Posts Tagged ‘Maths’

To adapt the opening to a well known book:

Alison Chabloz is an antisemite. There is no doubt whatsoever that Alison Chabloz is an antisemite. This must be distinctly understood, or nothing wonderful can come of the stories I am going to relate.

(She’s also a holocaust denier, white nationalist, and avid and vocal supporter of literal Nazis, but that’s a bit of a mouthful and it ruined the flow of the paragraph above. However, it’s equally important to understand and appreciate all of that as well.)

Chabloz was convicted at trial in 2018 of offences relating to malicious communications, and then, upon appeal this year, her convictions and sentences were upheld.

I’m not going to go into the whys and wherefores of whether she should have been charged, and then convicted; there are coherent and rational arguments on both sides. If you want to read more on it, well, Google is your friend.

But I attended most of the days of the pre-trial hearings, and then both trials.

Leaving aside the specifics of the trials themselves, attending them was a genuinely fascinating experience. Y’see, I’d never been to court before. I came close a couple of times, professionally, but in the past couple of years I’ve been in court a few times. Never as a defendant, I hasten to add, nor as a witness, merely as an interested – a very interested – observer.

What surprised me – continued to surprise me, on each occasion – was how genuinely interesting it was. I’ve heard the tales of how boring it is, how technical much of the legal argument is, how painstakingly slow the days go; also of the arcane and nitpicking over points of law to the point of absurdity…

Well, not in my admittedly limited experience.

All the barristers and advocates I’ve observed have been at pains to explain to the court, to witnesses, and to the judges, in the plainest possible language, their cases.

Sure, there have been plenty of technical details, but nothing that was even mildly difficult to follow.

Maybe I’ve just been lucky. Or maybe it’s that like so much else:

a) things have changed, and
b) the worst steoptypes are the worst, not the typical.

So, anyway, back to Chabloz.

STORY 1: Zionist… maths?
A pre-trial hearing, fairly early on in the process. As I recall, it had to do with formally reading the charges, and legal argument as to whether the court had jurisdiction over two of them.

While we were waiting, I pulled out of my bag the book I was then reading: Things To Make And Do In the Fourth Dimension by Matt Parker. (If you don’t know Matt, he’s an Australian mathematician and standup comedian, part of The Festival of The Spoken Nerd.)

It’s a great book; funny, clever and lots of thought experiments and things, as the title promises, to make… and to do. I’d picked it up in the hope it would refresh my enjoyment of numbers and maths; it quickly did both.

So, there I was, in the public gallery at Chabloz’s pre-trial hearing, and as on previous occasions, I was one of the few who wasn’t there to support her. Oh, yes, she had her supporters; a dozen or so people there, some wearing offensive t-shirts, some with tattoos that wouldn’t be out of place at a far right rally… for the obvious reason.

Before the hearing started, I was reading the opening chapter of the book… which deals with “how high can you count with your fingers?”

It’s an obvious question, and an even more obvious answer, yes?

No. It’s only obvious if you a) count in Base 10, and b) allow each finger to count as a single unit.

The moment you switch to other bases, or take advantage of knuckles, etc…

Look, here are some pics of the illustrations, at a decent size so you can appreciate them.

So there I am, reading away, chuckling at the gags – it’s a genuinely funny book – when suddenly A Shadow comes over me, and a very large bloke is looming over me – give him credit, he was very good at looming – and staring at my Star of David necklace, which was revealed by my just-open shirt.

Now, it’s not a huge Magen David, but yes, granted, it’s noticeable.

He clocks the diagrams of the hand counting on the page and is suddenly in my face – “Are those Zionist hand signals then?” he demands. (I’d add ‘belligerently’ but be fair, that’s a given.)

I look up in surprise and he gestures to the court room before us. “Are you going to signal the zionists in the court…?”. And then there’s suddenly two more people, equally knuckle draggers, pointing at the page, and muttering.

There was a lot of muttering.

I merely raise the book, so they can see the cover… the idea of mathematics is apparently but very obviously beyond them; they make some further comments about zionist and jews… and signals.

There is more muttering.

Apparently, it’s well-known, ‘we’ have secret hand signals. You didnt know that? Well, now you do.

But before I could actually say anything… the clerk of the court called us to order and the case began; they returned to their seats, glaring at me… and muttering.

