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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 after the death of his old dog, Kosmo, he also has a new bulldog puppy, Clara, since September 2018 :-)

Some of my bikes

My Crypto Pages

My Maths Pages

Thursday, December 13, 2018

... Interesting Times

People believe there was an ancient chinese curse "May you live in interesting times!" But this is fake news, there was no such chinese curse. That said, some people collect analogue clocks with non-standard displays, aka interesting times. I bought this one from MathsGear last week; now sold out :-(

Standard clocks have a circular clockface, a short hour-hand and a long minute-hand. Some have a seconds-hand too. But this is a Fibonacci clock! The short straight hand is the minute hand. The longer hand is in the shape of a Fibonacci spiral curve. You read off the hours where the Fibonacci spiral curve intercepts the vertical central line on the oblong "clockface".

The photo on the left shows 12:02, the photo on the right shows 1:50.

A practical tip : mount the clock at eye level to make it easier to read. Leave room for the spiral end at 3 and 9 positions. The cheap drive is powered by an AA battery.

If you thought this was scurrilous, wait until you see the hyperbola display clock!

The little hand centred on the baseplate is the minute hand. As the baseplate slowly rotates the straight black rod moves around and intercepts the hyperbola slots where you can read off the time : 3:30 here :-) Sadly, already sold out :-(

For the New Year's Eve countdown, I also have a candle I calibrated myself :-)

May you too live in interesting times ;-)

Tuesday, December 11, 2018

This pencil, sharpened, stays in its prime :-)

Around this time of year, I'm always on the lookout for really nerdy presents for my geeky STEM friends. So I was quite happy to find this pencil at MathsGear , in the UK. It came in boxes of 11 :-)

The pencil is embossed with a 24 digit prime number (see close-up, below).

Now, as you use the pencil, you will need to sharpen it at times. So first of all, you will remove the leading digit, 3, by sharpening the pencil. The great feature is that the remaining 23 digit number 576...37 is also prime :-)
Continuing, you'll sharpen the pencil again some time later, removing the now leading digit, 5. The remaining 22 digit number 76...37 is also prime :-) This goes on, all the way down the pencil, until you are left(sic!) with one remaining digit, 7, which is also prime. How geeky is that!

That 24 digit prime number is the largest continuously left-truncatable prime number. Dr. James Grime has the details in a 10 minute YouTube video.

I managed to get one of the last pencil packets, these are sadly now sold out :-(
However MathsGear have plenty of other stuff; go see if there's anything you like. Comments (4)
Cop Car (USA) wrote " "boxes of 11" - Well, of course! A prime number of pencils that degrades to a prime number in whichever direction it is truncated. Thanks for the link. They have some neat stuff!" Rubbish! One is not a prime number! The definition of a prime number is a positive integer that has exactly two positive distinct divisors :-)
Cop Car (USA) replied " Back at you, Stu. Not everyone abides by the definition of "prime" that you quote. You use your definition and I'll use mine. At one may access "The History of the Primality of One | A Selection of Sources" by Angela Reddick, Yeng Xiong, and Chris K. Caldwell. It includes a statement from D.N. Lehmer, "A prime number is defined as one that is exactly divisible by no other number than itself and unity. The number 1 itself is to be considered as a prime according to this definition and has been listed as such in the table. Some mathematicians [a footnote here cites E. Landau [76]], however, prefer to exclude unity from the list of primes, thus obtaining a slight simplification in the statement of certain theorems. The same reasons would apply to exclude the number 2, which is the only even prime, and which appears as an exception in the statement of many theorems also. The number 1 is certainly not composite in the same sense as the number 6, and if it is ruled out of the list of primes it is necessary to create a particular class for this number alone." Of course, 1 was not always considered to be a number. ; )" Quoting your own source "Modern usage dictates that the number one be called a unit and not a prime." So there ;-)
Cop Car (USA) replied " "Modern usage" is not something that I, who learned about prime numbers in 1952 and who am well past my prime, recognizes. I'll slink off, tail between legs, and drop the subject." That'd be 1951, 'cos it's prime ;-)
Petra (A) begs "Sold out ? :-( Can I have one from your box of 11 please pretty please?" Mail me your address then and pay the postage.
Andrew (GBM) asks "If 1 has one divisor, and primes two, what do you call numbers with three divisors?" Those are the squares on the primes, Andrew.

Sunday, December 9, 2018

Blogroll changes : ave atque vale.

Time to tell you about some (forthcoming/past) changes to my blogroll.

It seems that Badtux the snarky penguin hasn't updated since the start of november - instead of almost daily - so I'm assuming he's hospitalised or even deceased. What a shame, it was a good blog which I liked a lot. But I'll be dropping it from my blogroll for the new year. Learning from this, I've instructed SWMBO to put up a one-liner "This blog stopped here" should I shuffle off this mortal coil before she does.

