Eunoia
 
> Most recent Blog Comments Policy Impressum Maths trivia Search this site RSS Feed Eunoia, who is a grumpy, overeducated, facetious, multilingual expat Scot, blatantly opinionated, old (1944vintage), amateur cryptologist, computer consultant, atheist, flying instructor, bulldoglover, Beetledriver, textbookwriter, longdistance 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, July 31, 2015
An upsidedown houseRiding our motorcycles along the road downstream of Lake Eder, just outside the village of Affoldern, Frank and I came across a house which had been built upside down!You are supposed to think that some stupid builder held the architect's plan the wrong way up; but of course it is just a tourist
All the regular fittings are in place and screwed to the "floor" which is of course the ceiling. The photo below shows the bathroom fittings in their normal orientation, which means that Frank appears to be upside down :) Of course the toilet paper "hangs" wrongly as does the electric cable and none of the taps worked, so it's an approximation. The illusion is quite good, but occasional minor details are a giveaway. Can you see the conceptual error in the photo below? The window is tipped open at the "bottom" instead of the "top". More attention to detail needed! I want my money back!! ;) This normal view of the children's bedroom (below) shows how the bed is screwed to the ceiling as if it were the floor, and Teddy "laying" on the bed. Notice too how the prohibitory stickers on the door frame spoil the illusion by being displayed legibly, i.e. in normal orientation :( Plenty of visitors though, mostly families with small children. The owner probably makes far more in entrance fees than he would have gotten in rent if the house had been built right way up! Comments (1) : Wednesday, July 29, 2015
Mayan NumeralsMayan heiroglyphs show us that they used a number system counting to base 20 (rather than 10, as we do). So we can deduce that they either went barefoot or wore sandals, so that their toes were visible, so they could count on them :)A dot, such as you would get by sticking your finger in clay, represented one. Five dots were replaced by a line, like looking at a hand sideways. Four lines (think 2 hands and 2 feet) thus represented 20 and were replaced by a dot written one level up. Larger numbers were then written vertically, think boxes stacked on top of one another, a positional notation. A positional notation needs a symbol for zero, the Mayan symbol looked like an empty shell (or a rugby ball in profile). So a dot over a shell meant 20. A dot over a shell over a shell meant 400 (=20*20). A dot over a shell over a shell over a shell meant 8000 (=20*20*20). So a bar and 3 dots over a shell over 2 dots meant 802 to base 20 = 3202; that clear? Addition was easy, just group the levels together and apply replacement rules and upshifts as necessary. It's a bit like doing Roman Numeral arithmetic, except that the Romans didn't have a zero. Subtraction is easy too, multiplication a little harder and division quite a bit harder (do repeated subtraction and level shifts as needed). This is slightly confused by the way dates were recorded. They grouped 18 (instead of 20 things) together at the second level to get a group of size 18*20 =360. Probably a rough estimate of the number of days in a solar year, some think. I, personally doubt this, because we know that the Mayans had a quite accurate calculation of 365.2422 days for the solar year. YMMV. Now the Babylonians counted to base 60, which is three times 20. So we can deduce that they went barefoot AND were into threesomes ;) But that's a subject for a different (censored) blogpost ;) Comments (2) : Monday, July 27, 2015
Darwin Awards @ KulmbachTwo young men (20,24) in Kulmbach  a small town in Bavaria famous for its beer  were obviously frustrated at the weekend by the big sign at the openair swimming pool "Closed for repairs". Hint 1.So that dark and moonless night they climbed over the tall fence to go for a swim. They clambered up the outside of the 10 meter (33 feet) diving tower, because the staircase had been removed(sic!) as part of the maintenance. Hint 2. They dived simultaneously from this height expecting a cooling splash. What they failed to notice in the dark was that the pool had also been drained for the announced repairs. Both dead, one quickly, the other slowly :( It is not known whether drugs or alcohol or just being Bavarian contributed. Comments (2) : Friday, July 24, 2015
How come black holes suck so much?I don't really understand gravity. But then neither do theAn example: How come black holes suck from the inside too? A black hole results when a star of mass more than about 5 suns collapses. Gravity pulls in all the material. The simple imaginary model shows spacetime as a rubber sheet bearing (sic!) a heavy ball in a 3D cusp called the gravity well with the singularity at the "bottom". The steepness of the walls on the gravity well are a measure of strength of the gravitational field. This corresponds to the escape velocity needed to escape the gravity well. At some position the steepness of the gravity well walls imply that the escape velocity is equal to the speed of light. So nothing traveling at or below the speed of light can get out of the gravity well here. This limit is called