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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

Leapday, February 29, 2020

Getting to 365.2425 days

When society became agricultural a couple of thousand years ago, calendars were needed to let the farmers know when best to plant their crops etc. It also became important that the calendars stayed in sync with the solar year and didn't drift along by a day or a few days every year. The first calendars were probably lunar rather than solar ones and they didn't know back then that the Earth's orbit around the sun (=the solar year) took about 365¼ days.

The original Roman calendar, alledgedly dating from Romulus, consisted of ten months beginning in spring with March; winter was left as an unassigned span of days. The winter period was later divided into two months, January and February. Weeks had eight or nine days. This scheme was somewhat short of the solar year, and it needed constant intercalation to keep farming in the proper seasons. Intercalation was done in february to keep in sync with the solar cycle. The Greek (Attic) calendar was not entirely dissimilar.

Then along came Julius Caesar who introduced the Julian calendar in 46 BC. The Julian calendar was supposed to have a single leap day on 24 February every fourth year, which would have made the average year 365¼ days long; quite accurate until the priests screwed it up by making a leap day happen every 3 years. The revised calendar remained slightly longer than the solar year :-(

Finally in 1582 AD Pope Gregory introduced the Gregorian calendar to get the seasons back into place, which most countries use until this day. An average Gregorian year is 365.2425 days long. Compared to the tropical year, the Gregorian calendar is still off by 1 day every 3236 years.

But that was just within the sphere of influence of the Catholic church which had "inherited" the Roman empire, so to say. Other religions had - and still have - their own calendars.

The Hindu leap year includes an extra month, often referred to as Adhik Maas or Purushottam Maas. It typically occurs once every three years or four times in 11 years. Therefore, the yearly lag of a lunar year is adjusted every three years.

The Chinese add a whole leap month approximately every three years : The Chinese Calendar has a leap month added about every three years.

Months in the Islamic calendar are directly tied to the timing of the Moon phases. The length of each month is determined by the duration of a Moon cycle or lunation, specifically the time from one Waxing Crescent Moon to the next. Even though the sum of 12 lunar months consistently falls 11 days short of the length of a solar year, Islamic time reckoning does not employ any correction mechanisms, like the leap days in the Gregorian calendar.

A leap year in the Jewish calendar has 13 months and occurs 7 times in a 19-year cycle. In Hebrew, a leap year is referred to as Shanah Me'uberet, or pregnant year. Months in the Jewish calendar are based on the phases of the Moon. A new month begins on the day of the Crescent Moon after the New Moon phase. Because the sum of 12 lunar months is about 11 days shorter than the solar year, a 13th Jewish month is periodically added to keep the calendar in step with the astronomical seasons. In a Jewish leap year, an extra month is added after the month of Shevat and before the month of Adar. It is called Adar Aleph, Adar Rishon, or Adar I. The month of Adar is then referred to as Adar Bet, Adar Sheni, or Adar II. According to Jewish tradition, Adar is a lucky and happy month.

If I had my way, I would scrap February 29 (leap day) almost every 4 years and replace it every 8 years or so by an extra weekend in the summer when it's warm here :-)

Tuesday, February 25, 2020

Our nearest neighbour

When asked which is our nearest neighbouring planet, many will answer Venus. But this is not always true. The picture most people have in mind is shown below. But it is misleading. Yes, it shows the planets in the correct sequence, moving left-to-right away from the sun, and it shows the relative sizes of the planets (and the sun) to scale. However the distance between the planets is far from being to scale, and they are hardly ever in a straight line as shown below.

So, in order to answer the question Which is our nearest neighbouring planet? I put the four inner stone planets on a straight line using the correct distance for their mean orbital radii (distance from the sun). The distance Sun-Earth is defined as one (1) Astronomical Unit (AU). Mercury orbits at 0.39 AU, Venus at 0.72 AU, and Mars at 1.5 AU. These are average distances, i.e. assuming circular orbits whereas in fact the orbits are slightly elliptical. So, IF and only IF the inner planets were in a straight line, Mercury would be 0.61 AU away, Venus would be 0.28 AU away and Mars 0.5 AU away from Earth.

