Stu Savory's Blog Anglo-German website. http://www.savory.de/blog.htm
Wednesday, April 27, 2005

How to square the circle

Please make the effort to get out your schoolday compasses and actually DO this exercise, then you'll believe me. Learn it by heart to impress your geeky friends (and/or your school's mathematics teacher), by squaring the circle !

  1. Draw a horizontal line in the middle of the paper and mark a point R at the right end.
  2. Open your compasses about an inch (roughly) and mark a point T on the line.
  3. With unchanged compasses, mark a point O on the line so that distance OT=2*TR.
  4. Draw a circle centered at O, and label point P at the left of the diameter line. This will be the circle POR whose area we are trying to equal with a square.
  5. Construct point H halfway along the line PO, (you should know how to do that).
  6. Raise a perpendicular at T, intersecting the circle at Q.
  7. Draw a chord RS of the same length as QT.
  8. Join PS and draw MO and NT both parallel to RS.
  9. Below the horizontal diameter, draw a chord PK of length PK=PM.
  10. Construct a vertical tangent PL of the same length as line segment MN.
  11. Join RL, RK and KL.
  12. Label point C on RK so that RC has length RH.
  13. Construct CD parallel to LK, meeting RL at D.
  14. Construct a square on base RD. It will have the same area as the circle! You can verify this by measuring the length RD as the radius RO times the square root of (~1,7724539). So the area of the square is *r2. Quod erat demonstrandum.

Does that knock your socks off, Euclid, or what? :-)

There is an amusing anecdote from my schooldays about this construction. We had a good maths teacher, Jeb, who often spoke ex cathedra though, that is, he didn't prove what he said. So Anthony and I set him up one day. At the start of a lesson, my good friend Anthony asked "Sir, can you show us how to go about squaring the circle?"

Jeb replied "Certainly not, boy! It is impossible to construct a square of the same area as a circle using only straightedge and compasses (Euclid's toolkit)! I told you that last lesson, pay attention!"

At this point I butted in "But you didn't prove it, sir! And you're wrong; I bet I could get the whole class to square the circle right now! Then we'll measure everyone's square and we'll see it's *r2"

Jeb of course knew that squaring the circle is impossible, but couldn't prove it there and then. To cut a long story short, Jeb fell for it and I had the whole (unwitting) class each do the construction given above after admonishing them to go for maximum precision. Given the chance of embarrassing one of us (Jeb or cocksure me) they all made a maximally precise effort as I took them step-by-step through the construct which I had learned by rote. Everybody then measured the length of the side of their square and we averaged the result, getting ~1,7725, about the square root of . Jeb was dumbstruck, but he shook my hand and gave us the rest of the hour off, which upped my class status no end. A week later the school was still buzzing :-)

But of course, squaring the circle using only straightedge and compasses (Euclid's toolkit) IS impossible (because is transendental {proved by Lindemann in 1882}), so what have I done? The construct actually draws a square of area (355/113)*r2 and the fraction 355/113 is an approximation to which is accurate to the seventh digit. So if the pencil lead of your compass is so fine that it can draw a line only 1/100th of an inch wide, then you would need to draw a circle over 4 miles in diameter before you could notice the error. So, pure geometry apart, for all intents and engineering purposes, the construct which I showed you above DOES INDEED square the circle :-)

Of course, the construct was not mine, I was just a precocious teenager (15 or 16) then. After the previous lesson, when Jeb alleged but did not prove the impossibility, I had spent several hours in the library until finding this construct which is due to Ramanujan (originally published in the Journal of the Indian Mathematical Society, V, 1913, p132). I learned it off by heart, just to set Jeb up. Not until several weeks later did I show Jeb Ramanujan's paper. So I hope it was for some of my other maths work that they gave me the maths prize that year ;-)

But of course, if you (only just) don't restrict yourself to using compasses and straightedge ONLY, there is a much easier way to square the circle.

Assume you give me a coin (yes please) and ask me to construct a square of the same area as the coin. Just draw draw a line on the paper, and mark a point A. Draw a diameter on the coin and roll the coin along your line until the other end of the coin's diameter meets the line at point B. The length AB = r by definition. Extend the line AB to point C where BC = r = the radius of the coin. Find the centre of the line AC and draw a circle centered there so that points A and C are on a diameter of it. Now drop a vertical from point B to intersect the circle at D. Now we know that BD*BD = AB*BC = r*r. So a square drawn with side BD has the same area as the circular coin. QED!
NB: I already showed you how to take square roots using only ruler and compasses.

Today's blog is for Viktor (Kiev) and Alaskan teacher Mike Mathew (all the best for Paxen!).


Monday, April 25, 2005

Sum-thing easy?

Edinburgh teenager David mailed last week and asked me for another maths puzzle for himself and his classmates.

So here it is David, a little brainteaser. Expected solution-time is four (4) minutes. Off you go, the stopwatch starts NOW!

Currently I seem to be running out of steam, bloggers' block or whatever, finding it increasingly difficult to find stuff to write about and to motivate myself to do it. So I'm just going to write the stuff I promised Viktor (squaring the circle) this week, then take a creative break for a while. In the meantime your suggestions and requests for subject themes would be appreciated, any thing but the Hommingberger Gepardenforelle!

Kevin Drum (Washington Monthly) and Betsy Devine point me to a website which enables one to "measure" the readability of one's blog just by plugging in its URL. First comes your Gunning-Fog index, which is a rough measure of how many years of schooling it would take someone to understand the content. The lower the number, the more understandable the content will be to your visitors. My Gunning-Fog index (for this month's blog) is 9.7 (years of schooling it would take someone to understand me). The second result is the Flesch Reading Ease number. It is an index number that rates the text on a 100-point scale. The higher the score, the easier it is to understand the document. Authors are encouraged to aim for a score of approximately 60 to 70. My Flesch Reading Ease result is 67.57, so that's on target too. The third result is the Flesch-Kincaid grade level. Like the Gunning-Fog index, it is a rough measure of how many years of schooling it would take someone to understand the content. For this blog the number is 6.65, so people with a mental age of >= 12 to 16 should be able to read and comprehend this blog.

