Out of the Blue . . .

. . . I got an Email from Joe Faust who is putting together a History of Hang Gliding online. Joe had seen a 1976 photo of me hang-gliding in the Sauerland Hills at Villingen, Germany in 1976, so asked if I had any more old photos. Here they are Joe, enjoy:-

Later I went on to fly regular planes, complicated ones as well, and became a flying instructor. On a flying-instructor ongoing-education course years later I got a chance to fly an historic (1938) SG38 glider, the oldest hang glider I've ever flown (3-axes controls, though!). In this close-up below you can see how primitive it is :-)

Photo of an SG38 training glider taken at the Wasserkuppe Museum of Flight in 2007.

I'll do a photoseries on the Wasserkuppe Museum of Flight next month, OK Joe?

We put the clocks back one hour :-)

Here in Europe we put all our clocks back by an hour today (3->2 am) and so got to stay in bed for an extra hour; it has been much appreciated by all concerned as y'all see in the photo (right ;-)

Eagle eyes will have noticed the timestamp at the bottom of the posting rolled back from CEST to CET.

This 1 hr time change is normal for us here in Yurp. In the USA - just for comparison - sitting Presnit George Dubya Bush has put the clock back by a thousand years :-(

Copyright ^© Stu Savory on 28th Oct 2007 at 06:28 CET permalink Comments Email

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Messiah's Handbook^*

Just yesterday I was waffling on about some trapdoor functions which go easily one way and are much harder in the other direction. Today I want to introduce you to a very readable book which is constructed like that. Let me show you.

Richard Bach's Messiah's Handbook is one of those rare books which actually contain instructions for their own use :- "Hold a question in mind, please. Now close your eyes, open the handbook at random and pick left page or right".

Each page contains a single Zen-like aphorism, purportedly the answer to your question, and every single one is so very true. Example? "The only thing that shatters dreams is compromise". Anyone^** who ever worked for a large corporation understands that ;-)

The corollary of the instruction-for-use is that the book contains no table of contents, no index, and consequently the pages are deliberately not even numbered ;-)

Now think about the structure of other books. Novels have no index, often no table of contents, but the pages are numbered so you can remember your place if interrupted while reading them. They are meant to be read serially, from front to back. Textbooks have additionally at least a table of contents so that you can refer to specific subjects. Many have an index to let you look up specific ideas, words, equations, quotations. Regular dictionaries are sorted alphabetically so that you can look up words assuming 1) you know the alphabetical order (not always true for foreign languages), and
2) you can spell the word. I have a question (e.g for Wendy) . How do dictionaries for ideogram languages like Chinese work, where there is no alphabet?

Scrabble dictionaries sort the letters of each word into alphabetical order and then let you look up if there is such a word. Homonymic and/or phonetic dictionaries let you look up the spelling of a word if you just know how it sounds. Do Chinese dictionaries work like that, Wendy? Crossword-puzzle dictionaries are sorted by word-length :-)

This book is haptically great too (= it even feels good). It is bound in blue suede, presumably from the late Elvis's shoes ;-) Interesting title too, omitting a leading "The" as more presumptious monotheistic books would use. Other classical Messiah's stories are the Torah, the Koran and the Bible, all of which are so full of contradictions that they just confuse their readers. The Bible is particularly gross in this respect, I could quote you a gross of contradictions from it, but that's a subject for another post. Of course any system of logic which contains the axioms X and NOT-X (a contradiction) will let you prove ANYTHING! Richard Bach's excellent little book sums this up neatly with the implicitly recursive aphorism "Everything in this book may be wrong" ;-)

Curious? The ISBN is 1-57174-421-5. BTW, one more thing, it has 208 pages ;-)

^* : Today's blog is dedicated to the memory of Don Shimoda :-)
^** : Dilbert is the archtypical case in point ;-)

Copyright ^© Stu Savory on 27th Oct 2007 at 06:27 CEST permalink Comments Email

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On Trapdoors

Adrienne asked for a simple explanation of trapdoor functions, so here it is. Let's first consider the traditional trapdoor. This is a horizontal hinged hatch providing access to e.g. an attic or a cellar. Due to the force of gravity it is easier to open downwards than upwards (which is why it doesn't work in space in freefall).

Trapdoors were also used during the 18th and 19th centuries for hanging people. Two half-trapdoors were used, abutting in the middle, the hangee standing initially in the centre (Try to work out why two half-trapdoors are better than one whole one; I'll explain in a footnote^* if you can't work this out for yourselves). The cheap alternative was for the hangee (suicide?) to stand on a bucket (pail). The bucket was then kicked away and the hangee dropped. Hence we have the idiom "kicking the bucket" meaning death. Some people think another idiom "beyond the pail" means the same thing, but this is not the case. It uses a different spelling "beyond the pale", meaning the Palings which were an early form of fortification for villages and towns. Thus "beyond the palings" means (behaviour) outside civilisation (nowadays referred to as something equally pale, such as "The White House" ;-)

Getting back on topic, one-way functions which are easier to do in one direction than in the other are called trapdoor functions. Believe you me, they are hard to find. Some examples are discrete logarithms, elliptic functions and (the simplest example) factoring large numbers.

