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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

Stardate : -307841.51474505325

Dif-tor heh smusma*

Goodbye, Leonard Nimoy, and thankyou on behalf of all Trekkies.

* : That's Vulcan for "Live long and prosper" :-)

Comments (2) :
Schorsch (D) has a Spock joke for us : " Spock in a Swiss cheese shop : the more cheese you have, the more holes there are. The more holes there are, the less cheese there is. Therefore, the more cheese there is, the less cheese there is. (Spock's mind blows!)" Oh nice one, Schorsch. I'm so stealing that for the cheese-and-wine party tonight :-)
Fritz Jörn, who blogs a little (in German) here, and is a friend of my old boss Dr.Hartmut Fetzer (to whom, Hi :-)), writes that "Spock's hand sign is Aaronitic, see here. To just use it as a greeting takes tradition lightly. And here is a photo thereof taken in the Jewish cemetery in Schwarzrheindorf." Yes, I knew that. Nimoy's family was Jewish. There's a YouTube video of him explaining the blessing in the synagogue, seen when he was a child :-). LLAP!

Friday, February 27, 2015

Lanzarote Cactus Garden

One of the (tourist) attractions on the small Canary island of Lanzarote is a cactus garden with its collection of over 1000 different types of cacti, ranging from the very tiny to the absolutely huge. Here are some of the photos I took during our one hour visit. Mouse-over the photos for a short description.

The cactus garden was established by local artist César Manrique (1919-1992) about whom more in a later blogpost in March.

Comments (1) :
Cop Car (USA) wrote " One can see so many different species within a well-designed garden! Your photos are lovely and I can appreciate how much work has gone into garden design. Given a choice, I prefer natural scenes (a high desert after an April shower provides a beautiful display of cacti); but, few of us (relatively speaking) have the choice, so gardens are most welcome. Looking forward to more photos of your trip." De nada :-)
Jenny (Ibiza) asks "Are the cacti labelled?" Yes. In photo 4 you can see a typical small black nameboard, see this close-up.

Wednesday, February 25, 2015

Lanzarote Lava

Being fed up with the freezing German winter, SWMBO and I flew to Lanzarote (Canary Islands) last week for some sunshine (20°C) while my sister-in-law looked after our dogs for us. I found the national park at Timanfaya to be most impressive. The world's biggest lava flow - over 10 miles wide - from a volcanic outbreak 300 years ago which lasted 6 years. So here are four photos to give you an optical impression of the bleak, black landscape with plants few and far between as far as the eye can see!

Subsequent blog entries will show you the cactus garden, diverse sporting activities and some local artist's work etc.

Comments (1) :
Cop Car (USA) wrote " Being a lousy geographer, I had to look up to see where-in-the-world Lanzarote is. Sounds like a wonderful place to spend a bit thawing out. I'm happy to hear that you and your wife got a break." Thankyou, CC. I've just added a link to the Wikipedia description of Lanzarote to make it easier for other readers :-)

Sunday, February 22, 2015

Annual Clout Shoot

Regular sport archery focusses on accuracy. In winter, in the sports hall, we train at 18 and at 30 meters. In summer, outdoors, at 50, 70 and 90 meters too. Hit a golfball at 18, a tennis ball at 30, a hand at 50, a head at 70, a body at 90 meters in terms of 14th century military archery.

But in the middle ages the distance between battle lines was 180-250 meters. So back then the archers trained elevations to achieve specific ranges, relying on the target areas being densely occupied by opposing forces. Once a year we try shooting at these ranges too, it is called "clout" shooting. A pole is put up 180 meters away and target rings drawn on the grass around it. It looks like this after a round, after you've got the elevation about right. Once I actually hit the pole, but that was a fluke, which cost me a round of beers :-)

The annual clout shoot is in memory of the battle of Crecy - 26th August 1346 - where the 9,000 English beat the 30,000 French resoundingly thanks to the English longbow. The battle lines were drawn up 230 meters apart, a tactical mistake by the French, because they had mercenery Genoese crossbowmen which they had put in the front lines so they could earn their pay first. However, in 1346, no-one really thought about just-in-time logistics and the crossbowmen's shields (pavese) were at the end of the 5 mile long French baggage train which had to file single tracked through the muddy woods of Crecy. So the crossbowmen were exposed.

