Archive for Science

Phrygian = subtonic – Dorian

A bunch of musically related posts are being re-hosted on another site. This one specifically is now over here.

Major minor teatime diner

A bunch of musically related posts are being re-hosted on another site. This one specifically is now over here.

Pitch Axis Considered Harmful

A bunch of musically related posts are being re-hosted on another site. This one specifically is now over here.

Odds and Sod’s Law

Facebook competitions. Lovely aren’t they? The sort where you’re invited to supply some of your contact details in exchange for a token in a pile, one of which will be randomly picked and its owner be declared the winner. The prizes are often rather nice, rather desirable, so you’re tempted. “Facebook already has my contact details“, you think, “… this company isn’t getting any more than I’ve already chucked in Facebook’s general direction anyway“. What’s the harm?

But then they invite you to be a virus. They give you an opportunity to increase your chances of winning. “Invite five friends“, they cry. For every friend that joins in, we’ll give you an extra vote. So the deal here is that, in exchange for you doing their work for them (increasing the likelihood of their getting the large amount of contactage they’re after), you get more tokens in the pile.

Of course you instinctively ‘know’ immediately that this is bollocks. Obviously the more people in the game, the worse your chances are, but you’re thinking “yes but I get more votes, so maybe …?
Let’s do some sums.

Clearly the best way to win is to be the only player. One participant, one token in the pile, it’s the only one that can be drawn, chance of winning – 100%. Easy. Your strategy – kill all those you know who’ve entered. Which means, pretty much – since you don’t know who’s entered, kill everybody but the guys with the prize.

But that sort of behaviour is deemed unacceptable. We know, it’s health and safety gone mad, but what are you to do?

So, like an idiot, you invite your five friends. Let’s assume the worst – they all take up the offer. You’ve now won an extra token for each friend so you have six tokens in the pile. And there are now six people in the game, most – five – with only one token. So you’re better off than they are, for sure. There are eleven tokens in the pile – your original one plus the extra five you just earned, and the five new ones from your friends. Your chance of winning just dropped from 1 in 1 (certainty) to 6 in 11 (about a half) and theirs went up from zero to 1 in 11.

Suppose that each of these friends is as equally idiotic as you. They aren’t going to invite you back because you’re already in, so they each invite five new friends. That’s twenty five brand new people. There are now thirty one people in the game – you, plus five, plus 25 – and there are your six (the number didn’t increase, sadly) tokens sitting in a pile with twenty five new ones from twenty five new people, plus thirty tokens – six each now – from your five successful friends. Your chance of winning is now down to 6 in 61, about 10%. And you’ve lost control over what happens next.

Except it might not be twenty five new people of course. Because your friends’ friends may each be shared by more than one of your friends. That’s quite likely. In the extreme case, your little coterie may well comprise only you, your five friends, and one other person you don’t know but who happens to be the common friend of each of your friends. The competition runner is only ever going to get seven sets of contact details out of this sorry bunch – so you have that satisfaction – but what are your chances of winning now? They can’t be quite as bad because your universe is so small.

Well, your five friends each invite the maximum five friends, but four of those friends were (unbeknownst to them – they knew only not to bother inviting you) already in the game (you brought them in) and it’s only the fifth person (the one you don’t know) who is a new joiner, and only one of your five friends is going to succeed in trapping that individual. So there are seven individuals and a pile of thirteen tokens. That’s the eleven before the new round of invitations, plus one for the new individual, plus one introducer’s token for your successful friend inviter. Your chance of winning dropped a tad, from 6 in 11 to 6 in 13. One of your friends has a 2 in 13 chance of winning and your other four friends, and your ‘friend-in-law’, have a 1 in 13 chance. The universe can have a little snigger at this though since it knows that your friends believe – erroneously – that their chances of winning may still increase at any time when their untaken invitations succeed (which of course they never will). So there’s that.

