, which lead to the common expression "By Jove!", still used (in the UK) today. Hurler of lightning bolts as a form of rapid justice, from which today's legal system could learn a thing or two!

Thor (right) - shown bearing his boomeranging hammer Mjollnir - is one of the Nordic Gods, son of Odin the father God. These Gods are still around today, we get the names of some of the days of the week from them :- (Wodan's-day, Thor's-day, Freija's day). Tues-day - thought by some to be the Jews' day - actually came from Tiwaz'-day (Tiwaz is a Germanic version of Tyr). So the Norse Gods are still part of our daily(sic!) lives. Thor features heavily in the Prose Edda an early islandic text by Snorri Sturluson (1178-1241), a classic well worth reading (in translation).

So these are just three of the Gods with more seniority than today's swaddled infant. And all this talk about Jesus being the Son of God did not even start until 160 AD, it was not mentioned in any of the original texts. And not all of these got into the bible. What texts were included (and which not) was not decided until 325 AD at the First Council of Nicaea (which is in present-day Turkey). Once they'd decided what books were to be in the bible, they got around to more serious stuff like 1) the prohibition of self-castration and 2) prohibition of the presence in the house of a cleric of a younger woman who might bring him under suspicion (older women are OK?). One of the gospels they threw out was the Gospel according to St.Judas. So much for fair and balanced reporting, even then! If you are curious, try reading any of these :-

• The Gospel of Judas. By Kasser, Meyer and Wurst.
• My Name was Judas. by C.K.Stead.
• The Lost Gospel. The Quest for the Gospel of Judas Iscariot by Herbert Krosney.

And of course, when the Jews were asked which books should be in the bible, they gave the same reply the Japanese did in Pearl Harbour, "Torah! Torah! Torah!" ;-)

So, folks, whatever is your cut from the opium of the masses, have a nice day :-)

Copyright ^© Stu Savory on 25th December 2006 at 06:25 CET permalink Email

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In a state of indecision (or two) ...

Originally I was going to blog about the life or death conflicts in places such as Gaza (Palestina/Israel) and Kashmir (Pakistan/India), places which are in two states. But then my australian blogfriend Anna Pashen sent me the poster shown below, which she bought for a Brisbane beach party. It was to be a surfers' reception, but it was unexpectedly cancelled (i.e. the wave function collapsed ;-)

For those of you unacquainted with quantum theory, let me point out that Professor Erwin Schrödinger was famous for two things :-

• His cat, and
• His assertion that all geeks have zits^* (especially Wigner's friend ;-).

^* : "Daddy, do all geeks have zits?"
"Yes, Virginia, but don't use that word 'cos it's rude; they're called 'fizzy cysts' " ;-)

Copyright ^© Stu Savory on 21st December 2006 at 06:21 CET permalink Email

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Blogging for the Old Bats ;-)

Fallow moonlight casts shadows on a dark dank night in an old graveyard in Golders Green. It is where HE lies, eternally undead, awaiting the full moon. What rough beast is this, his bloody thirst unslaked, dreaming of white throats, bared unto His thirsting fangs? It is Dracula, wompyr, vampire.

Costas Efthimious from the University of Central Florida has - methinks - never been in this graveyard at midnight. Otherwise he would not allege that there are no vampires. He arbitrarily assumes the first vampire arose(sic!) spontaneously in 1600 AD and that each vampire bit a victim once a month, thus doubling the number of vampires every month. Therefore - after only 29 months (which is not even 2 ½ years) - there would have been 2²⁹ vampires, and that was the total population of the Earth around 1600 AD. Therefore, he says, either everyone is already a immortal vampire or there never were any.

Let us now - in the immortal memory of Bram Stoker ( author of 'Dracula' ) - examine this hypothesis. Prof. Efthimious assumes vampires are immortal. But Stoker and even more so Hollywood, tell of several methods for killing vampires. There is the traditional stake through the heart. More likely is accidental exposure to sunlight. It might be that every time the clocks are put back the vampires clamber out of their coffins an hour late by mistake and inadvertently expose themselves to sunlight :-) Surely the strongest reason yet for maintaining summer-time ;-)

Then there's holy water, and/or being touched by a cross (presumably a star of David if they are Jewish vampires [not unlikely, as vampires do bleeding kosher kills] ;-).