Like I said, the battle lines were drawn up 230 meters apart, way beyond the 150 meter range of the Genoese crossbows, so their flight of arrows all fell short. The English longbowmen however had a range of 300+ meters. So their flights of arrows decimated the Genoese merceneries who were shieldless. As was much of the French infantry. The Genoese merceneries fled from this massacre as they could not hide under their big squarish pavese shields.

The French infantry had to clamber over the Genoese corpses and through the deep mud from the previous day's incessant rain to mount their attack. The English longbowmen waited until they had done so, then took them down in masses at 100-150 yards, thus making the field full of corpses wider in order to slow down a subsequent French cavalry charge.

The French knights were dying (sic!) for a fight and mounted their cavalry charge next. Now the English longbowmen had interchangeable warheads for their arrows and so put on broadheads to attack the (unarmoured) French horses as they picked their way through the mud and double-wide field of corpses. A knight without a horse is useless. As some knights got through the fields of corpses, for their 100 meter cavalry charge, the English longbowmen changed warheads again, this time to bodkins, which are armour piercing at these short ranges. Thus they could take out the French knights, firing a half dozen arrows per minute.

As the knights were just a few meters from the English bowmen and at full gallop, they fell into pits full of piked staves which the English had dug in front of their lines under cover of darkness the previous night, before the French had even reached the battlefield. The English archers could then draw their short swords ("mercy-givers") and stab any remaining French knights through their visors!

About 4,500 French knights were killed plus uncounted infantrymen and mercenaries. The English lost at most 200 men; it was an asymmetrical slaughter which founded the reputation of the English longbow and gave rise to the V-for victory two-fingered sign in the UK. This was reinforced at the battle of Agincourt in 1415, where the English also had a 6-1 victory due to the longbow and to better tactics. But that's enough of a history lesson for today :-)

Comments (1) :
Doug (Canada) wrote "One of my favourite movies is is the 1989 Kenneth Branagh version of Henry V. To my mind one of the greatest tracking shots in all of film history is the one near the end as the scene of the carnage at Agincourt is surveyed. It's a remarkable bit of cinematography and very moving. You can see it here - shot starts at 2 minutes in." Ah yes. And Shakespeare wrote some good stuff, didn't he? :-)

Friday, February 20, 2015

2048 : A win at last :-)

Way back in May of 2014 I told you about an addictive new game called 2048. Finally, after 8 months of playing it on and off, I have managed to win at it, see the 2048 score in the top left corner :-)

No, I don't honestly know how that happened and have been unable to reproduce it during the last 2 weeks, so I'm calling this one a fluke :-(

Comments (1) :
Jenny (Ibiza) asks "How many tries?" Dozens? scores? but less than a hundred.

Wednesday, February 18, 2015

Oshkosh, 1984

A while back, fellow pilot and blogreader Cop Car asked me about the flying I'd done in the USA. Turns out I have very few photos. This bunch was taken in 1984 when I flew into Oshkosh; analog photos back then, which I subsequently scanned. So apologies for the quality.

Oshkosh is on the west side of Lake Winnebago about 180 miles north of Chicago. Once a year their airfield (Wittman Field) hosts the EAA (Experimental Aircraft Association) meeting and Oshkosh is the busiest airfield in the whole WORLD! Like 7000+ planes, experimentals, homebuilts, warbirds and regular small planes. They borrow tower staff from Chicago, who call you out visually without your callsign (you don't use your own radio). We were told to stack up clockwise over the lake and when it was my turn, I was called "Blue-striped Aerostar, you are number EIGHT on finals now, maintain 105 knots". That got me wide awake, could I see all seven in front of me? You land in threes, the first lands long, the second midfield and takes a left off the runway, the third lands short and takes a right off the runway, then the next three & so on.

Anyway, Oshkosh is THE place to see planes you might otherwise never see, so here are the ones which were new to me back then :-)
Mouse over the photos for a descriptive title/identifier.

If you fancy hopping the pond for a visit to Oshkosh yourself, Bob Webster has a useful website, albeit in the other direction, USA->Yurp.