PS : I don't have many US Republican readers ;-)


Friday, April 22, 2005

Get well, Michelle!

Habemus Papam. And now that the Poop-a-thon is over, it having blocked the internet news pages and occupied sundry TV-channels, we can get back to the important things in life. Such as your feedback and comments during the past week. NB, Photo (left) : new world view by the Vatican's Papa Ratzi ;-)

For us, the saddest news of the week was that Michelle aka Mandarin Meg has quit her job due to her permanent pain (see her blog comments for details) and will be having to undergo surgery to alleviate it somewhat. Michelle, we both wish you all the best and a speedy return to a pain-free world!

Joel missed the (UK) political satire in my Cherry Blossom post, so let me point out that my Deep Purple Haze post was a political metaphor too (The mixture of red and blue [=purple] that you see on the net may not reflect political Reality either). That I mentioned Rock therein had nothing to do with the first Pope (that's an Ancient Greek pun, stolen from the Bible, made by an early scribe, Petros(gr.)=Rock and 1st Pope = Petrus; not His words, He said His prayer in Aramaic). Maybe I shouldn't write so cryptically and get back to simple Bushwhacking ;-)

Apropos Bushwhacking, Ray Wilson (Australia) picked up my thread about US Bioterrism, and mailed :- "Hi Stu, I logged into your site this evening to catch up on what you have been doing and coincidentally was reading your April 14 blog on the danger of bio-terrorists, when ABC TV started running a story on the USA flying "surveillance" sorties over Columbia. The story from Foreign Correspondent is précised at: http://www.abc.net.au/foreign/content/2005/s1344908.htm.

Good old Dubya has apparently been sending single engined planes to check out Coca crops in Columbia. Of course when these surveillance planes are in the area farmers on the ground suffer from breathing difficulties, burning throats and eyes and their children and wives burst out in boils and other skin afflictions. Yep, you've guessed it - to protect the youth of US from shoving Cocaine up their noses, their beloved government sprays a cocktail of potent herbicides over a foreign country to kill the Coca crop and bugger any person or unfortunate animal caught in the resultant spray. I had heard of the CIA being involved in spraying Agent Orange in Mexico on marijuana in the 1970s (probably left over from the Vietnam war) so there's nothing new in the bio-terrorist field. Whoops, that's right the US government are the good guys, right?

Interestingly the contractor who flies these sorties is Northrop Grumman a company that earns $56B from defence contracts and manufacturer of the Stealth Bomber. Of course they deny all knowledge but have offered a widow of one of their employees $350,000 as long as she stops asking questions about her husband's employment. He was one of the pilots of these small planes that crashed in Columbia. Have this country's leaders lost all semblance of morality?"

In a word, Ray, YES!

Visual design specialist Robin Kirkey appealed to my Inner Mathematician by pointing me to some interesting fractal Flash animations, but she also pointed me to some politically good Bushwhacking Flash movies. The URL for a freeware mouse zoomer to aid colour sampling also came from her; thanks, Robin!

For those of you visitors who came looking for some rather specific biographical mathematical stuff, here is the biography of Valentina Mikhailovna Borok (1931-2004), who used to teach a great course in rigorous analysis. Here is the biography of Paul Appell (1855-1930). You can follow this link to get to Don Knuth's home page. Don has a pipe organ in his own home and is a good organ player, so when he was visiting here we took him to see the Paderborn cathedral organ, the second largest in Germany (we're talking a 49 foot sub-bourdon here!)

Dianne, who speaks with a Texan drawl, likes my "British accent" on the phone. Ma'am, we are speaking English, so by definition, YOU have the accent! BTW, the History of the Union flag is given via that UK royal URL, or did you mean the US Union flag?

For the biker fans, I recommend The Zen of Motorcycling, in and around New Hampshire (USA).

Jakarta girl Beyondsky/ShugoreI sent a link to her photo contribution to my Skyline Meme, it is Sydney CBD skyline, as seen from The Rocks.

This week I seem to be running on empty, bloggers' block or whatever, finding it increasingly difficult to find stuff to write about and to motivate myself to do it. So I'm just going to write the stuff I promised David (a puzzle) and Viktor (squaring the circle) next week, then take a creative break for a while. In the meantime your suggestions for subject themes would be appreciated.

Addendum (Saturday) : Sadly the Champion bulldog bitch from whom we were expecting to get a pup was empty, and has no pups. So we're back to square one and pretty depressed here :-(


Wednesday, April 20, 2005

Deep Purple Haze

For the fans of 1960's rock music, that's a confusing blog header today, moving across the spectrum of musical taste from Deep Purple to Jimi Hendrix's unforgotten Purple Haze.

But today I want to talk about the optical spectrum. Last week Robin and Michelle helped me out by colour-sampling some oak leaves, which I didn't know how to do myself. The variability of the results got me thinking about colour-sampling, and what it is we actually are seeing (here).

Forty-odd years ago, at university, my fellow student Laszlo and I tried measuring the breadth and flatness of our colour perception. We set up a rotatable prism and a positionable slit whose width we could vary to vary the brightness of spectral lines. Then we projected randomly chosen colours in random positions and of varying brightness. We recorded where(if?) we could see a coloured line and its theshold intensity. After we checked the whole class for colour-blindness, we chose Laszlo and myself to do the experiment, because it turned out that Laszlo could see a few Angstoms more red than I, and I could see a few Angstroms more violet than he could. What was still violet for me was ultra-violet for him and what was still red for him was infrared for me. Not by much, but just measurable, on the lower corners of the chromatic curve.