Gloriously, a few weeks later I met up with Matt at a comedy gig and told him what happened. I bet him – before I told him the tale – that no matter what reactions he expected the book to have… that wasn’t one of them.

I won the bet. And I got his permission to tell the story, and use the images above, for which he has my grateful thanks.


So, Chabloz was tried in magistrates’ court in 2018, and was convicted. She appealed her verdict and, in early 2019, she faced… well, it wasn’t merely a new hearing; the prosecution and defence cases were presented again, calling witnesses and everything.

And it wasn’t merely an appeal, because it wasn’t on a point of law; the entire case was reheard in front of three district judges. It was, effectively, a new trial. So I’ll call it that.

STORY 2: “One of us?”
The first day of the trial, post pre-trial hearings, is due to start at 10am. I get there about five to, but the display screen is showing the case is now due to start at 10:30 in Court 8. The usher outside the courtroom confirmed “an urgent court matter” had to be dealt with. (I guessed a bail matter or search warrant or somesuch… the usher just said he ‘couldn’t say’ why, but that it shouldn’t take long.)

So, I’m waiting outside the courtroom, checking Twitter, playing a game on my iPhone, and A Very Nice Older Lady comes across.

Very polite, very unsure. Think Miss Marple, but a bit taller, a bit less bird-like. But basically… her.

Hello, are you going into Court 8?” she asks.

Now I have no idea who she is, or why she’s asking, and previous experience has taught me the wisdom of wariness. I merely look up and reply with “Hello, can I help you?”

Very Nice Older Lady: “Oh, I’m supposed to be going in there but I thought it was due to start at 10.

I explain about the delay and she’s full of “Thank you so much, oh dear, but thank you…”

“Not a problem,” says I, and go back to my phone.

Anyway, 20 minutes later, we’re let in. I find a seat at the end of the front row, directly behind the row reserved for the press.

She immediately comes over to me, suddenly very animated.

Oh!” She says… “Oh… I didn’t realise you were… ‘One Of Us!’

Now, as I’m sure you’ll appreciate, dear reader, ‘One Of Us’ could mean a multitude of things. It could mean:

Oh, you’re also Jewish!’

It could alternatively mean:

Oh, you’re also interested in the trial

Or it could be:

how lovely, someone else coming here to support our dear friend in her hour of persecuted need!

Could be anything…

So I say, politely, with a smile, “I don’t know if I’m ‘one of you’… what do you mean?”

One of us!

“Er…” I smile. She’s not making this easy.

Here to see the trial?” she ventures.

Me: “Well, yes… but whether I’m ‘one of you’, I guess, depends on which side you’re on.”

Pardon?” The Very Nice Older Lady looks shocked, as if the very idea that someone could be ‘on the other side’ is inconceivable, literally inconceivable. Still not helping, though. But she starts to look less ‘very nice’.

I offer: “Well, whether I’m ‘one of you’ depends on whether you’re hoping she’ll be acquitted, or whether she’ll go down for a couple of years.”

Well, acquitted OF COURSE!” She looks at me, the penny finally starting to drop…

“Ah. Then I’m very much not ‘one of you’…”

Oh?…Oh!

“No, I’m hoping she gets convicted again and is sentenced for as long as the judge can possibly send her down for…”

“…” (And for once, that’s not a conceit… her mouth opened and closed a couple of times, but nothing came out.)

I smile very sweetly at her.

Ah, she finds her voice. “Ooh,” she says. Yes, she said “ooh.” Then “I should bash you…” and raises a mildly shaking hand…

“I really, really, wouldn’t advise it…” I say, and fuck knows what she sees in my face when I say it… but she scuttles to the other side of the box so fast, your eyes would spin…

And then spent the rest of the session muttering to her companions and pointing at me…

So, that was nice.


 
So, what did I learn from the two stories above? Antisemites who support Alison Chabloz like to mutter, and to point. And to point and mutter. And that they are very, very stupid.

(I was curious later, so had a look online. According to a revisionist – i.e. holocaust denying – website, the woman’s name is ‘Sophie Johnson’, or at least one identity she’s used is, and she’s one of Chabloz’s chief supporters. She’s on the left in the pic attached.)

See you tomorrow, with something very different.

This post is part of a series of blog entries, counting down to my fifty-fifth birthday on 17th August 2019. You can see the other posts in the run by clicking here.