the event horizon and the size of the black hole at this position on the wall is given as the Schwarzchild radius (yes, I'm ignoring the emission of Hawking radiation and the fact that the hole is most probably rotating, KISS). On the other hand, we are taught that gravity travels at the speed of light. If the sun suddenly disappeared, we wouldn't notice until 8 minutes later, when the sky went black because the light takes 8 minutes to get from the sun to us. And only then would the Earth shoot off in almost a straight line because the gravitational pull of the sun had disappeared too. And yet objects orbit around black holes (the Milky Way orbits a massive black hole near its centre) tighter than if the black hole merely had the mass outside the event horizon. So gravity must be permanently "escaping" from below the event horizon of a hairless black hole??? Making the black hole suck harder??? My brain imploded too :( And so I was duly pleased to read an article by astrophysicist Jillian Scudder on June 30th explaining how gravity escapes from a black hole; she has corrected my mental model and put my mind at rest. Thankyou, Jillian :) Comments (3) : Wednesday, July 22, 2015
Village tractor fans' meetAcouple of weekends ago, the tractor fan club in our village (see sweatshirt logo on the left) held a meet in a nearby meadow and brought along their oldtimer tractors for display and mutual admiration.Here are some of the photos I took, first photo is of a Fendt, probably dating from the 1960s/70s. Hanomag (see below) produced tractors from 1912 until 1969, when Hanomag was sold to MasseyFerguson. This is an R22, from the fifties(?) Even Porsche built a diesel tractor. This is powered by an aircooled, fourstroke, 2466 cc, threecylinder diesel producing 35 hp. One farmer even had a Landau as a trailer, so that his family could come along for the ride. The aftermarket green sunshades were a good idea, at least until the thunderstorm squalls came :( In anticipation of the intense sunshine (it was 39°C, about 100°F) a makeshift tent was put up between the beerstand and the grill. Then came a rain squall. The rain accumulated in the tarpaulins, as you can see in the photo. Later, a guy with a broom came around and poked at the paulins, so the water ran off. Below is one of the rarer spokedwheel Hanomags. Addon silencer underneath to let the driver breathe clean air! There is a local artist who makes sculptures from scrap metal. This 35 cm long model of a tractor uses old ballbearings as wheels :)
Monday, July 20, 2015
Uranus is a strange place ;)Been getting some complaints about the blog being too highbrow again, lately. So here is a deliberately lowbrow schoolboy humour type blog entry. YMMV ;)Scientists probed Uranus with a robot probe called Voyager 2 in January 1986 and concluded that Uranus is a gas giant. It also examined the rings around Uranus. Humanity has not been back since :( Uranus is indeed strange. When planets form from the accretion disc around a nascent sun, they tend to adopt their spin from the accretion disc, so the polar axis is usually aligned so that their equator is roughly in line with the accretion disc. This is not the case for Uranus, whose polar axis is pretty much at right angles to the plane of its orbit. We think that there was a collision of the accumulating planet Uranus with another planetsized body early in the history of the Solar System. After all our moon was formed similarly from a collision with the Earth. So the polar regions are either dark or bright (sunward side). Indeed the sunward pole of Uranus has a UV dayglow. The moons of Uranus are 50 shades of grey, due to the UV radiation darkening any methane trapped in the icy surfaces of the inner moons. Uranus has more methane than Saturn and Jupiter, cause unknown, and has 4 times the diameter of Earth, so Uranus is quite big and smelly. Herschel originally called his planet Georgium Sidus (George's Star), sucking up to the UK king who financed his observatory. But other nations objected and so it came to be called Uranus after the Greek god of the sky. It is the only planet whose name is derived from a figure from Greek mythology, the rest are Roman gods' names. If you drew a cone from the centre of the Earth out to the perimeter of Uranus, it would intersect the Earth's surface with an area the size of a soccer pitch, that's how big Uranus is! FWIW, with a similar cone for the dwarf planet Pluto, the intersection area would be about the size of the goalkeeper. Again, FWIW, the massive black hole at the centre of our galaxy would have a cone intersecting the Earth's surface with an area the size of the exclamation mark's dot on your laptop. But now that NASA's New Horizon probe is delivering such great photos of Pluto and Charon, noone is interested in Uranus anymore, so there! Hey wow, lowbrow AND informative ;) Comments (3) : Saturday, July 18, 2015