In natura the flowers like the one shown at the top of this article are a vibrant deep purple to me. Then I add "but the photo does not do them justice". So what is happening? Let's say I photograph them with an analogue camera. Then their image is recorded on a film whose spectral response is different across the visible bandwidth from my eyes. Different film manufacturers and different film development procedures render spectrally differing results. I find that Agfa photos are bluer than Kodak which seem yellower to me. Personally I find Fuji gives the most natural results. And slides are much better than paper positives too.

So then this negative film is used to produce a positive image on (a choice of) papers using different chemical procedures again. I might then scan this positive photo. My scanner may have a different spectral response from yours, I don't know. Then I put this scanned image on this web site and you look at it on your monitor which may have a different colour temperature than mine. WYSIWIG? What YOU see is what I gardened? No way, there have been these four spectral filters in between, negative-positive-scan-monitor. Even if I had used a digicam, we still have its spectral response and your monitor to consider, so that's two filters there.

So when Meg and Robin did a sampling for me, what was happening? Their digicams probably had differing spectral responses, so they each captured a different representation of their individual oak-leaves (which differed too). Then they looked at these representations on their own monitors, pointed to a point on their monitors and "sampled" that, mailing me the hex values. I then plugged those hex-values into my webpage and chose the one nearest to my oak-leaf, as I see it. So when you do colour sampling ask your Zen self : "What is reality?" :-)


Monday, April 18, 2005

In Memoriam : Albert Einstein

E=mc2 was not the only thing he wrote, here are some other Einstein things for your delectation.

This year is Einstein year, as we celebrate the centenary of his theory of special relativity. General relativity came 11 years later, and, FYI, the covariant equations thereof were actually first published by David Hilbert. But fifty years ago today, April 18th 1955, was the day on which Albert Einstein died peacefully, aged 76.
So let's remember him with some of his great non-scientific lines :-

  • Do not pride yourself on the few great men who, over the centuries, have been born on your earth through no merit of yours. Reflect, rather, on how you treated them at the time, and how you have followed their teachings.
  • It is a mistake often made in this country (USA) to measure things by the amount of money they cost.
  • We are faced with the dismaying fact that the politicians, the practical men of affairs, have become the exponents of international ideas.
  • Force always attracts men of low morality, and I believe it to be an invariable rule that tyrants of genius are succeeded by scoundrels.
  • Democratic institutions and standards are the result of historic developments to an extent not always appreciated in the lands which enjoy them.
  • It may affront the military-minded person to suggest a regime that does not maintain any military secrets.
  • Few people are capable of expressing with equanimity opinions which differ from the prejudices of their social environment. Most people are even incapable of forming such opinions.
  • All of us who are concerned for peace and the triumph of reason and justice must be keenly aware how small an influence reason and honest good will exert upon events in the political field.
  • One misses the elementary reaction against injustice and for justice - that reaction which in the long run represents Man's only protection against a relapse into barbarism.
  • In order to be an immaculate member of a flock of sheep, one must above all be a sheep oneself.
  • One is born into a herd of buffaloes and one must be glad if one is not trampled underfoot before one's time.
  • One has been endowed with just enough intelligence to be able to see clearly how utterly inadequate that intelligence is when confronted with what exists. If such humility could be conveyed to everybody, the world of human activities would be more appealing.
  • One can organize to apply a discovery already made, but not to make one.
  • Do not worry about your difficulties in mathematics; I can assure you that mine are still greater.
I'm sure that if I'd written some of these great lines - and how I wish I had - some of my American blogreaders would dismiss them as mere Bushwhacking :-(

Although Einstein is mostly remembered as a theoretical physicist, he also had a practical streak as a minor inventor. In fact, together with his junior (by 19 years) partner, the hungarian physicist Leo Szilard, he had 27 patents, eight of which were for various kinds of refrigerators, like the Swiss patent shown here right.

Einstein worked on 50 patents, either as the inventor himself or as a background research partner. He was also a patent clerk of course; amusingly enough, one of the patents he was to approve during his time as a patent clerk in Bern (the Swiss capital) was for a device to synchronise clocks at e.g. railway stations "to ensure they show exactly the same time". Sounds ironic, especially as this (1905) was the same time (sic!) as he came up with Special Relativity.

In 1914 he was to adjudicate on the Anschütz-Kaempfe patent case, where an American company illegally misused the Anschütz patent on gyro-compasses. After WW 1 Einstein improved the Anschütz-Kaempfe gyro compass with his own patented method of suspending the gyros to make the gyro keep an "absolute" heading. This was ironic too, because General Relativity imples a relativistic precession of the gyros anway ;-)

Einstein also cooperated with Goldschmidt on a hearing aid for a deaf lady singer, and even suggested the cooperation (which led to their patent 590783 in 1934) via a poem of his own :

"Ein bisschen Technik dann und wann,
auch Grübler amüsieren kann,
Drum kühnlich denk ich schon so weit:
Wir legten noch ein Ei zu zweit".

Finally, in 1935 Einstein (who was at Princeton then) and Bucky took out an US patent for the camera with a photocell to set the exposure; remember this when you use your digicam. The photocell is based on the quantum effect for which Einstein got his Nobel prize. Full circle!


Friday, April 15, 2005

Helpful Blog Friends' Feedback

Help is never far away, especially with good friends in the blogosphere. When I was writing Tuesday's article about Why Aspirin® should be Oak-green it suddenly occurred to me that I could display it in an oak-green colour, but I had no colour-sample. But I do have two good friends in the blogosphere who are graphics experts so I popped off (pun, geddit?) an urgent email to Robin and to Michelle, asking for the hex-code for oak-green. Within an hour both had found an oak leaf in their garden, scanned it, sampled the colours therefrom, and mailed me a choice of answers! Wow!!

