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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 called 'Kosmo'.

Some of my bikes

My Crypto Pages

My Maths Pages

Saturday, July 28, 2018

Dark Side of the Moon

Well actually, it was a lunar eclipse last night (as seen from Germany) because the moon doesn't have a dark side, being tidally locked with the same face turned towards the Earth all the time (aside from a small libration). This implies that all of the surface of the moon gets turned towards the sun at some time in the moon's monthly orbit around the Earth.

The red colour - a so-called blood moon - is caused by the Earth's atmosphere scattering sunlight's shorter wavelengths (blue and green) out of the way, leaving the longer wavelength red light to pass on towards the moon.

This time, the moon was at almost the farthest point away in its elliptical orbit, and so - as Kepler taught us - travelling slowly. Thus we had a really long lunar eclipse (at 103 minutes, the longest this century). Totality started at about 21:30 here (we are quite westerly) and continued until 23:13. It was quite hazy at the start so a good view peaked around 22:22 pm. Meanwhile, the ISS came overhead orbiting west to east at 21:47 and again at 23:24 so that was an additional spectacle. BTW, I can recommend this ISS tracker web page which lets you see where the ISS is in real time :-)

A couple of other spectacles at the same time : the Perseid meteor shower - well, about 2 per minute - was visible to the east and Mars at its closest to Earth just to the south-east of the moon was visibly red. The haze was too dense here for me to get a good photo of the Mars disc, so I put my tabletop telescope away again :-(

Donald Trump - ever publicity hungry - claimed he had learned from his last experience with an eclipse because he's a stable genius and so wore dark glasses for this one (this despite the fact that it was not even visible from America) ;-)

I hope all my Yurpeen/Australian/African readers got a good view too :-)

Meanwhile - if you came here looking for Pink Floyd - here's the 1974 Wembley live version :-)

Comments (1)
Petra (A) sent me this unique lunar eclipse photo, supposedly from Ignoramia, Texas ;-)

Tuesday, July 24, 2018

Sunday's oldtimer meet

On sunday I drove my oldtimer Porsche to the oldtimer meet in nearby Büren town. There were several vehicles there I hadn't seen there before, so here are my photos of them.

Above : Mercedes 190 SL cabrio, which were built from 1955 to 1963.
Below : Mercedes 190 SL 4 cylinder 105 hp SOHC engine, with twin carbs.

Above : Heinkel Trojan bubblecar, built 1956-1958, 175cc 10hp 1 cyl. 4 stroke engine. That's my 163 hp red Porsche 944 oldtimer behind it :-)
Below : Two Heinkel Tourist scooters, built 1953-1965, same engine as the bubblecar.

Above : BMW 700 30 hp engine at rear, built 1959 - 1965.
Below : 647 cc flat twin (from the R67 bike) 30 hp, or 40hp in the Sport version.

Above : Ford Mustang convertible, this first version built 1964-1973.
Below : The 1968 289 cu. in. (4.7 litres) V8 engine delivered about 200 hp.

Above : MG A convertible, built 1958-1962. In British Racing Green :-)
Below : MG A dashboard with its strange pull-on knobs. 108 hp 1800cc inline four.

I didn't stay for the afternoon tour through the countryside, to avoid being stuck behind the 10hp bubblecar and thus never getting out of first gear :-(

Comments (2)
Cop Car wrote " You saw a bunch of good-looking cars, Stu. Surely, your Porsche held its own, though. Your photo of the 190 SL looks (to the best of my memory) like my brother's 1961 SLC 2-dr roadster - down to the interior and exterior colors. It proudly takes up 1/3 of his garage space in Colorado while the other 2/3 is occupied by an SLC 4-dr sedan (purchased in 1974 - don't recall the model year of the car) and a 1992 W124 4-dr sedan (the only new car he's ever purchased!)" Those cars I showed get polished, mine gets driven daily ;-)
Liz wrote " So I called Mike to look at the cars. Like you he's a walking encyclopedia. His friend had a Heinkel scooter back in the late 60s, the only in Derby amongst the Vespas and Lambrettas. But he queries your MGB saying it's an MGA? He had an MGB (sold it to buy carpet and a cooker when we got married)." Mike is right. Narrower radiator grille, rounded bonnet at the front, so it's an MG A. I'll change the text and wikipedia link. Thanks Mike, for the correction.

Sunday, July 22, 2018


Back on Friday, July 6, I blogged about doing exact multiplication quickly by mental arithmetic. Cop Car commented that she mostly uses guesstimates. So I've been trying to think of when I use guesstimates too, to get a quick approximate answer.

So let me show you today how to calculate square roots by guesstimating. I'll show you three examples.