If I ask you whether 614,889,782,588,491,411 is prime, that is difficult for you to answer. You would have to use the Sieve of Eratosthenes and test-divide by all the primes up to 784,149,081 (the square root of 614,889,782,588,491,411). Even using the known divisibility test simplifications and/or high-precision integer arithmetic, this would take you quite a while.

Now if I tell you to multiply the first 14 primes and then add 1, you know that the result is prime because 614,889,782,588,491,410 has these 14 prime factors and so 614,889,782,588,491,411 always gives a result of 1 when divided to modulo these 14 primes. I derived a generic proof of this and showed it to you already. Easy-peasy!

And so factoring large numbers (e.g. of the order of 10¹²⁸ and more) is a one-way (= trapdoor) function; easy one way but really hard (maybe even NP-hard?) in the other.

What do trapdoor functions have to do with cryptography? In 1874 (sic!), a book by William Stanley Jevons described the relationship of one-way functions to cryptography and went on to discuss specifically the factorization problem used to create the trapdoor function in the RSA system (late 20th century). During the 1970s we Brits invented asymmetric key algorithms by using trapdoor functions; It was James H. Ellis, Clifford Cocks, and Malcolm Williamson at GCHQ in the UK (the Brit version of the NSA). GCHQ managed to keep this secret until 1997. Rivest, Shamir and Adleman at MIT reinvented it in 1978 and used it in their RSA algorithm. For the details of trapdoors in Public-key cryptography I refer you to the excellent article in Wikipedia. Also read about Diffie-Hellman key-exchange there too (and the Merkle problem).

Was that understandable enough, Adrienne?

^* Footnote : The centre of gravity of a trapdoor drops with 1 g acceleration. So the non-hinge side drops with 2 g. So using 2 half-trapdoors beneath the hangee assures the abutting joint drops away faster than the hangee's feet, avoiding any entanglement. We humans are good at optimising death for others :-(

Copyright ^© Stu Savory on 26th Oct 2007 at 06:26 CEST permalink Comments Email

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How to write Shaggy Dog Blog Stories ;-)

This is your chance to help US bloggeress Kay over at Kay's Thinking Cap :-)
Kay blogs what she calls "groaners" - what we here in Yurp call "Shaggy Dog Stories" -, every monday one from her stockpile and every friday one sent in by her blogreaders. I have contributed a couple; you could too, which would help keep her thread going. People I have asked to do this often answer that a) they don't know any, much less b) how to make up new ones. So I thought I'd tell you how to do it :-)

'Shaggy-dog story' has come to mean a joke where a pun is finally achieved after a long (and ideally tedious) exposition. The humor in the punch line is usually due to the sudden, unexpected recognition of a (pun on a) familiar saying, since the story has nothing to do with the usual context in which the phrase is normally found, yet the listener is surprised to discover it makes sense in both situations.

However, if the audience is not already familiar with the phrase used in the punch line, or is not aware of the multiple meanings of the words in the phrase, the surprise ending of the joke cannot be recovered by "explaining" the joke to the audience. Thus you need to take the cultural environment of the likely audience into account. Mine are thus restricted to the anglo-saxon (= native English-speaking) cultural environment; I can't do it in Japanese or for the Islamic cultural circles (are there any jokes in Islam?).

So I start off by coming up with a pun on a familiar saying (idiom). I may make it up myself - usually by saying the words aloud and then deliberately mispronouncing them - or I may have read the pun somewhere or heard it on TV or radio. Then I concoct a story for each of the words in the punned saying so that each word appears (usually only once) innocently within the context of the concocted story. So I really work backwards from the punchline to get an innocent lead-in story. Just be sure not to give the game away too soon, lest you spoil the punchline for your readers :-)
In the 1^st example shown below the words 'battle hymn' give the game away too soon. It would be better to leave off the word 'battle' perhaps, but then some of your readers might not get the punchline. Note too that the punchline is aimed at a US audience, other nations - especially non-christian ones - may never have heard of the 'Battle Hymn of the Republic' :-(

Here follow three examples I made up. Once you have grasped the principle I would ask you to make up some of your own and then mail them to Kay (her address is on her blog) for her Friday-Groaner Thread. Thanks to those who do so, in advance :-)

So my american friends and I were discussing the Iraq war. "Those christian fundamentalists in the White House started a war of unprovoked aggression! They are probably the most bloodthirsty killers in history, 100,000 Iraqi dead you know!"

"Naah. The most bloodthirsty killers in history were the hordes of Genghis Khan's mongols. They swept across Asia to the Middle East in 1206 AD, pillaging , raping, and bloodletting. The villages and market squares were KNEE DEEP in bodies, blood and gore as Genghis Khan combed the countryside for enemies."

"Yes but the american fundamentalists approved of and still encourage that sort of gory bloodletting rampage. In fact, during their civil war, one of them even wrote a hymn about battling Genghis Khan!"