Then I found one other photo, where I am flying a Cessna 180/182(?) on floats out of Sausalito for Lake Tahoe, probably in the late 1970s. However, thorough research by Cop Car's friends (all aviation history buffs?) identify the plane as a Stinson 108. Now I have no memory of ever flying a Stinson, so I've taken the photo down, my memory must have deluded me. However, I do remember flying a Taylorcraft floatplane N96292 floats at Sausalito on August 5th 1978 for 1:25 as my introduction to floats, but I can't find a photo thereof, seems I didn't do many photos back then :-(

Comments (2) :
Cop Car (USA) wrote " Several times I meant to go to Oshkosh; but, crowds are so unpleasant for me that I never made myself do it. I have flown at least one aircraft that was displayed there in the late 1970s/early 1980s, however - the Merkel Mark II , an all-metal biplane designed and built to aerobatic loads. The MM II was the first tail-wheel (and first stick) airplane I ever flew. The late Ed Merkel and I flew together a great deal in those days, and I helped maintain his airplane - especially when he was out-of-town for extended periods. His widow still owns the plane as far as I know - although it's in a bit different configuration, now, and has been painted. Stu's floatplane aircraft is somewhat of a puzzlement to me since I cannot see the tail section. I would say it was a Cessna 185 except I've never seen a metal-skinned Cessna with the Vee wing struts. This is embarrassing since I, during 1978-1981, was the group engineer with structural responsibility for all of the tail-wheel models - current and past production versions. I flew each of the then-currently-produced tail-wheel models - never on floats or skis!) I've forwarded the photo to a friend who is better at recognizing the older models than I am. He is nearing his 50th anniversary as a structures engineer on Cessna single-engine models and is quite the historian.)" I no longer have my old logbooks, to look that flight up :-( So if your friend can ID it, that would be great :-)
Jenny (Ibiza) asks "What a funny plane that 11th photo shows. Which end is the front?" It's the Rutan Voyager, which is a canard, so it is flying left to right in my photo.

Tuesday, February 10, 2015

Twinkle, twinkle, little star...

Except that stars don't. Twinkle, I mean. It's our atmosphere that twinkles. Apollo astronauts on the moon looked up at hard, pointlike dots. Untwinkling stars. Because the moon has no atmosphere. The ISS crew reports the same thing. Even the robot on Mars which took a photo of the Earth in the martian sky saw nary a twinkle. Because the martian atmosphere is so thin.

The stars are so far away that they appear as point sources despite their size (UY Scuti, the largest known star, is over 1700 solar diameters in size). The eye's pupil is about 7mm across at night, so it's a narrow beam that one sees. The atmosphere contains regions of warm and cold air which have different refractive indices and whose surfaces are neither parallel nor perpendicular to the beam of starlight. These regions thus act like prisms and deflect the beam slightly. There are many such deflections as the beam passes through the atmosphere, changing from millisecond to millisecond. So the apparent direction to the star changes minutely very quickly, almost randomly about the centre of the beam. It is this which we call twinkling.

And stars are point sources. If you see them through a reflecting telescope with an apparent cross, what you are seeing is the diffraction pattern of the spider-leg thin arms which hold the secondary mirror in place.

Two myths busted for the price of one ;-)

Sunday, February 8, 2015

Grexit part II (deserting the sinking ship)

Estimates by the ECB and JP Morgan Chase report that within the last two months alone 21 billion (aka 10↑9) Euros have left greek bank accounts for elsewhere. That's 10% of their deposits :-( The Target accounts - which are a measure of the severity of the Euro-crisis - showed this capital flight too. The german Bundesbank Target account went up by 54 billion to 515 billion in january alone. At the same time the greek Target account deficit rose from 42 to 49 billion (december figures). So the rich Greeks distrust their government so much they are deserting the sinking ship rather than trying to save their own country. That's selfishness winning over patriotism for you!

Now let's look at how those Target accounts work. When those rich Greeks move their money abroad, the greek banks obtain a refinancing from the ECB, increasingly in the form of Ela-emergency credit, in part therefore from the german Bundesbank. The Ela-emergency credits therefore are being misused to finance rich Greeks' capital flight :-( The Target accounts are being misused as a licence to print money :-(

And who do you think is going to have to pay for all this sinking-ship desertion? Why, you and I of course :-( So I think it is time Greece set up capital flow controls such as were used in Cyprus in 2013 to prevent their banks collapsing! And should Grexit asap :-(

