Use Ctrl+ to enlarge this blog page if you need to.
Nav Tools

--> Most recent Blog

Comments Policy
Maths trivia
Search this site
RSS feed for Stu Savory's Blog RSS Feed

Stu Savory ;-) School report for Stu Savory
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, May 28, 2020

Homeschooling Maths : Root(2) is crazy!

During this Coronavirus lockdown, parents are having to homeschool their children, sometimes in areas where they are not qualified to do so. Friends of mine are struggling to tutor their teenager in maths, claiming they were "bad at maths" themselves in school and ever since. So I offered to do the homework with the parents alone, so that they could then help the teenager do the homework. And thereby hangs this tale :-)

First thing I did was to get them to self-estimate their maths abilities on Pergelator's chart :-

They thought they might manage some algebra, but nothing more complicated. This is probably true of most parents???? The dad said he didn't even understand the homework question , claiming it said Prove that Root(2) is crazy. Neither did I, so I asked to see the homework question. It actually read Prove that Root(2) is irrational :-)

So I explained that irrational did not mean crazy in this maths context, but meant that root(2) could not be expressed as a ratio, i.e. a fraction like a/b where a and b are whole numbers.

Now the easiest way to do this is to assume the opposite and show that this assumption (root(2) is rational) is self-contradictory and thus wrong.

So we write a/b=root(2) as the irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) which is a fraction in which the numerator and denominator are integers that have no other common divisors than 1, so both a and b cannot be even, one of them must be odd.
Then we square both sides, getting a2/b2 = 2.
Multiplying each side by b2, we get a2 = 2 * b2, and so a2 is an even number, and thus a is an even number too, because even*even=even and only odd*odd= odd.

Now because a is even, we can rewrite it as a = 2*c. So 2*c/b=root(2). Square both sides, getting 4*c2/b2 = 2. Multiplying each side by b2, we get 4*c2 = 2 * b2, and so b2 is an even number, and thus b is an even number (as is a) too. But one of a or b must be odd, as we showed above. So the assumption (root(2) is rational) is self-contradictory and thus wrong. Q.E.D. :-)

We went through this a couple of times until they could reproduce the proof reliably and were quite pleased with themselves that they could do an algebraic proof after all those years after leaving school themselves :-) And yes, I do expect teenagers to be able to produce that proof themselves.

Now for some historical background, dating back to before 520 BC. Hippasus of Metapontum was a philosopher attending the school of Pythagaros. Pythagoreans preached that all numbers could be expressed as the ratio of integers, but Hippasus of Metapontum drew a square (of side 1) and looked at the diagonal in the square (root(2)). He used the proof I just showed you to discover irrational numbers. This so shocked the Pythagoreans that Hippasus was later "drowned at sea". History does not record whether this was an accident, suicide or murder for his discovery!

Whatever. Root(2) is so crazy it could get you killed back then :-(

Comments (2)
Gertrud (D) wrote (I translate) "So where are you on that graph?" Just to the left of the peak, near the top. I would be the first to admit that my maths has got rusty since I retired. Haven't used a Hamiltonian (e.g. to calculate the total energy of a particle in quantum mechanics) for fifty years. I can still do matrices, but haven't done any tensors for over 35 years. Can still do statistics (e.g. for quality control); that's about it these days.
James twittered this hilariously realistic dialog with his child :-

Monday, May 25, 2020

Told you so!

Just a week ago in this blog I opined that here (in Germany) we are reopening too soon and that this was likely to cause new Covid Infections. Sadly, I was right.

In a restaurant in the state of Lower Saxony on 15th May, guests held a closed private party, disobeying all the separation and hygiene rules to be applied in restaurants. Now 18 are confirmed as infected and 118 have been put in quarantine. The landlord is likely to be fined 25,000 Euros. The restaurant has been shut down again.

In Frankfurt in the state of Hessen, Christians (Baptists) crowded into their church, sang hymns loudly, thus spraying the virus around them. 107 are now infected with Coronavirus. So the Blood of the Lamb didn't work, despite what Mike Pence thinks! Way to go, Xians!