You invited your own competition. How silly of you. If you’d invited only one friend – you had a gun pointed at you, the devil made you do it, whatever – you’d’ve been better off with a 2 in 3 chance.

But you know you’re not the one in control here. Others are going to come in regardless of your meanness in attempting to keep knowledge of this competition to yourself. So having more of your tokens in the pile is always going to be better. In fact, if you’re the only one keeping your friends out, and everyone else is being all lady bountiful with their invitations, then you’ve no chance. So you have to bring in more competition. It’s really annoying.

The Errr. The Errr.

They do go on about the problem of evil, don’t they? There is no problem of evil. It’s the problem of good that’s the issue.

Why be good when stupidity and ignorance are so readily rewarded? That‘s the problem.

The above is an example of a category error. At first glance it seems to have the required cynical insight. But on further inspection it can be seen to miss its mark.

It’s a common mistake. The topic, the category space (if not quite the subject itself) of the argument is good and evil. But the discussion takes the issue into a different topic – that of right and wrong. There’s nothing evil about (personal) stupidity and ignorance. Whilst they’re not generally regarded as being amongst the set of encourageables, it’s not a crime to be stupid or ignorant. Indeed the point of ‘the point’ is that stupidity and ignorance are commonly accepted as – if not always positively amongst the rewardables – by no means excluded from the unrewardables.

Evil is not being rewarded (here), so the fact that Good is also not being rewarded is beside the point. Wrong may be being rewarded, but the arguer’s not claiming that Right isn’t. So the point is, as they say, moot.

You’ve got to stay on category.

Naturally it may well be still the case that evil and/or wrong is rewarded more than is good and/or right, but that’s not what this (argument) is about.

Slum it?

We now bide on the outer edges of the big pin wheel. But did we come from inner parts? Were we flung out of town by a flail, an arm, a slide, of stars?

This may seem like idle spec – how could we ever know if, over the 22 or so rings round the big whirl in the sky that our sun and chums may have made since the earth was born, we have been moved out from its midst as well as round it? The earth has had bags of time to wipe out any such signs – many, many times over. But the moon, on the other hand, has been quite samey over all that time. It’s got no land drift, no snow, wind, fire or ice to wear stuff down – only the thump by the odd space rock. So it may hold a long note of the sun’s and its kids’ many turns round the thing we see as the milky way (and we don’t mean the snack), now going round at about once every 200 mega years.

That’s still way too long ago for any early human to have seen more stuff in the sky than now. Not even tiny vole like chaps were out and about back then. But t-rex and chums may have gazed upon a night more dense with stars, on the other side of the sky, 100 mega years ago.

If we go back to the moon and dig a bit, we may find signs of stuff found only in the hot busy core – and then we’d know. The mere fact that we could know means it’s not an idle idea. But it looks like we’d have to go some place else than stay here on earth.


Had an idea to find my dad’s Bacon Number. Though not in the film business, he had featured (as half of the double act ‘Johnnie and Ronnie’)- playing the accordion alongside his drummer chum – in Stewart Mackinnon’s 1993 film Border Crossing. This is a difficult film to track down. Amber Styles was in that, so she’s the obvious link, and indeed it turns out that her Bacon Number is three and so his is four.

However, Gerhard Garbers – also in Border Crossing – was in a 1990 film called Werner – Beinhart!, which also featured Ludger Pistor, who was in this year’s X-Men First Class with the man himself, old Kev. So Gerhard (also in the highly enjoyable Run Lola Run) beats Amber (sorry Amber) with a Bacon Number of two, so my dad’s is three.

Except – there’s a route with even more cachet. Border Crossing’s Les Wilde was in Stormy Monday with Tommy Lee Jones, who was of course with ‘the Bake’ in JFK. So, though my dad’s Bacon Number is still three (which is pretty good for a non-player), that’s a fairly decent path.

But whoa hang on there and hold your horses just a cotton’ pickin’ minuteStormy Monday? My sister was in that! OK, it was a bar scene and she didn’t say anything and she’s uncredited, but still – that means she’s got a Bacon Number of two.


