Friday, February 27, 2009
Painting by Numbers : XN :-)
Upon reflection, I seem to be framed . . .
For any non-mathematicians/computer geeks among you, let me explain :-
In the picture below, X is about one third. So X4 is about 1¼% of the original size.
Which is why the pictures above only go to depth 5 which is about 5 pixels across!
And for those of you into basic S-u-r-r-e-a-l-i-s-m, or on LSD or magic mushrooms, here's one using a Moebius Strip as a mirror, which can't possibly make you (two-)edgy ;-)
Mirror, Mirror, off the wall . . . ;-)
Wednesday, February 25, 2009
An odd way to get e
mrit, writing from India, asks "My calculator doesn't have an 'e' button. I can get 'PI' (nearly) by keying in 22/7, but what can I do to get 'e' ?"
Actually, Amrit, you would get a better approximation to PI by using 355/113, that's 7 digits of accuracy instead of just 3. To get 'e' you can combine the single digit odd numbers in decreasing order like this :- Take the 9, multiply it by 7 (=63), take the reciprocal (=1/63), multiply it by 5 (=5/63), take the square root [I'm assuming your calculator can take square roots, the CALC on your PC can], subtract the result from 3 and what you get is 1 approximation to 'e', accurate to the 7th digit also ;-)
Or of course, you could just memorise the decimals ;-)
Monday, February 23, 2009
Atheism......... At least it is not anthropomorphic ;-)
Notice that Dalek religion has much in common with any of our Abrahamistic ones...
"The God of the Old Testament is arguably the most unpleasant character in all fiction".
Saturday, February 21, 2009
Solar Power = Clean Power ?
Not at the generating end, it isn't! :-(
Friday, February 20, 2009
Gone , but by no means forgotten :-(
ush the lesser has been out of power for a month already, but we must nevertheless never forget the serial misuse of executive power, the wars started, the torture and incarceration, the corruption, the whole EVIL reign.
Let us hope that Obama's presidency will be more enlightened, open and honest.
Thursday, February 19, 2009
Doing big numbers
nother maths anecdote? No, two!
Back on Tuesday 10th, I mentioned Ackermann's Function A(m,n) which gets really big very quickly. Over at his blog Pergelator, Charles picked up the ball and ran with it, programming Ackermann's Function for his computer. As expected, his PC crashed with a stack overflow because Ackermann's Function is calculated using non-primitive recursion. It also soon delivers VERY big numbers, so Charles would not have got very far using only 32 bit integers. Even 64 bit integers wouldn't help, nor a four gigabyte stack size, because even A(4,2) would need a 65536 bit integer to be calculate correctly! Using floating point numbers is not the solution either, because the rounding/truncation combines with the recursive calculation to make nonsense of all the intermediate results. So if Charles wishes to proceed, he'll need an arbitrary precision arithmetic package (like, 20,000 digits of precision!). Really slow too!
All of which reminds me of my first encounter with REALLY big numbers, I think I was about 10 at the time. We'd learned the four basic arithmetic operations (+,-,*,/) to the teacher's satisfaction, so he introduce us to modulo and exponentiation. Now Modulo means just keeping the remainders after doing division, and Exponentiation is repeated multiplication. Thus he gave us 22=2*2=4 and 33=3*3*3=27 as examples.
Then we were shown that 34=81, but 43=only 64, because the exponents make the number bigger faster than a larger radix does. He then went on to nest exponents, and had us calculate 333=327=150094635296999121. Such stacked numbers get very big really quickly. For example, 999=9387,420,489 which has 369,693,100 digits!
Then he gave us the digits 1 through 9 and asked us to write the largest number we could. Donald, who had either been asleep, or had missed the point entirely, wrote 987654321 ;-) And dozy Brian - who often spelled his own name 'Brain' (sic!) - remembering that 34 > 43, wrote 123456789 ;-)
The rest of us noticed that one(sic!), used a radix of 2, writing 91 in the top line :-)
Sorry about the headline, which sounds like some kind of juvenile crap, but it is better than the first headline I used which was "How to get really big very quickly", which I rejected because it sounded like one of those Viagra spams or feel-thy p0rn pages;-)
Wednesday, February 18, 2009
Teach the Talented!We have a problem with the education systems here in Yurp. Instead of stretching the talented, which would benefit the economy more, we try to get the under-average to pull their socks up enough to reach the government defined MINIMAL education level.
