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Eunoia, who is a grumpy, overeducated, facetious, multilingual ex-pat Scot, blatantly opinionated, old (1944-vintage), amateur cryptologist, computer consultant, atheist, flying instructor, bulldog-lover, Beetle-driver, textbook-writer, long-distance biker, geocacher and blogger living in the foothills south of the northern German plains. Not too shy to reveal his true name or even whereabouts, he blogs his opinions, and humour and rants irregularly. Stubbornly he clings to his beliefs, e.g. that Faith does not give answers, it only prevents you doing any goddamn questioning. You are as atheist as he is. When you understand why you don't believe in all the other gods, you will know why he does not believe in yours :-) Oh, and he also has a neat English Bulldog bitch 'Frieda'.

And her big son 'Kosmo'.

Some of my bikes

My Crypto Pages

My Maths Pages

Friday, November 28, 2014

Smell my nuts!

But of course, dear blogreaders, you cannot. If only because the internet does not have an olfactory channel (yet), so we're restricted to audiovisual communication. These walnuts are small but tasty this year, slightly oily and with a heavenly fresh scent, not like the american walnuts the local supermarket sells, dry and wrinkly, like Grandpa Walnuts ;-)

Imagine if we did have an olfactory channel though. Then government websites would be phishy, or maybe the porn sites would be too :-( neither would be in good taste (sweetness, sourness, saltiness, bitterness, or umami). For smells, the primary odors are Musky- perfumes/aftershave, Putrid- rotten eggs, Pungent- vinegar, Camphoraceous- mothballs, Ethereal- dry cleaning fluid, Floral- roses, Pepperminty- mint gum, I've learned. But I'm not sure how these would look on a mass spectrogram, certainly not simple. Any other smells could be made by combining these in various relative concentrations, it is claimed. But odour chemistry is so complex that it took until 2004 for a Nobel Prize to be awarded for work that teased out the nature of smell and the remarkable combinatorial mechanism by which the human nose senses odour.

So when someone suggests we should perhaps be communicating with ET using odours instead of audiovisual messages, we would need to be sure we were not sending Ethyl Mercaptan (C2H5SH), whoever she is ;-)

This post inspired by the use of a so-called network sniffer, made in Japan :-)

Comments (3) :
Doug (Canada) wrote "That's so rotten, you bad egg :)" Methinks it comes from playing too much Pong ;-)
Cop Car (USA) wrote " FYI, in the States, one may find TWO kinds of walnuts: 1) English - thin-shelled, lightly colored shell and meat, mildly-flavored nuts, and 2) black - native to the USA, thick-shelled, dark-colored shell and meat, strongly-flavored nuts. We have several old, black walnut trees growing in our woods; but, I've never figured out how to get the tough outer shell off of the nut; so, if I want black walnut meats, I buy them. One of my favorite ice creams is black walnut. has a photo of a couple of black walnuts. I should have included this excerpt from the web site referenced below (I added the underline to the text) :-
Black Walnuts have a bold and rich flavor but they don't crack open easily like English walnuts. It is hard work and our best advice is to let us do it for you. But for those who enjoy the challenge, here are some helpful hints to get the nutmeat out and into your favorite recipes: Gather the nuts after they fall during late autumn. Pick them up by hand or by using our "Nut Wizard," a handy nut-gathering tool. The Nut Wizard has a long handle with a barrel-like end that, when rolled over black walnuts, picks them up like magic! Spread the nuts onto pavement after gathering them and run over them with your car 'till the hull is pulled off. The nuts are covered with a greenish outer hull that should be removed so the nutmeat isn't spoiled. While in your vehicle, make sure to rev the engine and pretend you're in a monster truck crushing cars and not black walnuts. This does not help in any way but can be entertaining for kids and confuses the squirrels. Spread the nuts on a screen in a covered area with good ventilation. A carport works well. This dries the nuts and makes cracking much easier and cleaner. Crack the nuts with a hammer or strong nutcracker. Watch for flying shell pieces! To ease this tiresome and messy process we sell a large steel nutcracker designed for cracking black walnuts. Great for all kinds of nuts as well, this cracker is freestanding and easy to use. Pick out the nutmeat using a nut hook or other device. It is difficult but worth it, kind of like digging for buried nutty treasure. "
I'll get me some, to compare taste with ours :-)
David (NY,NY) jokes "You asked who Ethyl Mercaptan is : she is the wife of that military guy from poetry class, Captan Mercaptan ;-)" GROAN!

Thursday, November 27, 2014

Ferguson coincidence?