However, the planets orbit the sun in (almost) the same plane. Mercury orbits the sun in 88 Earth-days, Venus in 225 Earth-days, Earth in 365¼ days, and Mars in 687 Earth-days. Thus, starting from the straight line assumption shown above, I calculated where the planets would be after one year and drew their positions to scale both as regards distance (described above) and angles resulting from orbital rotations. See my sketch below.

Mercury makes 365¼/88 = 4.15 orbits, so is 54 degrees past the initial straight line Sun-Earth. Venus makes 365¼/225 = 1.623 orbits, so is 224 degrees past the initial straight line Sun-Earth. Mars makes 365¼/687 = 0.53 orbits, so is 191 degrees past the initial straight line Sun-Earth. These angles and AU distances are to scale in the diagram above; planet sizes are not to scale. As you can see, after 1 year, Mars and Venus are on the far side of the Sun and SURPRISE perhaps, Mercury is our nearest neighbour.

When I do the calculation using the correct, elliptical, orbits and integrate the distance over a whole century, then Mercury is our nearest neighbour for 46% of the time, Venus for 36% of the time, and Mars for 18% of the time.

This doesn't mean that Mercury is easiest to get to. The amount of energy needed to get to each of the planets can be related to the square of the difference in their orbital velocities (Delta-V). Now Delta-V from a low Earth orbit (LEO) to a Mercury orbit is 7.5 km/sec, for Venus it is 2.5 km/sec, and for Mars it is 2.9 km/sec, so Mercury, although nearest to us for 46% of the time, is almost thrice as difficult to get to.

Nearest in terms of distance is not nearest in terms of Delta-V aka energy to get there.

Friday, February 21, 2020

Palindromic number surprises

Today I want to tell you about a couple of things that surprised me about palindromic numbers. I guess that's what comes from playing with number theory ;-)

Most people know that palindromes are words or phrases that read the same from back to front as from front to back. Example word level, example phrase "Evil rats on no star live".

Similarly, palindromic numbers read the same from back to front as from front to back. So 15651 and 82374647328 are palindromic but 191919 is not.

There is a conjecture (that's math jargon for : we believe it to be true but we can't prove it) that if we flip a number and add the result we will always get a palindromic number as a result. If not, just repeat the operation as often as needed and we'll always finish up with a palindromic number.

Examples : 23 flipped is 32, adding them gives 23+32=55 which is a palindromic number, immediately. 159 flipped is 951, adding them gives 159+951=1110 which is NOT a palindromic number, so we repeat the operation again 1110+0111=1221, which IS a palindromic number, after just one repetition of the operation [flip and add].

So far, so good. But SURPRISE there are numbers where we don't know if the final result is a palindromic number or not. Take 196 as (the smallest) example. 196+691=887 is not palindromic, so repeat the operation. 887+788=1675 is not palindromic, so repeat the operation. 1675+5761=7436 is not palindromic, so repeat the operation. 7436+6347=13783 is not palindromic, so repeat the operation. At this point I gave up doing it in my head and wrote a little program (in PROLOG, Cop Car) to repeat the [flip and add] operations. This what Pergelator would have done. After over a billion iterations, it still didn't have a palindromic number result. So we don't know if the conjecture is true or not.

So I researched around the web for palindromic numbers and discovered the second surprise (to me) : Every number can be written as the sum of three palindromic numbers! There is a paper by Cilleruelo, Luce and Baxter proving this for any base, not just 10. Thanks guys, for blowing my mind! ;-)

Comments (1)
Pergelator sent me a link to a gaudy program which, given any number, will display one of the palindromic triples which add to that number. It implements the Cilleruelo et al algorithms.