"Oh come on, I've never heard of THAT! How does the battle hymn go then?"

"My knees have been so gory since the combing of the Horde..."

Once upon a time - when Britain had an Empire ( or at least a larger Commonwealth) - the young Queen Elizabeth the Second (or first if you happen to be a Scot) did a tour of the Commonwealth and visited several places in Africa, including Southern Rhodesia as it was then called. She visited several kraals and the local villagers carved a specially magnificent wooden chair for her to sit on, upstaging even the local chief's throne. After the ceremonial dancing and prancing was done, HM remarked what a comfortable chair that had been and that if she ever came back she would like to sit on it again. And so it came about that the proud natives stored the comfortable chair away in the chief's hut in the vague hope that Her Majesty would one day return.

And indeed, fifty years later, to celebrate a half-century of queening about, Her Majesty DID revisit many countries and even got an invitation to visit once again the aforementioned kraal, even though that was now in an independant country (I think it's called Zimbabwe now). The new chief, grandson of the one she had first met, even pulled out her original chair - all dry and dusty - had it carefully dusted down and let her sit there for the traditional war-dancing demonstration. Unfortunately, it seems that during the intervening five decades the infamous african termites had gotten into the seat and weakened it considerably. As a result the chair collaped in a cloud of dry dust, dumping Her Majesty unceremoniously onto the ground. How embarrassing :-(

The moral of this tale? People who live in grass houses shouldn't stow thrones ;-)

In Australia and New zealand Xmas happens in the summer, so it can get very hot then. This reminds me of the story about an NZ dairy farmer who needed to get the roof fixed on one of the sheds used for making cheese. He had two such sheds, one for processing the curds into cheese and the other for storing the skimmed milk left over after separating the curds. The skimmed milk was later packaged as a diet drink for sale in supermarkets across NZ. It was this second shed whose roof needed repair.

So the dairy farmer called a roofing contractor and asked for pricing for a clay-tiled roof versus one of wooden shingles. The latter came out cheaper so that this was what he ordered. The roofing contractor then explained that he had no men available to do the work short term, but that he could send over two pretty young ladies to construct his wooden roof. Just to be on the safe side, he also pointed out that the girls would work in bikinis rather than overalls, due to the terrible heat when the sun was burning down. Would this be OK with the farmer's wife?

Since the dairy farmer's wife was away anyway, he happily agreed to this condition ;-) However the girls turned up late in the afternoon, thus avoiding the worst of the sun's heat. Unfortunately this meant that the dairy farmer had to go off for church choir practice so that the choir could sing the Xmas carols correctly at Xmas. It must have been with the Xmas carol practice in mind that he left specific instructions for the roofing contractor's girls telling them which shed needed the new wooden roof :- "Shingle belles, shingle belles, shingle o'er the whey!"

Copyright ^© Stu Savory on 24th Oct 2007 at 06:24 CEST permalink Comments Email

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Thirty-seven tips (inter alia from Rob Yest)

37 is interesting for a number(sic!) of reasons.

Here are the first dozen ;-)

1. There are 37 genes in the mitochondrial genome.
2. 3×7×37 = three 7s = (777).
3. There are 37 points in a "perfect" bridge hand.
4. There are 37 bars in the digits of a digital (seconds) watch in 12-hour mode.
5. Tyrannosaurus Rex has 37 vertebrae in its tail.
6. William Shakespeare wrote 37 plays.
7. Hannibal brought 37 elephants with him on his conquest of Rome.
8. The 37th ASCII character is '%'.
9. The (european) roulette wheel has 37 numbers (greedy Vegas wheels have 38).
10. The 37th chemical element is Rubidium.
11. There are not 37 items in this list, which is a miracle...
12. but there are 37 miracles in the Bible ;-)

Having got your attention with this list of 37-trivia, let me introduce a rare guest blogger. He is Robert Yest, who teaches maths at ARC in Sacramento (California), AND at Yuba College in Marysville(CA) AND at Solano College in Fairfield, CA. He returned to teaching a few years ago after working in the corporate world since getting his PhD. He doesn't have a personal homepage yet since teaching at three institutions eats up his personal time, which is why I'm giving him blogspace here today.

Rob read my maths page about divisibility tests for the prime numbers up to 50, wherein I stated that 37 is a slightly more difficult case. But Rob has a simplification for the divisible-by-37 case. Let him tell it in his own words (all credit where credit is due :-)

Hi there Stu,
I found your divisibility tests for primes up to 47 interesting. You indicate that the divisibility test for 37 is where the test gets (slightly more) difficult. Let me add assistance. 37 * 27 = 999. So 1000 = 1 modulo(37). Thus, if X = 1000*y + z, where 0 =< z < 1000, then writing to modulo(37) we get X = y + z . So the divisibility rule could be simplified by adding in groups of three digits at a time :-)

For example, consider the number 205,346,966
Now 205 + 346 + 966 = 1517
and 1 + 517 = 518.