Is it just coincidence or divine intervention that "Darren Wilson" is an anagram of "Insaner World" ? That'd be AmeriKKKa :-(

Comments (1) :
Cop Car - who knows I'm an Atheist - wrote "I will give you an iron-clad, money-back guarantee that it is, indeed, just a coincidence, Stu." That's only because "iron clad money back" is an anagram of "Balanced Mock Irony" ;-)

Wednesday, November 26, 2014

Testing Prime

We buy a lot of books etc from but/thus get a lot of advertising from them (in German). The newest said "Test Prime 2860486313" wherein they wanted me to try out their premium service (aka Prime) and sent me a ten digit password or lottery number. However my mathematical brain interpreted "Test Prime 2860486313" as asking me to check whether 2860486313 is a prime number! It is :-)

How do you go about checking whether a number N is prime? Well you can use the Sieve of Eratosthenes but that gets big for an N with 10 digits. Prime sieves are almost always faster, but you can do trial divisions by all the primes up to the square root of the ten digit number, in this case 53483. There are more efficient methods, e.g. Sieve of Atkin but these are not widely known.

There is also another (highly inefficient) way I know to see if N is prime. This is something that Pergelator might like to try out in one of his famous spreadsheets. Except that it does need really high precision :-

A number N is prime if and only if factorial(N-1) modulo(N) = -1 .

Bet y'all didn't know that! :-)

Somebody is bound to ask how come we have a negative remainder. Well, we're working with modulo arithmetic, so -1 is the same as the positive remainder N-1, OK? E.g, 6 modulo 7 = -1 too.

The proof tree has four branches, 1) with N=a*b, 2) with N=c2, then 3) special case with c=2, and 4) where N is prime. In case 1, the remainder is obviously zero (because both a and b are factors in factorial(N-1)). Similarly in case 2, it is obviously zero, in case 3 the remainder is 2 by trial. But case 4 is harder to prove. Try it. Hints : You will need to use Fermat's little theorem, the fact that a factorial is a field and that multiplication is commutative.

USA blogreaders have the whole of the Thanksgiving weekend to think about this and come up with part 4 of the proof, except that on friday they'll all probably get blacked out ;-)

This post "inspired" by Amazon Prime, to whom no thanks ;-)

Comments (2) :
Jenny (Ibiza) asks rhetorically "Is there anything you can't prove?" Thanks for the implicit compliment, but yes, lots of stuff. I can't even understand Wiles' proof of Fermat's last theorem, nor Perelman's proof of the Poincare conjecture. We all have our blind spots. I remember when Freeman Dyson - a famous professor at Princeton IAS - wrote in 2005 that he believes, but cannot prove, that there is no power of two, whose digits reversed, are simultaneously a power of five. But within seconds I gave him the counter example 20=50=1 and also said that it is provably the only counterexample! My insight - his blind spot - was to count to a base other than 10. Counting to base 5, any power of 5 is a 1 followed by some number X of zeroes. Reversing the digits gives you X leading zeroes and the trailing 1. The only power of 2 which is 1 is 20. Therefore this is the only counterexample :-)
Pergelator (USA) wrote "I don't understand how you can get a negative number from modulo arithmetic, unless you start with a negative number. I thought X % Y (C programming language notation) always gave you a value in the range 0..(Y-1)" I explained that in the blog. N-1 modulo N can be written as N-1 AND as -1 :-) Use N-1 if you're more comfortable with a positive remainder.

Monday, November 24, 2014

A bang-on book :-)

Those of you who have ever worked in a (UK) defence research (nuclear) establishment will have a severe attack of deja vu when reading this hilarious book; I know I did :-)

David Langford, the author, must have worked in one too because he can caricature the people, the WW2 buildings, the petty burocracy, the "security"-men, the rule-breakers and the sheer humdrum day-to-day life of military R&D so well.

You will emerge from reading this tomb tome in a gentle radioactive glow of delight, stockpiled with anecdotes that will raise the hairs on your neck in a chain reaction of sniggers and outright unclassified laughs from the pits :-) Although it says $17.95 on the cover, I paid less via Amazon, then read it all in one 6 hour session. Very funny indeed, but scary for some maybe :-)

ISBN : 1-59224-125-5

Comments (5) :
Cop Car (USA) wrote " Is there a pun there, somewhere? I'll check to see if I can get the book through Inter-Library Loan. If not, I'll check online for purchase. Thanks for the review and for not (graphite) piling it on too deeply." Pun on 'leaky'? yes, radioactivity leaving the site.
Doug (Canada) gave this hint : " I have a sneaking suspicion you'll really like this site . " ´My word! You know me well! I'll certainly keep my eye on it ;-)
Kees (NL) sent a link noting "You would have enjoyed saturday's Blind Book party in Amsterdam :-)" P'raps. If there is one locally, I shall try to attend :-)
DeeDee (USA) quips bitterly "Here's a worse horror story : Dick Cheney to be the new SecDef!" Really? I thought it would be Darren Wilson :-(
Jenny (Ibiza) asks "So what are you reading this week?" Be patient! Next book review coming on monday, 1st december.