To get the square root of (say) 41, use the next lower perfect square, 36, which is six squared. So the answer will be six plus something. To get the something, take the excess 5 (=41-36) and divide it by twice the six, getting 6 + 5/12 = 6.41666 which is only about 0.2% high.

Now try 51, so 49 is the nearest lower perfect square. So the answer will be seven plus something. That something will be the excess 2 divided by twice the seven = 7 + 2/14 = 7.143, instead of 7.142.

Now try 137. So that's 11+something. The something will be 16/22= 0.727 making 11.727 instead of 11.705 so 0.2% off.

You see, the guesstimates are quite good :-)

Comments (2)
Cop Car wrote " I think you hit the nail on the head with your comment several days ago that we oldsters learned to do math in our heads and that the youngsters may not have had that experience." True.
Hassan (Teheran University?), I'm afraid I couldn't understand what or why you wrote; try again but clearer please.

Wednesday, July 18, 2018

Helsinki Body Language

Who needs body language? The facial expressions say it all :-(

And we can't trust either of them :-(

Comments (2)
Derek (UK) said "... and Trump contradicts himself a day later :-(" Because he has a new pet = Schrödinger's cat ;-)
Liz (UK) wrote " I keep saying, 'Why don't the Americans do something about their president?' There seems to be so much that is dubious if not downright illegal about him. And 'How could they elect him in the first place?' But then I think about Britain and Brexit and I remember: people are stupid. What really amazes me though is that Christians support Trump. I have a Christian friend - a very serious knowledgeable Christian who puts me to shame - and he continues to support him. At first he said Trump was a better bet than Hillary but I don't know what his excuse is now." At least one American (Mueller) is doing something about Trump and his cohorts ;-) Apropos Brexit : I think it's going to be a hard Brexit, even no agreement at all, Liz, which is why I've taken a second (German) nationality so that I can continue to live here!

Sunday, July 15, 2018

Bastille Day Bloopers

Yesterday was Bastille Day, much celebrated by the patriotic French. As usual there was a big military parade, but this year the parade included a couple of magnificent bloopers ;-)

The parade included a display by the national motorcycle display team demonstrating their skills, e.g. by riding in interweaving figure-eight patterns. Except that this time two of them collided and fell off their bikes with the whole country world watching on TV :-(

The next blooper involved the Patrouille de France, who traditionally fly along the Champs d'Elysee over the Arc de Triomphe, trailing a Tricolore (the French national flag) of red, white and blue smoke behind them. Except that this time the outside plane in the blue team had been loaded with red smoke instead of blue! Sacre bleu! Again with the whole country world watching :-(

This much to the amusement of other nations who believed the French military flag is all-white anyway ;-)

Thurday, July 12, 2018

Lost Letters

One of the benefits of the internet is that it provides access to old - like a thousand years old - documents which would otherwise be hidden away in libraries, monastries etc etc. I've been trying - with difficulty - to read some old (english) documents and it seems they use some letters which are no longer in our modern alphabet.

Singing : Where have all the letters gone, long time passing?

Old English used the Futhark alphabet , socalled because instead of a,b,c... it went f,u,t,h,a,r,k... But I can't really read that runic stuff anyway. But some of the Futhark letters survived into the middle ages, the first I encountered was Thorn, written in upper case as Þ and in lower case as þ. It was the predecessor of "th" used nowadays, you may still see it on british pub signs "þe olde pub". When the French took over (1066ff), they didn't have thorn and so replaced it with a "y", hence you also see "Ye Olde Pub" in Britain. But it is still pronounced The and not Ye ;-)

Next I found Eth, written Ð and ð respectively. It came from the Irish regional accent and also evolved into "th".

The ampersand & is still with us. The name came from "and, per se, and" because it was the final letter of the alphabet and stood on its own.

Another cropped up frequently, Eng , written as Ŋ and ŋ. It has been replaced by "ng", e.g. in an ending.

Some letters were graphemes, merging two letters such as "ae" and called Ash. The merge of "oe" was called ethel and was the transcription of the futhark rune Odal.