A school head has publicly said that he/she thinks it would be better if all the children had to repeat a year's schooling than even one child die avoidably from Coronavirus. Nevertheless, politicians insist the schools be reopened. We'll see how that turns out :-(

Now the governor (minister-president) of the state of Thuringen has decided to remove ALL restrictions (such as wearing masks in public and the 1.5 meter separation rule) claiming he is down to 133 infections per 100,000 residents. Stupidity indeed. I expect a reopening catastrophy there! Shit happens when politicians, not scientists, decide :-(

Thirsty, May 21, 2020

Fathers' Day Edition

Back on the 10th of May, we had Mothers' Day here in Germany, an overly commercialised thankyou-day when the moms got a present, e.g. a new handbag.

Now today, we celebrate Fathers' Day here in Germany, where young males (mostly singles) go in large groups on a hike, dragging a handcart filled with crates of beer and schnaps (=shots). Due to Corona (the virus, not the beer) this year the groups should be gone, so the beer brewers have introduced handbags for men, Fathers' Day edition :-)

A dozen different bottles, each ⅓ liter. That's 8 pints. I'd be smashed out of my mind!

Comments (3)
Doug (Canada) sent this great collection of beer quotes :-

This cartoon I stole from the web, but don't remember who to credit, probably a blogger in the USA somewhere (I'm told it was Hermann) :-

John (USA) wrote " Your post of quotes really cheered me up! Must admit that I'm jealous about the Fathers' day handbags. Stay safe." You too, John!

Monday, May 18, 2020

Reopening too soon! Change my mind?

Coronavirus is changing the world. In our country we were first shown this graph and told that strict measures were needed to flatten the curve so that our health system did not become overloaded. The measures included 1.5 meter social distancing, wearing masks when out, shutting schools, churches, large sports events, demos etc. They worked, because people followed the new rules, so the health system did not become overloaded. Other countries were less rigorous and so less fortunate.

So we are now on the green curve. Flatter but much longer. We have robust data from the outbreaks in China and Italy, that shows the backside of the mortality curve declines slowly, with deaths persisting for months. So we are probably just past the peak of that green curve here in Germany. USA and UK are still on the rising side of the curve, UK maybe peaking. But now unwary people are protesting and disobeying the shutdown. Politicians want to reopen the country asap, in my opinion far too quickly :-(

I wish the politicians were more careful and not causing a second wave of infections by reopening far too early. They should listen to the scientists like Dr.Fauci in the USA.

This shipwreck (below) is the impression I have of e.g. Trump's daft rapid-reopening policy. The white House has daily testing, frequent temperature checks, and daily environment disinfections. And still: Trump's valet was infected, as was Pence's press secretary, Ivanka's assistant and a dozen secret service personnel.

Many politicians want to "save the economy" and so are reopening far too fast because they think it's all over and recovered patients cannot be reinfected (NOT proven!). Currently we have an infection rate R hovering around one, I'd like to see it consistently less than ½ over at least a month. Personally I think we will have a second and maybe third wave as suggested in the sketch below. These later waves will be bigger and will go on for longer. Note that I can't put calibrated scales on either axis, but you get the gist.

Now shops are reopening, cafe´s too, restaurants and pubs. I regard this as highly dangerous. I only shop (masked) for comestibles/vittles etc twice a week, buying non-comestibles online. No sitting in cafes, restaurants or pubs, just take-out food maybe once a week. Nobody needs to see spectator sports live, just watch the soccer etc on TV. I'll be staying home even if barbers, physotherapists etc are open again. I'll wait until hospitals are reopened for visitors again, because then I'll know it's a scientist's decision, not an ignorant pro-capitalism politician greedy for popularity!

This Peanuts cartoon summarises my present opinion succinctly :-)

So, do you also think we are reopening too soon? Try to change my mind!