And this is possible. There are some really talented kids out there who are (usually) being neglected by the state school system. Here is an example from the UK. Two seven-year-old twins have set a triple world record by becoming the youngest ever children to pass an A-level maths exam. Peter and Paula Imafidon both achieved a Grade D in AS-level maths designed for candidates of 17 years. Other high achieving pupils who have enrolled on the Excellence in Education Programme are Israel Nwesi from Greenwich, who wrote a GCSE exam paper aged six last year, and Joy Osariemen Monene of southeast London, who got a C in maths aged 10.
For my German-speaking readers, I have a book tip here.
Andreas Salcher has written an excellent book bearing the title "Der talentierte Schüler und seine Feinde" (= "The talented pupil and his enemies"), ISBN 3902404558, which I can thoroughly recommend. Dr. Andreas Salcher studied inter alia economics at Harvard, and in 1993 was co-founder of the first Austrian school for the highly talented. He writes from experience.
Who are the 'enemies'? We all are; even PISA is. We need to change the whole system as suggested by my bell-curve shown above. We need to amplify good teaching and good teachers. As parents we have a reponsibility for the upbringing of our children ourselves, and not just leave it to the (state-) schools. Salcher's book is about the Austrian school system, but our schools here in Germany are not vastly different.
If you are the German-speaking parent of an A+ schoolchild, please read this book and act on its suggestions. Not only to benefit your own children, but to push for change in the system to support talented children better, starting even in primary school.
So how do other countries' education systems compare? Well, the Russian secondary schools are going downhill too :-(
It always focussed on learning by rote in an almost encyclopaedic manner,
but over the last few years the exams are simple multiple choice ( 1 of only 3 answers!) tests,
introduced just 'to make the marking easier' :-(
In the UK, there are a couple of new approaches worth keeping an eye on, to see how they turn out. Monkseaton high school is experimenting with high intensity courses (aka force-feeding pupils' memories?). Meanwhile, in the USA, Professor Harry Brighouse (University of Wisconsin-Madison) has blogged some obvious comments about school improvement and the achievement gap, a blog article well worth reading by US parents.
Comments : My artistic friend Claudia points me to another book, one which contains a diatribe against incompetent/unprofessional/disinterested/helpless/overstressed/lazy ... teachers. Das Lehrerhasser Buch by Lotte Kühn, ISBN 3-426-77834-3. Reviews thereof are polarised, either for or against, few opinions in the middle ground. I haven't (yet) read it myself, and so can only pass on Claudia's tip on this paperback.
Tuesday, February 17, 2009
Pressure on the pound : visualising inflation :-(
Visualisation of a monthly decrease in real purchasing power :-(
Monday, February 16, 2009
Airfoil Icing :-(
There are reports in the press that last week's crash of a DH Dash 8 near Buffalo (NY) was due to icing. So today I'll explain in general about de-icing an airplane's wings.
It's not the weight of the ice on the wings that brings the plane down, it's that the ice-buildup destroys the airflow over the wings. And if one wing loses lift before the other (almost always the case), the plane will just spiral in :-(
To prevent ice-buildup planes have de-icing systems. On a jet, with its plentiful supply of heat, this will be done by passing hot air from the jet along the leading edge of
the wings. Propellor planes have inflatable rubber 'boots' along the leading edge of the wings, see topmost sketch of an airfoil cross-section; they are the black bits of the wings in the photo at the top.
In icing conditions - cold, moist air - ice deposits on the leading edge of the airfoil, see the second sketch.
The ice can build up quickly - as shown in sketch three - and the aircrew need to keep a permanent lookout for ice buildup. Usually an aircraft will have lights to illuminate the leading edges at night, so the crew can see any ice building on the wings.