Then you can use your divisibility test on 518 instead of 205,346,966 which makes it MUCH simpler :-)

Also you can look at the three digit number and subtract the minimal (of the three) digit numbers from all digits to simplify your number again. (This will effectively subtract a multiple of 111). In the example I give above, there is a zero in the 3-digit number 205. The only possibilities with 0 as a digit are 37, 74, 370, 740, 407, and 703. Only the last two are worrisome, but easily testable. And so with 518, you would get 407. Just some number theory in action,

Robert Yest

Another Maths comment came from a young french blogreader Adrienne who read my cryptography pages (which are in German) and asks "What is a trapdoor function?". I'll cover that in a separate post later this month, Adrienne, OK?

Copyright ^© Stu Savory and Robert Yest on 22nd Oct 2007 at 06:22 CEST permalink Comments Email

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The stamp of friendship

W hen me mate MAD-Eddy hits you, you stay hit. You do not get up again. Not if you know what's good for you. Eddy is a sharp dresser too. Has lotsa belts in his wardrobe. All of them black. None of them for holding his trousers up. To give him all of his sporting titles is to sound like a thirty-year-old MZ single cylinder two-stroke engine running at tickover - Dan, Dan, Dan, Dan, Dan.

So I'm glad to call him a friend. A generous friend. Generosity is stamped on 'im.
On friday he gave me an old "Lettre Anglais". No, not THAT kind, luv. This one :-

First day cover. 900th Anniversary of the Battle of Hastings^*. Loadsa stamps with pics from the Bayeaux Tapestry across the top. All different (e.g Harald II claspin' his eye. 'Cos 'e got an arrow in it). Just 'cos Eddy thought that as a Brit I'd appreciate it mor'n 'im. I DO, MATE. Gets a place of honour on the study wall. Inna frame too, innit.
Thanks, Eddy. Cheers mate. Must lend you my copy of "1066 and all that"; good laff ;-)

^* We're a week late, the Battle of Hastings was on 14th October. And it was at Senlac Hill anyroad ;-)
941 years ago last week, that's a prime result by any count ;-)

Copyright ^© Stu Savory on 21st October 2007 at 03:03 CEST permalink Comments Email

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A Beautiful Mind Model

Theoretical physicist Sean Carroll - who is one of the contributors to the Physics Blog Cosmic Variance - recently blogged about the Beauty of Equations. It seems that Edge.org has a cooperation with the Serpentine Art Gallery (London, UK) wherein selected famous people get to write down their favourite equation and these are hung on display in the said gallery. What a great idea. I wish I'd been to see it, but you can see it online (cf. previous link). Doubtless C.P.Snow is turning in his grave ;-)

What's YOUR favourite equation or model? Show me yours and I'll show you mine ;-)

And thereby hangs a tale :-) Forty+ years ago I did an Honours B.Sc in Physics as my first degree (here's the 40 year re-union bash report), so I have a geeky inkling about stuff. Sometime later I had a relationship with a rather beautiful girl who made the mistake of saying in exasperation "I wish I understood better how the world works". So I told her, turning to my big whiteboard to write :-

This is the Standard Model of particle physics, a quantum field theory which describes three of the four known fundamental interactions between the elementary particles that make up all the matter in our world, just leaving out gravity (the weakest force). {Even today we still don't have a good ANY understanding of quantum gravity :-( }.

It seems that she really didn't want to know that and left me shortly afterwards ;-) Which is what you blogreaders will do if I continue in this mathematical vein, so I'd better leave it there, having told you about a beautiful model (Hi Babe ;-).

Copyright ^© Stu Savory on 20th October 2007 at 06:20 CEST permalink Comments Email

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Your comments this week

Brian (South Africa) replied to my mortality rate statistics (life expectancy) (see the 11th) and points us to these useful tips :- 24 Warning Signs You Cannot Afford To Ignore.

Liz Hinds has three book tips for us :-

• Salmon Fishing in the Yemen
• The Kite Runner
• Curious Incident of the Dog in the Night-time

Four Dinners asks "Have you read any of the 'Red Dwarf' books yet? It's not that they're particularly well written really. Just hysterically funny if you have a schoolboy like sense of humour." He also asks about the language I used for Chrissie. It's Gaelic.

Kay features one of my shaggy dog stories as Groaner of the Weak Week ;-)

Greta Christina has an angry piece on Atheism :-)

Sarah (UK) liked the title 'Ground Control to Major Tom' I used the other day and tells us that David Bowie is to appear in Doctor Who sometime in the future (Who's?). Meanwhile Lewis has blogged about a new danger to aviation (idiot pilot not on board!).

Ivan (Moskow) points us to a page telling us how to do rounded corners in CSS.

Jacky (NZ) read my piece on the world's oldest blogger and points us to what may be the world's youngest blogger. We both agreed to exclude the ones where an overly ambitious Mom blogs (allegedly) for her small child, even claiming the relevant domain.