Hilbert's HotelSince I was already visiting the old town graveyard in Göttingen (see previous post), I took the opportunity to walk over to plot number 83 to pay my respects to the worldfamous mathematician David Hilbert (18621943) too. The footnote on his headstone is one of his favourite sayings (I translate) : "We must know. We will know. "Hilbert is famous for a number of things (see Wikipedia article behind the link). He compiled a list of 23 unsolved problems at the International Congress of Mathematicians in Paris in 1900. This is generally reckoned the most successful and deeply considered compilation of open problems ever to be produced by an individual mathematician. He is also popularly known for the Hilbert's Hotel paradox. Hilbert's Hotel has an infinite number of rooms, all full. But it can accomodate a new guest just by having all the existing guests move (in parallel, thus in a finite time) to the room with a number 1 more than their allotted one! The new guest is then put into room one :) Not only that. Since each number has a unique double, if each existing guest moves to a room number twice his alloted one, then the hotel can accomodate infinitely many new guests! They are put in the oddnumbered rooms. Not only that. If infinitely many coaches each with infinitely many seats arrive, then even all these new guests can be accomodated in Hilbert's Hotel (which was already full!) via an appropriate mapping function. Below this headstone, Hilbert sleeps alone... By wry coincidence(?) there are no other graves on plot#83 to the left of David Hilbert's grave ;) I wonder who came up with that positive idea ? ;) Comments (4) : Tuesday, July 14, 2015
Pilgrimage to GöttingenJust as every Moslem should take a Hajj to Mecca, every Catholic a pilgrimage to Rome, so should every scientist visit the old town cemetery in Göttingen. And since it is barely 70 miles from here, I rode my motorcycle over there recently to pay my respects to the eight Nobel prizewinners buried there.During the first half of the 20th century, the university at Göttingen was the leading place in the whole world for scientific study and research. Then along came Hitler, fired all the Jewish professors, and German science went downhill suddenly :( But 44 Nobel prizewinners were/are associated with Göttingen, and eight of them are buried in the huge old town graveyard where I took the photos below. Alfred Nobel (18331896) was the man who invented dynamite (and had 350 other patents too) from which he made a fortune (he owned Bofors). This fortune was used posthumously to institute the Nobel Prizes for scientific excellence etc. There is no more famous award. The graveyard itself has a small, peaceful, idyllic lake near the 8 graves. A special Nobel rondell has been erected nearby too. It has the form of a regular 17sided polygon; this is a hattip to Gauss, who was also a professor at the uni there. As a boy, he was the first person to construct a 17gon using compass and straightedge only (Euclid's toolkit). The central plinth bears a round emblem of Alfred Nobel, weathered and hard to see in my photo. Most of the Nobel prizewinners' graves are kept uniformly simple. No religious symbolism, no lists of degrees and titles, no dateofbirth or dateofdeath, just the name at the top. And, very interesting, a scientific footnote at the bottom! First time I have ever seen a gravestone with a footnote on it :) On the left below, Max Planck's gravestone footnote displays the quantum Planck length. On the right below, Otto Hahn's gravestone footnote displays the fission equation for uranium. These are the things for which they were awarded their Nobel prizes. One other has no headstone (I assume he didn't want one), just a small groundlevel plaque at some random position in a bed of ivy, as if they were uncertain where to put it exactly, lest it jump around ;) The eight Nobel Prize winners buried here are (in alphabetical order) :
More about this graveyard in a later post, to follow . . . Comments (2) : Sunday, July 12, 2015
Silver Wedding :)SWMBO and I married (late) 25 years ago today  a thursday  narrowly avoiding a friday 13th for which  mysteriously  no registry office bookings seemed to have been made ;) So today we're quietly celebrating on our own  no guests, no party, just us.I got her this bouquet of 25 longstemmed roses by way of a thankyou :)
Comments (2) : Friday, July 10, 2015
Mean StatisticsBlogreader Ed (USA) sent me this White House claim and asked "How can this be? I thought the average is always 50%?"There are different kinds of average Ed. The MEDIAN has 50% of the children above and 50% below by definition. Here they are using the MEAN. Sum all the IQ scores and divide by the number of children to get the Mean. Example : assume 9 children get a score of 100, but one dumbass gets 90. Then the total is 990, divided by 10 children gets a mean IQ of 99. Lo and behold, 90% of the kids have above average (Mean) IQ. Now if that dumbass was bright and had scored 110, the mean would be 101 and 90% would be below average (the mean) :( But 50% would still be above the median :) Now a whole different kettle of fish is to ask "What do IQ tests actually measure?". They are an ordinal scale which correlates with problemsolving ability, we are told. But different psychologists may explain it differently. Results may depend on your background and culture : if I gave you a test written in German you might score far less than one in English. And if the test was really about knowledge of the Koran, we'd both fail ;) It's difficult as a tester to design tests without a bias. But children who score higher on IQ tests will, on average, go on to do better in conventional measures of success in life: academic achievement, economic success, even greater health, and longevity. This is regarded as an advantage in meritocratic societies (not all are, some are theocratic, some oligarchic etc). If I were among the politicians responsible for claim shown above, I'd not have used it. Because as the example I gave above shows, it means they have "educated" some (25%) kids so badly that those kids dragged the MEAN so far down that the other 75% scored above the mean :( If I were in their shoes, I'd want to track the MEDIAN score over the years and decades. A downward drift of the Median score is what you call the "dumbing down of America", always assuming the testdifficulty remains the same. Weaker tests and scoreinflation may be used to (supposedly) counter that trend :( Did that help? Comments (4) : Wednesday, July 8, 2015