Using fine judgement, the aircrew will let a little ice build up and then quickly inflate the rubber 'boots' pneumatically to crack the ice thus breaking it off the front of the leading edge, see sketch four. Small amounts of ice may remain on the top and bottom of the airfoil, causing some loss of lift, as shown. The 'boots' will need to be cycled often - depending on icing conditions - to keep the ice off the airfoil.
If the 'boots' are cycled too early, a thin ice sheet may be pushed out by the 'boot' and then re-freeze instead of breaking off and being blown away. The 'boots' are now totally ineffective and ice can build up in an uncontrolled manner, leading to loss of lift by the airfoil, in the worst case assymetrically, whereupon the airplane spirals in for the fatal crash :-(
The Dash 8 was flying in known severe icing conditions on approach to Buffalo.
Slowing down for the landing and lowering flaps may cause the airflow to be disrupted even earlier. This MAY have been the cause of the crash near Buffalo, I GUESS. We shall have to wait for the official accident report though, to know for sure.
If the runway is long enough - Buffalo has a mere 813 meters and no lights marking the ends of the runway :-( - it may be a better choice to leave the flaps up, keeping the speed up, and make a long landing, relying on reverse thrust to stop once down.
FWIW, the propellor is also an airfoil and will have electrical heating to keep it free of ice. The pitot tube and static ports will be heated electrically too so that speed and altitude information is kept always available. If these freeze up too, you are in a VERY difficult situation when flying in instrument conditions (as the Dash 8 was).
Saturday, February 14, 2009
I'm sure all our sympathies go out to those Australian families who lost their homes and belongings - indeed, some of them, their lives - in the ongoing firestorms there.
The very word firestorm rings a sad bell today, especially in Dresden. Back in WW2 'Bomber' Harris instigated an attack on the civilians of Dresden, beginning 21:45 of February 13th 1945 and continuing through the night into the 14th. Many tens of thousands civilians were burned, asphyxiated, or crushed under collapsing buildings. Harris saw this as merely revenge for Göring's Luftwaffe attack on Coventry, 1940.
Using Firestorms as a hook, let me recommend a great book to you. It is famed Kurt Vonnegut's SF novel "Slaughterhouse 5". The narrator begins the SF novel telling his connection to the Dresden bombing, why he is recording it, a self-description (of self and book). Slaughterhouse-Five is a commonly-censored book in the USA, frequently banned from American literature classes, removed from provincial school libraries, and struck from literary curricula, so it may be hard for you American blog-readers to get a copy. It is censored there because of its realism - Vonnegut has American soldiers behave as soldiers; they talk and swear and curse; his language is irreverent ( "The gun made a ripping sound like the opening of the zipper on the fly of God Almighty"); and the book depicts gays. In fact, it was one of the first literary acknowledgements that homosexual men, referred to in the novel as "fairies", were among the victims of the Nazi Holocaust, as were Roma and Sinti, the Shoah was not just about the Jews.
The fire-bombing of Dresden in World War II is the central event mentally affecting Billy Pilgrim, the protagonist. Vonnegut claims the firebombing killed 135,000 German civilians; he cites "The Destruction of Dresden", by David Irving, also worth reading.
Go read this SF novel by Vonnegut, it's a Firestorm for the mind! "Poo-tee-weet?"
Friday, February 13, 2009
(Street-)Fighting the recession! Go BUY STUFF !!
ow I am NOT at all an economist, nor do I play one on the stock market, so I have no well-thought-out idea how to save the economy :-(
But then, neither do the pundits, nor the banks or professionals!
Nowadays we have 'nanny state' Republicans supporting socialistic takeovers of banks and indeed partial nationalisation thereof, and Liberal Obama will be bailing out huge corporations. Overstretched credit for profligate spending - especially in the USA - is what got us into this US-housing/banking/credit-card mess in the first place, so is more-of-the-same going to help us? This question applies to all our economies.
But it seems to me, we could all help by buying stuff (but NOT on bad credit).
