I'm dreaming of a white ...

Easter ? Methinks they'll have to rewrite the old Bing Crosby song :-)

Although Xmas and New year were green and warm, these Easter hols here have turned out to be cold(-8°C), white and a couple of feet deep in snow :-(

In places, the snowdrifts were a couple of feet deep and the dogs kept disappearing ;)

But when the blizzards blew and the snow was whirled around I put the dogs on the leash, lest they disappear completely in the reduced visibility! But they still had fun, mostly consisting of pulling me off my feet and then jumping on me and licking my face to ensure I was still unhurt :-) Two (even one!) young bulldogs are capable of pulling me along on a sled, no problem there. Maybe I'll train them for the Iditarod '09 race ;-)

Here's wishing all my blogreaders a warm(er) springtime in the coming month :-)

Copyright ^© Stu Savory on 30th March 2008 permalink Comments Email

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A Mole turns 90

Heinz Felfe, double, triple, nay quadruple agent turned 90 recently. There was a congratulatory column in RIA Nowosti (the Russian news agency) just this week, written by the FSB (which is the current incarnation of the old KGB).

Felfe in his twenties spied for the Nazis, where he lead the department forging pound notes during WW2 and cashing them in via Switzerland and Lichtenstein. After the war he was a POW for a while before becoming a spy for the Brits in 1947. After they dropped him as being too suspect he joined the KGB in 1951 as 'Paul'.

Barely two months later he was smuggled into the West German Organisation Gehlen as a mole, where he was known as "Fresian". When the Organisation Gehlen evolved into the BND he worked his way up the ranks quickly until he was discovered to be a mole in 1961. In 1963 he got 14 years jail for treason. In 1969 he was swapped in Moscow for 3 CIA agents. Amusing in retrospect, since he had been running as a well paid CIA agent himself since 1956. He disappeared for a while (on the Krim?) before reappearing as a lecturer in East Germany. In 1986 he wrote his memoirs there : "Im Dienst des Gegners; 10 Jahre Moskaus Mann in der BND". He betrayed about a 100 CIA agents and 90 West German spies besides handing over 15000+ classified documents to the KGB, so it is no wonder the FSB have said 'Thankyou' this week. Think of him as their equivalent of John le Carre's Smiley, spying quietly, successfully, in the background.

As any gardeners amongst you will know, it is really difficult to get rid of any moles :-(

Copyright ^© Stu Savory on 28th March 2008 permalink Comments Email

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Golf in Ireland

B logreader and motorcycling friend Paul Gockel sent me this joke in reply to my St. Patricks Day anecdote and the subsequent One-True-Church^® satires.

An American golfer playing in Ireland hooked his drive into the woods. Looking for his ball, he found a little Leprechaun flat on his back, a big bump on his head and the golfer's ball beside him. Horrified, the golfer got his water bottle from the cart and Poured it over the little guy, reviving him.

"Arrgh! What happened?" the Leprechaun asked.

"I'm afraid I hit you with my golf ball," the golfer says.

"Oh, I see. Well, ye got me fair and square. Ye get three wishes, so whaddya want?"

"Thank God, you're all right!" the golfer answers in relief. "I don't want anything, I'm just glad you're OK, and I apologize." And then the golfer walks off.

"What a nice guy," the Leprechaun says to himself. I have to do something for him. I'll give him the three things I would want.. a great golf game, all the money he ever needs, and a fantastic sex life."

A year goes by (as it does in stories like this) and the American Golfer is back. On the same hole, he again hits a bad drive into the Woods & the Leprechaun is there again.

"Twas me that made ye hit the ball here," the little guy says. "I just want to ask ye, how's yer golf game?"

"My game is fantastic!" the golfer answers. I'm an internationally famous Golfer now." He adds, "By the way, it's good to see you're all right."

"Oh, I'm fine now, thankye. I did that fer yer golf game, you know. And tell me, how's yer money situation?"

"Why, it's just wonderful!" the golfer states. "When I need cash, I just reach in my pocket and pull out hundred dollar bills that I didn't even know were in there!"

"I did that fer ye also." And tell me, how's yer sex life?"

The golfer blushes, turns his head away in embarrassment, and says shyly, "It's OK."

"C'mon" urged the Leprechaun, "I'm wanting to know how many times a week?

Blushing even more, the golfer looks around then whispers, "Once, sometimes twice."

"What!" responds the Leprechaun in shock. "That's all? Only once or twice a week!"