Hollywood would also have us believe that vampires only bite virgins. This was a rumour spread by the local lads who then explained to the virgins how they could avoid becoming vampire food, the lads would volunteer their help ;-) And thus there became a dearth of virgins in Hollywood and the vampires died (again) of hunger :-)

Once the vampires' expiration rate exceeds their creation rate, Efthimious equation has a decreasing effect and the race of vampires dies out unnaturally. That this is the fact is celebrated by the traditional English greeting - particularly popular around Golders Green - of "Hallo Sunshine!" ;-)

As an aside : if we are to believe Hollywood, most of the victims were pulchritudinous blondes - virgins as mentioned above - and so most of the 2nd and subsequent generation of vampires were women. Tradition has it that you could also kill a vampire by burning it like a witch at the post on a bonfire. Indeed the etymology of the word 'vampire' comes from the Transylvanian word anglicised as 'Wompyr', which is a truncation of the phrase "women's pyre" . Q.E.D ;-)

However - as Efthimious does not seem to know - real vampire bats (native to South America, not Transylvania) are NOT promiscous (fact!). They tend to suck the blood of the same host (cattle) over and over again rather than switching to a fresh host at every gorging. In fact, they fly low over the heads of the bovine herds, listening intently. Apparently each cow has a slightly different breathing pattern which the bats can identify. They fly above the herd until they identify the breathing pattern of their previous host (which they have remembered) and then suck from the same beast again using the holes they made the first time. This makes the skin-penetration much easier for them, since they also inject a substance so that the holes do not heal well.

But you really didn't want to know all bat, did you, dear blogreader?? ;-)

This post today is for Liz Hinds, who has a bat house in her garden.

Copyright ^© Stu Savory on 18th December 2006 at 11:42 CET permalink Email

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Heiko's bipolar problem ;-)

T his being the festive season when Xians - despite it being explicitly forbidden - make graven images of the Baby and put them in a manger under their Pagan trees, and the more fundamentalist members of the One True Church^® (whichever!) see that the pattern in their burnt offerings (in their break-fast toast) is an image of His mother, it is the dog's bottom when I get to see the semblance of the Holy Ghost (see photo left). Either that, or I'm still a little tipsy from an office Xmas party :-) And thereby hangs a non-canine tail tale...

... Heiko's tale. We were down at the boozer yestreen swapping enigmatic puzzles for entertainment - simple things please simple minds - when Heiko asked this one :-

"OK, OK, OK. It's my turn to pose a puzzle now. You walk a mile south, then a mile west, then a mile north and are back where you started from. Where are you?"

People suddenly took an extreme interest in their beers and the sound of (almost) silent slurping prevailed. We'd had several pints already :-)

Then Heiko - who can't stay quiet for long when he's had a few - added :- "Come on! It's a unique answer!" Stop reading now dear blogreader and try to solve it.

Various quiet mumbles followed, surpassed in volume by the sound of supping.

"S'obvious, innit," the irrepressible Heiko answered himself "It's the North Pole!!! Only there can you walk 1 mile south, one west (or east) and then 1 mile north to get back to where you started from! Elementary, Watson!" he crowed triumphantly.

We returned to the study of the froth on our beers until I interjected "But you misled us, Heiko, that's not a unique answer, there are an infinite number of correct answers." Stop reading now dear blogreader and try to find them.

Heads perked up at the prospect of Heiko having to buy the next round :-)

So I explained : "Assume you were one mile north of a circle 1/(2*PI) miles north of the South pole. Then you could walk a mile south to get to that circle, then a mile west, walking one complete orbit of the south pole, then one mile back along your original tracks to get you back to your starting point, which could be any one of an infinite number of answers all on a circle around the pole. Indeed you could start at an infinite number of points on an infinite number of circles being 1+1/(2*PI*N) miles north of the south pole for N = 1,2,3,4,5,6,7 etc orbits of the pole. So it's anything BUT unique; I think you owe us all a pint! Mine's a smooooth Guinness :-)"

Needless to say, the seasonal merriment increased loudly as we all enjoyed Heiko's discomfort. NB: This tale has been retold with his permission, he's a good loser.