Friday, November 21, 2014

Murphy multitasks :-(

Sometimes when Fate has it in for you, she gets Murphy to multitask and all the crap happens on the same day. Like early last week.

The heating boiler in the cellar went on strike, error code 3, whatever that is. On the bright side, after a cold night, the plumber came first thing next morning (I know why I always tip him generously). Almost simultaneously, the decade-old ground-water pump failed and went into a nerve-wracking permanent alarm failsafe beep mode. Luckily, the plumber was still here :-)

Then our trusty household help got long-term ill and has sadly quit, so I'm looking for candidates for next year while wishing her a recovery soon.

The dark areas on the top of my head and upper left thigh turned out to be skin cancer, so I had to get them removed. The clinic burned/froze the ones on my skull off with liquid nitrogen (almost painlessly) but had to cut a chunk out of my thigh, so no bicycling for a month till the scabs fall off :-( Nervously waiting for the histology of the bits they cut out to see if they got it all out.

Large medical bill for my previous hospital stay, with more to come from the skin-cancer clinic. So tight purse strings for a while. OTOH, the price of heating oil for the forthcoming winter is at an all-time low since 2010 :-)

My car key fell apart, the blade separating from the handle. Turns out that welding an old large coin to the blade as a substitute handle doesn't work, because the original handle contains a transponder for the immobilizer and has to snug up to the lock to allow engine starting. That was something I just learnt :-( New keys cost upward of $100 including transponder handles :-(

Some spammer used my Email address a while back so some spamfilters now regard e.g. my comments on your blogs as spam and remove them (so reported by Hattie (Hawaii) and by Cop Car and by Ed (all USA)). Finally, my own spamfilter failed, due to overflow. So I'll have to recalibrate it.

After the favourable revues (and hype) for the movie Interstellar I went to the cinema thursday night to see it. Well, the special effects were really GOOD and they must have had a consulting physicist, but the plot was too full of Hollywood bathos and the film was so long-winded and slow at times that I thought I was suffering from relativistic time dilation myself :-( Making no spoilers, suffice it to say that on the way home the car stereo was playing Pink Floyd's A momentary lapse of reason ;-)

Still, all just first-world problems I suppose, so I shall stop complaining and just get on with life :-) Expect me back to merry-blogging next post :-)

Comments (6) :
Cop Car (USA) wrote " You really have been having a time of it, lately, Stu. From experience I can tell you that having your body removed, fractionally, is a heckuva weight-loss program. Let's hope all of your margins turn out to be "clear". P.S. I really don't know why TypePad treats your comments as spam. I've known others whose email has been hacked, sending out spurious emails by the dozens; but, AFAIK, they don't get black-listed." For my sins? ;-)
Cop Car (USA) replied " We may do lots of wrong; but, can an Atheist "sin"? " In the eyes of a religious beholder, yes. The beholder defines what is sin, indeed for that matter, what is right and wrong. For example, our politically overcorrect Ministry of the Interior has just produced this gem : "Muslims living in Germany who receive at the end of the year the special payment, a so-called "Xmas bonus", should not feel hurt in their religious feelings." So change the name of the bonus??? Done correctly, right and wrong are merely Darwinian survival rules for the species, surely?
Jenny (Ibiza) asks "Does your leg hurt? When do you get the biopsy results?" Yes, usual post-OP wound pain. Results coming next friday I'm told.
Ed (USA) suggests supergluing the key blade back onto the old handle.
John (UK) asks "So what's the status now?" Heating works, pump works, new household-help signed up to start 1/1/2015, biopsy results not coming until friday, 2000 liter heating oil purchased, sharing SWMBO's key, my spam filter reset, and eagerly awaiting "The Imitation Game" at the cinema next month. So, fighting back Murphy on all fronts, if I may say so without hubris. Pierre (F) asks "OT, but why do you always include our nationalities after our names in your blog-comments?" To give other blog-readers info about the cultural background from which you write, which MAY be relevant????