Robin Kirkey picked up the ball and ran with it, and has written a whole tutorial on the subject! That's one fast-responding girl! She wrote to me as follows :- "I posted a new tutorial on my website this morning about creating a graphic web interface using Paint Shop Pro, CSS and XHTML. In it, I cover one method I use to sample color from images. While the tutorial is specific to Paint Shop Pro, Photoshop has a filter similar to the one I used in Paint Shop Pro. Access it through Photoshop's Filter | Pixelate | Mosaic menu. Colors are then sampled from the resulting squares with the eyedropper tool and can be saved to your color swatches. A quick double-click on the color will bring up Photoshop's Color Picker where you will find the HEX code for the color."

Maybe I (at 60) have time to study this IT stuff, too? And maybe avoid the bogus blog scams?

Referring to my same posting ("Which discoveries are attributed to the wrong person?"), Malcolm, a UK policemen, tells me that some sources attribute the discovery of unique fingerprints to Francis Galton, an eccentric cousin of Charles Darwin, but this is wrong, he writes. In fact they were introduced in British India in the 19th century for the signing of deeds. Scotland Yard picked up the idea and by 1905 had nearly 100,000 fingerprints on file, Malcolm writes.

On the cryptography front, John Alexander relates his news that he has recently tied up with Royal Holloway University who will take Bletchley Park's machines, including his, and write them up in some agreed format. They already had his Hagelin C36 and now have his M209 and NEMA; so I'm looking forward to seeing John's machines appear on their websites soon (John doesn't have his own website [yet]). BTW, I sold my NEMA last year for a fair price to "Anon". Funnily enough, the Patriot Act allows US citizens to import cryptographic equipment, but it probably forbids them to export any, I bet. Peculiar, because I for one wouldn't trust any ciphering gear (pun!) I'd bought from a foreigner. It's a paranoic business, cryptography is ;-)

Anna Pashen emailed "I only just read that your dear dog has passed on. I am very sorry. I know how heart breaking this can be. Over Christmas my mother and I had to take in my childhood dog, Jess (aged 16), to be put to sleep and it was heart-wrenching." Plans are afoot, Anna!

I had reported to Eric Kastner that his Spell words with flickr doesn't seem to work correctly here (I'm using a German version of Opera) and he's promised to look into it; Javascript bug?

US polyglot Dave commiserates with me on the lack of language training in the (US) military and wrote "Until language acquisition and maintenance is part of every officer's performance evaluation, DoD efforts are doomed to fail. It is really that simple!" Teasing Dave, I wrote back with a quote from Ambrose Bierce, (1842-1914): "War is God's Way of Teaching Americans Geography" and I added "And languages, maybe?" ;-) Having written that, it must be said that Dave is far more language-gifted than I am; I can speak 4 and read another 3, but Dave outstrips me quite a ways. I find learning a new language so difficult that I have to admire all you folks who pick them up quickly and speak/understand them by the handful! Volpuk or Esperanto anyone?

Old friend Carl Rose sent me a 44 year old photo of us playing in our old school cricket team. Carl is 4th from the left (next to the headmaster) in the back row, I was 12th man and scorekeeper and am seen standing next to the groundsman. Hey look! We had HAIR then!

Currently I'm researching an article for a russian SF magazine about contact with alien cultures and looking for historical evidence from the European invasions of America, Australia etc and the culture clashes associated therewith. As it happens, our old history teacher Geoff Partington wrote an article once about the problems aborigines had learning maths. What a small world! Geoff is 75 now (and online!) and had a good academic career with lots of publications in the field of education. Geoff has also written about the history of cricket, so I took pleasure in being able to forward Carl's cricket photo to him :-) N.B: The great english mathematician G.H.Hardy, about whose famous taxi ride anecdote I wrote just last sunday , was a great cricket fan too.

Carl points out that I had 500 visits NOT 500 visitors per day, as I wrote. He writes "In Opera I can keep several pages open at once, and can open them from a previous session. As your page opens here automatically, then your visit counter will clock up each time I open Opera. If all your readers have this system, how many people are actually reading your missives, or do your 5 readers log into Opera 100 times per day ;-) ?" Hmmm, visits vs. visitors is obviously true, I stand corrected. But when Opera starts a tab from a previous session I've always thought it just gave the locally cached page copy, unless that page contained a "Cache-Control" with the content = "no-cache, must-revalidate". The cached copy should not influence the hit-counter IMHO.

Viktor (Kiev) wants me to blog some maths again and, this being Einstein year, asks for the derivation of E=mc2. That'd be a couple of pages of college algebra though and would bore most of my readers, so go use the Wikipaedia, Viktor. I'll show you how to square the circle soon though, that'll get Euclid turning in his grave, and Gumz (Sri Lanka) having a hissy fit ;-)

Wilfried showed me how to put our local current weather report into my right sidebar's base.

Frank Paynter sent a few visitors here, Meg too. Thanks, both.

Gary Williams blogged a photo of me opening the outdoor chess season here. Thanks, Gary!


Thursday, April 14, 2005

An American kind of War

Just a thought : a lot of the American soldiers who died in Iraq and more who have been injured for life, losing limbs etc. are black brothers and sisters.

So how come, when Rumsfeld was in Iraq yesterday, pinning gongs on the cannon-fodder, was he pinning medals on white guys only ? (see photo, left).

Just a question, but likely to piss Jeneane Sessum and others off. What'll Melanie Mattson say to that?