Comments (5)
Anon (D) wrote (I translate) "You're a pensioner with a fixed income. Some of us workers are on half-time/pay, some have been fired. Mini-savings exhausted, rent due, HP payments due. We need the money, so reopen asap!" Apply for gov. benefits!
Liz Hinds (UK) agrees with me, writing " Much too soon. I am desperate to hug my grandchildren again but their - and our - lives are too precious to risk. As for schools reopening! Nonsense. I'm sure you'll have seen that Eton, Harrow and the like aren't even thinking about it until September. And, yes, I understand that like you, we're in a comfortable position, retired in a safe, warm house with a garden, but I can't believe the government can't find the money somewhere to support those who need it. That said, I am in bit of a down phase, feeling not depressed exactly but restless - more like I need to punch someone! And I can think of a few who would top my list for target practice." Violence is never the answer, but maybe you are a paciFIST? ;-)
Anon (D) wrote again (I translate) asking "If you chose to stay locked down, how are you going to save the economy?" By buying stuff ahead of delivery. For example : friends have a restaurant, closed until recently. So I buy take-out meals there and buy gift-vouchers from them (so they had a cash flow during lockdown), redeemable when they are economically back on their feet. If many people followed this gift-voucher strategy, cash flow would keep businesses going.
Neil (UK) asks "So what do you see as still dangerous?" Public transport (Busses, trains, airlines) and schools reopening. Church services and other gatherings.
Ferdi (D) tells us that " The number of positive corona tests in Germany rose to 176,486. The number of new infections was 814 on Wednesday. This is a significant increase. The number of new infections was 499 on Tuesday and was 401 on Monday." So yes, reopening was too soon!

Friday, May 15, 2020

Out of the blue, nice hearing from you :-) ...

Coronavirus is having some nice side-effects : e.g. people are more helpful and others are remembering old friends. I've emailed several to check on how they are coping in the shutdowns in their countries, and I've been getting emails out of the blue too. Thanks to all of you.

First off was Gerald (D), a geocacher friend from years ago. He'd been in a second-hand bookstore where he found a copy of a (crappy) novel I wrote thirty years ago. So he bought it and sent it to me for me to sign it, which I did before returning it to him :-) So now he has two signed books :-)

Then Iwan (RU) wrote that he'd be AFK (away from keyboard) and not blogreading for the next few months. He's leaving his Moscow apartment and going to live in a Datscha in the Urals (800 miles away) to avoid getting Covid-19, he wrote. I replied "Good luck if you need any medical help way out there" Out into the wild blue yonder in those backwoods. Methinks we're unlikely to meet again :-(

This week, Lyn (UK) wrote to check on how we were coping in the shutdown. I've known Lyn for over fifty years now, but haven't seen her for a decade since my last trip to Oxford (for John's meeting of our old university friends).

Paul (D) sent a photo of the Domiracer he is restoring; looks good!

Now let's make this a shout-out to all those with whom I have lost touch : should you read this or have it forwarded to you, drop me a line to the email address below, it's nice to hear from old friends :-)

Comments (1)
Klaus (Alaska) wrote " Assuming I'm an old friend, turning 75 in about 6 weeks, still alive, Alaska is probately the best State to be within the US because of its size and not so many people. ( 660 million sq.miles, 730 k population) . However we do have 392 cases and 10 death as of today, last year AK had about 2.0 M. visitors, this year we may see 5 k or less, I still live in Talkeetna (population 950) , in the summer we usually have 350 k- 400 k visitors within the summer month and in the winter it is a ghost town, this year it will also be a ghost town in the summer, no cruise ships, no passenger airplanes, Cornelia did visit Talkeetna many years ago. I'm still selling real estate but keep the physical distance and have a mask on, for the most part I stay at home and read books or be on the computer...." Thanks for the update, Klaus.

Monday, May 11, 2020

Good Golly, Miss Molly

Sometime in the mid-fifties, my father bought a radio-cum-record player and one of the first single records he bought was Good Golly, Miss Molly by Little Richard. I still have that 45 rpm record :-) Then, Little Richard was seen as lively but not as sexy, so that when my parents decoded the next line of the lyrics (Good golly Miss Molly, you sure like to ball), they hid the record away from us children :-) I don't think they knew he was a gay/bisexual voyeur, even when they heard the lyrics to Tutti Frutti which were openly about lubing up for anal gay sex, viz. " Tutti Frutti, good booty, If it don't fit, don't force it You can grease it, make it easy..."