Wednesday, November 19, 2014

Illegitimi non carborundum

My friend Frank and I rode south to the Alps in august, stopping over in Rothenburg-ob-der-Tauber on the 2nd, where I got this parking ticket (see left). Frank got a similar one too. This pissed us off enormously, because we had both paid a parking fee and displayed the receipt exactly as demanded on the parking fee machine :-(

Rothenburg-ob-der-Tauber is a medieval walled town which lives from tourism. For this reason almost all the parking lots are outside the town walls, so that tourists get an internal view of the town as it might have been several hundred years ago, without any modern traffic.

But I knew from previous visits that there is one small hidden square - right in front of our hotel - where you can park in the town centre. Parking there used to be free but as we found out the town now charges for parking there. Squeeze the tourists right? Their only source of income. Clever, huh? :-(

So Frank and I inspected the parking fee machine which turned out only to have a tarif for cars (see photo below). So logically the parking for our motorcycles should have been free if the town is too stupid to have a tarif for motorcycles. However the receptionist at our hotel said the traffic wardens would give us a ticket if we didn't pay the car fee :-(

So - reluctantly - we each paid a car fee and then had to park both bikes into one car slot as there was only one available, thus effectively doubling the town's profit :-( As demanded by the text on the machine (see bottom line of the photo above) we displayed the receipts behind our windscreens although putting them in our transparently-topped tank bags would have been more sensible on this rainy day. But the town hadn't thought of this possibility :-(

When we came back from our evening stroll through the old town, we had got the parking ticket shown at the top of this post :-( Furious, I took a photo of my parking receipt, wet, but still legible behind my windscreen. See snapshot below, which plainly shows we had paid until 9:28 the following morning!

Not only that, the parking ticket als claims my bike is black. But it is white, they don't come any whiter, as you can see in the photo below.

Three weeks later, a summons came in the post that we should pay the €10 fine. NO WAY!!! So I wrote a furious letter, showing the photographic evidence given above and citing two witnesses that we had paid at the machine. I further questioned the traffic warden's suitablity as a witness, given that she could not tell black from white, nor could she see the receipt on plain display EXACTLY where the text on the machine demanded that it be displayed. I then went back and deleted all the swear words, merely leaving the heavy sarcasm.

A week later we got an unsigned reply stating that the summons had been withdrawn :-) The town wouldn't have had a leg to stand on in court :-)

So, what do we learn from this? It's always good to have a camera with you to document evidence. A mobile phone camera will do. Keeps 'em honest!

BTW: Illegitimi non carborundum is ostensibly a mock-Latin aphorism meaning "Don't let the bastards grind you down" :-) Wrong! The actual latin word for Bastard is spurius, which is most probably why this is such a numinous & spurious blogpost ;-)

Comments (2) :
Klaus (Alaska) catches my typo "You must have been really upset about that ticket you received in Rothenburg, as a revenge you spelled Rothenburg wrong in your blog "Rotenburg", I think it sounds even better without the "h" because the name came from all the red roofs and if you scratch the "n" than it even sounds better in German "rote Burg" or "Roteburg" " Told you it was beyond comprehension (=numinous); anyway, spelling is not my 4tay. I'll go back and put all the Hs in right now :-)
Rhea (currently in Rome) opined "She really blew it - and your mind ;-)" Indeed! And my cool too :-(

Monday, November 17, 2014

Astrostump :-)

Recently the cherry tree in our back garden gave up the ghost. No cherries, leaves fell off, and the whole tree started leaning towards the house. Time to chop it down. So I got the OK from the local council (everything has a burocratic regulation here in Germany) and got a professional tree-feller to do the work. He climbed the tree upto the highest safe branch, fixed his abseiling gear there, abseiled down and started lopping off branches piecewise from the bottom up. That way, falling branch pieces land on the ground, not on lower branches. Then, back up at the top of the trunk, he moved the abseil hook down 6 feet at a time and lopped off the trunk top-down. Lastly, take the sawdust tarpaulin off the lawn. Neat :-)

I'd decided to leave the roots in the ground rather than dig up half the lawn and had him leave a stump at knee height. Then I rubbed plenty of salt into the stump so that it won't rot away and now I have my very own astro-stump. I can place my small portable astronomical telescope, Dobson-mounted, on the stump and now sit or lie on the garden lounger to do my star-gazing :-)

And in the summer, for garden parties, we can place the top lid off an old wine barrel on the stump and, hey-presto, we have a neat table for the snacks and bottles. The untreated lid even adds a wine aroma to the garden party :-)

Now I'm sure someone will ask "Why don't you just use a bigger telescope and get more magnification too?". This little one has a 3 inch aperture and so the maximum useful magnification is 3*30 = 90. But being so small it cools down to usability within 2 minutes when taken outside. The 8 inch aperture scope could optimally give 8*30=240 magnification but the seeing is rarely that good. And it takes ¾ hour to cool down when taken outside. Plus, it is only semi-portable. I have to take it down into 4 parts to get it in the car. This little one is really portable and so suitable for spontaneous use.