PS : Jane has suggested that we ALL put some Sudoku in our sidebars. It's her new sidebar meme :-)
She - and several others - have said they are working on my 'Invention' meme (see wednesday's post).

Copyright ^© Stu Savory on 16th December 2006 at 07:42 CET permalink Email

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Light(-bucket) humour feedback

M onday's post about light buckets (large aperture astronomical telescopes) attracted rather varied responses. Here are some of the star replies ;-)

Anna Pashen (Australia) wails too about the issue of light pollution, viz. "Here in Brisbane it is nigh impossible to see much in the way of stars at night as any low level cloud reflects the city lights back. We have some very confused crows here that spend entire evenings calling the the dawn/dusk because of how bright it is." She recommends I go to the Nullabor plain. 1-way.

Someone calling himself The 12 inch man - which I sincerely hope is just a reference to the aperture of his telescope - tells us about a current ESO (European Southern Observatory) mega-light-bucket project. "The ESO have begun the €57 Mio. study phase for a mega-light-bucket, completion 2017 at the earliest. It's called the E-ELT (European Extremely Large Telescope). Question : How many meters is the E-ELT's aperture? The answer is 42 :-) It will have 960 hexagonal segments each of 145cm diameter. Even the secondary mirror is 6 meters across! It will have adaptive optics, correcting the position/height of 5000 supports at a rate of about 1000 times per second. No decision yet on where it will be located; expect political infighting :-("

Doug Alder recommends the clear skies of backwoods Canada at Roswell Rossland ;-)

Winston Rand wishes he too had a light bucket or even a telescope at all :-(

Jane^** jokes "Are we to assume that light buckets are to see pail stars ;-) ?" and wants to know whether I am expecting to see ET :-) , or even H.R. Giger's Alien :-(

Ivan tells us that there are plans for space tests to see if there is a fifth dimension and suggests that UFOs may come from it, rather than from elsewhere in our galaxy, whereas the SETI group think we may be talking to aliens within 20 years. It seems the Carnegie Institute have already decided where to look for ET. However, in the UK, the confidential Ministry of Defence report on UFOs (Unidentified Flying Objects) has concluded that there is no proof of alien life forms. UK evidence notwithstanding ;-)

Before I get snowed under by mail from the more wacky convinced and dedicated UFO believers, I'm going to pick up Jane's request and blog about the Fermi Paradox at some future date. [Fermi Paradox : The belief that the universe contains many technologically advanced civilizations, combined with our lack of observational evidence to support that view, is inconsistent. Either this assumption is incorrect (and technologically advanced intelligent life is much rarer than we believe), our current observations are incomplete (and we simply have not detected them yet), or our search methodologies are flawed (we are not searching for the correct indicators)].

And before we worry about communication with extra terrestrials, lets just consider some of the iconic trash tossed down before us Terrans. The toolbar shown above is a snapshot taken from Firefox (any other toolbar would have done just as well). There are no plain-language drop downs here to assist you. Now I defy any (non-Firefox) users to tell me what ALL these icons do, left to right, off you go now! OK?

^** @Jane : As you requested, I have put some simple Sudoku in the right sidebar again.

Copyright ^© Stu Savory on 15th December 2006 at 06:15 CET permalink Email

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Inventing : a meme :-)

A ssume you could invent something - just one thing - in the coming year, what would it be? I'm just starting this (new) meme - inventing it, so to say - to see which of your bright ideas takes the biscuit.

Just come up with an idea for a device you would like to see invented in 2007 and blog about it in the Q&A format shown below. Link to this blog post somewhere in yours. Then mail me the permalink of YOUR blogpost, so that I can point to all the inventions from here. Oh, and tag your blogfriends to do so too. We're blogging market research for inventors, right? And outlining a business plan for them too. If this meme encourages the invention of just ONE of the things outlined in our meme, then it has served its purpose (ideally of course, to make for a better world, but also - the capitalist motivator - to make YOU rich ;-)

So let me kick off with the meme :-

Assume you could invent something in 2007, what would it be?

I'd invent the Personal Power Pack.