Tuesday, February 18, 2020

Hiking through Patagonia

No, it's not me doing that trip, it's my old friend Mike. He and I went to City University (London,UK) together for our B.Sc (hons) degrees in Physics back in the early sixties. Mike currently hails from Canada and is into long distance hikes. And when he hikes, he blogs about each daily walk. This time he is in Patagonia and has been blogging some photos of the spectacular scenery. So I would like you all to follow this link to Mike the Hike and go give Mike the readership his photos deserve :-)
P.S: Right clicking on his photos gets you to the enlargements.

Personally, I'm trying to get a group together to go hiking the Faroes in summer, but first plans have fallen apart as there are not enough local takers (it's expensive) :-(

Thursday, February 13, 2020

My 60's Coding history

Last sunday, CopCar started a meme, asking What was your first coding language?.

So that was a memory test (for me), as I started coding over 55 years ago. Let's see what I can reconstruct, trying to put my coding languages into a semblance of the chronological order I used them in the sixties.

My first encounter with a computer was using a huge military R&D analog computer to program the differential equations involved in guidance systems for ship-to-ship guided missiles, ship-to-air interceptor missiles and torpedoes. So the programs consisted of wiring lists between amplifiers and feedback factors for each amplifier.

But my first experience with coding for digital computers was a (cross)- assembler. We typed code into a teletypewriter, storing it onto paper-tape. This was later read into a big (for those days) computer which assembled the code, emitting another paper tape of object code which would (when correct) be uploaded - again via a teletypewriter - into the target hardware aka a tiny missile guidance electronics. You learned to write tight, fast, code to fit into a minimal amount of memory.

The first stand-alone computer that I got to use all by myself was the Ferranti Pegasus, one of which still survives to this day in the Science Museum in London, UK. The next one, used in batch mode, was a Ferranti Mercury. It was a huge machine (weighed over a ton) with about 2000 tubes (=valves) and even a floating point unit. So I learned to program it in Autocode, a UK forerunner of BASIC I suppose. My first experience with a (batch) compiler and interpreter.

Next up, I wrote my own interpreter which took the wiring lists etc from the aforementioned analog computer and stepped through a Runge-Kutta integration loop to simulate the analog machine. Turned out to be slower! I also ran up against stability problems (differential equations for missile guidance are usually stiff enough for a Runge-Kutta method to be stable) which decades later I recognised to be fractal issues, but Mandelbrot had not written about fractals at that time.

The first real compiler and high-level language I learned was GPSS, a batch oriented simulation language. Next up were Algol 60 which I preferred for its elegance to FORTRAN which followed. All these were in batch mode on the Ferranti Atlas, at the time the fastest supercomputer in the world. They claimed that when it went offline, the computing capacity of the UK was halved;-) Then came the mind-blowing APL.

Next up was COBOL because a team of us wrote an 18-pass COBOL compiler for the AEG TR86. I also used JOVIAL for a MIL project, this was WAY before ADA became a requirement for MIL projects (around 1980). And so, the 1960s came to a close before I got a chance to learn all the exciting languages which followed :-)

I hope this answers CopCar's question :-)

Comments (4)
Cop Car wrote " So many things I never used and never accomplished. Very, very good, Stu. Thank you. Ah, yes, Runge-Kutta methods. I doubt that I've explicitly used them since completing my thesis (Investigation Concerning Non-Uniform Beam Vibrations). As I recall, I did indeed run into numerical instability - even when using double precision mode. Boeing had been kind enough to let me use their IBM mainframe (1974 - I no longer recall the machine designation). As you mentioned, our (USA) military was in love with ADA for a number of years. Interesting posting." Thankyou.
Ivan (RU) grinned "So much obscure stuff : APL, GPSS, Jovial etc. And such obscure HW!" Ferranti was big in the sixties in the UK, later it was ICL that was big in the UK.
Schorsch (D) asks "What about BASIC and C?" I didn't encounter them until the nineteenseventies.
Brian (UK) asks "So you probably knew some of the pioneers?" Well, 'knew' is too strong a verb. Remember, I was very much a junior nerd then. But I did get to meet some of them : Bauer (ALGOL), Hopper (COBOL), Schwartz (JOVIAL), Strachey (GPM) spring to mind :-)