Neither gives the resolution needed to achieve these professional NASA shots.

Jupiter shown with its moon Ganymede transiting the Red Spot storm.

Comments (8) :
Paula (D) wrote "See also Cheeseburger here ;-)" Nice link, thanks!
Jenny (Ibiza) also has a YouTube link about tree-felling ;-)
Claire (IRL) asks "What are the 4 pieces of the larger scope and how big are they to fit in the car?`" The scope has an 8 inch aperture tube, 4ft. long, which fits across the back seat. The Dobson mount fits in the boot (=trunk), as do the finderscope and the eyepieces. Drive through the cold night well wrapped up and with the heater OFF to keep the main mirror cool :-(
Pergolater (USA) has his own cherry tree memories :-)
Cop Car (USA) wrote " Good grief, Stu. With all of the complaints about the regs (parking and tree lopping) in your part of the world, I'm surprised that you don't find somewhere that is more to your liking! BTW: Around here, when a tree is taken out, one may pay the arborist a fee to grind out the stump. It takes a few minutes and a few dollars; but, planting of a replacement tree (or other vegetation) can commence immediately. When I am the one who cuts down the tree or trees (such as the other day when I sawed down four trees - the largest of which was about 15" Diameter), I leave the stump(s). I use all the energy that I have just getting the trees sawed down and the carcass sawed into lengths/pieces small enough for me to woman-handle them back to a brush pile in the woods. The birds love the brush piles!" I'm going through a grumpy old man phase at the moment, Murphy struck several times on the same day :-(
Hattie (Hawaii) wrote (on her blog, 'cos the mails to me failed) " Hi, Stu! Your blog has been especially lively of late. I really like your cherry tree stump solution. [He's making a table out of it.] I'm a big fan of figuring out how to use things that are around instead of going out and buying more stuff! I'll probably put one more post up about the Seattle Museum of Flight. The lava seems stalled for now but I'm wary. Glad I don't live out there in the flow path. Take care." Looking forward to the Seattle Museum of Flight post :-)
Claire (IRL) asks "What eyepieces do you have for the little scope?" The main mirror has only a 300mm focal length, so the 20mm Plössl gives a wide field of view with only 15x magnification. The other one is a 4mm Plössl, with 75x magnification. OK for the moon and planets.
John (UK) questions "The photo has you stargazing in the daytime???" Sure, you can see the moon and Jupiter etc in daylight if you know where to look:-)

Sunday, November 16, 2014

RIP Alexander Grothendieck

Genial mathematician Alexander Grothendieck has died, aged 86. His speciality was Algebraic Geometry, for which he was awarded the Fields prize in 1966 (the Fields prize is the Nobel prize of mathematics). His work provided the foundations upon which others achieved fame, e.g. Andrew Wiles proof of Fermat's last theorem, Gerd Faltings (Fields medalist 1986), etc. He quit mathematics in 1991 for a monkish existence (meditation, religion and philosophy) after learning his research institute was in part financed by the French ministry of defence. RIP.

Comments (1) :
Claire (IRL) asks "And what, pray, is Algebraic Geometry?" Just a different way of looking at geometry. Where you might draw a ball, he would write x2+y2+z2=1, then he could use algebra and all known algebraic results before turning the final expression back into some geometrical object. BTW, that is very much a simplification...

Friday, November 14, 2014

40 years on and still going strong :-)

A fortnight ago, indeed On Any Sunday you might say, my motorcycling friends & I go for a spin, often to Rainer's place Gut Albrock which does a huge sunday breakfast for bikers.

It was there that we saw this nicely done restoration. Judging by some details, it is a Norton Commando 850cc dating from 1974, so 40 years old this year.

Impeccable! The owner even wore a Cromwell helmet - alias skid-lid, standard in the 1960s. But his goggles were a terrible mismatch, foam framed with a Union Flag design, they were only worn by Mods (scooter riders) back in the day. We "Rockers" all used RAF type 9 pilots' goggles. I know, I was there and part of the Ace Cafe and 59 Club scene :-)

But nice to see that someone (from the Paderborn area) likes old Brit bikes :) The bike behind it is a cut and modded 1970's Honda CB750 four, also in good condition. He probably has the number 49 because my 1969-vintage Honda CB750 Cafe Racer oldtimer had already taken the 59 registration.