Describe what it does

It'd be a jam-jar sized device, weighing not more than 3 kg (6 lbs), that could generate up to - say - 15kW of electricity efficiently while staying cool.

What would be the major use?

Fitted in your house or apartment it would generate enough power for all your family's electrical needs (average approx. 5kW) including heating/cooling the house. You would no longer need a mains connection (unless you wanted to sell surplus power to the power company's network). We would no longer need those potentially dangerous nuclear power stations. We would no longer need those dirty, smelly, coal and/or oil powered ones either. No more strip mining -> unviolated landscapes.

What might be a secondary use?

License to automotive makers who would produce electric cars, one such device per wheel ( 4*15 = 60 kW = 80 hp) would suffice, given the torque characteristics of DC motors. No more reliance on imported oil, independence from fossil fuels, no pollution.

How would it work?

Cold fusion. Just feed in water as fuel. Electrolyse it to oxygen (released to the atmosphere or bottled for resale?) and hydrogen. Fuse the hydrogen to helium (released to the atmosphere or bottled for resale?) releasing the energy as electricity into your house's wiring system or into electric motors in each wheel of your car.

How big is the market?

One per household. Four per car. Comes out at about 1 per person.

What would be the price?

Present household power and heating costs are about €2000 p.a. here. Cars here average about 15000 kms/year = 1500 litres of fuel = €2000. Four units per car, assuming a unit replacement interval of 8 years (like for a car) makes €4000 each. Whoever corners the market^* on this device makes a mint ;-) And we all benefit from a cleaner world with a simplified (decentralised) energy infrastructure. Way to go!

Correspondance - but especially blogging your own desired inventions - welcome :-)

Feedback : Some of the inventions you'd like made in 2007 :-

• Scott Adams wants a room-temperature superconductor.
• Doug Alder wants to invent two things : 1) a small remote control device that when pointed at an [excessively loud] car will cause all electronic components in the car to overload and basically fry. And 2) A Pinnochio chip in the TV set for watching political shows :-)

^* Bill Gates need not apply ;-)

Copyright ^© Stu Savory on 13th December 2006 at 06:13 CET permalink Email

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Santa, I want a Light Bucket from you pls :)

Because I can't afford to buy one for myself :-(

A Light Bucket is an astronomical telescope with an aperture so large that it has a field richer than the diffraction limit. Like this one ;-) It enables you to see (and/or take photos of) things like these magnificent photos I 'borrowed' here :

• And this shot of the cloud formations on Jupiter.
• Or the serene rings of Saturn.
• And the glory of the Whirlpool Galaxy.

But as it is, I'm grateful for a small 8-inch Dobsonian^* small enough to fit in the car and be taken to places with dark skies. This world is suffering increasingly from light pollution so that we no longer have the contrast they had 200 or more years ago. That's the downside of electric (street) lighting :-( I remember on my first African safari many many years ago being gobsmacked at how many stars there were! And different ones from here of course. I saw the full glory of the Milky Way (BTW, the word 'Galaxy' comes from the Greek for 'milky way'. Chocolate anyone? :-)

When I was 13 I was gobsmacked by Sputnik transiting the heavens and wanted to become a cosmonaut. I'd listened avidly to Journey into Space on the BBC radio and subscribed to the Eagle comic just to read Dan Dare ;-) . Then went on to do a first degree in physics and later became a flying instructor, subconciously thinking all this might help qualify me. But no, it was not to be. Sadly, I'll never get to see this view :( Unless Sir Richard Branson seriously reduces his prices ;-) However, almost seven years ago, I did make the acquaintance of a couple of Mir cosmonauts, 2 very nice men.

But now, yes, the goddess Fortuna smiles on me, for it turns out that there is a Light Bucket just 50 miles north of here, in Melle. And Santa has granted my wish, for they are having an open night on the 25th december, so - hoping for reindeer-clear skies - I shall go there, queue for my few (arc-)seconds of jaw-dropping amazement and get to see all the glory of the heavens - new stars - through a one-meter aperture 'scope.

Now where did I put that unread copy of Chapman's Homer ? ;-)

^* John Dobson - The Sky Monk - is a VERY interesting man, sidewalk astronomer, MacGuyver of the stars. Please go read his biography, or buy the DVD there to get the full force of his charismatic personality.