A motorcycle trip to TrierMost tourists visiting Trier on the Mosel river go there to see the Porta Nigra (Black gate). It's the largest Roman city gate north of the Alps.The second most popular place amongst the tourists is Karl Marx's birthplace, which is now the Karl Marx museum, well worth a visit. Much less well known is the Löwen (=Lion) apothecary, Google has a bunch of photos, because I forgot to take one of the impressive reddish entrance. This is Germany's oldest apothecary, deeded in 1241 AD and family owned since 1660. The inside was rebuilt in 1966 by the Berlin architect Glahn in a very modern minimalist style; be sure to take a look inside. The Colognestyle ceiling is still from 1695 however. An insider tip from my good friend Marion :) Monday, July 6, 2015
The Weierstraβ Lecture, 2015Karl Weierstraß (18151897) attended the local grammar school where he passed his university entrance exams at the top of his class. He went on to become one of the famous mathematicians of the 19th century as the founder of modern analysis. Friday we celebrated his 200th birthday.In his memory, the mathematics department of the local university invites famous guest lecturers each year to give public lectures, understandable even to those of us with less developed mathematical muscles(?). This year the historical introductory lecture was by Professor Dr. Peter Ullrich (University of KoblenzLandau) "On the influence of Karl Weierstraβ on modern mathematics". Most of this we all knew already. This was followed by the main invited lecture : Fields medalist Professor Dr. Wendelin Werner (ETH Zürich, Switzerland) who talked about the construction of special selfavoiding random walks. The Fields medal is awarded every 4 years to worldclass mathematicians aged under 40 for brilliant papers. It is the maths equivalent of a Nobel prize, there being no Nobel prize for maths. Werner won the medal in 2006. I printed out a copy of Werner's 2008 paper "The conformally invariant measure on selfavoiding loops" and took it along on friday, getting an autograph on the front page for my collection. His talk covered various methods (percolation, uniformspanning tree, random polymer) of doing selfavoiding random walks and calculated the fractal dimensions of each. Nigh on 2 hours of concentration and I'm not sure how much the local freshmen got from it. Probably too highbrow for them? Oh yes, and he ran late ;) Comments (1) : Sunday, July 5, 2015
Greek Referendum dayFlorence Margaret Smith, aka Stevie Smith summed up the situation leading to today's referendum in Greece already, Not waving but drowning...Mind you, I doubt whether you or I, but especially the Grecian poor, can even understand the question, let alone the consequences. OXI Morons :( Meanwhile, in Brussels, the temperature has reached 40°C (=104°F) . . . Comments (1) : 
Recent Writings
An upsidedown house Mayan Numerals DarwinAwards@Kulmbach Black holes suck... Village tractor meet Uranus is strange ;) Hilbert's Hotel Pilgrimage to Göttingen Silver Wedding :) Mean Statistics Trier Weierstraβ Lecture Greek Referendum day US geographic ignorance Toy Museum He He He, Efimov is right The Rudi Blues :) Hitstorm? Not really :( Napoleon's Waterloo Hat Waterloo Blogroll Ain Bulldog Blog Badtux... Balloon Juice Cop Car Curmudgeonly... EarthBound Misfit Fail Blog Finding life hard? Hattie (Hawaii) Making Light Mockpaperscissors Mostly Cajun Murr Brewster Not Always Right Observing Hermann Pergelator Rants from t'Rookery Scary Duck Spork in the drawer Squatlo Rant Yellowdog Grannie Archive 2015: Jan Feb Mar Apr May Jun Archive 2014: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec This blog is getting really unmanegable, so I am taking the first 12 years' archives offline. My blog, my random decision. Tough shit; YOLO. Link Disclaimer ENGLISH : I am not responsible for the contents or form of any external page to which this website links. I specifically do not adopt their content, nor do I make it mine. DEUTSCH : Für alle Seiten, die auf dieser Website verlinkt sind, möchte ich betonen, dass ich keinerlei Einfluss auf deren Gestaltung und Inhalte habe. Deshalb distanziere ich mich ausdrücklich von allen Inhalten aller gelinkten Seiten und mache mir ihren Inhalt nicht zu eigen. This Blog's Status is Blog Dewey Decimal Classification : 153 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 3narcissistic 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 153type blog. QED ;) Books I have written

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