Nay Survey

So this woman is standing with a clipboard inside the shop, which is Maplin’s, and I’m on my way out and I haven’t bought anything (but she wouldn’t necessarily know that) and she asks (yes she does), like, “Would you mind taking part in a survey?” and I say “It’s ninety pounds an hour” and she laughs and says “No thanks” and lets me go without further ado.

Time and Space

Looking for the phrase bigger than space results in (at the time of writing) about half a million google hits. By comparison we get six times as many with longer than time.

This is, one suspects, mainly due to the romantic idea, fairly commonly expressed in song, verse and prose, that our loves will outlast time itself. It seems that having something larger than the size of the universe is not a romantic idea. Or one at least six times less frequently expressed.

Whose Pyjamas?

One of your grandfathers” is one of two specific males (yes, I know it could actually refer to only one, but let’s avoid that bit of scandal).

One of your great aunts” is one of the sisters of one of your four grandparents.

Your great aunt” could, informally, still mean one of the (possibly numerous) great aunts you may have, but it could also tell someone that three of your parent’s parents have no sisters and that the remaining one has only one. I believe that you’d not typically infer that, though. Not in the culture I’m in, anyway.

One of your grandfathers’ sisters” (note the position of the apostrophe) is the same as one of the sisters of one of those two males. Each grandfather may have exactly one sister and we’d still be able to say this.

One of your grandfather’s sisters” (note the position of the apostrophe) is still one of your great aunts but we may now plausibly infer that one of your grandfathers had more than one sister, and that – if the other grandfather had only one sister – the great aunt in question is one of those rather than the single sister of that other grandfather. But you’re pushing things a bit there.

But in these last two we’ve already missed a possibility. It’s caused by the “One of” bit. It might actually not select a sister at all, as we have assumed here, but a grandfather. It completely alters the meaning. It’s the difference between “one of (his (either grandfather)’s or (this grandfather)’s) sisters” – which refers to one female – and “his (i.e. one of my grandfathers) sisters” – which refers to a whole slew of them.

Without further clarification, it’s not possible to tell which is meant. I’m reasonably sure that the default, natural, interpretation is the single female one. But even there it’s probably more to do with usage than syntax. In typical discourse of that nature you’re simply more likely to be referring to a specific individual.

Were you to continue the sentence and say “One of my grandfathers sisters have formed a choir” (I’ve omitted the grandfatherly apostrophe – it doesn’t elucidate and you can’t hear it anyway) it sounds wrong. You might eventually work it out and realise it does both make sense and is accurate – precisely and concisely informative even – but I suspect you might be a tad annoyed at the speaker for having made you do all that work. In practice you’d be expected to say just “My grandfather’s sisters have formed a choir” and leave open the question (or even relevance) of which grandfather you mean. Or indeed of which sisters – since you still can’t hear the apostrophe, that choir may include all sisters of both grandfathers, but that would be an unlikely intended meaning – again mostly by dint of context rather than syntax.

The question is, is there a language where these ambiguities are removed by syntax alone? Note that I’m not talking about vocabulary and syntax helping out. For instance – and in (very) particular – in Latin we may distinguish a maternal great aunt (matertera magna) from a paternal one (amita magna) but any disambiguation therewith provided is simply an accident of vocabulary. What I mean is, is there a language anywhere (anywhen, even) which forces you – by syntax alone – to be specific so that there’s no doubt that the speaker means “the sister of one of your grandfathers” and not “the sisters of one of your grandfathers” or “one of the sisters of your grandfather” or “one of the sisters of your grandfathers” by synthetic possessive/genitive syntactic marking rather than by lengthy analytic expression?

And would it extend to the disambiguation of the rather large number of possibilities intended by something such as “one of your grandfather’s sisters’ cat’s pyjamas”, where the ‘one-of’ may select (one of) grandfather, sister, cat, or pyjama?