Tuesday, February 11, 2020

Stormy Monday Blues

Starting on sunday in the north of Germany and going south on the monday, we just had the first hurricane of the year here. The whole country was on red alert. Winds over 120 mph in places; in our valley we had just 75 mph though, with slightly less damage than the Kyrill storm in 2007.

The winds came from the northwest, pushing water from the North Sea into coastal areas. People who parked on the seafront promenade road - despite widely televised warnings - almost lost their cars! Some even went windsurfing!

On the autobahn some lightly loaded but high sided trucks got blown over, thus blocking the road for everybody else, so several autobahns had to be closed :-( The national rail system closed down completely on sunday evening and most flights were cancelled too. Only now are things getting back to normal.

The storm was named Sabine here (Ciara everywhere else), because in Germany you can pay €200 to have a low (or high) pressure zone named after yourself/your girlfriend etc. What the government won't do to collect a bit of extra money! FWIW, wind turbines in Sabine generated a record 47.3 GWatt!

In Berlin the scaffolding was blown off a building site and locally trees crashed into parked (and also moving) cars. A local cyclist was also hit by a tree. Personally we stayed in the house - to comfort our dog - while the wind howled even louder outside. No tiles lost this time, but several branches from our trees.

My good friend Frank has a carpentry and roofing business, so has been very busy, even with a waiting list of people who lost roof tiles. Helping has priority!

Now, for those of you who came for the music, here's Stormy Monday Blues, recorded during Alexis Korner's 50th birthday party/all-star-blues-jam in 1978 :-)

Comments (1)
Schorsch (D) warns "Another hurricane brewing south of Iceland, 952 hectopascals and 220 km/h winds. Expect it here by sunday :-(" Let's hope it weakens off before it gets here!

Sunday, February 9, 2020

Moscow's magnificent Metro

Most big cities around the world have an infrastructure for getting commuters in and out of and around in their city. This is often an undergound railway, variously known as the subway, metro, U-bahn, or tube. These have varying quality standards from country to country, from squalid and filthy through dangerous to magnificent. I have personal experience of several of them, so here's my little summary.

New Yorkers are by a short margin the filthiest, with no respect for the otherwise quite good subway their city provides for them.

New Yorkers just throw their garbage onto the subway tracks. Starbuck's beakers, McJunk burger wrappings, drug needles, cigarette stubs and empty packs. All inflammable, so absolute disregard for the danger of a fire.

Apropos fire danger, some years ago (1987) there was a huge fire on the London (UK) tube system. Wooden escalators, gunged grease had collected under them, one spark and the inferno was there. 31 dead and 100 injured. No wonder, the London Tube system dates back to 1863.

The London Tube system is regarded as the dirtiest place in the city (and that's saying something!), inadequately ventilated, with hot fetid air being forced into your lungs with filth over 10 times the WHO recommended limit.

Escalators in general are dangerous. In Istanbul (Turkey) recently (in 2018), an escalator on their subway opened up a hole during the rush hour and swallowed a man beneath it for over an hour until he was rescued :-(

In Tokio they have stocky, burly, men - albeit in white gloves - to jam you aboard the metro cars during the rush hour :-(

At the other (upper) end of the attractiveness spectrum - to be recommended to Americans and Brits alike - is the Metro system in Moscow (Russia). It is the busiest metro system in Europe (trains every 90 seconds), and is considered a tourist attraction in itself. Beautiful stations, like being in palaces.