Wednesday, November 12, 2014

Jonas Jonasson's books :-)

When in London last month, I went for a beer and a venison pie with Mike (of Canada) and Carl (who oscillates between London and Trinidad&Tobago). In the course of our rambling discussions, Mike raved about a couple of books by Jonas Jonasson. And rightly so! For I have just read both of them, they are hilarious, rambling, slapstick, Mr.Bean-on-crack style, comedies. I preferred The 100-year old man... slightly, but tastes differ. Both are can't-put-down, read-all-in-one-8-hour-session, funny stories.

The ISBN numbers, L2R, are 978-1-84391-372-6 and 978-0-00-755790-5.

The 100-year old man... has been made into a movie, also available on DVD, so the non-book-readers among you can enjoy it too :-)

Comments (1) :
Paula (D) asks "What's that second one called in German?" Die Analphabetin, die rechnen konnte, ISBN-13: 978-3570585122, about €20.

Monday, November 10, 2014

USA : a nation of losers :-(

America - the limited subset that is united (hah!) - had its mid-term elections last week. And voted to have a standstill for two years :-(

So their future - and probably ours - is hellish :-(

Now if the GOP tries to introduce legislation along GOP lines, Obama can still veto it. Tit for Tat, after the GOP fighting him over the last 6 years ;-) But if Obama tries to suggest any legislation, the GOP will kill it in the House and/or Senate. And Americans still oppose the idea of man-made climate change, and gun-control is dead in the water school(?), women's rights will be aborted [oops :-( ]...

The Tea-Party (aka batshit-crazies) gained nine seats of the +17 Republican gains. Schools - and whole states - will be be governed by mentally ill neo-fascists. The environment & economy will deteriorate, more spying, less jobs. Many of the Tea Party would rather see the USA fail than Obama succeed :-(
Fat-faced multi-chinned Mitch McConnell will be unable to contain the crazies in his own party, already lining up for the goat-rodeo of 2016 :-(

American voters seem to ignore all the good stuff Obama's been doing (despite GOP obstructionism), viz. :

  • brought the economy back from the brink of another Great Depression
  • unemployment steadily falling,
  • stock market has soared, underpinning the retirement hopes of many,
  • (mostly) discontinued pursuing "wars of choice",
  • Obamacare has been a measured success, allowing large numbers of previously uninsured American to have access to health care.
  • etc. etc.

Goodbye USA, you made the wrong choices mid-term. Shame....

Comments (3) :
Ed (USA) wrote "I wrote a full page reply, but then I realized you'd only tear it apart, so here's this one word summary instead!"

"I disapprove of what you [omitted to] say, but I will defend to the death your right to [decide not to] say it" (misquoting E.B.Hall, NOT Voltaire).
Doug (Canada) replied to Ed, saying " Then obviously it was a badly flawed response unless you think Stu is incapable of logic. You must be GOP if you think there was anything misleading, untrue about what Stu wrote. Well as the old saying goes - truth hurts. " You mean like this ? ;-)
Renke (D) wrote " The USians may be losers but they are in good company - Harper (Canada), Abbott (Australia), Orbán (Hungary), see also the advent of Afd (Germany) or UKIP. If Thatcher's goverment (11 years) is typical, we're looking at a lost decade, with new levels of political madness. *Very* scary, and Ukraine is a prime example of the result: A new cold war, and both sides (The East and The West) are quite happy with a hot proxy war in the area formerly known as the Eastern oblasts of Ukraine." My text editor couldn't cope with your Cyrillic text, Renke, so I've just included the English bits you wrote. Sorry.

Sunday, November 9, 2014

"Get away from through The Wall!"

Today we are celebrating the 25th anniversary of the fall of the Berlin Wall & Iron Curtain, on 9th november 1989 :-)

At 18:53 the Italian journalist Ricardo Ehrmann, in a DDR press conference, asked Günter Schabowski (DDR-Politbüro) exactly WHEN the new travel rules would apply and he stuttered and answered "...As far as I know, immediately". By 21:20 thousands of East German (DDR) people were gathered at the Bornholmer Street border gate in Berlin, demanding passage to the West. The border guards caved in and let them pass the border. First across were Siegbert Schefke (a protester) and Aram Radomski (a photographer). A hundred thousand(sic!) quickly followed, carrying hastily packed and overflowing suitcases, vowing never to return.

A peaceful revolution, not a shot was fired. A win-win situation for both sides. Albeit we are still paying that extra "solidarity tax" to help get East German up to West German living standards, even after 25 years. A long economic struggle to bootstrap the new eastern states.

The Berlin Wall was erected in 1961, which was when Ivor Cutler published his mad little Wall song as a subtle reply to Walter Ulbricht's big lie (see below).