Comments (4) :
Petra (A) reprimand "Politics is not your strong suite, go back to science and humour!" Maybe you're right? But sometimes I need to let off steam :-)
Klaus (Alaska) points me to Alan Greenspan's views on Grexit and the Euro.
Hattie (Hawaii) wrote " Hi, Stu. I don't pretend to know a lot about all this money stuff and have no head at all for mathematics. But I do think national debt is not the same as the family budget. It is too bad that Greece tied its economy to Germany's. How could that end well?" They are dragging us down!
Renke (D) wrote " One last comment before I shut up - your reply as quoted in the last line is only partly true. Most [for Greece, the NGO ATTAC (absolutely not neutral :)) calculated 77 %, Der Spiegel wrote for the second bail-out that 25 % were given directly to international creditors. The truth is somewhere in the middle] of the Euro crisis bail-outs (Greece, Portugal, Spain, Ireland, ...) were not used to lower the country's debt but for financing debt conversion programs. Greece is heavily indebted and has a horrible track record in corruption and misgovernment but "our" money is not part of the obscure Greek national budget - the tax money is used to stabilise the underfunded European (including German) banks. There may be good points to rescue the financial institutions (I'm fortunately not an economist) but arguing Greece is destroying Good Old Germany is not exactly true. German banks invested in high-interest (and high-risk!) Greek bonds [in 2011 (before the huge debt conversions) according to FAZ about 22.7*10^9 EUR] after Greece defaulted the troika invented a scheme to shell out those banks via tax-financed kick-backs. Rant end, as promised :)" FWIW, their current (new) finance minister specialises in Game Theory :-(

Friday, February 6, 2015

Grexit NOW, please!

A few years back, around 1981, Greece joined the EU (European Union). Then around the turn of the century, Greece applied to partake of the Euro. You would think that some of our politicians and some of the socalled "experts" in Brussels would have checked to see how financially reliable Greece had been in the past?

Did they? Did they hell! They turned a deliberate cyclopean blind eye :-(

Otherwise they might have discovered that :-

  • Greece went bankrupt in 1824.
  • Greece went bankrupt again in 1843.
  • Greece went bankrupt yet again in 1860.
  • Greece went bankrupt for a fourth time in 1890.
  • Greece went bankrupt for a fifth time in 1932.
  • Greece was thrown out of the currency union it was in, in 1908.
If you or I had a credit history like this, defaulting on our debts FIVE times in the last 200 years, we would NEVER be trusted again! But the feckless eejits in Brussels welcomed them on board, GAVE them the Euro in 2001, and now have a partial default on their hands. Now the unproductive, freeloading, tax-avoiding, finagling Greeks want to default even more and are blackmailing the EU for even more "free" money which you and I will end up paying :-(

And of course, the incompetents in Brussels conveniently "forgot" to include a clause in the Euro-participation contracts to enable them to expel the bankrupting ingratiates! The only way to get rid of them is for them to leave of their own "free" will and go back to the Drachma :-(

Time for that "Grexit" - Greece exiting the Euro, back to the Drachma - NOW!

Methinks this "gimme!" attitude of entitlement has been a grecian trait for millenia? After all, was it not Archimedes who said

GIVE ME a lever and GIVE ME a place to rest it and I will move the world.
See, "GIVE ME" crops up twice! :-(

PS: FYI : Portugal has also defaulted on its national debt five times since 1800, and Spain no less than seven times (and 13 times in all since 1500). The UK has not defaulted even once in over a thousand years!