He is replaced by Sabine Hossenfelder, a theoretical physicist, who blogs over at Back Reaction. She writes a science-heavy blog and so may not be for everyone, but I'm trying it at least for a while.

For a month or so I've been reading Infidel753, an American allrounder, which I like for his weekly roundup of links he enjoyed during the previous week.

This year I've been following a fellow biker, Kinga Tanajewska, who is returning home to Poland from Australia on her motorcycle. She blogs about her adventure at On Her Bike with lots of great photos; she was in Bulgaria in her last posting and so almost home. I expect I'll stop following the blog when she gets home unless she sets off on another adventure.

I like to keep my blogroll short (currently 20 links) so I can visit everyone daily, but if you know of a blog which you think might appeal to me, please email your favourite link to me :-)

And before anybody asks : "ave atque vale" is Latin for "hail and farewell", it originated from the last line of poem 101 by Catullus, as classical scholars will well know :-)

Gratuitous puppy photo of Clara for all who asked :-)

Comments (5)
Good news! Badtux tells us he's still alive, just been away for 6 weeks :-)
Peter (UK) wrote "hi Stu, you seem pretty content with your lot, an interesting item might I say.... best wishes for christmas and the new year...." Always open for new suggestions though, Peter.
Astrid (S) implores "Just don't go 100% science blog please, max. 50%" OK, I'll try to remember to rant occasionally, Astrid ;-)
Pierre (F) asked "I love the RoboBulldog! Who sculpted that?" Local man Jürgen Linnemannstöns, from scrap metal. Here's his LilleArt website.
Karel (CZ) wrote "I suggest xkcd." Often good, but not consistently so.

Thursday, December 6, 2018

Galileo saw Neptune!

Way back around 1610 the prevailing opinion of the solar system was the geocentric claim by Ptolemy. This held that the Earth was at the centre of the universe; in particular The One True Church® held that the Vatican was the centre of the universe. It still does :-( This was what got Galileo into trouble because he suggested that the Sun was at the centre of the solar system (aka heliocentric model). Hence "E pur si muove".

He had deduced this by observing 4 moons around Jupiter, using his improved but still primitive refracting telescope. His first home-made telescope was like an opera glass nowadays, the main lens convex and the eyepiece a concave lens, magnification 3 ;-) His later improvements gave his best telescope a magnification of about 20, albeit with a narrow field of view and lens defects causing blurry images. Nevertheless he saw Jupiter as a disc and the four larger moons of Jupiter. In order of decreasing size, these are Ganymede, Callisto, Io and Europa. The first three are even bigger than Pluto, which was why Pluto was recently degraded to the status of a dwarf-planet, leaving Neptune as the planet farthest out in our solar system.

In 1612 Galileo was observing Jupiter again when he observed what he at first thought was a fifth moon but later wrote that it was a fixed star although documenting its movement relative to the background stars. Here are his notes made at the time :-

Nowadays, every decent amateur astronomer has a solar-system-simulator running on his or her PC. By setting its date to winter of 1612, it can calculate what the night sky looked like back then. Galileo's notes show the 5th object, a faint blue dot, in the plane of Jupiter's moons. The simulation places Neptune - the outermost planet of the Solar system - exactly where he saw the 5th object. So I conclude : Galileo saw Neptune!

Now we can test if this was indeed feasible. Tonight and tomorrow night Neptune is right next to Mars making it very easy to find in the sky. So I shall use my small portable reflecting telescope - Galileo would have eaten his heart out for one of these - choose an eyepiece to set the magnification to about 20x, and look at the red disc of Mars. Right next to it I shall expect to see a pale blue dot, Neptune, thus "confirming" that Galileo could have seen Neptune with a 20x magnifying telescope. You can do this too, so give it a try! You can see Mars with the naked eye, it's really close right now, just 8 light-minutes away. But you will need either high-power binoculars (20x) or a telescope to see Neptune. Just like Galileo did :-)

In all fairness, mine is the better instrument, a reflecting telescope like the one invented by Sir Isaac Newton in 1688. His primary mirror had a 2 inch aperture and magnified about 35x. Mine has a 3" aperture and so a maximum useful magnification of 150x, viewing permitting. Still not enough to see Neptune as a disc though (needs 200x+ AND good viewing).