Kiss of Death : Mrs. Cheney has let it be known that Barack Obama is Dick Cheney's eighth cousin. Well, I guess that's the end of his chances then! :-(

Lorena (India?) asked for Sarva Jagannadha Reddy's contact info so she could get a copy of his book "The True Value Of PI" ; glad to oblige, Lorena.

Finally, inspired by Richard Bach, let me leave you with this thought for the weekend : Everything that ever happens, happens between your ears. Think about that ;-)

Copyright ^© Stu Savory on 19th October 2007 at 06:19 CEST permalink Comments Email

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Quedlinburg revisited

I've shown you photos of Quedlinburg before, but here are some photos from a recent revisit to show our friends from Alaska how nice it looks. Quedlinburg is a small town on the eastern side of the Harz mountains; it is a UNESCO World Heritage Old Town and still has some 1200 old wooden-beam buildings, some shown here. Beautiful town, always worth visiting.

Copyright ^© Stu Savory on 18th October 2007 at 06:18 CEST permalink Comments Email

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Ground control to Major Tom ... --- ...

Blogging today as a flying instructor, let me tell you that one of the most important things for a pilot in (heavy) traffic is Situational Awareness. That means you need to not only to know where YOU are, etc but also at all times where other aircraft, terrain, ground vehicles etc are also (and their speed vectors).

I write this because there was a ground collision of two aircraft at LHR (London Heathrow) on monday evening, as reported here. A lack of Situational Awareness :-(

The person you are all taking to on the radio is called ATC (Air Traffic Control) and is theoretically responsible for separation. Sure. He/she is "responsible", but is you and your passengers who die when ATC screws up. So you need to listen to ALL radio conversations - not just those directed at you - so that you have that critical awareness of what is going on around you at all times. If ATC appears to be screwing up (again), just refuse the clearance they give you or ask for clarification. Don't fail to ask for clarification if you don't fully understand the situation. There is such a (potentially deadly) thing as false pride, i.e. not wanting to appear non-professional.

Here are some examples of ATC getting it wrong even while the aircraft concerned were still on the ground. Yes, it happens, just read on here please:-

North Las Vegas, September 2003 : A Piper Arrow on final for runway 12R was cleared to land when a Piper Mirage was cleared for takeoff on the crossing runway 07. The two planes collided at the intersection of 12R and 07. Clearly an ATC failure, which could have been avoided by them looking out of the window at the crossing runway. Or even (surprise, surprise) only using one runway direction at a time, as is done here. Luckily there were no fatalities.

Saraseto, March 2000 : a Cessna 150 was cleared for takeoff on runway 14. ATC then cleared a 172 onto runway 14, believing both were using the full length of runway 14. However the 172 was at an intersection AHEAD of the 150, followed instructions and taxied onto runway 14 where it was hit by the departing 150. Four dead. Again ATC's fault, which could have been avoided by just looking out of the window. Situational awareness by the 172 pilot - who should have been listening to ALL the conversations on the radio - should have prompted him to get confirmation of the clearance. Looking left and right before entering the runway would have caught the ATC failure as well. Personally in such a situation I would have asked specifically for an "Intersection Take-Off" just to help jog ATC's situational awareness too. No-Brainer!

Los Angeles, February 1991 : A Boeing 737 on final was cleared to land on runway 24L. ATC then positioned a Metroliner half way down 24L with the intention of clearing it for takeoff before the Boeing touched down. They never did clear the Metroliner for take-off and the Boeing was unable to avoid a collision. 34 people died. Again ATC's fault, controllers not being aware what the other was doing. Situational awareness (listing to ALL conversations on the same Tower frequency) should have triggered the Metroliner pilot to query his entry clearance and/or have triggered the Boeing pilot to initiate a go-around. ATC may be 'responsible' but it is you who dies!

Finally, I would like to recommend a useful online facility, the Air Safety Foundation to all my pilot readers. You can use their online training courses to keep yourselves up-to-date and aware of accident causes. If you are a certificate-freak who needs to document what you know, you can even print out a pretty little course certificate :-

Coming back to that LHR ground incident which triggered this post, we all realise that the ATC controllers are under tremendous pressure; understaffed, overworked etc etc. It may be only a matter of time before it happens in the air. ATC keeps suspiciously quiet on 90+% of 'near misses'. Unless two planes do actually collide in mid-air - thanks to ATC 'control' (as happened one night over southern Germany thanks to Swiss ATC a couple of years ago) - only the odd passenger taking a quick photo of a 'close encounter' exposes them. So fellow pilots : keep on your toes at all times!

Copyright ^© Stu Savory on 17th October 2007 at 06:17 CEST permalink Comments Email

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World's oldest blogger?

B oing Boing gets it wrong! It is not some 93 year old american guy. It is (AFAIK) Maria Amelia Lopez - aged 95 ! - from Muxia in Spain. I guess Boing Boing can't read Spanish, which is why they missed it. I think that Ms. Ronnie Bennett, who runs the ElderBlogger blogroll, should give her a place of honour :-)

Any blogreaders know of anyone older who is blogging? People with a provable age?
Don't tell me about that Ukranian guy who claims to be 118. He just can't count ;-)

Addendum(noon) : Madame Levy points us to The Life of Riley, which although Ollie Riley is 108 is actually written for her by Mike Rubbo from transcribed conversations. Hmmmm, does that count then? Is it like the difference between an auto-biography and a biography? Or is it like having a ghost writer? Do ghost-bloggers count?