Another kvetch. That Miserable Failure, Bush, has been going on about the dangers of terrorists having bio-weapons. But who has been sending potential bio-weapons to more than 3700 sites in 18 countries? The USA of course! The bio-weapons (viral samples) are Asian flu, which killed between one and four million people (in 1957). Because the virus has not been in circulation since 1968, people born after that do not have antibodies against it - and current vaccines do not guard against it. The College of American Pathologists sent out the bio-weapons (viral samples) between October 2004 and February of this year. ALL of the 3700 need to be recalled. Can Bush and Rumsfeld count up to 3700 without making a mistake? I doubt it, they can't even count votes properly :-(


Wednesday, April 13, 2005

Return of the shoe polishers . . .

Spring is here and down in the valley near the Brit army barracks here the cherry trees are in full bloom. There is such a bumper crop of Cherry Blossom in the UK too that we can expect the return of the boot-lickers and -waxers (as we call them here) in Britain on May 5th :-(

PS : That was a bilingual (UK/D) joke; sorry all you monolinguals, but tough shit if you miss it!


Tuesday, April 12, 2005

Why Aspirin® should be Oak-green

Continuing the science thread I was writing last week, young David (Scotland) asks "Which discoveries are attributed to the wrong person?" Here are three examples, David, and "what I tell you 3 times, is true!" :-)

The Playfair cipher, which I blogged about on February 9th, is wrongly attributed. It was actually invented by the British inventor Charles Wheatstone, he of the Wheatstone Bridge for measuring electrical resistances. Lyon Playfair, the first Baron Playfair of St.Andrews, was a good friend of his; they even looked very much alike (short and bespectacled). Playfair had much better political contacts though, and was able to demonstrate this system to Lord Palmerston (who was Home Secretary at the time) and to Prince Albert (Queen Victoria's husband). Although the Admiralty rejected it, the British Army used this cipher in the Boer war and in WW1, referring to it as the Playfair cipher. Given only pencil and paper and no computers, it is in its striated form a pretty good cipher, as long as the messages are kept fairly short. Lt. J. F. Kennedy (USN) used it too. Although Wheatstone invented it, Playfair was the Marketing guy who took the credit :-(

Also a case for disagreement, the differential calculus was invented/discovered by Newton and Leibnitz more or less in parallel. Each accused the other of stealing his ideas.

More recently (WW2) we have the case of Aspirin®. The name derives from the willow tree, whose bark is analgesic. This was reported as early as the 13th century, when bears were seen to strip the willow bark and chew it when they had toothache (broken teeth and/or infected gums). Salycylic acid (the active component) was not identified until the late 19th century, when chemistry had progressed sufficiently. It is too bitter to use, however. The giant German chemical company Bayer put people to work on derivatives. By 1898 Aspirin®, acetylsalycilic acid or HOOC-C6H4-COOCH3, came on the market, its discovery being attributed in the mid '30s to two assistant chemists at Bayer, namely Heinrich Dreser and Felix Hoffman.

This is not in fact true! Aspirin® was invented by Arthur Eichengrün at Bayer. Hoffmann was just his assistant and Dreser was not involved in any way! The Dreser/Hoffman story was put about by the Nazis, because Eichengrün was a Jew and the other two were Aryan! Eichengrün meanwhile languished in the KZ (concentration camp) at Theresienstadt, but survived the war.

Eichengrün fought to re-establish his name, but it was not until 2000/2001 that Walter Sneader of the University of Strathclyde managed to track down the over 100-year-old lab-books at Bayer which confirmed that Eichengrün was the man who discovered Aspirin®. Now history has been re-written and the Nazi propaganda expunged at long last :-)

Oh, BTW : the German name Eichengrün translates as Oak-green, hence today's header :-)


Sunday, April 10, 2005

133.335

This is my own ghost story today, it scared me almost witless at the time. But first you need to know an anecdote about two famous 20th century mathematicians.

Back in the early 20th century there was a famous pure mathematician in England, G.H.Hardy who discovered a natural mathematical talent from India, Ramanujan. Hardy brought Ramanujan to England (Trinity College actually) and they cooperated for a while, but just two years after the war, Ramanujan fell sick and died of tuberculosis aged only 33. Let me relay the famous incident of the taxi licence number in Hardy's own words:-

"I (Hardy) remember going to see him (Ramanujan) once when he was lying ill in Putney. I had ridden in a taxi-cab number 1729, and remarked to him that the number seemed to me a rather dull one, and I hoped it was not an unfavourable omen. 'No' he reflected, 'it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways". [Hardy, 1940]

FYI, 1729 = 123 + 13 and = 103 + 93. Hardy then asked Ramanujan if he knew the answer to the same problem for 4th powers? Ramanujan replied 'No, but it must be very large'. FYI, it is 635,318,657 = 594 + 1584 and 1334 + 1344. BTW, 1729 is also interesting because it is a Harshad (divisible by the sum of its own digits, 1729 = 19*91). It is also the largest number which factorises into the sum of its digits times its reversal. 1729 is also the smallest number that is a pseudoprime simultaneously to bases 2,3 and 5. So Ramanujan had only seen one aspect of what makes 1729 interesting, but a great mental performance nevertheless.

That was the background, now back to MY ghost story. A few years ago I took a taxi from the railway station to the University at Kaiserslautern where I was due to give some lectures on AI (Artificial Intelligence). I got in the front, next to the driver. You can do that in Germany, they're not Hansom cabs, just regular cars painted beige, usually a Mercedes. The waiting driver had been playing chess against a handheld chess-computer (called 'Mephisto', incidentally), so we talked about chess during the drive. Then I saw the cab's licence number and said, almost jokingly "5282, that's a pretty boring number".