Copyright ^© Stu Savory on 11th December 2006 at 06:11 CET permalink Email

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Mrs. Salmen's Luxury Jams Manufactory

Breakfast at a small hotel in october introduced me to the superb taste of Lucullus jams and spreads. And I learned from the label on the jar that the jams were made less than 40 miles from where we live. Guess the rest ;-)

So I called the number provided on the label and talked to the owner, Simone Salmen, asking who my local distibutor is. Sadly, there isn't one, but she invited me to the factory because I enthused so much, especially about her Latte Macchiato breakfast spread. The factory is wholesale only, so I got some friends together ( Jana, Hasibaer etc) and we went there on december 1st and left with over €200 worth of jams, spreads, mustards and pastes as delicious Xmas presents (see photo above, of a three-pack that my young friend Jana put together). And a six-pack of Latte Macchiato breakfast spread just for me ;-)

Somehow, before talking to Mrs.Salmen on the phone, I had had a romantic image of her as a grey-haired old grandmother stirring her lonely secret-reciped pots in a cottage in the woods. It turns out that she is a smart and industrious young woman - in her 30s I would guess - who employs 14 people mostly busy with the logistics of delivering their jams etc to resellers worldwide, all 15 are friendly and very helpful.

They have a HUGE choice of available mixtures - I'm just trying the Bailey's Cream Spread as I write this, yum, yum, yum. Does this blog post have you salivating now? Then there is good news for you, dear blogreaders, because Mrs. Salmen now has an online shop where you can order her goods online and have them shipped to you directly, thus obviating the need for a local dealer (I choose that word advisedly ;-)

The URL of Mrs. Salmen's online shop is http://www.marme-laedchen.de. Enjoy! Sometimes the window I've given doesn't open properly, in which case just open a window yourself and copy the URL provided. Oh and I've just noticed the shop is only in German, but others should be able to guess their way through. You can't go wrong whatever you choose, everything I've tried so far has been deeeeeeeeeeeeelicious :-)
Minimum order is for €15 by the way, >= €30 postage is free (in Germany anyway).

This info for Cowtown Pattie, for Liz and for Doris, all of whom have a sweet tooth ;-)

Copyright ^© Stu Savory on 9th December 2006 at 06:09 CET permalink Email

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A message for the gits stuffing my mailboxes : »In a perfect world, spammers would get caught, go to jail, and share a cell with many gay men who have enlarged their penises, taken Viagra and are looking for a new relationship.«

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Discovering the Complex Primes as a kid :-)

B eing an account of how - at the early age of 16 - my flabber got ghasted.

Back in the halcyon days when Carl and I were at school, back before ancient dinosaurs became extinct, 1960 actually, some of those dinosaurs were our teachers, and some of them were rather good. We had John E. Blamey (acronymically named JEB) for maths. Jeb didn't so much teach by answering our questions but rather by asking us pertinent questions in reply. It really annoyed me at the time, but I now realise how genial this method was, because it taught us to think independently. So here's a reconstruction of one of the times Jeb blew my hungry teenage mind ;-)

We had learned much earlier about prime (natural) numbers and how we could use the Sieve of Eratosthenes to find them. We had even learned how to prove that the factors of all composite (i.e. non-prime) numbers are unique (see my blog-post from 14/11/2006. Then, our GCE O-levels safely behind us, our first 6th form lesson was about complex numbers (points in a plane) and how to do arithmetic with them (see the shifting and twirling blog post dated 20/11/2006). So I asked teacher Jeb :-

"Sir, are there such things as prime complex numbers?"

And Jeb replied "Well are there? As always, class, define your terms first!"

The whole class groaned as we saw our workload just increase in a complex way ;-)

Anthony proffered cautiously "Well, prime numbers are positive whole numbers not divisible by any smaller numbers other than 1".

"Good definition" said Jeb, "So what would complex whole numbers be?"

"Erm... complex whole numbers are where both the real and imaginary terms are integers?" I suggested "Like the intersection points on squared graph paper?"