"Well," says the golfer, "that's not bad for a Catholic Priest In a small parish." ;-)

As related to me by Paul Gockel permalink Comments Email

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I-less in Gaza -(

A nonymous often ain't :-(

There are two kinds of bloggers. Anonymous bloggers and the upfront ones. When I started blogging, I decided to go upfront and avoid all the hassle of hiding behind a wierd pseudonym. The corollary was that I chose not to blog about my job, my oh-so-gray employer, etc. Whistleblowing is not my thing.

Other bloggers have made the other choice, blogging perhaps indiscretions about their job, and thus having to hide behind anonymity for fear of losing said job. There are policemen, teachers, ambulance workers, council employees etc etc who did this. Experience has shown how difficult it is to remain anonymous. Some bloggers close down from sheer paranoia. A young lady in France was fired when discovered. No joke.

The latest in this line is Civil Serf, a 33year old UK female civil servant. Last week her blog was pulled from cyberspace. A pity, because it was quite amusing. Simultaneously, Gus O'Donnell (the Prime Minister's chief of cabinet), who is mentioned also in her blog BTW, has announced that there is to be a compulsory code of behaviour for UK government employees in cyberspace just as there is in the real world.

So it is not just in Iran, Russia or China where censorship takes place. I wonder what the Sharia has to say about blogging? They'd probably cut out your tongue :-(

I'm just writing this as a caution for those friends of mine thinking of starting blogging and who live in repressive regimes (eg. the UK). Similarly, think twice about whistle blowing, the protection mechanisms are very poor, especially when corruption goes all the way to the top of an organisation. Oh yes, I too have also worked for S??m?ns ;-)

Here in Germany, we are required to put an Impressum on our websites, revealing our names, adresses etc etc. But there are still many who do not comply. Cave Canem.

The ultimate in anonymous blogs has to be the new Shin Bet blog, designed to get the IP addresses of curious Hamas readers, wouldn't surprise me. I-less in Gaza, indeed.

Copyright ^© Stu Savory permalink Comments Email

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A positive sign today ;-)

L ittle Moishe - otherwise a fine Jewish boy - was doing very badly at school in maths. His parents had tried everything... tutors, mentors, flash cards, special learning centers, computer assisted training. In short, everything they could think of to help his maths.

Finally, in a last ditch effort, they took Moishe along and enrolled him in the special maths class for retards at the local Catholic school. After the first day, little Moishe came home with a very serious look on his face. He didn't even kiss his mother Hello. Instead, he went straight to his room and started studying. Books and papers were spread out all over the room and little Moishe was hard at work. His mother was amazed. But nevertheless , she called him down to dinner.

To her shock, the minute he was done, he marched back to his room without a word, and in no time, he was back hitting the books as hard as before. This went on for some time , day after day, while the mother tried to understand what made all the difference. Finally, little Moishe brought home his report card. He quietly laid it on the table, went up to his room and hit the books. With great trepidation, his Mom looked at it and to her great surprise, little Moishe had got an 'A+' in maths. She could no longer hold her curiosity. She went to his room and said, "Son, what was it? Was it the nuns?" Little Moishe looked at her and shook his head, no. "Well, then," she replied, "Was it the books, the discipline, the uniforms? WHAT WAS IT ALREADY?"

Little Moishe looked at her and said, "On the first day of school I knew they weren't fooling around in maths class when I saw that guy nailed to the plus sign!" ;-)

Copyright ^© Stu Savory, Easter 2008 permalink Comments Email

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Copyright ^© Stu Savory permalink Comments Email

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I imagine that the the eclipse of the sun over Golgotha Hill roughly 1975 years ago today might have looked something like this ;-) Here is W.B.Yeats version ;-)

In the run-up to the bloody crucifixion, the Vatican is doing it's best to return to the middle ages. Father Gabriel Amorth - 82(age or IQ?) - at the Pope's university Regina Apostulorum is setting up a training course for exorcists. Not the guided missile that sank HMS Sheffield, that was an Exocet, but those Catholic nutters who torture people (mostly defenceless women) both physically and psychologically. The Vatican wants to have 3000 new exorcists - one in each diocese - plying their devilish superstitious trade. 3000 new exorcists? I would have thought 666 would be enough. It's not only Islamic religious fundaMENTALists we have to worry about, but Catholic nuts too!
The One True Church^® - trying to distract us from more news about Father Peter K. buggering poor choirboys in Regensburg - is excelling itself again. SHAME ON IT!!!

Embedded photo original at the top can be found on the Sevenload portal, to whom thanks.