Time slowed to a crawl as I remembered these were almost the very words in the anecdote as told by Hardy, as quoted above. "Not at all" replied MY taxi-driver, "it's the number of ways of placing 8 mutually non-attacking rooks onto a chess board". Thus spake the Mephisto-man.

As I heard this Ramanujan-like reply, the hairs on the nape of my neck stood up and a cold, cold shiver ran down my spine. The whole world stopped moving and I knew in that very moment, I just KNEW that I daren't turn around, or I would have seen two ghosts sitting in the back seat of the cab, Ramanujan and Hardy, grinning evilly. I'm telling you, that line scared me witless!

And what does all this have to do with today's subject line (133.335)? 133.335 is an interesting number because it is the Dewey Decimal Classification for 'numerology'. But it is also scary in a devilish way, because if you reverse it (like one of those Heavy Metal records of yore) and add, you get 133.335 + 533.331 = 666.666 the Number of the Beast, repeated. Mephisto again ???


Friday, April 8, 2005

The big D ; 500 daily visitors reached now

500+ of you visited here on Wed & Thur, which I regard as positive feedback. So let me say thankyou to all my new readers and of course to the true, blue readers from the US (I don't have many red-state ones). Now for your comments this week :-

Jimmy McCarthy (Wick, Scotland) wrote "I enjoyed your coverage of Hans Christian Andersen's 200th anniversary. Like you I remember the fairy tales. Among my favourites was The Emperor's New Clothes One might say that it is apt as a parable about the media driven obsession with celebrities!". Jimmy also read Wednesday's blog about Jenner's cow-pox vaccination discovery and sent a link pointing to his great photo of a Hielan' Coo.

Jeneane Sessum had a close shave, but scraped through OK ;-) Glad to hear it went well!
Anna Pashen pointed me to Jaakle, who points to another Pentagon incompetence story. Michelle confirmed getting our revenge present for the one she and Rob sent us from Hawaii. Jane reminds me that the MotoGP season starts on Sunday & sent me a photo of Rossi's 46:-) Biker friend Matthias Sander (Germany) spent a tiring, but adventurous and worthwhile weekend learning to race a Supermoto bike, and recommends the Supermoto training school. Alex spent the weekend racing a friend's little 600cc Honda Supersport in Mugello (Italy).

Graham Lawrence (Geneva, Switzerland) tells me he has a Swedish colleague who has met Frode Weierud, the crypto-collector at CERN; it's a small world! John Alexander (Leicester, UK), also a crypto-collector (usually M209s) was here a couple of weeks ago to collect a 'wet and rusty' 1944 Schlusselgerät 41 for delivery to a friend in Scotland. Myself, I've just got hold of a Confederate cipher disc from the States, trivially simple of course, but historical :-)

Several blogs I'd like to have read have been often down this week, I'm told that is because Blogger sucks big time :-( Public utility reliability? No way. And that's why all the HTML and CSS on THIS blog is handwritten, folks! My provider's host only went down for a few hours last year.

Referring to yesterday's subject, Ivan thinks that ALL the major discoveries (wheel, fire, etc) were made by accident (or better, by chance observation). There may be some truth in that!


Thursday, April 7, 2005

Discovered by accident

Yesterday I left you with the thought "Science does not always progress as cleanly as we would like to think", so today I'd like follow up on that with some anecdotes about "Discovery by accident" as opposed to experimenting to confirm a theory.

Let's kick off with that classical (sic!) example, Archimedes (287-212 BC). Archimedes was a Greek polymath, of whom many tales are told, some true, some probably not. It is true that he invented the compound pulley, using it in the several war-engines he had built (ballista?). The water-snail, a screw in a pipe used to raise water for irrigation, is also attributed to him. He was also good at maths and came up with formulae for calculating volumes; indeed Plutarch tells us that his grave was marked by a sphere in a tight-fitting hollow cylinder, engraved with the formula for calculating the unoccupied volume remaining between the two.

Vitruvius (a Roman historian) tells us the following anecdote: King Hieron asked Archimedes to determine whether his crown was made of pure gold, or had been diluted with silver. Archimedes came up with the idea of calculating the crown's density by dividing its weight by its volume, the volume of its irregular shape being equal to the amount of water it displaced. Vitruvius says that Archimedes came up with this idea when getting into a full bathtub and seeing the water overflow, being displaced by his own body's volume and then running naked through the street shouting "Eureka!" (I have it!).

Personally, I think this tale of intuition unlikely, Archimedes was quite capable of performing a thought-experiment to come to the same conclusion. Stick a (cylindrical) wooden branch into a piece of clay. Let the clay dry in the sun, then cast some metal into the hole in the clay. Afterwards fill the hole with water. It is obvious that the volume of the metal equals the volume of the wooden branch equals the volume of the water. Volume not weight, Archimedes could have deduced, even without taking a bath and running naked through the street.

So let's look at another accidental discovery, in recent recorded history, this one by Otto Stern (1888-1969). [BTW: Stern and Einstein used to go to brothels together, asking the girls to leave, so that they could discuss physics together with no fear of being disturbed by the rest of the faculty!] Now, quantum theory predicts that atoms such as silver should possess a magnetic moment. So Stern and Gerlach did an experiment to measure the deflection of a beam of silver atoms by a magnet, with the electromagnet turned on versus with it turned off. The difference was expected to be miniscule. They observed a hairline of silver which gradually turned black and resolved into two barely separated hairlines, but only when Stern peered at the hairline. It turns out that Stern's breath contained sulphur from those terrible cheap German cigars Stern smoked. The sulphur blackened the silver, turning it into silver sulphide and revealing the two separate hairlines more clearly. This accident made clear a result otherwise diffuse.