Getting off-topic here, but if you want a semi-portable scope that will show ALL the planets as discs, you will need something like this one shown on the left. This has an eight inch aperture (and so could reach 8*50=400x magnification with best viewing), and when dissembled into its 4 main pieces will JUST fit in my car (a VW New Beetle). The tube goes across the back seat, the mounting in the trunk/boot, the box of different eyepieces behind the passenger seat and the sight behind the driver seat. The sight has no magnification, it just projects a red spot into the sky so you can aim the main tube. Mind you, you'll need to drive (in winter!) with the car's heating off or you'll find it will take the main mirror ¾ hour to cool down after arrival at your dark-sky observation site ;-)

Now let's just hope the skies are clear on 6th and 7th :-)

Comments (4)
Brian (UK) asks "What do those scopes cost?" They're cheap. The small tabletop one is a Celestron First Scope and cost just 73€. The bigger one is an 8 inch aperture Galaxy d8 on a Dobsonian mount. An equivalent Orion XT8 model costs just 380€. Add 4*30=120€ for four different Plössl eyepieces of your choice of focal lengths. That's how I got started. But don't expect to see the quality of satellite-based imagery like Hubble or Kepler photos.
Petra (A) asks "What else did Galileo see?". He also saw sunspots, the phases of Venus, craters & mountains on the Moon, and Saturn. But the lenses on the first refractors were so bad that early observers thought Saturn had ears rather than rings. There was even a publication by a Vatican astronomer - in Latin - suggesting that the rings of Saturn - I translate from the title of the publication - were "...the foreskin of our dear Lord..." ;-)
Brian (UK) replied, asking "So, did it work for you? Did you see Neptune at 20x ?" Sadly no, we had 8/8 cloud cover both nights until after Mars set. The best laid plans of mice and men gang aft aglay :-(
Jack Kinker (USA) corrected my introduction, as forwarded by Pergelator, writing " Wasn't this the Ptolemaic claim? Copernicus moved the Sun to the center...?" Yes indeed Jack, my bad! In 1543 Copernicus published De revolutionibus orbium coelestium putting the sun at the centre of the solar system, although Aristarchus of Samos had initially suggested this around 250 BC. The model with the Earth at the centre and everything else in nested spheres around it was due to Ptolemy (around 130 AD, in his book Almagest). I have corrected the initial blogpost, thankyou Jack!

Saturday, December 1, 2018

Bar bet questions

Regular readers will know I like bar bets to win a beer or three. So here are some tricky questions for you to try yourselves. I always warn people to think deeply first before replying. No Googling allowed!

Question 1 - What is heavier, an ounce of gold or an ounce of feathers? Many immediately shout "They're the same!" but that's not true, the gold weighs more than the feathers! Proof : Gold is weighed in Troy ounces, non-precious metals (and feathers) in avoirdupois ounces. A troy ounce weighs 31.1 grams and an avoirdupois ounce weighs 28.35 grams. So an ounce of gold weighs more than an ounce of feathers. Mine's a Guinness.

Question 2 - What is heavier, a pound of gold or a pound of feathers? Having heard my previous reply, many immediately shout "The gold weighs more than the feathers!" but that's not true, the pound of gold weighs less than the pound of feathers! Proof : There are 16 ounces in an avoirdupois pound but only twelve troy ounces in a troy pound. A troy pound weighs 373 grams but an avoirdupois pound weighs 454 grams. So a pound of gold weighs LESS than a pound of feathers. Mine's a Guinness again;-)

If these troy vs. avoirdupois weights are confusing any of you, let's try a simpler but worldwide question for my internet blogreaders.

Question 3 - You and I each get a ton of bricks delivered to our building sites. Whose brick load is heavier, yours or mine? Some cautious thinking takes place across the web ;-) It's the same item (bricks), so there can be no difference you might think. But I live in Germany, so my ton is a metric ton (1000 kg = 2206 lbs). If you are in the USA, you use short tons (2000 lbs). In the UK you use long tons (2240 lbs). So the answer to the question "Whose brick load is heavier, yours or mine?" depends, dear blogreader, on where you live! So let's each have a third Guinness ;-)

Aside : What have we learned today? When using a measurement make sure you know the exact units used. When stating a measurement, be sure to quote the exact units used. Preferably, use the metric system too ;-)

Recent Writings
... Interesting Times
This pencil...
Blogroll changes
Galileo saw Neptune!
Bar bet questions
Attractive numbers
InSight on Mars :-)
Bigger than you'd think
"I am a jam donut!"
Marriage made in heaven
Hessen's election :-(
9/11, a fateful day
The Hill of Crosses
The centre of Europe
Space museum, Moletai
Six :-)
The Glory of Autumn
Discworld discovered
Tallinn, Estonia
Riga, Latvia :-)
Speech-to-Text ;-)
Amber Museum, Palanga
Baltic Coast Road
Sculpture Park Klaipeda

Ain Bulldog Blog
All hat no cattle
Back Reaction
Balloon Juice
Cop Car
Earth-Bound Misfit
Fail Blog
Finding life hard?
Greg Laden
Mostly Cajun
Observing Hermann
On her Bike
Rants from t'Rookery
Starts with a Bang
Yellowdog Grannie

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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 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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