Copyright ^© Stu Savory on 16th October 2007 at 06:16 CEST permalink Comments Email

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More about books.

Wendy Templeton, blogreader in Hong Kong, recommends Bill Bryson's The Life and Times of the Thunderbolt Kid which had her "continuously braying with laughter and wiping tears from my eyes". His other books are good too!

Young Jennifer(16) wants to be an airline pilot when she grows up {fairly recently I recommended she read Aviatrix's blog, now she's hooked}. She asks what is the best book about the Zen of Flying I can recommend. Well, Jennifer, it has to be Richard Bach's Illusions ISBN 0-440-20488-7. He is the guy who also wrote "Jonathon Livingstone Seagull", but all his other books are pretty good too. I have them all :-)

Germany's most widely read plebian newspaper Bild, recently conducted a survey asking "Have you read a book this year?", and the answers shocked me :-

• 22% of those asked have not read a single book this year!
• 16% of women and 28% of men.
• 35% of those with no occupational education (e.g. an apprenticeship).
• 20% of those with O-levels, = US high school graduates.
• a mere 8% of schoolchildren,
• but a shocking 7% of people with university degrees!

Just for comparison, I read about 50 books per year, and recently was reading 1 daily. But the people I admire most are those like Terry Pratchett who can write two every year whilst maintaining an excellent quality. I've written a few & know how hard it is!

Addendum (monday evening) : Hans Peter Pfersich recommends "How would you move Mount Fuji?" by William Poundstone, with questions from Microsoft interviews. Four Dinners likes movie/showbiz bios and recommends David Niven's "Moon's a Balloon", the late Sir John Mills "Up In The Clouds Gentlemen Please", Lauren Bacall's first book "By Myself" and one on Tommy Cooper "Always Leave Them Laughing" by John Cooper - fascinating insight into a naturally funny man.

And what about the rest of you? What book tips do YOU have to share?

Copyright ^© Stu Savory on 15th October 2007 at 06:15 CEST permalink Comments Email

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Shrinking my piles...

Of all those as-yet-unread books, that is! NOT what you were thinking ;-)

Having been confined to a sickbed for a couple of days recently, I was able to enjoy the peace and quiet. No telephone, no neighbours, no handymen, no blogging(!), no internet, just some rest and convalescence. So I took the opportunity to reduce the pile of unread books and would like to recommend three of them to you.

On the left, Terry Pratchett's "Making Money", ISBN 978-0-385-61101-5. Master con-man Moist von Lipwig is appointed head of the Ankh-Morpork Royal Mint. It is a job for life, which is not necessarily very long ;-) An enjoyable romp in the best Discworld tradition, but it does presuppose you read pTerry's previous novel "Going Postal" if you are to get all the jokes. Australian blogreader Anna Pashen should enjoy this one :)

In the centre, bloggeress WPC E.E.Bloggs(sic) has put together an amusing - if sometimes repetitive - little soft-cover book from her blog articles. She explains the ineffably burocratic workings of the UK police forces today, when trying to cope with your friendless neighbourhood ASBO git. I think that Four Dinners would like this one. The ISBN number is 978-0-9552-8547-9, orderable from Amazon.de by clicking here.

On the right, US mathematics schoolteacher Margeret Tent has written quite an exceptionally engaging narrative of Gauss's life from his working-class boyhood 200 years ago to the heights of world-class mathematics. The book is written for young readers (e.g. 13 year olds) and the little amount of maths used therein is easily understandable. The ISBN number is 1-56881-261-2. I recommend this book specifically to blogreader Madame Levy, for her teenage daughter's maths education. This book was a get-well present from Alaskan blogreader Klaus Steigler, to whom many thanks.

In a failed attempt to understand the evangelical subculture of American christian fundamentalism I also read "Mine eyes have seen the glory", a book I cannot recommend (except perhaps to Liz Hinds), which is now - most deservedly indeed - out of print.

The other book I read was recommended to me as typical Jewish humour. Stomping the Goyim, a 1969 novel by Michael Disend is however twee, pointless, overly cute, and just plain badly written. It is about being gay, ungoy, drugged-out, and psychodelic in the late 1960s; none of which are, or ever were, desirable aims. It is also hard to read due to Disend's so-called 'style'. If this is the epitomy of Jewish novels, then all I can say is "Oy vey!". I gave up ½ way. Definitely NOT recommended. On the other hand, I'd recommend you get a grip on yourself and read Philip Roth's funny "Portnoy's complaint" if you're looking for 1960's Jewish wanker's humour ;-)

Copyright ^© Stu Savory on 14th October 2007 at 06:14 CEST permalink Comments Email

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Congratulations Chrissie! Freewoman in spe.