Comments (4) :
Klaus (Alaska) tells me that last sentence about the UK is wrong : " According to this 2008 report (pages 40 & 41) the UK has defaulted 5 times since 1822. Germany did it 3 times, here you can see the list of sovereign debt defaults of all countries. But as you know it is not only Greece that causes the Euro crisis, its also Italy,Spain, Portugal, France, all those countries have missed the "Maastricht Treaty" when it was agreed on that the deficit to GDP should not exceed 3% and debt not to exceed 60% of GDP, even Germany missed those marks in the last few years. The US had a deficit to GDP of 10.1% in 2009, in 2014 it was 3% (recovering), the US debt to GDP was 101%, but Japan topped that (227%) in 2014. Our whole world lives on debt and sooner or later (rather sooner) that will come to an end, hyperinflation, devaluation of paper money, etc., however have a nice weekend. P.S. the power of a currency is also the result of a strong economy and there are signs that Europe is getting weaker in that regard." I was quoting from memory from a Civics class I took 50 years ago, wherein we were taught that the UK just scraped by going broke by restructuring their debt, which is what your 2008 report says in Table 3 on page 42. However, we may need a real economist to interpret this for us, so Guido, if you read this perhaps you'd comment?
Klaus (Alaska) replied : "It maybe also important to explain the difference between Bankruptcy & debt default,countries cannot go bankrupt, who would they file it with ?, speaking for the US that matter is covered in the constitution: However, the Constitution was amended to specify that the validity of the debts of the United States cannot be questioned, which means that the U.S. cannot avoid its debts by filing bankruptcy. This change in the Constitution also said that when part of the U.S. revolts and forms its own "country" (this last happened 140 years ago, starting the Civil War), that country's debts are not valid and do not have to be paid, so there is no need for that country to file bankruptcy. I don't know how that matter is regulated in other countries but I think similar. So coming back to your statement about the UK "never defaulted in thousand years" is wrong, they defaulted 5 times but solved it through restructuring and so did other countries that dealt with debt defaults.If you would wrote the "UK never went bankrupt in thousand years" that would be correct but also nonsense because a country cannot go bankrupt. In private business affairs we have bankruptcies, first comes debt default ( company cannot pays its bills) and than at least in the US a company files bankruptcy (Chapter 11) that way they are allowed a time frame of 120 days to either pay or restructure the business in a way to pay their debt and or renegotiate new terms with the Debtors (maybe lower payments, etc.) to settle the debt. There are more legal terms within chapter 11 but everybody can look them up on the internet. P.S. in the US it is not even allowed that a State files bankruptcy." Aha, the (in) the red states?
Renke (D) wrote " I'm not sure if I like the trendy tabloid style of your article, very similar to Bild's Pleite-Griechen campaign. But whatever - it's your blog :) Shortly before your rant Andrew wrote also about Greece, personally I prefer his unagitated point of view." Chacun à son goût.
blog a bissl (D) wrote " NO country will ever pay back ist debt. They all just recycle the money they don't have. (Like the whirlpool of a flushing toilet, see Once interest rates are zero, debt doesn't cost. So it's written off silently, just stays in the books for a while, until it will be forgotten one day. This holds true to states, to banks (who create money nowadays), to all official A-rated entities. Unfortunaltey you and me aren't: We have to pay back debt, we pay interest, thus massively adding to the common wealth ( " I'm sure the Greeks would like to have negative interest rates on their debts ;-)

Monday, February 2, 2015

Doing big numbers :-)

A few years back, I gave a lecture to a class of schoolchildren, entitled Doing big numbers :-) and since I've finally found my notes, I thought I'd reproduce it here for your esteemed edification :-)

Of coarse (sic!) the class thought it might be a talk on personal hygiene so we got the usual "No shit!" jokes out of the way first and began with the question "What is the biggest (whole) number?"

The first to answer proffered "A million million million!" soon followed by undisciplined shouts of "Whatever anybody else says, plus one!" and "Then times itself!". Good answers, I said, and we'll come back to them later.

So I rephrased the question to "What is the biggest number to which you can count?" The same answer "A million million million?" was suggested, but more with a query at the end. So I had them do this calculation: Assume it takes you on average 6 seconds to enunciate a number, and you can count - without making a mistake - for 70 years of your life, how high could you count? 14,400 per day times 365 days/year times 70 years = 367,920,000 so not even 400 million, let alone a million million million :-(

Just for comparison, assume a blade of grass is 1mm wide, then a square meter of dense grass could hold a million blades, so a standard football(soccer) pitch could hold 7,140 million densely packed blades, which you couldn't count out loud! At most a 20m square patch.

An objection came "But 367,920,000 is so small it's not even interesting, tell us about some really big numbers!" Wrong, I said, 367,920,000 is an interesting number, and you can prove it. Ask yourselves what the smallest uninteresting number is? After several suggestions - aka a race to the bottom - one of the kids twigged that "There is no smallest uninteresting number, because that would make it interesting! And therefore there are NO uninteresting numbers :-)"

Correct, and when somebody answered "Whatever anybody else says, plus one!" it implies that there is NO largest number, you can always add one. But what is the biggest number you can write down? - writing it down is called a notation. Again "A million million million!" was proffered and corrected to "With the millions going on until you die!" Probably in a bank in Zimbabwe ;-)

OK, I said let's look at notations. What do you call it when you add up the same number several times, for example 10+10+10=30? You call repeated addition "multiplication" and write 10*3 = 30. Now what do you call repeated multiplication and how do you write it? So they learned about exponentiation which is just repeated multiplication, so 10*10*10=1000. This can be written as 103 with the count of the repeated multiplications as a superscript or written inline as 10↑3 which is easier to typeset. So your million million million is 1,000,000↑3 or (10↑6)↑3 which is 10↑18, you just multiply the exponents. You also have a billion, a trillion etc. as named numbers.