Now Little Richard (a euphemism for the opposite?, which was deemed too blatant at the time) has died of cancer at 87. Thanks man, for inventing rock-and-roll!

On his way down below, he will doubtless be accompanied by a chorus all shouting " A wop bop a loo lop a lop bam boo" ;-)

Comments (1)
Cop Car has a different interpretation of the Miss Molly lyrics : " From Like most of Little Richard's songs, this contains a lot of innuendo ("sure like to ball") but most people were too busy listening to the music to notice, or didn't get the reference. At the time, the most common meaning for "balling" was dancing; only later did it became a popular euphemism for oral sex. The term later took on a new meaning when it came describe a lavish and extravagant lifestyle, with these guys flashing their cash known as "ballers."
A video, only tangentially related: - a dance by Gene Kelly to Ballin' the Jack
From ballin' the jackunknown An obsolete expression meaning "to make haste", such as grossly exceeding the posted speed limit when operating your vehicle. Usage appears to be limited to the southeastern Oklahoma geographical area among men born pre-WWII. The origins of the phrase are unclear but several possibilities exist. Railroad crews used a jack with a ball on the end when laying and bending the rails of a new track so it could have originated from some tech specific aspect of the track laying procedure, or, more likely, it is derived from a dance of the same name popular during the late 1910's. The dance was derived from an obscure song popular in dance clubs of the era, "Ballin' the Jack". Contrary to the first impression one may experience upon first hearing the phrase it apparently has no connection with a sexual act performed on a male donkey(a jack). "
I stay by my version :-)

Tuesday, May 5, 2020

Learning from The Stig

Back in 2002ff there was a very popular and humourous UK TV series ostensibly about motoring, called Top Gear, presented by James May (Captain Slow), Richard Hammond (Hamster) and the mostly insufferable Jeremy Clarkson (the Loudmouth). It also featured a silent, anonymous (always helmeted), racing driver whose face and persona were never revealed. Some say. . . it was Ben Collins, and indeed for much of the series, it was he.

The Stig's primary role was setting lap times for cars being tested on the show, plus he would also instruct celebrity guests, off-camera, for the show's "Star in a Reasonably Priced Car" segment.
Ben Collins was fast, faster than both World Champions Nigel Mansell and Jensen Button; but of course he knew the circuit much better.

So when I saw his 2014 book, I picked up a copy and have been reading it with much pleasure. Anecdotes, often hilarious, and much driving instruction, some of which was new to me. Learner drivers in the UK get just 18 hours of instruction (for comparison, a Starbucks Barista gets 20). It's more here in Germany and less in the USA, I'm told. So this book picks up with more advanced stuff, explained better than in your run-of-the-mill driving school.

The Stig's main emphasis is on smoothness, achieved by situational awareness, allowing you to anticipate ahead of time what is going to happen next. I wish I could have had this book 58 years ago! He also describes different ways of doing things, so I've been trying them out in my 1985 oldtimer, a Porsche 944, but it is difficult to break old habits, even if there are better was of doing things (e.g. I don't usually heel-and-toe).

Besides being The Stig, Ben Collins does Hollywood car chases such as driving as Bond in Skyfall, Batman in The Dark Knight Rises etc. He also raced in The Le Mans 24 hour race, NASCAR, Touring Car world series etc. So yes, he is a well qualified driver AND an amusing author, despite the style-breaks :-)

I just have one bone to pick, and that's with the publisher. In places, some of the book is printed in light orange on white background, which makes it difficult to read. Black on white, yes. White or orange on black, yes. But light orange on a white background is a big NO! NO! imho.

I can recommend this book to other petrolheads, such as Liz Hinds' husband, who also has an old 944 , and old friend Peter (UK) who has a Porsche Boxster S and Gian in Switzerland with his old Morgan :-)

Size? 288 pp. Price is about 15 Euros. ISBN is 9787-1447272847. Publisher : Panmacmillan, London,UK. Written in English, sometimes colloquial.