About 35,000 employees; train drivers' health is checked before every shift, clean platforms and tunnels. Punctual. Their own safety record is very good except for Islamic terrorist bombings every couple of years or so :-(

A single ticket to get you from A to B is valid for 1½ hours irrespective of distance travelled and costs about 70 cents. Cheap! I used an all-day tourist ticket and visited a lot of the beautiful stations shown by Google. Google has a great collection of photos of magnificent Moscow Metro stations.

If you are ever in Moscow, be sure to see the Metro system, well worth it :-)

Friday, February 7, 2020

Telescope resolution revisited

Last month I ranted about stupidly bad astronomy Inter alia, I wrote that "Back in 1969 we didn't have telescopes powerful enough to even see the moon landing from Earth. And the Moon is only 1¼ light-seconds away from the Earth. We didn't have them by 1991 and we don't even have them today!"

Several of you have since asked "Why not?" and "What can our best telescopes see?" and "What about space-based telescopes like Hubble?"

The resolution of a telescope is proportional to the size of the main mirror. The Hubble telescope's mirror is only 2.4 meters across (because it had to fit into the Space Shuttle's bay to get into orbit). Hubble is in a close Earth orbit and so 1¼ light seconds away from the Moon. This means that a single pixel of visible light as seen by Hubble's camera is 90 metres across on the Moon. But the 1969 Eagle lander is only 5 meters across, so Hubble can't resolve it.

The biggest Earth-based telescope is the GTC on the Canary Islands. It has a 10.4 meter mirror. So the smallest object it can resolve on the Moon would be 20 meters across. Still not enough. It would need a mirror 80 meters across to see Eagle as two pixels; that's Why not :-)

So, if we want to see Eagle, the other option is to get closer than 1¼ light seconds. NASA did this by putting the LRO (Lunar Reconnaissance Orbiter) into close orbit around the Moon (12 to 100 miles altitude). Sure, the LRO camera is smaller but really close in. So it can resolve items only 18 inches across into one pixel. So here's the LRO photo of Tranquillity Base :-)

The white blob is the Tranquillity Base lander. You can even see the tracks where the astronauts Armstrong and Aldwin walked over to the crater called West and down to set up the scientific instruments, so YES, you doubters, Nasa was there in 1969 :-)

Next conspiracy theory? Perhaps NASA is not humans, but aliens (guys from Area 51 ?) trying to get back home using our very primitive technology? ;-)

Monday, February 3, 2020

Domino puzzle

Can you rearrage the dominoes shown below so that both vertical columns and both horizontal rows all add up to the same number?

Hint : it's an Illuminati puzzle, so the four sums are each twentythree.

Update 7/2/2020 : Oh come on, no takers? It's not THAT hard.

Jan (D) wrote " The hint made it easy. The total of the rows and columns would be 4 x 23 = 92 while the pips on the pieces add up to 69, leaving a difference of, too, 23 which must be the sum of the four corners. So the corners must be 6, 6, 6 and 5, making the (4,4) the only piece that can not be in a corner. This narrows it down enough to find a solution:"

Correct. Well done Jan! :-)
Pergelator has a thorough computerised solution now(18/2), see his blog.

Link to the previous month's blog.
Recent Writings
Getting to 365.2425 days
Our nearest neighbour
Palindromic numbers
Hiking through Patagonia
My 60's Coding history
Stormy Monday Blues
Moscow's Metro
Telescope resolution
Domino puzzle
Brexit tonight :-)
Scud Running kills
Pizza my arse!
Astronomically Stupid
U.S. Aircraft Carriers
No memory lockout :-(
Factorial fun
Going to Mars
Holiday avian dining
Good Omens & Puckoon
Khoroshevskoye Shosse
Winter solstice
Torn ligament :-(
Custom Bike Show
PISA results worsen
Hundertwasser brewery

Ain Bulldog Blog
All hat no cattle
Balloon Juice
Billions of Versions...
Cop Car
Digby's Hullabaloo
Earth-Bound Misfit
Fail Blog
Finding life hard?
Greg Laden
Mostly Cajun
Observing Hermann
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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