"Correct, Savory" Jeb replied "They are called the Gaussian integers after Karl Friedrich Gauss, a famous 18th & 19th century (1777-1855) German mathematician, who first came up with them. Gauss also proved the unique factorisation theorem for them too, namely complex integers can be uniquely factored into prime Gaussian integers. Oops, now I've told you that complex primes exist. Now I want you to work out the first dozen or so. You may restrict yourselves to positive real components and imaginary components less than or equal to the real components, because they are distributed symmetrically."

Heads lowered and a busy scratching out (as with the Sieve of Eratosthenes) of points on the squared paper of our notebooks ensured. "Well, (1+i) is obviously the first one" I said. "And there is no way to twirl that to get to (2 +/- i)" I added.

And so we ended up with the points shown in my sketch on the left. The sketch on the right shows you the complex primes within a larger radius; they are symmetrical about the X and Y axes.

Now lets look at some composites obtained by multiplying these complex primes.

• (1 + i) * (1 + i) = 1² +2i + i² = 1 +2i - 1 = 0 + 2i.
  { Plausibility Check in polar coordinates: R,θ=(root(2),45°)² twirls to (2,90°) }
• (2 + i) * (2 - i) = 2² - i² = 4 + 1 = 5.
• (3 + 2i) * (3 - 2i) = 3² - (2i)² = 9 + 4 = 13.
• (4 + i) * (4 - i) = 4² - i² = 16 + 1 = 17.
• (5 + 2i) * (5 - 2i) = 5² - (2i)² = 25 + 4 = 29.
• (5 + 4i) * (5 - 4i) = 5² - (4i)² = 25 + 16 = 41.
• (6 + i) * (6 - i) = 6² - i² = 36 + 1 = 37.
• etc. , etc. , etc. . . .

My mind short-circuited, my ghast was flabbered (and vice versa), and I worked through the numbers thrice^*** before I announced in shock and awe (pace Rummy):

"It seems that 5,13,17,29,37, and 41 and probably several more, which as natural real numbers are prime, are NOT prime numbers when they are complex numbers!"

Jeb grinned delightedly at us having made this discovery ourselves and added : "That is indeed so, young Savory! Well done, class. A real prime number P factorises in the complex (Gaussian) way only iff P+1 is NOT a multiple of 4. This and Pythagoras' theorem lead us to Fermat's two-square theorem" (See the yellow box on the right).

This post is for maths-loving Jax, daughter of Four Dinners, who is as old now as I was then, who is going into hospital tomorrow. All the best Jaxx, we'll all be thinking of you :-)

Thankyou, all you others for staying awake while reading this ;-)

An Aside : After reading in mid-november my proof of the Unique factorisation theorem wherein I mentioned that there are rings in which the factorisations are NOT unique, Pjotr, writing from Vladivostok, asked for an example as he couldn't think of any himself. OK, Pjotr, we've just looked at the complex Gaussian integers (N + Mi). Now let's insert a constant C which multiplies only the imaginary part. So we get (N + C*M*i). For this example, I'll choose to set C = root(5). So with N = M = 1 we can multiply the term (1+root(5)*i) by (1-root(5)*1) thus getting 1² - (root(5)*i)² = 1 + 5 = 6. But we also know that 2 * 3 = 6, thus in this ring the number 6 does NOT have unique factors! Q.E.D

Finally, a poem from Dave Pleacher (now retired from Handley's Maths faculty) :

By the way, 'Iff' stands for 'if and only if'. Just thought you'd like to know, folks.
^*** : Why thrice? "What I tell you three times is true" (Lewis Carroll, in one of the 'Alice' tales).

Copyright ^© Stu Savory on 7th December 2006 at 06:07 CET permalink Email

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Lunch @ Paganini @ Erfurt

YAPTR 12 Yet Another Photographic Trip Report in which I show you another place we visited. This time we were driving back home from the Erzgebirge mountains on the Czeck border and decided to do lunch in Erfurt.

Erfurt is the capital of the state of Thuringen (in Germany). Erfurt still has an intact medieval city centre. We wanted to visit the the Krämerbrücke, an ancient bridge crossing the narrow Gera River. The bridge is covered with inhabited buildings, mostly shops nowadays. It was built in 1325 AD with a church on either bridgehead, one of which still exists, and you can climb the tower for a magnificent view of the city. We also wanted to do lunch at Paganini's place, a high class Italian restaurant with great game meals (e.g. venison and wild boar etc). Let's start with a shot of Paganini's.