Copyright ^© Stu Savory on Good Friday, 21st March 2008 permalink Comments Email

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Match it for Pratchett !!!

T riggered by Four Dinners writing about The Grim Reaper yesterday, I'd like to remind you of the fate of my favourite living UK author pTerry. Terry Pratchett (alias pTerry) is the author of the Discworld series of fantasy novels and is IMHO a better writer than AK Rowling, sales notwithstanding. pTerry announced a few months ago that he was suffering the onset of Alzheimers :-( Just last week at a press conference he gave, he announced that he was donating a million US dollars to Alzheimers research which is still seriously underfunded. Well done. Now fellow blogger Chris Tregenza has started an appeal amongst fans called Match it for Pratchett. The aim is to donate an equal amount (or - preferably - lots more) from those who have gained much pleasure from pTerry's books. If we fail to reach this low target, it really WOULD be an embuggerance! So please go contribute now, before you forget !

Copyright ^© Stu Savory permalink Comments Email

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Almost finished with PI?

J ust-turned-thirteen blogreader Ranjit (India) commented on my PI-day post and wrote "Two questions : our much respected old maths teacher says PI goes on forever, but what happens to that PI mnemonic when it encounters the first zero digit? And is there a convenient place we could cut off PI as being 'nearly' finished?"

Good questions, my lad. The first zero occurs at the 32nd place after the decimal point. So those poems wherein you count the number of letters/word stop there :-(

As regards being 'nearly' finished, you can of course truncate (or round up) PI anywhere to get results with whatever precision you need. Thus some people use 3.14(truncating), some use 3.142(rounding up), and some 3.14159(truncating again). But by "a convenient place" I assume you mean places with recurring zeroes (truncating) or recurring nines (rounding up)? Then let's look at those places.

There are two recurring zeroes "00" first at the 307th place after the decimal point, three "000" first at position 601, four "0000" at 13,390, and five "00000"at 17534. The six zero string 000000 occurs at position 1,699,927; seven 0000000 occurs at position 3,794,572; eight 00000000 occurs at position 172,330,850; but nine 000000000 does not occur in the first 200,000,000 digits of PI. You could thus use any of these positions as being 'nearly finished' by truncation.

As far as finding a convenient position to round up is concerned, two nines 99 occur first at position 44, three, four, five and six nines 999999 occur first at position 762 (in context : 77130996051870721134 999999 83729780499510597317). Seven nines 9999999 occur at position 1,722,776; Eight nines 99999999 occur at position 36,356,642; But nine nines 999999999 do not occur in the first 200,000,000 digits.

Another blogreader, Charles Pergiel (OR,USA), has asked "What if PI isn't really an infinitely long number? What if it really stops after, say, N digits? Would anyone be able to tell the difference?". So I pointed him to my proof that PI is irrational. Here 'irrational' means that it is not expressible as a fraction A/B. Which in turn means that it does not contain a recurring cycle of digits. If it were a fraction A/B then it would contain a recurring cycle of digits of maximum length B, and thus - expressed to base B - would have just a single digit after the point. An example? 22/7 = 3.1 to base 7. As a decimal, 22/7 contains a recurring cycle of digits: 3.142857 142857 142857 ...... And thus 'irrational' means PI does not terminate when written to ANY base at all :-)

PS: I have another page with a short history of PI approximations. Go PI-ruse it ;-)

Copyright ^© Stu Savory on Wednesday, 19th March 2008 permalink Comments Email

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A St. Patrick's Day anecdote, begorrah ;-)

Once upon a time there was a salesmen's conference being held in New York , coincidentally on St. Patrick's day so that the attendees could attend the celebrations there 'for free'. There were three Italians attending who were not acquainted with the disgusting American-Irish practice of putting green colouring in their gnat's piss "beer" on that day. One of the salesmen was from St.Peter's Square (Rome), one from Naples and one from that place half underwater (Venice). They went into an Irish Pub.