Seo an 104mh Mòd, a tha ga chumail am bliadhna-sa anns a' Ghearastan. Bidh an fhèis a' ruith gu 20mh den Dàmhair - nuair a bhios gach còisir-ciùil a' seinn ri cheile. Cuideachd, thèid òraidean agus tachartasan neo-fharpaiseach a chumail tron t-seachdain. Thèid Saorsa Loch Abair a buileachadh air Chrissie NicEachainn, 72, aig an fhèis. Ghabh i pàirt anns a' Mhòd son a' chiad turas ann an Dùn Omhain nuair a bha i 9 bliadhna dh'aois ann an seinn, na h-aonar, seinn ri neach eile agus còmhradh, 's bhuannaich i bonn òir tradiseanta aig a' Mhòd anns an Eilean Sgitheanach ann an '82.

Copyright ^© Stu Savory on 13th October 2007 at 06:13 CEST permalink Comments Email

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This mortal coil : life expectancy statistics

Many thanks to all of you who wrote concerned for my health after reading the pastiche song I wrote last thursday. I am now cut out for a longer period of blogging and just have to go for cancer checks every six months. That having been said, the turn of events did get me thinking morbidly about my own mortality and so today's blog will share what I found about life-expectancy statistics.

I drew the graph shown above from UK government actuarial tables for 2005, the newest I could find. The median life expectancy for a newborn UK male is 79.5 years. The 5 numbers for the boxplot are :- 47.9, 70.4, 79.5, 85.5 and 108.1 years.

However, having already reached age 63.4, I am not one of the 14% who have already died. Thus we need to renormalise the statistics to show 100% alive at age 63.4 :-) The 5 numbers for MY boxplot are thus :- 56.1, 75, 81.5, 87.5 and 106.4 years.
Having already made it to 63.4 thus increases my life expectancy by 2 years to 81.5.

The chart I have drawn above comes from the same source. It shows the absolute number of UK males who die within the year following their N-th birthday. We see that the mode is at age 82 (compared with the median of 79.5 years). The curve turns down afterwards because the number of survivors is getting smaller. So we really need to divide by the number of survivors to get a percentage deathrate within the following year. The chart below shows the percentage chance of dying before your next birthday for those aged N. What a morbid blog this is today! The next will be more cheery :-)

PS: The sample size of the actuarial tables is n=100,000 so the numbers are reliable.

Copyright ^© Stu Savory on 11th October 2007 at 06:11 CEST permalink Comments Email

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Pisa? Bad Frankenhausen church leans more!

Most people have heard of the Leaning Tower of Pisa. But not many know about the Leaning Tower of the 14th century church in Bad Frankenhausen (in Thüringen, Germany), which leans over quite a bit more, and in two directions to boot! So Klaus and I went to see it before it falls over (well, they are trying to shore it up now, as you can see in the photos). Klaus originally did a university degree in Civil Engineering, specialising in statics, so this would have been an interesting statics project for him :-) Me? I just stayed well on the upside of it ;-)

Copyright ^© Stu Savory on 10th October 2007 at 06:10 CEST permalink Comments Email

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Robust statistics using boxplots

Just last month I blogged about different kinds of averages. Now young blogreader Jeff (NZ) has commented "In our school they only taught us about the mean . Tell us please : when would you use the median, and why?"

The median is more robust than the mean, Jeff, it copes better with occasional data errors. Here's an example. Assume we have 10 numbers in our data set and sorting them into sequence they are : 1,2,2,3,3,3,3,3,4,4,5. These add up to 30 so the mean is 3. With these 10 numbers the median (central value) is also 3. So far so good. Now assume you made an error entering the 5 in your data set, your finger jiggled, the key bounced and the number you entered is now 55 :-( The data now add up to 80 so the mean is 8. But notice that the median is still 3. The median is thus said to be more robust because it is less influenced by such data errors.

Now lots of statistics are done using the mean (and the standard deviation as a measure of spread). But these require that the data be distributed 'normally'. That means they are in the bell-shaped curve you may have heard about (also known as a Gaussian distribution after the german mathematician Gauss). But an awful lot of the data sets we encounter are not like this. They may be 'flat' (random). They may tail off (survival rates). So it would be nice to have some robust way of doing statistics regardless of the way the data are distributed.

Back in 1977 John Tukey came up with the box-and-whisker-plot for showing a 5-number summary of datasets whose distributions were not bell-shaped. Anyone remember John Tukey? He was the man who invented the FFT (Fast Fourier Transform).

How do you draw a boxplot? First find the first and third quartiles of your dataset. 25% of the data are below the first quartile, 25% are above the third quartile. In the dataset we used above (1,2,2,3,3,3,3,3,4,4,5) the first quartile is 2 and the third is 4, as you can easily see. Now just draw a box shape with its edges at the quartiles. Also draw a line across the box where the median (= second quartile) is. The distance between the first and third quartiles is called the inter-quartile-range (IQR) and is a measure of the spread of the data. The IQR in our dataset here is thus 4-2=2.
The central 50% of our data always lie within the inter-quartile-range.