A googol is the name of the large number 10↑100; that is, the digit 1 followed by 100 zeroes. The word "googol" was invented in 1938 by a 9-year-old called Milton Sirotta. It is bigger than the total number of elementary particles in the universe which is around 10↑80. He also came up with the Googolplex. A googolplex is the number 10↑googol, or equivalently, 10↑10↑100). Written out in ordinary decimal notation, it is 1 followed by 10↑100 zeroes. But since a typical book contains only a million characters, just think how many books you would need to fill (hint 10↑94) to write that down, which is why we give the number a name "Googolplex".

Are there even bigger numbers? If so, how would we write them?

Now let's ask ourselves, what about repeated exponentiation? This is a hyperoperation called tetration. It is written with TWO up-arrows (e.g. 10↑↑4) using the up-arrow notation invented by Donald Knuth, or, to give him his full title, Prof.(em) Dr. Dr(h.c)26 Donald E.Knuth, that's how famous he is. I met him once many moons ago when he was less famous, a mere (h.c)19 ;-)

Repeated tetration is called pentation and is written with 3 up-arrows in Knuth's notation, e.g. 10↑↑↑7. Repeated pentation is called hexation and is written with 4 up-arrows in Knuth's notation, e.g. 10↑↑↑↑3. And so on....

As one child pointed out, you could even have a googolplex, followed by a googolplex of up-arrows, followed by a googolplex and that would be a really HUGE number :-)

These numbers are HUGE, you may say, far bigger than anything we would ever need. But even 10↑↑↑↑3 is really a SMALL number, because there are infinitely more which are bigger, but only 10↑↑↑↑3 - 1 which are smaller;-)

I hope I could show you how to do big numbers painlessly ;-)

Comments (6) :
Cop Car (USA) wrote immediately " I want your "Math is one of them" tee shirt!" Get your local T-shirt shop to print one for you, it's cheaper than transatlantic shipping.
John (UK) complained "We were only taught as far as exponentiation. But now you've explained it, it's obvious how the idea is extended. Thankyou!" Don't thank me, it was Don's idea, I'm merely passing it on.
Renke (D) asks "Why did you use football fields as example? The other well-known surface scale results in much more impressive numbers: One Saarland could hold about 2569690000 million grass blades :)" Football fields are well-known wordwide; you cannot say the same for Saarland. So it serves the international readership better to use soccer fields ;-)
Ivan (RUS) said "We learned about 'power-towers', e.g. 33333 at university. How would you & Don Knuth write that?" 3↑↑5 which is about 4.4 * 1038.
Schorsch (D) shows us a video How to do SMALL numbers ;-)
Klaus (Alaska) notes "So "Graham's_number" is larger than "googolplex", according to this article . " Indeed : Graham's_number is 3(64↑s)3. See how compact Knuth's uparrow notation is :-)

Recent Writings
Dif-tor heh smusma
Lanzarote Cactus Garden
Lanzarote Lava
Annual Clout Shoot
2048 : A win at last :-)
Oshkosh, 1984
Twinkle, twinkle...
Grexit part II
Grexit NOW, please!
Doing Big Numbers
A Thousand Years ago...
Budding Scientists
Winston Churchill
Reacting to Charlie
American Sniper
German Aircraft Regs.
Pegs in holes
The Ultimate Cafe´Racer
Pirating cartoons
Lilienthal Archives Online
2000 blogposts :-)
Sympathy for the Devil
The Maze Maker etc.
Stupid is as stupid does
Never annoy the wife!
Best of 2014

Ain Bulldog Blog
Balloon Juice
Cop Car
Earth-Bound Misfit
Echidne of the snakes
Fail Blog
Finding life hard?
Hattie (Hawaii)
Making Light
Mostly Cajun
Murr Brewster
Not Always Right
Observing Hermann
Rants from t'Rookery
Scary Duck
Spork in the drawer
Squatlo Rant
The Magistrate's Blog
XE Express
Yellowdog Grannie

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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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