Anyway, I needed an excuse to buy yet another motorcycle, so that'll be my little contribution to propping up the economy, which has its own nonpolitical rules anyway. But which economy to prop up? Looking at the way that Sterling has been falling against the Euro recently, and with a twitch of patriotism, I decided that the British economy needed propping most (let the dollar and the yen look after themselves). Patronisingly altruist? Nah! It was sheer biker's hedonism that led me to choosing to order a 675cc, 106hp, 3 cylinder, white streetfighter, the Triumph Street Triple.
The wife and I took a couple of test rides last autumn on the 2008 model, making sure it was small enough for the wife to ride it solo too, and sporty enough for me. I'd wanted a bike 100 kilos lighter than my big tourer, a Yamaha FJR1300, which we'll be keeping for trips two-up and for the long trips (a Norway tour is planned for this year).
We ordered this bike back in December 2008 for delivery in March 2009 (that's just 2 weeks away :-) and it's been getting cheaper by the
Folks, if you too want to save the economy, it's your duty to go out and buy stuff!
Wednesday, February 11, 2009
WW2 Fighter Warbirdsy good motorcyclist friend and occasional blogreader Paul Gockel sent me these two photos taken in the UK (Duxford, or Biggin Hill?) I'm afraid I don't know who the photographer was, to duly credit him/her. Good shots though!
Our local German law forbids that I display a swastika on my website, which is why I have elided part of the tail from the Me109, so you have to use your imagination, OK?
The aircraft are kept in good flying condition :-;
and are demonstrated regularly ;-)
Tuesday, February 10, 2009
No Boni ? :-(A blogreader who works in the financial sector (Deutsche Bank) has sent me his own bankers' bus slogan in response to my call for your bus slogans on the 5th of february.
Lemme see now, if I remember correctly, the boni for the very top brass at the Deutsche Bank depend upon a deep evaluation of Ackermann's function ;-)
Even if we only plug in REALLY small numbers such as :-
You know, Obama may have a point :-)
Monday, February 9, 2009
Missing the Gold :-(logreader James (USA) thanked me "for the moving piece on failed ambition ( February 4th)" and sent me these 2 photos of his own 2 failed ambitions ;-)
Yeah, right, James! You, me and about 6 ¾ BILLION other people in this world....
Sunday, February 8, 2009
The One True Church's® Obsession with Sex ;-)
here has been yet another report in the press about a Catholic priest fellating the altarboys. So this mouth-watering(!) scandal was discussed down at the pub, where Johannes asked what causes the One True Church's® obsession with sex? Maria (sic!) suggested it was to do with the requirement for celibacy which caused suppressed sexual urges. Big Peter (sic!) thought it was all an oral tradition ;-) After we stopped falling about laughing, I pointed out that there is actually a religious background. After all, Leviticus 21 : 16-20 (New International Version) forbids anyone from approaching the altar "who has festering or running sores or damaged testicles". And therefore the priests are required by their god to make regular and stiff checks of the testicles of anyone wanting to go near the altar, whether they be brother priests or able young altarboys, and ensure that their testicles come up fully functional ;-)
Mind you, this is the same Leviticus 21 which (in verse 5) forbids the monks' tonsures "They shall not make baldness upon their head..." which they don't take so seriously.
In this same Leviticus 21, priests are not actually forbidden from marrying (a decent woman), Verse 7 only forbids recycling : "They shall not take a wife that is a whore, or profane; neither shall they take a woman put away from her husband" ;-) In fact the priests are required to marry, verse 13 says "He shall take a wife in her virginity*", thus contradicting the requirement for celibacy which Maria had mentioned.
But at least necrophilia is forbidden (in verse 11) " Neither shall he go in to any dead body". I wonder why the author thought it necessary to add that grave rider ? ;-)
Comments(1) from Suzy(F); see this report on Sex Crimes and the Vatican.
Saturday, February 7, 2009
"Scramble : Go get 'em!" : 50 years ago...