Some of you older Brits may recognise today's blog-title. Back in 1961, Scottish comedian Ivor Cutler published a crazy EP entitled "Get away from The Wall!". The original is available online for 99c as an mp3 file from Amazon. But there's a choir version on YouTube for free here. Enjoy ;-)

Friday, November 7, 2014

Babbage's Engines

The History of Mathematics exhibition in the Science Museum (London, UK) displays full-size replicas of Charles Babbage's mechanical computers.

Charles Babbage was an english mathematician and engineer who lived 1791-1871, the last 42 years of which was in Marylebone, London.

Babbage invented the first mechanical computers, all brass and spit and polish, no electricity involved. Three replicas are on show in the aforementioned exhibition, so here are my photos of them.

Shown below is Babbage's Difference Engine Number One. Beginning in 1822, it was designed to calculate a series of values (e.g. tables of logarithms) automatically. By using the method of finite differences it was possible to avoid the need for multiplication and division, thus making the machine easier to build. Had it ever been finished, it would have been 8 ft. tall, and contained 25,0000 pieces totalling about 15 tons of brass!

He is probably better remembered though for his Analytical Engine (shown below). It could do fully-fledged general purpose computation (i.e. was Turing complete). Sequential control, branching and looping were all implemented in it. Programming was to be via a form of punched cards, loops of Jacquard's loom punched cards. The world's first programmer Ada Lovelace (after whom the strongly typed programming language ADA was named) developed an algorithm to calculate a sequence of Bernoulli numbers for the Analytical Engine. BTW: there will be an Ada Lovelace exhibition in the nearby HNF (the world´s biggest computer museum) in 2015 to celebrate her 200th birthday.

The third exhibit is Babbage's Difference Engine Number Two. The selfie photo below is just to give you an idea of the scale of these big brass engines. His drawings were used 1989-1991 to build this replica at the Science Museum from his blueprints. And yes, it works, delivering results to 31 digits of precision. By 2000 AD the Science Museum had also built the printer designed by Babbage (which you can see on the left here).

The next exhibit really surprised me. For size comparison with the Difference Engine Number Two, the jar contains Babbage's brain, pickled and preserved for eternity! Anatomists have sectioned the brains of several famous people to see of they have a different physical structure from the brains of the rest of us. This has - afaik - turned out not to be the case :-(

Doing my own size comparison, here is my photo of a plug-in circuit board for the 1951 Pegasus computer, which was valve(=tube) driven as you can see. Just one of these boards is about as large as Babbage's Brain. The Pegasus had several hundred of them and was even larger than Babbage's Engines. Your mobile phone - even your iWatch - is far more powerful!

And that's enough about the history of steampunk mathematics for now :-)

Comments (4) :
Cop Car (USA) wrote " "...delivering results to 31 digits of precision." I could have used that in 1974 for my thesis work. Unfortunately, I had to work with the available 16 digits of precision and I ran into mathematical instability. Oh, well. There are lots of precision resistors on that circuit board!" I love the engineering in all of that brass and cogs :-)
Jenny (Ibiza) wrote "You are one of the few people I know who can make maths interesting. Love your nerdy selfie :-)" De nada.
Kees (NL) asks "Does size of your brain matter?" Probably not. Cro Magnon had larger brains than Homo Sapiens. Whales have huge brains, probably through having to remember acoustic maps of all of the world's oceans, but also containing a lot of fatty cells to keep the brain warm. The structure of the brain matters more than size. But before you make any sarcastic remarks, yes, my skull circumference is 63 cms. And yours? ;-)
John (UK) asks "Why did he go for 31 digits of precision? Who needs that many :-(" Just by looking at the Difference Engines, we can deduce that he was using a fixed point number representation. No part of the mechanism is built for the exponent part of a floating point number representation. (Maybe I should blog about floating point maths or indeed generally about different number representations at a later date). So his 31 digits are to be able to cope with both large and small numbers in a fixed point scheme rather than any need for high precision (which was Cop Car's problem). But remember, this is a Difference Engine. It subtracts 2 large numbers to get a small result. Repeatedly. Which is why he needed many digits to retain accuracy, avoiding truncation/rounding errors.

Wednesday, November 5, 2014

A history of logs

While I was visiting the Science Museum (London, UK) last month I took a stroll through the History of Mathematics exhibition which was where I took the photos for this article about Logarithms.