And here is a selection of photos of some of the other neat looking things in Erfurt :-

• The Art Museum
• Detail of the frieze of the Art Museum
• The Atlantan Doorway
• Children's bookshop on the Krämerbrücke
• Shop for hand-made chocolates on the Krämerbrücke. Yum, Yum, indeed :-)
• Pair of typical beamwork houses
• Detail of a beamwork house nr. Market Place, note bottleglass windows.
• Entrance to the Krämerbrücke bridge, 1325 church tower entrance on left.
• Facade of Paganini's restaurant building
• Detail of the frieze on Paganini's place
• 1832 mural in Paganini's, with original Covent Garden poster
• An original score hangs framed on the wall there.

Now for a warning for all of you poor folks who get your coffee from St*rB*cks or similar. Paganini's place makes a coffee that will knock you right out of your socks! I usually drink a Latte Macciato which is normally mild enough not to interfere with my β-blockers. Not so the case here! They served me a tall glass of blown milk and a tiny, really tiny, copper thumbful of Triple Espressi. It sat there, black and evil, glowering at me like the Beast from the Pit! I poured it carefully over the back of the traditionally long hollow-handled silver spoon, to get that layered effect that a true Latte has, then enjoyed sipping it as it cooled. About 13 ¼ seconds later, Wham! Bam! my pulse was way up over 100 - despite β-blockers - and it remained that way for the wide-eyed and quivering 2 hour drive home. Wow! Triple A⁺⁺⁺ whammy! Be warned!

Copyright ^© Stu Savory on 5th December 2006 at 06:05 CET permalink Email

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Half a Million readers so far ;-)

This blog reached a milestone yesterday, the 500,000th blogreader stopped by :-)

I started this blog on 1/1/2003, so I'm in the 47th month now. Readership is now up to ca. 35,000 visits/month, which means 1162 visits per day. Now is a good time to say THANKYOU to my 1162+ readers daily. Of course, some of you don't come daily, so the number of actual blog-readers may well be larger. Thanks to you too!

The number of readers is (still ;-) on an upwards trend, and would have reached 34,000 for november 2006 if SiteMeter had not lost a whole week's data :-(

From the blog-writing point of view, I have written just over 760 blog-articles during that time, with a mean of 16.26 blog-entries per month (median=15, mode=14). That's a blog-article about every other day, OK? Mind you, the quality varies ;-) My blogging rate has been fairly steady, here's count-per-month over the 47 months.

The most popular archived month is February 2006, though I'm not sure whether that's for the entry about the death of Harry Potter or the one about how to scrub a disc really clean before you sell it. Mind you, it could also be the article on Bloody Theocracies or the pilots' trip report on visiting 10 countries in a single day. Dunno. So why don't you send me a mail, telling me the kind of stuff^* you would prefer here?

^* : Pace Four Dinners, only 21 so far were about maths. Another maths Post is in planning though ;-)

Copyright ^© Stu Savory on 3rd December 2006 at 06:03 CET permalink Email

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On World AIDS Day (and some other STDs)

While we were suffering from an Autobahn gridlock here in Germany (see my post dated 11/11/06), a UK bloggeress was reporting about her younger son's car breaking down, whereupon he had to walk home through the rain, clad only in a T-shirt (sic), she reported. So, inspired by this vision of bottomless humour, I wrote in her comments :-

"Always keep suitable supplies and clothing in the car (if not on you) should the car break down. For my friends in Alaska this means 2 sweaters and a parka and always a mobile phone. For my friends in Namibia it means having 4 litres of drinking water and a sunshade in the car. Given UK weather, a pair of swimming trunks might be de rigeur. Of coarse(sic) at his age it's probably good sense to keep 'emergency' condoms in the glove box ;-)"

My e-Friend objected to this idea, I quote "Excuse me! This is my car we're talking about. He is only allowed to use it because I'm nice."