Fifty years ago (hence excuse the quality of the photo) the UK's English Electric Lightning interceptor went operational. Oh boy , what a fun hot ship that was :-)
In British Airways trials in April 1985, Concorde was offered as a Mach 2+ intercept target for NATO fighters. Lightning XR749, flown by Mike Hale, was scrambled. Within 500 meters she was off the runway, wheels up, and at 50 feet. Supersonic over the airfield hedge and on full re-heat, she passed 36,000 feet after only 2 ½ minutes. Concorde was going at over Mach 2 at over 60,000 feet. The Lightning caught and overtook her in a tailchase! No other NATO fighter , including F-15s, F-16s, F-14s, Mirages, F-104s managed to do that. The Lightning's initial rate of climb was 50,000 ft per minute (15 km/min). The contemporary Mirage IIIE climbed initially at 30,000 ft/min (9 km/min), the MiG-21 managed 36,090 ft/min (11 km/min). The recent Tornado F3 does 43,000 ft/min (13 km/min). Even the Eurofighter is slower.
In 1984, during a major NATO exercise, the Americans sent a U-2 over at 80,000+ feet to keep an eye on things. Again, Mike Hale scrambled his Lightning. Records show that Hale climbed to 88,000 ft (26,800 m) in his Lightning F3 XR749 as he intercepted the surprised CIA pilot ;-) Must have been in coffin-corner for both of them! Similarly, Brian Carroll took a Lightning F53 up to 87,300 feet on a hot day over Saudi Arabia.
Disadvantages? A tiny, cramped, cockpit (see photo); very short-range radar (30 miles only, if I remember correctly); and minimal armament - being two Firestreak missiles (only a 4 mile range and not much faster than the Lightning) and two Aden cannon, fer Gawd's sake! You had to be careful not to overtake your own Mach 2.25 bullets!
Friday, February 6, 2009
Geocaching 102 : the Internet view of Geocachinghen I introduced you to the hobby of Geocaching (January 21st, 2009), I just told you about the physical part of finding caches. I omitted to outline the Internet database views provided i.a. by Geocaching.com. So here goes :-
When you find a cache, you sign its logbook there and then. But you (can) also log each find in their Internet database. After you have found a few, your personal logroll will look something like mine. Smileys indicate caches found, frownies not found.
After I'd found about a dozen, I decided to hide my own first cache (MMIX-A). I knew of an attractive outlook platform on the side of a steeply wooded valley side which overlooks our village. There is a shrine there and several ancient trees, a good place to hide a cache and attractive to visitors. Using my GPS, I took the coordinates of the hide and entered them in the Internet database; said entry looks like this :-
To these bare coordinates, you can add other useful notes. Mine looked like this :-
Barely 3 days later it had been found (congratulations OpaTheo) and within a week the cache's find-log had half a dozen entries and looked like this :-
As you see, finders can write their own comments about the cache and and any difficulties encountered finding (or NOT finding) it. I'd made my first one very easy, and in my cache notes, I had marked its attributes as 'not accessible for wheelchairs'.
And since in the initial cache load I'd put in a ticket for a free coffee for the first-to-find (FTF), I'm waiting for OpaTheo to show up. He has found some 1120 caches already, and so will doubtless be able to give me a lot of tips from his experience :-)
In the meantime, I'm thinking of places to place my second cache (MMIX-B). My main aim is to show other geocachers various beautiful places in my local area, this hermit monk's tiny church with a single room house attached, for example. Neat, huh?
Off the beaten track, in beautiful woods, but this neat place is wheelchair accessible too, to let the few disabled geocachers play also. However, checking against the map of the existing caches, I found that someone else has had basically the same idea. Oh well, just have to come up with yet another idea, I guess, one with a long hike in and rather difficult terrain? :evilgrin: :-)
Thursday, February 5, 2009
My Atheist Bus Slogan ;-)
theist bus slogans have been in the news lately, in London, Toronto etc. Now you can make your own Atheist Bus Slogan, over here. If you do blog yours, send me a link for inclusion here please. It's safe, 'cos Hell don't exist either.
Wednesday, February 4, 2009
Too old, dammit! --- Just! - Too! - Damned! - Old! :-(
Per spera ad astra
Ever since I was an impressionable little boy I've wanted to be a space-/rocket-jockey.