Another accidental discovery was made by (Sir) William Herschel (1738-1822). Herschel wanted to see how much heat there was in the various colours of sunlight. So he set up a large prism to split sunlight into a spectrum and hung his thermometer into the violet, the indigo, then the blue, the green, the yellow, the orange and finally the red, recording the temperature rise against his room thermometer which was out of the light. Having measured all the colours he went for lunch. When he came back, the sun had moved the spectrum around so that the thermometer was beyond the end of the visible spectrum. Nevertheless, the thermometer was showing the highest temperature of all. Thus did Herschel accidentally discover the infrared!

Finally, a Jesuit anecdote, in particular about Father Rheinberger in 1954. Some Jesuits have had an interest in science too. Around 1900 Father Odenbach (Cleveland, Ohio,US) built a seismograph and started keeping seismographic records. Then in 1909 he had the idea of equipping many Jesuit colleges around the world at a small capital outlay with seismographs in order to follow the movements of the Earth's crust globally. Sydney, Australia was part of this network. In 1954 Father Rheinberger there found a seismographic signal which appeared to coincide with the H-bomb test on Bikini Atoll. Confirmatory checks with all the other Jesuit seismographs correlated in four cases, all of which had been secret nuclear tests, and the Jesuits could even plot the sites of the test. This was the accidental beginning of worldwide nuclear test monitoring! "Jesus sees everything, we are merely his agents", the monks said :-)

Science does not always proceed by theory, experimental confirmation OR alternative theory, experiment, etc. etc. Quite often discoveries are accidental, giving rise to new theories.


Wednesday, April 6, 2005

Another jab at Etymology

Stop reading now if you are squeamish, and go elsewhere.

Continuing monday's etymological thread, I'll explain today how we got the word "vaccinate".

Edward Jenner (1749 - 1823) was a country doctor in Berkeley (Gloucestershire (UK), not the San Francisco area one) who noticed that milkmaids had a resistance to smallpox, then a prevalent and often fatal illness. Jenner was short on the ethical front though, so when in 1796 a local herd of cows suffered an outbreak of cowpox, he did an ethically dubious experiment. Cow pox transfers to humans too, but is only a mild affliction in humans. Jenner found a milkmaid (one Sarah Nelmes) with the cowpox boils and jabbed his lancet into her suppurating pustules (well, I did warn you, in the very first line, today!), extracting the pus. Yeuch!!

With the same infected lancet he injected the pus into an (unwilling) idiot farmlad, one James Phipps. A month later he extracted pus from a smallpox corpse (smallpox being fatal) and injected it into the poor farmlad Phipps. Phipps survived, confirming Jenner's vague theory. This practice ("Jenner's jabs") was then generally adopted, it working far more times than not.

A half-century later, Louis Pasteur (1822 - 1895) honoured Jenner's discovery by naming this process vaccination , from vacca(I) or vache(F), meaning cow, instead of the Brits' Berkeley dialect idiom "Jenner's jabs". Science does not always progress as cleanly as we would like to think ;-)


Tuesday, April 5, 2005

A short political note

That's an interesting juxtaposition of headlines on the BBC News this mourning (sic!).

In the UK, Tony B. Liar is about to declare a new election for May 5th, it is reported. That doesn't give the Brits much time to fix the gaping holes in the UK election laws in order to assure a fair election. I'll submit an application as an international observer again, like for the US election.


Monday, April 4, 2005

An Etymological Thread

Just the other day, over at English Cut, Tom Mahon explained the Savile Row origins of the English idiom No strings attached, which was new to me. It got me wondering about how other (peculiar) words came about, a not unrelated thread (groan!) :-

People with no knowledge of the classical languages - Latin and Greek - often made up new words with one syllable coming from the Greek and the other coming from the Latin. This grates on my nerves even now, although the words have long since been accepted into the English language. Example : Auto-mobile should have been either Auto-kineticon or it should have been Ipso-mobile, but not the bastard mixture of both languages which we've got now.

Examples in German : During the Third Reich they tried to replace all classic words with a wholly teutonic vocabulary. Thus we still have Fernsprecher (far speaker), now in parallel to Telefon, and Verschluckung (swallowing) instead of the perfectly valid Absorption, and Umweltlehre (whole-world-theory) instead of Ecology. Of course in German we just string other words together to make new ones too. Example : Donaudampfschiffgesellschaftkapitänswitwespensionsfund (Danube steam ship company's captains' widows' pension fund). If the English were to do this too, I would estimate it to be completely worthless (floccipaucinihilipilification) ;-)

FYI, floccipaucinihilipilification is the longest word in the English language which does not contain the letter 'E'. Incidentally, there is novel "A Story of Over 50000 Words Without Using Letter E", by E.V. Wright, published in 1939 by Wetzel Publishing Co of Los Angeles. Wright wrote this (lousy) novel of 267 pages(!) without using letter E at all, which is otherwise the most frequent one.

Inventor's personal names are often adapted for the product they invented. To vacuum cleaner the floor is known in England as Hoovering it. Making a photocopy is known in German as 'eine Xerox machen'. Coats made waterproof by rubber coatings, were invented by one Charles Macintosh. Charles Goodyear's process for curing rubber is however known as vulcanisation, after the classic god 'Vulcan'. The very word 'rubber' was given by the British chemist Joseph Priestley, who noted that "a piece of caoutchouc will rub (erase) pencil markings from paper". Such a 'rubber' is also known in the USA as an eraser. Now I just need to establish the etymology of the american noun "a rubber", as used in the poem "Where the hormones, there moan I" ;-)


Saturday, April 2, 2005

A Fairy-Tale Bicentennial

Today is the 200th birthday of Hans Christian Andersen and it seems the whole of Denmark is celebrating. Andersen was born on the 2nd of April 1805 in the coastal town of Odense (which is on the danish island of Fünen) and he died aged 70 in Copenhagen.