Now it is my understanding that the UK government is running a huge campaign against STD, and specifically recommend omnipresent condoms. Surely, if I were a responsible mother - or just a motherf*cker - I'd want to be sure my offspring did not get any STD, even at the price of having potentially embarrassing contents in the glove compartment. You could always hide the condoms there in old empty tin of pipe tobacco (these are already conveniently mnemonically labelled "Shag" ;-)

I recommend that responsible parents inform one another if they do this for their offspring in the family (sic) car, lest there be divorce-inducing repercussions if the spouse finds out by accident, e.g. rummaging through the glove box while the bridge-playing spouse says he/she has "Just gone out for a rubber or two." ;-)

Of coarse(sic) in catholic countries (like Eire) the One True Church^® makes it nearly impossible for you to buy condoms, so the local youths buy rubber gloves and a pair of kitchen scissors instead, storing these innocent items in the car too {this is most probably an Urban Legend, after too much Guinness ;-)}. Bearing in mind the intended use of the offcut fingers, I suggest that's why they call it the glove-box ;-)

As I said, the UK government is running a huge campaign against STD (Subscriber Trunk Dialling (?) ), allegedly to stop people calling their preferred sexual partner to arrange a date for a bit of rumpy pumpy, then getting the clap. Condoms are supposedly useful here. Presumably you put the condom over the phone dial/keyboard and so electrifying contacts are inhibited. But mobile phones fit inside ;-)

Aha, you cry, the acronym STD does not mean Subscriber Trunk Dialling in this context, but rather Sexually Transmitted Disease. Penny drops. Thankyou Penny. Venn a real girl turned up, I was always itching for her to drop 'em ;-)

Tony B.Liar's UK Government ministers, who can't stop f*cking about blindly themselves, would perhaps be better understood if they used good old anglo-saxon names for the STDs, like clap, tripper, pox. Instead they use the longer medical names, which are harder to remember. These names allegedly came from the Latin, but I have a different etymology for them :-

• Gonorrhoea : What you get when your boyfriend says "I'm gonna rear you!".
• Syphilis : The local slag whore was called Phyllis, you got the STD when you called her for a quick shag, crying frustratedly : "I gotta see Phyllis".
• Chlamydia : When your frigid wife gets excited and starts to thaw, she reports "I'm clammy, dear"
• AIDS-de-Camp : Military gays buggering with intent within tent.

Follow the four links provided above, kids, to get yourselves better informed!

No, seriously folks, this is a big pub(l)ic health issue, so make sure your offspring are well-informed in advance of any sexual activity (ever younger these days, I'm told), supply your sons and daughters with condoms and explain how to use them properly (yes, you may use a banana), even if it is an embarrassing lesson. Don't let them get an STD and/or pregnant just because of a false sense of shame. And the One True Church^® ? Tell it to get stuffed! This blog-entry was worth you having to put up with my bad puns even if it just saves one person from getting an STD. AIDS-be-gone!

In France today, the gummint is starting a 'Make Love' project by subsidising condoms. A 5-pack for only 1€! At those prices you'll get customers coming again ;-)
By contrast, in the UK, in a survey of 800 parents (commissioned by Teachers TV) they found that 74% of parents did not know whether their child was sexually active! On top of that, 44% say they have never had an in-depth discussion about sex with their offspring and 27% of parents do not want homosexuality to be mentioned in school sex lessons. May I suggest that parental prudishness is a contributory factor? Just FYI, here are some relevant stats from Germany : 12% of girls and 10% of boys aged 14 have already had sex. For 15 year-olds it's 23% of the girls and 20% of the boys. For 16 year-olds it's 47% of the girls and 35% of the boys. For 17 year-olds it's 73% of the girls and 66% of the boys. So teach them about condoms early!

BTW, rumour has it that the arsey RC-church is bending over and opening itself to a re-think on the use of condoms. Cardinal Barragan (president of the papal health board) has produced a working paper for bishops' review. Presumably the bishopricks are the scene of much choirboy hands-on experimentation ;-) Don't hold your breath.

Video : Doug Alder has a funny and appropriate advertising video here (2 MB .wmv).

Link of the day : Here's the link to the World AIDS Day website. Go read and learn.

Copyright ^© Stu Savory on 1st December 2006 at 06:01 CET permalink Email

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