Somewhere in the boxes I possess which contain the books I don’t actually have up on the bookshelves is a book entitled The Dictionary Of Misinformation. It’s a cracking book based upon the simple principle that most trivia books tell you things that, in the title of this entry, you didn’t know you didn’t know.

However, this book takes a decidedly different tack, by debunking loads of things you know… that are flat out false. Old wives tales, misquotes and the like, every incorrect item is taken seriously and the common fallacy is, for want of a better description, destroyed.

Music hath charms to soothe the savage beast? Quite possibly, but the quote actually refers to the savage breast, and it’s has, not hath. (It’s from… no, not from Shakespeare, but from William Congreve’s 1697 play The Mourning Bride, Act 1, Scene 1.)

Surely there’s no-one who still thinks the ‘wherefore’ in “wherefore art thou, Romeo?” means where? Well, yes, there surely are.

Urban myths don’t escape – the authors are merciless in describing the belief that a drowning man surfaces three times as the rubbish it is. Similarly, while they acknowledge that some people have amusingly appropriate surnames, they obliterate the concept of nominative determinism with some relish.

So, the book seems to address the idea of things you knew, but were wrong, and trivia books by the hundred tell you things you didn’t know you didn’t know, and there are more than a few volumes addressing the things you knew you didn’t know. (They’re in the non-fiction section of the library.)

You know, every so often on my blog I ask you to teach me something, to show (or tell) me something that you know about that I probably don’t. And I’ve been rewarded by lessons on cornering at speed, on how to judge wine, how to light a photograph correctly.

But I’ve never returned the favour, so what follows is something that you may have known, may not have known or might never have even thought about.

mathfun1How to tell if a number is divisible by any number between 2 and 12

I had a great maths teacher at school. He understood that to get kids interested in maths as a subject, he had to make it interesting as a subject. And to that end, he taught his class what he called the ‘tricks of the trade’.

So, for example, he taught us how to discover whether any number was divisible by any number between 2 and 12.

Some of them are, you’ll see, obvious; some of them make sense, and one or two you’ll have to trust me on until you test them out and find out they work

2: duh, the number’s even

3: if the number’s digits sum to a number divisible by 3, the number itself is divisible by 3.

4: If the last two digits of the number are divisible by 4, the whole number is. (Remember this, I’ll come back to it.)

5: the number ends in 5 or 0.

6: if the number’s even and the number’s digits sum to a number divisible by 3, the number itself is divisible by 6. (Makes sense, doesn’t it, but most people never combine them…)

7: hmm, he didn’t teach us this one.

8: If the last three digits of the number are divisible by 8, the whole number is.

(A slight bit of explanation here: Notice anything? If the last digit is divisible by 2, the whole number is; if the last two digits are divisisble by 4, the whole number is; if the last three digits of the number are divisible by 8, the whole number is. That’s because 2, 4 and 8 are 2 to the power of 1, 2 and 3 respectively, and the similar powers of 10, i.e. 10, 100 and 1000 are, respectively divisible by 2, 4 and 8. OK, explanation over.)

9: if the number’s digits sum to a number divisible by 9, the number itself is divisible by 9.

10: the number ends in a 0.

11. If the sum of every other digit, starting with the first, is either equal to the sum of every other digit starting with the second, or the difference is exactly divisible by 11, then the number is evenly divisible by 11. It sounds complicated, but it really isn’t, I promise. Couple of examples to show you what I mean.

Try 13,057. That’s 13,057. Add the bolded numbers, and then the non-bolded. So 1+0+7 = 8. Subtract the non-bolded (3+5 = 8), and you get 8 – 8 = 0, therefore it should divide evenly by 11. And indeed it does: 13,057 divided by 11 = 1,187.

Take 92,807. The bolded (9+8+7) sum to 24; The non-bolded (2+0) sum to 2. So… 24 – 2 = 22, which is divisible by 11. Therefore the ‘big’ number should divide evenly by 11. And it does: 92,807 divided by 11 = 8,437.

12: Another combination one; if the number’s digits sum to a number divisible by 3, and the last two digits of the number are divisible by 4, the whole number is exactly divisible by 12.

Nice and easy, eh? Well, easy-ish, I’ll grant you. All the numbers from 2 to 12. All the numbers from… hold it, I hear you shout. What about 7? You skipped over that one pretty bloody quickly, didn’t you, budgie?