Now we'll add some whiskers to our box. Find the smallest data point above 1½ IQR below the first quartile. In our case this would be the datapoint with value 1. Find too the largest data point below 1½ IQR above the third quartile. In our case this would be the datapoint with value 5. These two values (1,5) are the ends of our whiskers.

So our box-and-whisker plot summarising our dataset now looks like this. I've drawn in a small cross (X) where the mean is too (you'll see why later).

Now let's look at the boxplot for the dataset containing the erroneous 55 instead of the 5. The median stays at 3 but the upper whisker is now at 4 because the 55 data point is WAY outside 1½ IQR. In fact it is even outside 3 IQR. Datapoints outside 1½ IQR are called mild outliers (and represented by a closed dot), and datapoints outside 3 IQR are called extreme outliers (and represented by an open dot), because they are extremely unlikely and so are suspicious and thus worthy of further inspection. We need to see if they are errors (as is the case here).

Box and Whisker plots are easy to sketch by hand from the data, you don't even need a computer, any arithmetic (e.g. 1½ IQR) is so easy you can do it in your head :-) This makes them a useful tool in your maths toolkit. And now you've just learned how to make them and how to use them to catch outliers. Dead easy wasn't it? :-)

Of course since the distribution of the data is irrelevant for boxplots, they also apply to normal distributions. Here is a Wikipedia sketch showing you how they compare :-

One disadvantage as I see it, is that the boxplot does not show you the number of data points in the set (the so-called sample-size), so that I, personally, always write it next to the boxplot, e.g. n=10 here. That's 'cos I trust larger samples more :-)

In a later post I'll be showing you some non-normal data distributions (e.g. actuarial tables) and you can practice by drawing their boxplots if you'd like to try your hand :-)

Copyright ^© Stu Savory on 9th October 2007 at 06:09 CEST permalink Comments Email

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PS : Yes, I'm still an atheist; this poem is just artistic licence, OK ;-)

Copyright ^© Stu Savory on 4th October 2007 at 06:04 CEST permalink Comments Email

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My friend's crackers^* !

Blogreaders Klaus and Doris popped over from Alaska yesterday for a short stay. I say popped over, but it took over 30 hours door to door :-( And on the last hop - London (Heathrow) to Düsseldorf - they hungrily forwent the airline pretzels and crackers just so they could present me with this punny package ;-)

How many of you blogreaders can claim to have your own name branded foods? ;-)
OK, OK, Jock MacDonald, that's excluding you ('cos I was talking about edibles!) ;-)

^* Yes, I do know that the apostrophe should be behind the S, but that would have spoiled my little pun.

Copyright ^© Stu Savory on 3rd October 2007 at 06:03 CEST permalink Comments Email

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Getting the job application wrong ;-)

Last saturday I got to meet blogreader Peter who has his own head-hunting company. During my time with major corporations I probably interviewed a three-digit number of job applicants, so we were able to swap (anonymous) anecdotes about job applications and interviews. Here is a short excerpt.

Get yourself a decent photo for your letter of application, not one from those 2 € 'portrait' machines at the railway station or airport. They make you look cheap.

Don't look too scruffy in the photo;
ladies, in this photo you don't have to look seductive ;-)

If applying for a white collar job, wear a suit and tie for the photo. And for the interview too. Just make sure they are not the same ones, lest it look like you own just one (thanks to Peter for this tip). Been there, done that ;-) Ooops, double oops.

I once knew a lady who interviewed for a job at a small jewish bank in London(UK) while wearing a crucifix necklace, then wondered why she didn't get the job :-/

Not to mention the rather beautiful and deep-necklined young lady who came for one of those interviews over lunch who, upon seeing the menu, meant to say "I don't eat pork, you know" but forgot the word "eat" ;-) Perhaps I should have offered her a beef sausage? Sorry, girls, that is not an appropriate joke, I know.

There was a guy who answered his mobile phone whilst I was interviewing him :-(

And another guy who claimed fluent English and French on his application and was then speechless when I did the interview with him in both. That called his bluff. So don't brag with stuff you really don't know well, it can be very embarrassing!

Equally embarrassing is when the personnel department - trying to save money - used the old letterhead paper on the interview invitation and so the guy turned up punctually at the old address from which we'd moved 2 months ago :-( He was so pissed off at them he didn't come on the re-arranged date. I don't blame him, but we lost a good applicant. If you are reading this, I apologise again. Very embarrassing.

That was the same personnel department which asked me for a list of my publications "classified papers too". Duh! Am I stupid or what? Daft burocrats, all of 'em!

I'm sure Peter has lots more stories than I do and probably each of my blogreaders has had an embarrassing interview. Go ahead and mail any comments to be appended here folks, but say if you want them anonymised. Or blog 'em for a link here.

Copyright ^© Stu Savory on 2nd October 2007 at 06:02 CEST permalink Comments Email

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