"Go forth and multiply!" saith7 the Lord (Genesis 1:286). Two snakes5 objected "We can't multiply, we're Adders", whereupon the Lord said "Then goeth ye unto Noark4, shipbuilder3 and carpenter2 for he shall build you a table of logs over which ye shall have a sly drool1" ;-)

I just made that last paragraph up, like the rest of The Book ;-)

But it is interesting to see how logarithms arose as a means of doing multiplication. It is thought that the Babylonians invented the quarter square multiplication algorithm to multiply two numbers using only addition, subtraction and a table of quarter squares, some time around 1800 BC. No real progress was made until Arithmetica integra was published by Michael Stifel in Nurnberg in 1544, which contains a table of integers and powers of 2 that has been considered an early version of a logarithmic table to base two. In 1614, in a book titled Mirifici Logarithmorum Canonis Descriptio (Description of the Wonderful Rule of Logarithms) John Napier propagated the idea of logarithms. In 1617 he also came up with a simplified device for doing multiplication, called Napier's Bones, basically a set of small squares each with an entry from a multiplication table on it.

Immediately after Napier's book, Henry Briggs published (in 1617) a table of the logarithms of the integers 1 to 1000 to eight digits of precision. Almost at once (actually in 1622) Willian Oughtred came up with the slide rule by engraving logarithmic scales on two pieces of wood which could be slid past one another. His original design was for a circular slide rule, the linear slide rule first appeared in the 1650s.

My very own VEB Mantissa DDR school slide rule shown above is perhaps typical, being about ten inches long with linear scales. This limits its precision to 3 or 4 digits. In an attempt to squeeze 5 or more digits of precision out of the idea, several different approaches were made over the following centuries.

At the bottom is a linear slide rule of greater length. Our maths teacher Jeb had one at our school of 40 inches length. Above that is a cylindrical slide rule whose scale spirals around the cylinder. You can tell it was deemed valuable by it being kept in its own special box. In the background is a multiple-scale rule whose partial scales are folded concertina-style to get a very long scale onto a compact device. Of course, you had to keep track of what sub-scale you were using, but you could get 6 digits of precision from it!

Mechanical calculators were being built in parallel to slide rules. Schickard made one in 1623, but it was unreliable. Blaise Pascal built a better one in 1643. Not until 1851 was there a commercially succesful robust mechanical calculator (Thomas' arithmometer). My own Brunsviga is only 60-odd years old, the last generation before the electronic calculators.

I'll tell you more about mechanised maths in a separate article about Charles Babbage, soon. But that's enough for today.

Comments (1) :
John (UK) asks "Do kids these days understand slide rules?" Enough to operate them after being shown how. Only problem is keeping track of the decimal point position. But there it helps if they already know about floating point numbers, slide rules are inherently floating point devices.

Tuesday, November 4, 2014

In Memoriam : Ralph Knight, sidecar-racer.

Another old friend gone :-(

Ralph Knight, amateur sidecar racer from the Isle of Man, died last week of a heart attack whilst gardening, he was just 61 I believe. Norton-Paule just called me with the sad news, for which many thanks Paul. Friend Michel Kamper will be delivering the bikers' funeral address, a painful task.

This just a week after the death of Monika Storz (63?), she and I overlapped when working for 2 different companies. She had just decided to go for early retirement, but died suddenly before even seeing her first pension :-( SWMBO went to her nice (atheist) memorial meeting, representing us both.

We don't shuffle off this mortal coil in the same sequence we came onto it, but I'm still always startled when a younger person goes first :-(

Comments (2) :
Ida (B) wrote "Get used to the feeling, because the older you get, the more people dying will be younger than you." True.
Jenny (Ibiza) asks "Does 'overlapped' mean what I think it means? " No. It means that there were some years when we both worked for NCAG and other years when we were both at Unilab.

Monday, November 3, 2014

Snowbirds : Flying-Vee

You know winter is coming when you see these huge V-formations of cranes heading for sunnier climes to spend their winter. Photo sent by Isabelle, who lives in Germany on the Polish border, quite a way east of here. Sometimes cranes and/or storks take a more westerly route and make an overnight stop at the big pond in our village. Keeps the frog population down :-) No photos of them though, because no-one wants to disturb them.

Have you ever wondered why they fly in that V-formation? Because it's less effort for them. The wings have a high pressure zone on the bottom and a lower pressure zone on the top, generating lift. But at the wingtips the air "leaks" and flows around the end of the wing from the high to the low pressure area, so there is rising air just beyond the wingtips. As the bird moves forward, a vortex is left behind the wingtip. The bird flying behind positions itself in this vortex so as to be in the rising air, thus needing to flap less hard itself to generate lift. And so on and so forth. Synergy! :-)

And, thanks to YouTube, here's another famous left-handed Flying-Vee :-)

Comments (1) :
Renke wrote " Whut? They don't fly in a V formation because it looks cool? Now I'm disappointed :/" Maybe they just wanted to stork each other? ;-)

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