Truth is, he didn’t teach us how to quickly find if a number was divisible by seven. I even told my lad Philip, when teaching him those same tricks, that there wasn’t a quick way.

Well, I was wrong, and it took me until well into my 40’s (25 years after I learned the rest of them) to discover an incredibly easy way… I have no idea why it works, but it does.

Take the number’s final digit and double it. Subtract that from the rest of the digits and if you end up with a number divisible by 7, you’re home and dry.

Take the number 364. Double the final digit and you get 8. Subtract that from the first two digits: 36 – 8 = 28. And what do you know? 28 is divisible by 7, so 364 is exactly divisible by 7.

903? 90 minus 6 [3 doubled] = 84, so 903 is divisible by 7.

Look, I told you I didn’t know why it works, but it does.

So, who’s still awake now? Anyone? Anyone?

Ah.

A number of things

Posted: 29 October 2011 in personal, skills
Tags: , ,

Skip this if you’re not fascinated by numbers.

I’m serious – this subject has been known to have a more soporific effect than laudanum.

OK, still with me?

I was talking with (isn’t that a great way of being polite, instead of saying “I was having a small argument with…”?) a friend last night about something and as part of it, said I’d prove that 1 = 2, and proceeded to so so, but more about that in a moment.

But it started me thinking about mathematics and the tricks those of who have a grasp of it use. Of course, I use mathematics and arithmetic synonymously, and they’re not the same, at all. But forgive me for using them this way, just this once? Thanks.

Now, I had a great maths teacher at school. He understood that to get kids interested in maths as a subject, he had to make it interesting as a subject. And to that end, he taught his class what he called the ‘tricks of the trade’.

So, for example, he taught us how to discover whether any number was divisible by any number between 2 and 12.

It remains a mystery to me how everyone doesn’t know this, but:

2: duh, the number’s even

3: if the number’s digits sum to a number divisible by 3, the number itself is divisible by 3.

4: If the last two digits of the number are divisible by 4, the whole number is.

5: the number ends in 5 or 0.

6: if the number’s even and the number’s digits sum to a number divisible by 3, the number itself is divisible by 6.

7: hmm, he didn’t teach us this one.

8: If the last three digits of the number are divisible by 8, the whole number is.

9: if the number’s digits sum to a number divisible by 9, the number itself is divisible by 9.

10: the number ends in a 0.

11. If the sum of every other digit, starting with the first, is either equal to the sum of every other digit starting with the second, or the difference is exactly divisible by 11, then the number is evenly divisible by 11. Try 13,057. 1+0+7 = 3+5, therefore it should divide evenly by 11. And indeed it does: 13,057 ÷ 11 = 1,187. Take 92,807. (9+8+7) – (2+0) = 22, therefore it should divide evenly by 11. And it does: 92,807 ÷ 11 = 8,437.

12: if the number’s digits sum to a number divisible by 3, and the last two digits of the number are divisible by 4, the whole number is exactly divisible by 12.

Except… he didn’t teach us how to quickly find if a number was divisible by seven. I even told Philip, when teaching him those same tricks, that there wasn’t a quick way.

Well, I was wrong, and it took me until the age of 40 to discover an incredibly easy way… I have no idea why it works, but it does.

Take the number’s final digit and double it. Subtract that from the rest of the digits and if you end up with a number divisible by 7, you’re home and dry.

Take the number 364. Double the final digit and you get 8. Subtract that from the first two digits: 36 – 8 = 28. And what do you know? 28 is divisible by 7, so 364 is exactly divisible by 7.

903? 90 minus 6 (3 doubled) = 84, so 903 is divisible by 7.

Look, I told you it was boring; don’t say I didn’t warn you. Be grateful, I could have taught you a quick way of working out the two-digit cube root of any number between 1,000 and 970,299.

Anyway, that proof.

I have no doubt that some of you will spot the flaw in this fairly quickly, but it’s genuinely astonishing to me how many people don’t.

(1) Let a = b

(2) Multiply both sides by b… ab = b²

(3) Subtract a² from both sides… ab – a² = b² – a²

(4) Factorise… a (b – a) = (b + a)(b – a)

(5) Divide both sides by (b – a)… a = b + a

(6) Since a = b… a = 2a

(7) Divide by a… 1 = 2

Ta-da!

Yeah – I know, but be fair, I said there was a flaw…