Comments (2)
David (NY,NY) grinned and asked "So how many cars have you crashed?" Three. In 1970 I spun out in my Alfa Romeo spyder due to not having seen the mud in a curve; my fault. In 1984-ish I was part of a concertina crash going down hill on black ice; I managed to stop before hitting anybody and get out, but then a trailer-truck came down the hill sideways and swept us all off the road (I threw myself into the ditch just before he passed over me :-) Not my fault. In 2017/18 I was parked in a supermarket lot when an old lady tried to park at speed next to me and bent my yellow Beetle. Not my fault.
Jimmy (UK) noted "Here's a YouTube video of bad UK drivers (NB we drive on the left here)" It seems not everyone in the video does ;-)

Saturday, May 2, 2020

R.I.P Wolfgang "Bulli" Klois

It is with sadness that I report the death of an old friend, Wolfgang "Bulli" Klois, who died last tuesday (28/4/2020), aged 75. He and I both worked at Nixdorf Computer AG for a quarter of a century, where he was i.a. responsible for the 8890 machine, a smaller clone of the IBM 370.

Bulli and I were friends for over 45 years. It was he who first took me parachuting, a hobby I did NOT adopt :-) However we spent many happy years hang-gliding together. The photo above shows him landing my "Adler" (=Eagle) in the winter of 76/77 after a flight from the Ettelsberg in Willingen.

We've flown from the Teide volcano on Teneriffa, in the hills behind Santa Monica, and in the Alps. Later our interests diverged : I learned to fly regular GA planes, becoming a flying instructor. Bulli went into ultralights, flying around the local area. Each claimed to have had more fun :-)

Now Bulli has taken that final flight, ascending as far as possible. He was 75, just two weeks younger than I am. He certainly earned his wings :-) So here am I, still stuck down here, but waving hallo in his photo taken in 1976.

May you enjoy eternity, Wolfgang, surfing those heavenly cumulus clouds!
Our condolences go to his wife, Ramona, and their (adult) children.

Comments (1)
Udo (D) reminded me that "... he also established and ran the regular 'Health' table in Paderborn... Indeed, but being vegan doesn't guarantee a longer life. He deserved more.

Link to the previous month's blog.
Recent Writings
Homeschooling Maths
Told you so!
Fathers' Day Edition
Reopening too soon!!!
Out of the blue...
Good Golly, Miss Molly
Learning from The Stig
R.I.P Wolfgang Klois
Logistic collapse soon?
A story for Legba
Coping with Eejitz
No spit, Sherlock!
Easter cancelled ;-)
Sudoku challenge
Measuring Earth's size
No more threesomes!
The Whisky Museum
Shutdown in Germany
PI day
Bike Shop Open Days
Getting to 365.2425 days
Our nearest neighbour
Palindromic numbers

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

Archive 2020:
Jan Feb Mar Apr
Archive 2019:
Jan Feb Mar Apr
May Jun Jul Aug
Sep Oct Nov Dec
Archive 2018:
Jan Feb Mar Apr
May Jun Jul Aug
Sep Oct Nov Dec
Archive 2017:
Jan Feb Mar Apr
May Jun Jul Aug
Sep Oct Nov Dec
Archive 2016:
Jan Feb Mar Apr
May Jun Jul Aug
Sep Oct Nov Dec
Archive 2015:
Jan Feb Mar Apr
May Jun Jul Aug
Sep Oct Nov Dec
Archive 2014:
Jan Feb Mar Apr
May Jun Jul Aug
Sep Oct Nov Dec
This blog is getting really unmanagable, so I've taken 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 : F?r alle Seiten, die auf dieser Website verlinkt sind, m?chte ich betonen, dass ich keinerlei Einfluss auf deren Gestaltung und Inhalte habe. Deshalb distanziere ich mich ausdr?cklich 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 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 ;-)
Books I've written

Index/Home Impressum Sitemap Search site/www