It all started back in 1950, when I was six years old. A new boys' comic came out in the UK, upon which I splurged my pocket money. It was called Eagle and my favourite comic strip therein was Dan Dare, a post WW2 RAF-type hero, fighting the evil ones of the solar system (such as The Mekon). Impressionable little me wanted to do that too. From 1951 to 1956 it also was transmitted nightly by Radio Luxemburg as a radio series, but I never could identify with the voices of the actors playing the parts :-(
A much better radio series was the 1953-54 BBC's Journey into Space. In the UK it was the last radio programme to attract a bigger evening audience than television. At ages 9 & 10, I was one of those avid listeners, positively devouring those first clunky sound effects. Shhhh-T-clunk, the sound of a closing airlock, I can still hear it to this day ;-)
Then, on the early evening of October 4th 1957 - I was 13 - father took me out onto a nearby hillock. It was a clear evening, and there were more stars to be seen back then (less light pollution). Suddenly, in all its unexpected glory, Sputnik came fleeting by, bright in reflected sunlight. I was hooked! I wanted to be a space traveller too!
I even considered becoming a RAF cadet, because in a book I had read (Space Cadet), the way to space was through an Air Force career. Be a better pilot and move up ;-) Sensibly, my teachers and parents put a stop to that idea, insisting "You can do better than that!" (nagging words which were to become the bane of my young life) and insisted I study for university. But when Gagarin did his first 3 orbits on 12th April 1961 - I was still 16 - I (secretly?) resolved to read Physics at university so that I would at least have a chance to qualify as a mission specialist. After graduation, I went to work for a UK defence company so that I could gain some experience with rockets.
But "the best laid plans of mice and men gang oft a'gley" and I ended up geekily
programming guidance systems
for Navy guided missiles and homing torpedoes.
And so it came about that on 20th July 1969 (I was 25) when everyone else was watching Neil Armstrong
live on TV take that one small step, I was on a submarine hiding somewhere below the Arctic ice,
most probably in a place we should not have been (but the captain didn't tell us ;-)
And so,sadly, I missed seeing the giant step live :-(
But I did learn to fly aeroplanes, since it still seemed that all the astronauts and cosmonauts were also qualified pilots. I went on to get commercial-, instrument- and multi-engine ratings and to qualify as a flying instructor. Most important (to me) was the aerobatic instructor qualification, to get me used to pulling 3,4,5,6 or more Gees.
Life progressed, there were no opportunities for UK astronauts, so I "forgot about it" and I worked instead in the IT industry, usually on R&D projects. It was there in the late 1980s that I met German astronaut Reinhard Furrer and was able to have a couple of long chats with him. A very motivating person, as is ESA astronaut Thomas Reiter whom I only met for a shake-hands. I've also had the opportunity of some talks with MIR cosmonaut Viktor Afanasyev, veteran of three long-duration missions. He has logged over 545 days in space, and 7 EVAs totaling 38.55 hours. Also a test pilot. I got a short chat too with Sergei Krikalev, veteran of six space flights. He has spent more time in space than any other human being, 803 days, 9 hours , 39 minutes in space. Had it not been for the collapse of the Soviet Union, Sergei might well have been the first man on Mars! He too is an acrobatic pilot (a good qualification then ;-)
All of these astronauts and cosmonauts are enthusiastic men, technically well educated and super-dedicated. But they are in a different league altogether, you or I cannot compete :-( I would have liked to meet , but missed, Yuri Baturin. Baturin was also a cosmonaut who graduated from the Moscow Institute of Physics and Technology in 1973 and is a former head of National Security (what kind of qualification is that ???). Well, if I couldn't fly into space myself, I thought, at least I have had first-hand accounts from several that did. That will have to suffice, I thought, albeit sadly :-)
And then along came Sir Richard Branson with Virgin Galactic and commercial manned space-travel! For a mere $200,000 you can have a sub-orbital lob to an altitude of 110 kms, including 6 minutes of weightlessness, starting in 2010 AD. That's next year already! Except that the waiting list is already looooonnggg, and the fact that I would have to sell the house (or my soul), that childhood dream might become realisable!