The barman - an ex-porter who claimed to be (or not to be) a shakespearian actor "between engagements" - was thus asked by these 3 salesmen if he had any REAL irish beers (stouts). He said he had a choice of Guinness, Mackeson's or Murphy's stouts. The bible salesman from Rome asked him what was the difference, so the actor/barman explained : "They are all dark stouts but the Guinness is bitter and has a fine creamy head, albeit spoiled by the addition of green colouring today." The mafiosi from Naples then asked "And the Mackeson?" Turning to the spaghetti salesman from Naples, he explained "The Mackeson's is sweeter, a hint of caramel, with a larger head with larger bubbles in the foam, spoiled today by the green colouring too." The third salesman asked "And the other one, is it spoiled by green colouring too?" Striking a Shakespearian pose, the porter/actor/barman turned to the Merchant of Venice ;-) and declaimed "The quality of Murphy's is not stained..." ;-)

Copyright ^© Stu Savory on 17th March 2008 permalink Comments Email

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Quoting Einstein on PI day ;-)

March 14th (3.14) is celebrated roundly in America today (because of the way they write dates). Usually 7 students will order a 22 inch circumference pie and divide it up fairly amongst themselves ;-) However, Californian hippies, being more precise, will take 355 grams of marijuana and share it fairly around between all 113 of them ;-)
Sharing this celebration, I thought I'd tell you an anecdote about Albert Einstein today.

As you may know, in 1922 the physics Nobel prize was shared between two people, Albert Einstein and Niels Bohr. Einstein got his, surprisingly NOT for the theory of relativity, but for his explanation of the photoelectric effect via light quanta. Bohr got his for the orbital model of atomic structure. Interestingly Einstein thought Bohr was barking up the wrong tree and vice versa. The two theories did not become unified into quantum theory until several years later. Indeed Einstein never did accept quantum theory as we know it today, saying "God does not play dice!"

Nevertheless, Einstein wanted to grasp these ideas and read a book on Bohr's ideas on this very day many decades ago. He finished it at exactly 33½ seconds to two in the afternoon. Thus a digital clock would have displayed 3.14 1:59:26.5 ;-) As he put the book down at this exact time he is reported to have said "How I need a drink, alcoholic of course, after the heavy chapters involving quantum mechanics." ;-)

If you don't think that's remotely a ghostly^* coincidence, dear blogreaders, I suggest you count and write down the number of letters in each word of his exclamation ;-)

BTW, 14th March is also Einstein's birthday, which is why I chose to quote him :-)

^* : Pun on Spukhafte Fernwirkung, geddit?

Copyright ^© Stu Savory on 14th March 2008 permalink Comments Email

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Car thief alarm : Our back seat drivers ;-)

NB: This is a fictional limerick, and 'Dakar' is the only word I could get to rhyme;-)
Copyright ^© Stu Savory on 12th March 2008 permalink Comments Email

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Code-Breaking for Kids, Part 2

A bout 20,000 of you came and read the first article on Code-Breaking for Kids. Here's the follow-on article. Firstly let me ask you this time NOT to send me pieces of code to break, because I won't be doing that, subsequent ad hominem attacks notwithstanding (you know who you are). Instead, this little series is intended to enable you to be able to break pencil-and-paper codes yourselves, OK?

Young Terry (Minnesota, USA) who is 13 (but going on 14, she insists) has asked "What is the next step, the next harder code, the first ones were too easy?".

The next step in complication, Terry, is the monoalphabetic substitution. Just write a mixed alphabet under the normal (plaintext) one. To get a mixed alphabet you can put Scrabble tiles in a bag, shake it thoroughly, and pull the letters out one by one. Do this, because we people are notoriously bad at choosing random numbers or letters. The mixed alphabet is the secret key you share with your communications partner.

Example Key:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

L P G S Z M H A E O Q K V X R F Y B U T N I C J D W

To send a secret message, you just substitute each letter of the plaintext (in the top row) with the corresponding letter of the ciphertext (in the bottom row). To make it harder for any wannabe codebreakers, you should leave out any punctuation marks and especially the blanks between words. Instead group the letters of the coded message into groups of five. That way noone can see where the word boundaries are.

Decoding is done by substituting each ciphertext letter by the plaintext letter above it in the key. After that you can see where to put the blanks back in. Now decode this:-

UZGBZ TGRSZ CBETT ZXMRB TZBBD.

For decoding, you may find it easier to sort the two key lines given above so that the ciphertext key (bottom line) is in alphabetical order. Thus :-

Key sorted for decoding :

H R W Y I P C G V X L A F U J B K O D T S M Z N Q E

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

This kind of monoalphabetic substitution code can be broken (for longer messages than this example was) by doing a frequency analysis. Those are just fancy words, Terry, for counting how often each letter crops up. For English, the relative ranks of each of the letters is ETAOIN SHRDLU... etc. So if the codebreaker found that the most frequent code letter was an I, the next most frequent a T, the third most frequent an H, he/she would guess that I=E, T=T and H=A etc. Depending on the message, that may not be quite right, but near enough to guess the rest :-)

There is a simplified version of this monoalphabetic substitution widely used (especially in America) for codebreaking puzzles. To keep things simple they leave in the original punctuation and especially the blanks. The secret message is also usually a famous quotation and is given with the attribution of whoever said the line. Now try your hand at codebreaking on this secret cryptogram (it does NOT use the key shown above) :-

OH’P YSH HLBH O’Z BCKBOF HS FOA.