I don't know how to display Ond, That, Wynn ,Yogh , the long S or the Irish G but they crop up too. We've lost 12 letters it seems. Don't think all alphabets have the modern English 26 letters either. Welsh has 29 letters not all of them being L ;-) Italian (like Latin) has 22, German has 30 (counting 3 umlauts and β) and Hawaiian just 13. Cyrillic, Greek and Latin alphabets actually share 11 letters. And if you thought 26+12=38 letters were hard, try Slovak with 46 or Cambodean which has 74 :-)

PS: In Trump's tweets the letter I seems to crop up a lot ;-)

Comments (4)
Engrumpled Curmudgeon (Canada) points me to a page showing how to display Wynn ,Yogh , the long S etc in HTML etc. Thanks, Doug.
Petra (A) asks "So, can you show us the others now?" Some of them : Wynn is ƿ, Yogh is Ȝ and ȝ in lower case, but I still couldn't find either Ond or That.
Petra (A) complains "Wynn and Yogh don't show up here!" Are you using a Samsung smartphone? Their browser has some defects. Try installing Firefox.
Derek (UK) "Are you implying that monasteries hide their books?" You'd better believe it! Not too far from where you live is Hereford Cathedral. They have the world's only?/largest? chained library (about 230 OLD books, 1500 total). Dating from 1611, when hand-written medieval monk's books were really valuable, they have a library wherein the books are all chained to the shelves and the shelves are barred off. See here for a video.

Monday, July 9, 2018

Biker News

Good knews from Kinga, who is riding her motorcycle back from Australia to Poland. She got safely through Iran, despite her big bike and her gender (officially motorcycles over 250cc are illegal in Iran and women are not allowed to ride). So now she just has to cross Aserbaidschan and Armenia (short rides) before the long east-west trip across Turkey to reach Europe. I enjoy following her blog 'cos I'm too old to do that ride myself.

The 5 of our lads who set out for a tour round the Baltic gave up and just toured southern Norway instead due to a mishap and bad weather. One ran off the road in Poland, breaking 2 ribs and damaging his kidneys. The bike was a write off. So the other 4 returned him to Germany where his GF picked him up. Re-planning took those 4 to Norway where one chickened out due to incessant rain (so I've bought him a "Norsk sutrer" T-shirt ;-) ) The remaining three turned south after Trondheim to get to warmer and dryer weather and did a tour of the fjords. Now all 5 are safely home again :-)

I've had lumbago which prevents me from riding right now. Originally I wanted to go to the LWL museum in Münster which has an exhibition about brains and even has slices of Einstein's brain on display. Macabre but interesting. More about that when I can make the trip :-)

Some bad news too though : William Dunlop was killed in a practice-session crash at the Skerries 100 road races in Northern Ireland, the third member of the family to die road-racing :-(

Comments (2)
Ed (USA) asks "What does 'Norsk sutrer'mean? Is it German?" No, Ed, it's norwegian for 'Norwegian wimp' ;-)
Ed (USA) replied "Sounds like that Beatle song - Norwegian Wood." It was more like Norwegian Wouldn't ;-)

Friday, July 6, 2018

Go forth and multiply...

.... it said in the bible. But it didn't say how to multiply ;-)

So here I'll show you yet another method to do mental arithmetic multiplication, this one suitable for numbers "near" powers of ten.

Single digit example, just to illustrate the method : 7 * 8 =56 which you learned by rote, so you know the answer already. Now this new method: How far is 7 from the next power of 10? 3. So subtract that 3 from the other term 8, giving 5. Write that down on the left. How far is 8 from the next power of 10? 2. Multiply that 2 by the previous difference, 3, getting 6. Write that down on the right. So you've now written the answer, 56 :-)

Now a double digit example. 96 * 89 =? How far is 96 from the next power of 10? 4. So subtract that 4 from the other term 89, giving 85. Write that down on the left. How far is 89 from the next power of 10? 11. Multiply that 11 by the previous difference, 4, getting 44. Write that down on the right. So you've now written the answer, 8544 :-)

Sometimes the second product will be above 100, so just add the one to the left half of the result. Example with a carry-digit : 88 * 87. How far is 88 from the next power of 10? 12. Subtract 12 from the 87, getting 75. Write that down on the left. How far is the 87 from the next power of 10? 13. Multiply that 13 by the previous difference, 12, getting 156. Write that down on the right. This has 3 digits not 2, so you add the 1 to the 75 on the left, getting 76. The total result is thus 7656 :-)

Let's try three digits. 977 * 963 = ? How far is 977 from the next power of 10? 23. So subtract that 23 from the other term 963, giving 940. Write that down on the left. How far is the 963 from the next power of 10? 37. Multiply that 37 by the previous difference, 23, getting 851. Write that down on the right. So you've now written the answer, 940851 :-)

And you did all of that in your head!

OK, OK, mostly people use a calculator (even the one in their mobile phone) but it's always useful to have another arrow in your mental arithmetic quiver.