I remember reading some of his fairy-stories as a child:-

  • The Emperor's new clothes,
  • The little mermaid, (have you seen the statue in Copenhagen harbour?)
  • The Princess on the Pea,
  • The Ugly Duckling,
  • Little Match Girl.

I'm sure many of you blogreaders will remember these with affection too. Altogether he wrote about 160 fairy tales. He also wrote drama, poetry, novellas, travel accounts and autobiographies (sic!). Although he always wrote in Danish, many of his works were translated into German (e.g. by Adelbert von Chamisso) and indeed published in German first. Somewhere (I need to sort our 7000+ books here thoroughly some day :-) I have a reprint copy of "Das Märchen meines Lebens ohne Dichtung", his autobiography from 1846, probably in the attic :-(

This bicentennial occasion is being celebrated in Denmark with ties bearing his signature, coins showing his face, newspapers printing day-by-day extracts from his diary etc. Yes, indeedy, Marketing is by Disney! There have even been "Hans Christian Andersen"-ambassadors appointed; these include Harry Belafonte´, Nina Hagen(sic!) and even Pele´. In Copenhagen there is a 62-stop "Hans Christian Andersen" city tour, which includes a visit to his nondescript grave in the 'Assistens Kirkegarden'. While you are there, take a look at Sřren Kierkegaard's grave which is nearby, then you've covered both ends of the Danish cultural spectrum ;-)

As a fairytale conclusion today, let me show you a photo of the wholly natural 'Faerie Ring' on our back lawn, an ellipse of pretty little violets. Sadly the photo doesn't do the 'Faerie Ring' justice, for it is a vibrant purple (well, violet, of course) contrasting brilliantly with the green.


Friday, April 1, 2005

Friday Feedback - your comments this week

Crispin Burdett (London,UK) took up the theme of absentmindedness which I blogged about last saturday and sent me the following anecdote about the mathematician David Hilbert :-

"Hilbert [...] was perhaps the most absent-minded man who ever lived. He was a great friend of the physicist James Franck. One day when Hilbert was walking in the street he met James Franck and he said, "James, is your wife as mean as mine?" Well, Franck was taken aback by this statement and didn't know quite what to say, and he said, "Well, what has your wife done?" And Hilbert said, "It was only this morning that I discovered quite by accident that my wife does not give me an egg for breakfast. Heaven knows how long this has been going on." -- from The Physicist's Conception of Nature, reprinted in T. Ferris (ed.), The World Treasury of Physics, Astronomy and Mathematics, Little, Brown & Co., 1991, p. 604."

Crispin, as it happens, I remember staying in a hotel in Göttingen, whose rooms were numbered Zimmer 1, Zimmer 2, etc. The big suite however was named "Hilbert Raum", an insider joke that only mathematicians as guests might understand ;-) Indeed, I always wondered thereafter if they could accommodate an infinite number of guests ;-)

Robin Kirkey (Baltimore, US) sent me her Pyansky (Ukrainian Easter Egg) picture, which she did using her stained glass method outlined on her website. She also links to this 6 MB flash film, knowing what a big Dubya fan I am ;-) N.B: This film is highly likely to piss Meg off ;-)
In answer to the question about our prettiest egg, it is this huge ostrich egg, professionally painted in South Africa (Hi Mike!), where I bought it. Here are its 4 faces: Pic1, Pic2, Pic3, Pic4.

Malcolm (a UK policeman) sent me a whole raft of police jokes, here are the best three :-

  • A cement mixer collided with a prison van on the Kingston Pass. Motorists are asked to be on the lookout for 16 hardened criminals.
  • I saw six men kicking and punching our superintendant. Another constable said 'Aren't you going to help?' I replied 'No, Six should be enough."
  • An armed criminal hijacked a bus full of Japanese tourists. Police are looking for him on the basis of fifty-three photos ;-)

Marshall Kirkpatrick (Eugene, Oregon, U$A) is starting up his own company and asked to use my Mt. Dachstein photo from the meme on his website. It's a blog for his just-begun consultancy, teaching social change organizations, small businesses and others how to use blogs, wikis, RSS, social bookmarking and podcasts. Permission granted, I'm all for startups :-)

Jane liked the aerobatic photo I blogged last sunday and asks to see what it's like in the cockpit during aerobatics. I don't have a good photo of that, Jane, but there's a good one over at Delta Aviation (UK). And for my good friend Ina, here's the ICAP II EA-6B Prowler cockpit.

Nicole (Switzerland) asks, since I'm such a polymath (it IS april 1st), maybe I can interpret these two juxtaposed traffic signs for her ;-) Since this is April 1st, and probably unaware of the connotations of the colour BRAUN hier in Germany, Anon (a US Army SSgt stationed here) is saluting the red,white and BROWN. BTW, Dubya's other 2 letters are U and H, as in Up His ;-) Thanks to the Dept. of Biometric Security, the Presnit's passport now contains his digital ID :-)

Phil points us to the statisticians' report that Dubya manipulated the vote (not just on April 1).

Finally, there's a tight little scottish joke (to coin a phrase) on Doug Alder's site :-)



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Dr. Stuart Savory, who is an overeducated, grumpy multilingual ex-pat Scot, blatently opinionated, old (1944-vintage), amateur cryptologist, computer consultant, flying instructor, bulldog-lover, Beetle-driver, textbook-writer, long-distance biker, blogger and webmaster living in the foothills south of the northern German plains. Not too shy to reveal his true name or even whereabouts, he blogs his opinions, and humour and rants irregularly. Stubbornly he clings to his beliefs, e.g. that he's not really evil, or even anti-american, in spite of Dubya's efforts to convince him that he should be. He sorely misses his late dog :-(


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