Per spera ad astra indeed :-)
But since a few weeks I've been suffering from acute lower back pain, not a slipped disc, but lumbago. But sciatica, lower back pain, and lumbago all mean that sufferers can no longer pull the Gees encountered in space flight, even sub-orbital lobs. So I have to say goodbye to the dream that Richard Branson had resurrected for me :-(
If you hear me wailing, it is not pain. It is my disappointment and frustration at my being too old and decrepit, dammit! --- Just! - Too! - Damned! - Old!!! :-( :-(
Tuesday, February 3, 2009
Jewish insurance, already ;-)
Not so ridiculous as the Two Ronnies thought when they did this TV sketch ;
Monday, February 2, 2009
Check Digitschoolboy blogreader Art, (USA), having read my pages on divisibility, has asked for an article on Check-Digits. So I've waited a month - just to make sure that I wasn't doing his homework for him - now here is the requested article, Art.
A check digit is a form of redundancy check used for error detection, a single digit computed from the other digits of the number, and usually placed at the end of the number. Now almost 80% of the errors made when transcribing an identification number are single digit errors. Examples? Someone writes a 3 when 'copying' an 8. Or omits a digit, especially when there are several identical digits together, e.g. writing '44444' istead of '444444'. To catch this type of error, just add up the digits of the identification number, appending a check-digit to make the whole divisible by 9. Thus the digits of 122333677 add up to 34, adding 2 gives 36, which is divisible by 9.
122333677 needs an appended 2 to make the sum of its digits divisible by 9. This digit 2 is the checksum.Now let's say the 6 was omitted. The total (including the check-digit) would be 30, not divisible by 9, and so the error would be detected. If instead, the central 3 had been written as 8, the total would be 41 not divisible by 9, and so the error would be detected again. Only an omitted 9 would not be detected by this elementary checksum.
However, over 10% of the errors made when transcribing an identification number are transpositions of adjacent digits, e.g. copying 42 as 24. The sum modulo 9 method shown above would not catch these. But you could go for divisibility by 11, writing an X if the remainder is 10. Just add up the digits in the even positions and subtract the digits in the odd positions. Thus 198376 gives 9+3+6 = 18 - (1+8+7) = 2 which needs a 9 to make it divisible by 11. Thus the whole ID would be 1983769. If the 8 and the 3 were swapped (=193876 with checkdigit 9), then 9+8+6 = 23 -(1+3+7) = 12, not divisible by 11, and the swap-error has been detected.
Inexplicably, the American social security numbers (SSN) don't use a checkdigit scheme
But if you look at any of your books, Art, they will generally have an ISBN number. ISBN numbers have 10 digits. The tenth digit is the check digit, calculated like this :- 10d1 + 9d2 + 8d3 + 7d4 + 6d5 + 5d6 + 4d7 + 3d8 + 2d9 + d10 = 0 (modulo 11) However, if the check digit d10 is 10, the letter X is used.
The ISBN scheme catches all single digit and all transpositions of adjacent digit errors. However, only works for identification numbers that have 10 digits in them. Recently, a 13-digit ISBN variant has been introduced whose checksum works differently. See if you can work out how the 13-digit ISBN variant works, Art :-)
The EAN (European Article Number) barcode on items you buy at the supermarket also contains a checksum. The check digit is computed modulo 10, where the weights in the checksum calculation alternate 1 and 3. Since the weights are prime relative to 10 the EAN finds all single digit errors. But since the difference of consecutive weights is even, the EAN does not find all adjacent transposition errors :-(
Belgian bank account numbers use modulo 97 check digits. Credit card account numbers use modulo 10 check digits,via Luhn's algorithm which catches any single-digit error, as well as almost all transpositions of adjacent digits except transposition of the two-digit sequence 09 to 90 (or 90 to 09).
And then there was that motorist in Prague who gave me the finger for sounding my horn at him as he dozed at a green traffic light; AFAIK, that too was a Czeck digit ;-)
Charmaine (USA) has suggested I change my 'About' text to reflect the fact that Dubya is no longer presnit. OK, babe, I've just done that for you; see sidebar :-)
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The Googling ;-)
Back out :-(
A bit on the side
Financial ripoff schemes
Six years of blogging :-)
The God of the Old Testament is arguably the most unpleasant character in all fiction.
Blogs I co-author
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