Science Man

It was quite amusing, listening to BBC Radio 4's Today programme on Wednesday morning, to hear yet another pair of eminent scientists launching yet another attempt to interest schoolkids in science, this time involving "celebrities" such as Terry Pratchett (huge fan), Bill Bryson (moderate fan), and Heston Blumenthal (the man needs help), who will be debating the promotion of science at Downing Street, no less. Setting aside the largely middle-aged fanbase of these guys, I'm afraid this is all missing the point.

The intention seems to be to demonstrate to British kids that "science" is involved in pretty much everything, and that therefore they should (a) take an interest and (b) consider a career as a scientist. Dream on, guys.

Consider cars. Pretty much everyone drives one, and you'd have to be beyond stupid not to realise some science and engineering are involved in making it go. But how many people, on lifting the bonnet of a malfunctioning car, do not feel an immediate depression of the spirits? This is not an exciting or empowering moment: no amount of understanding of the internal combustion cycle will help you. No, the spell that drives your magic chariot has broken, and it has been reduced to an inexplicable tangle of grimy components.

Ditto the interior of a malfunctioning computer. Or even a broken plastic toy, infuriatingly resistant to glue ("Never mind, maybe I could become a materials scientist!"). Few things are as frustrating, as existentially humbling, as a complex man-made object that is out of order... (I think Heidegger had something to say about this, but can't be bothered to find it).

And then, of course, there is science's dirty little secret -- the mathematics. I'm sorry, guys, I have nothing but admiration for scientists and, I admit, a sense of inadequacy shading into shame in the face of the achievements of science. But nothing -- NOTHING -- would ever have persuaded me to return to quadratic equations and calculus once my exams were over.

Now, it's clear that one of the forms of idiocy from which I suffer is that I am troubled by the sort of questions that only a scientist (or possibly a theologian) can answer satisfactorily. You need to have a full spectrum of talents in your friends, ranging from the infra-red warmth of a life partner to the ultra-violet coolness of an aloof ironist. But one essential part of the spectrum is often missing, because it is rare, and that's the deep reassuring green provided by a friend who combines a general all-round competence in scientific matters with the urge and ability to communicate them. I am fortunate enough to have several such friends, but of these my old squat-mate Andy S. is the one I call on when I need the help of ... Science Man.

Here is a classic example, re-enacted live before your very eyes, an email exchange concerning a puzzle in the book The Art of Looking Sideways, by Alan Fletcher:

Subject: Is there a scientist in the house?

Mike to Andy:

I've been staring at this conundrum in a book in our downstairs loo for days -- not continuously, obviously, or I'd be looking for a doctor, not a scientist :) -- and it's starting to drive me nuts. I'm at work, not in the downstairs loo, so can't describe it exactly, but it goes like this:

There are two identical isosceles triangles drawn on squared backgrounds. The first triangle is divided internally into two large right-angled triangles (one at each bottom corner), two small right-angled triangles (together in the top corner), and two interlocking L-shapes filling the rectangular space left by the triangles. The second triangle is filled with the same shapes, but with the two larger triangles together in the top angle, and one each of the smaller ones in the bottom corners; the two L-shapes are interlocked differently to fill the remaining rectangular space again. The conundrum is that in the second version the area of the triangle seems to have increased, because all the components are the same size but the rectangular area bounded by the two L-shapes has increased -- there's now a blank area in the middle between the Ls!

Is this a well-known puzzle? I just can't get my head round it! How can the area of the second triangle not be equal to the sum of the components that completely cover the first one??

Andy to Mike:

your description works fine. The puzzle feels familiar and I've got the sense of having seen an explanation somewhere. If you don't mind I'll let it fester until something turns up. I bet there's some odd symmetry being broken somewhere, but it's hard to see where with an isosceles triangle.

Mike to Andy:

Cheers. Please don't blame me if your mental well being suffers ... It's starting to feel like I've found a basic flaw in the Laws of the Universe.

I'm completely calm. (I need to be, I'm 50 tomorrow ...)

Andy to Mike:

Happy birthday!

Check that the sides of the triangles do actually meet in a straight line. It's easy to convince yourself that they do. A bit of convexity (or concavity) could be releasing the missing area. I was in doing an odd days work at the local sixth form today and mentioned it to a mathematician. He said some students had had a similar or the same puzzle and found that what looked like perfect alignment of the sides in fact wasn't.

Mike to Andy:

I don't think this is an illusion - I could try drawing it on paper. You don't even need the L shapes: basically, swapping the "inner" triangles creates rectangles of different areas ... Which -- I think! -- means that "sum of the areas of the four small triangles" subtracted from "area of the larger triangle" is not a constant value, which I find spooky. It's like the geometrical equivalent of cold fusion -- something for nothing! There has to be an explanation ...

Andy to Mike:

I've just had a look at the details of your triangles. Remember tangents?
Well, 13/6 is not equal to 9/4. Hence it's not really a straight line,

i.e 13/6 = 2.166666 and 9/4 = 2.25

The angle with a tangent of 2.1666 is 65.225 degrees

The angle with a tangent of 2.25 is 66.038 degrees

Hope this helps!

Mike to Andy:

I do vaguely remember Tangents, weren't they a bit like Juicy Fruits?

I've just drawn the thing on paper and, by Pythagoras, you're right! I will now track this Alan Fletcher down and perform some serious geometry on him with a compass ...

Thanks, Science Man! You've saved my sanity!

So, you see, there's a world of difference between knowing there's a lot of science about, and being able to apply it. And it usually involves maths.

One of my favourite sayings is that "to a man with a hammer, everything looks like a nail." There is, unfortunately, another sort of "science-inclined person" (let's not call them scientists) for whom everything can be explained with a very limited toolkit, usually acquired at school, and lashed together with "common sense." These people give science a bad name.

These are the same guys who wrote the geography textbooks -- the ones which explained how rivers start off flowing small and fast in the mountains, then gradually get bigger and slower in a sort of river "life cycle," until the things became so sluggish in old age that they have to be practically pushed into the sea. Makes sense, doesn't it? Then some bright spark -- yer actual scientist -- came along and actually measured the speed of flow in various rivers, and discovered that -- crikey! -- rivers get faster and faster, not slower and slower. Well, um, that makes sense, too. But the maths proves it.

Anyway. Lots of luck with your campaign, Lord Drayson (Science Minister), with its catchy "street" title Science: So What? So Everything. But, hey, maybe I should put him in touch with my very own Science Man? It can only help.