O NDPH FSY’H RBYH HS IA HLAKA RLAY OH LBMMAYP.

--- RSSFE BQQAY

If you haven't managed to break this code within (say) 15 minutes, then you may go read my method How to Solve Cryptograms. Don't go there yet, try it yourselves first :-)

Once you've mastered the method, here are three cryptograms for you to try to crack.

Just FYI: "ETAOIN SHRDLU..." is also the key sequence used on the top row of typesetting machines.

Copyright ^© Stu Savory on 10th March 2008 permalink Comments Email

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International Women's Day Pics for Machos;)

Copyright ^© Stu Savory on 8th March 2008 permalink Comments Email

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Next week's UK Budget 2008

Y ou've got a problem, Darling! The UK economy appears to me to be heading for its worst recession since 1992, or at the best for a mild stagflation.

The chancellor, Alistair Darling, has to cope with a society deep in debt, the over-heated housing market and a shaky financial sector, all while inflation is heading upside of 3% (earlier Gordon Brown had declared that under 2% was the British government's target). Pumping Fiat money into the market won't help in real terms.

Energy costs and food costs are driving inflation, as is the falling exchange rate (the Pound has lost 10% against the Euro since autumn 2007). Although the UK economy has been expanding by 3% in recent years, I guess that 2% is more likely this year; so it's slowing down there too. 1½ million fixed-interest mortgages expire this year and will need to be renewed at a higher interest rate. Or the dreaded word foreclosure :-(

With that expected inflation, the Old Lady of Threadneedle Street won't (can't?) follow the American's aggressive interest drop, lest they cause even more inflation. But expect another small (¼%) interest rate drop in april or may. Let's see first what Darling does in his budget on 12th of march. He'll be increasing taxes and throttling back on expenditures, you mark my words! State expenditure is running at 42% of the GNP already. Even if he cuts the expenditure expansion rate by half (ie. 2% instead of 4% under Labour so far) over the next 5 years, he'll only reduce that 42% to 41½% (which would be the lowest since 8 years). On the income side, the state currently takes 39.2% of GNP. Expect him to add 1% over the next 5 years. This would lead to the Brits suffering under their highest taxation rate for 24 years. All this just to keep the new-debt under 2.7% of GNP. And I doubt if he'll manage even that!

The slowing economy means less corporate taxes for Darling though, which is why he'll have to raise income tax :-( Now that is counterproductive of course, since it would slow the economy even more! So the UK government is between a (northern) rock and a hard place. I'm afraid my UK friends must expect a recession this year; it'll be more than just mild stagflation. Get out of Pounds and into Euros early, my UK mates!

Copyright ^© Stu Savory on 6th March 2008 permalink Comments Email

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More Mental Arithmetic Wizardry

S everal of you have written to say you enjoyed the piece I wrote on February 29th on taking cube roots in your head and have asked for more. Tim Brown tells me that some of my Maths pages, e.g On Squaring the Circle get listed by other maths fans in StumbleUpon which explains the sudden (but short-lived) surges of popularity they get (like 15,000 visitors in a week, then dribbling off to nothing).

But I do get interesting mails from some of the visitors, e.g. from Anshu, a 21 year old girl from India, who did undergraduate maths and is now studying cinematography. Inter alia, she looked at my Pythogoras theorem proof and has this to add. I quote :- "This is of Indian origin. By Bhaskara II in approximately 1185-1114 BC. Apparently no written proof was there and hence it wasn't considered clearly at first but was later accepted as probably the first proof of the pythogoras theorem though it was discovered seperately over the years in various other parts of the world. The proof itself consisted of the diagram where 'a' was in green, 'b' in blue and 'c' in red and below it there was one word written in Sanskrit (ancient indian language that is not in used while talking now, but which many still understand) that translated in english would mean BEHOLD!"

How about that! Half a millenium before Pythagorus. Thanks, Anshu!

And so, for you folks interested in more feats of mental arithmetic, I point you to a video on TED which shows Arthur Benjamin racing a team with pocket calculators to figure out multiple digit squares in his head, guessing birth days, and explaining what he does in real time (= thinking aloud). Go watch, learn, and enjoy :-)

Copyright ^© Stu Savory on 4th March 2008 permalink Comments Email

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