Comments (4)
Cop Car wrote " Dear friend Stu, You know a lot of neat tricks for mathematical manipulations. Cool beans! However, you live life closer to the edge than do I if you really need to be able to do three-digit multiplication (in your head) to provide a precise answer. In my life/career, if I was away from pencil and paper, a slide rule, a calculator, etc, my mental "guestimate" would suffice. It's obvious at a glance that 977(963)=something less than one million. (Of course, I didn't need to win bets in bars.)" If you can do mental arithmetic fast enough, it is indistinguishable from a "guestimate" ;-)
Ed (USA) wrote "There you go again, making it look trivial!" . . . indistinguishable from magic, Ed, indistinguishable from magic ;-)
Petra (A) wrote "Your assumption that I could do 37*23=851 in my head as per your 3 digit example, is mightily wrong. And I suspect that is true for most people." That's because you are young Petra; old fogies like me were taught mental arithmetic. But you may well be right :-(
Ed (USA) then asked "Does this ALWAYS work?" Yes, but only really suitable for numbers "near" powers of ten.

Tuesday, July 3, 2018

Factorial fun!

Sunday afternoon and five of us (bikers) were sitting in a quiet beer-garden in the woods near Lake Möhne when a nearby bell-tower started to ring its bells. One of the girls asked "How long is that going to go on?" to which I replied "Well there are 7 bells, so 2½ to 5 hours, depending on the interval in which each bell-ringer pulls his bell."

"How do you know that?" she asked.

"I don't, I just calculated it in my head" I explained in reply, "We hear 7 bells, so a full peal means 5040 individual bell-pulls --- that's factorial 7 --- which takes almost 3 hours to ring. An 8 bell extent takes about 19 hours and has only ever been rung error-free once, afaik."

"What's a factorial?" she asked.

"The number of ways you can arrange N items in a line. So factorial 3 is 6, and the 6 permutations are ABC, ACB, BAC, BCA, CAB and CBA. Factorial N is the product of all whole numbers up to N, so for 3 it is 1*2*3=6 and for 4 it's 1*2*3*4 = 24, for 5 it's 1*2*3*4*5=120, for 6 it's 6!= 720 and 7!=5040."

"I remember doing that in school," one lad replied, "but we were never told what you could use it for. And the maths teacher said factorial Zero was One, but never told us why, and I didn't understand why that is so. And you can't put a zero in that 1*2*3... sequence!"

"There are 2 ways to put 2 items in a line, AB and BA. There is just one way to put one item on the line. And there is also just one way to put zero items on a line. So factorial zero is defined as one." I replied.

"But what about the sequence 1*2*3*4*5...? No zero in it!" I was asked.

"Let's just rearrange the definition there" I answered "Four factorial is five factorial divided by 5, 3 factorial is 4 factorial divided by 4, 2 factorial is 3 factorial divided by 3, 1 factorial is 2 factorial divided by 2, and 0 factorial is 1 factorial divided by 1, which is 1" I explained.

Meanwhile the full peal of bells had stopped because one of the bell-ringers had made a mistake; sometimes known as dropping a clanger ;-)

Combinatorial bell-ringing was first described by Fabian Stedman (GB) in 1668 in a book Tintinnalogia co-written with Richard Duckworth and later in Stedman's own 1677 book "Campanalogia". Mathematicians thus see him as the first Group Theorist :-)

FWIW, the exclamation mark notation N! for N factorial was not introduced until 1808 by the French mathematician Christian Kramp.

Comments (1)
Ed (USA) wrote "You make the math look so easy!" It IS easy, Ed, but I had a good maths teacher Jeb who explained everything very well, giving examples of where the maths is used. I try to emulate him :-)

Recent Writings
Dark Side of the Moon
Sunday's oldtimer meet
Helsinki Body Language
Bastille Day Bloopers
Lost Letters
Biker News
Go forth and multiply
Factorial fun!
150 years of typewriters
Canstein Highland Games
Hilarious Blackmail Scams
Are these Skyhooks?
Brit Blades Ban
On the road again :-)
G7 Body language
Use less plastic!
NSU motorcycle museum
Blogroll additions
Marion's new book
Dambusters' Day

Ain Bulldog Blog
All hat no cattle
Balloon Juice
Cop Car
Earth-Bound Misfit
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Finding life hard?
Greg Laden
Mostly Cajun
Not Always Right
Observing Hermann
On her Bike
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Starts with a Bang
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FWIW, 153 is a triangular number, meaning that you can arrange 153 items into an equilateral triangle (with 17 items on a side). It is also one of the six known truncated triangular numbers, because 1 and 15 are triangular numbers as well. It is a hexagonal number, meaning that you can distribute 153 points evenly at the corners and along the sides of a hexagon. It is the smallest 3-narcissistic number. This means it’s the sum of the cubes of its digits. It is the sum of the first five positive factorials. Yup, this is a 153-type blog. QED ;-)
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