Malaga meals

I'm just back from Malaga in Spain, where I was a member of a PhD thesis defence panel.  It was a very interesting thesis, which I enjoyed reading, and I got to meet up with several colleagues, and have lots on good conversation.

And good food, of course. On the Thursday evening, the supervisors and I went out for a "tapas crawl" -- ham and cheese in the first place, anchovies, cod, and tuna in the next, then finishing up at a Moroccan tea shop.  Along the way we passed the Moorish Alcazaba Fortress and Roman Theatre.




Friday breakfast was churros (fried dough) which are eaten after being dipped in thick hot chocolate -- very more-ish.







Lunch was paella and grilled swordfish on the beach, "serenaded" by green parakeets in the palm trees.  The warm sunshine made a pleasant change from the grey and raining England I had left 24 hours earlier, but I did make sure to sit in the shade.




Dinner, after the defence, was a kind of "up market" tapas, in that there was lots of (relatively) small, varied, delicious and ... different ... courses.

1. Pear draped in salmon covered with blue cheese, accompanied by blackberries
2. Ham and honey crepes
3. Cod in a tomato sauce (okay, quite tame in comparison, really)
4. Lamb, goats cheese, and sweet onion chutney
5. Pork and pate rounds with strawberry sauce

There were several of us dining: the panel, the supervisors, and the successful candidate.  Although we cleared the early courses, it just so happened that we all left some of the final one.  And it was the final main course: next was delivered the sweet course.  So, was it coincidence that we all faltered at the planned final fence -- or would they have continued serving new courses for as long as we continued eating?

Oh, and in between all the meals, as well as the defence there were meetings, presentations, discussions ... and coffee.

climbing up onto the shoulders of giants

If I have seen further it is by standing on the shoulders of Giants – Isaac Newton 

Newton was not first to say this (and it may or may not have been a jab at Hooke), but the idea is sound: we can get further because we don’t have to invent everything from scratch; we can build on what others have done before. So, if we need to solve a particular problem that needs calculus, we don’t have to invent calculus from scratch to do so, we can use what Newton (and Leibniz, of course) invented. Standing on their shoulders, we can see further.

But how do we get to stand on the giant’s shoulders? (I’ll keep the metaphor to a single giant, as standing on the shoulders of multiple giants sounds too much like a circus act. And I am focussing on the mathematical giant.) We aren’t born up there on the giant’s shoulders. While we don’t have to grow into the giant (invent calculus), we do have to climb up the giant (study calculus).

And the giant is getting ever bigger. On the one hand, this is good: being so much higher we can see so much further. On the other hand, what happens when we have to spend our entire lives climbing up the vast growing giant, and never reach the viewpoint on the ever-distant shoulders?

We need short cuts up the giant. Fortunately, other are building ropes and ladders and lifts: tools to climb the giant more easily. So, we now have computer algebra packages that can solve our differential and integral equations for us; we no long need to spend years studying and practising how to do this.

But wait! cry the purists. That is cheating.

there is no Royal Road to geometry – Euclid

Understanding an idea meant entangling it so thoroughly with all the other symbols in your mind that it changed the way you thought about everything. – Greg Egan

There are no shortcuts, the purists insist. Mathematics is not a “spectator sport”. You have to do it, be immersed in it, internalise it, in order to really understand it.  The youth of today, with their fancy calculators and computers, they don’t really understand arithmetic and algebra and calculus.  Get off my lawn!

There is nothing new under the sun when it comes to criticism of youth, of course. Plato, in Phaedrus, has Socrates rail against this new-fangled literacy:

 [writing] will introduce forgetfulness into the soul of those who learn it: they will not practice using their memory because they will put their trust in writing, which is external and depends on signs that belong to others, instead of trying to remember from the inside, completely on their own. You have not discovered a potion for remembering, but for reminding; you provide your students with the appearance of wisdom, not with its reality. Your invention will enable them to hear many things without being properly taught, and they will imagine that they have come to know much while for the most part they will know nothing. And they will be difficult to get along with, since they will merely appear to be wise instead of really being so. 

This sounds suspiciously similar to those modern complaints about using calculators rather than mental arithmetic, or using computer algebra programs rather than slogging through pages of pushing symbols around. These devices give only the “appearance of wisdom”.

I do have some sympathy with this view. There does seem to be a lot of blind trust in the output of calculators and computers. However, I’m not sure it is purely the fault of the calculators. There can be uncomprehending blind trust in symbol pushing, too. I remember, many years ago, being in a computer shop, buying four items. The shop assistant wrote down the prices, and laboriously added them up, with much crossing out. When they announced the total, I said “that’s wrong”. They got a bit huffy, but then I pointed out their total was too small: it was less than one of the items on the list! As well as their huffiness, I detected a faint feeling of puzzled wonder from the assistant: how had I known? Despite the hand calculation, the assistant had no feel for the numbers. Maybe Socrates would have said that they should have added the numbers in their head? (Notice here that I didn’t know what the right answer was, but I knew the suggested answer was wrong.)

Another example comes to mind, again from many years ago. We were buying some new pillows: four for £4.99 each. The shop assistant wrote down 4.99 four times in a list, and added them up. Meanwhile I was going “£4.99 is a penny less than £5, so that’s £20 minus 4p, or £19.96.” I had the right money ready by the time the assistant came up with the answer, and was again met with puzzled wonder. (I’m sure that’s the real reason supermarkets took the prices off their goods: to stop some customers freaking out the cashiers by having the right money ready!)

I recounted this pillow story to my mother, who, faster than I did my shortcut calculation, simply multiplied 4.99 by 4 in her head, and got the right answer. I was almost as much in awe of this feat as the shop assistant had been in mine. But which approach shows more understanding of numbers: my short cut or my mother’s brute force calculation? Is it possible that slogging through all those exercises merely enable us to do calculations quickly, without thinking? And if there is no thought, then what have we actually gained? After all, one can learn by rote and merely “parrot” remembered answers.

Back to climbing that giant. What we need is a way of taking short cuts up and of having the “feel” for the numbers. An approach that could work is critical thinking about the supplied results (whether supplied by computer, or by our own unthinking calculations). We can keep the feel by using even shorter short cuts and heuristics that give an approximate answer, as a sanity check. Those shorter cuts and heuristics supply the feel, and when they are done automatically, they are the feel.

So, education shouldn’t be focussed on getting students to wade through pages and pages of exercises, pushing symbols (be they numbers or letters) around (unless they enjoy that sort of thing, of course). It should be more focussed on training in the use of short-cut tools, education on where and how to apply the tools, and meta-training in critical thinking about the results those tools give. Then we can climb the ever-growing giant fast enough to get to the top in time to see something before we die, and confident that we’ll understand what we do see when we get there.

other Grays

While writing about The Puppet of Dorian Gray my thoughts turned to alien grays (as you do).

These are all over the place around here.  There's the signpost on the A14 to Hemingford Grey (maybe the resting place of a famous historical alien?)  Locally, Greys of Ely are so well assimilated into the community that they run a transport business.

But what got me worried recently was seeing a van with a logo warning of Grays Surfacing.  I didn't even know they lived underwater!

fake fake moon landing site

As I was trawling the web to find a particular picture for my "Angry Birds * Space" post, I came across the "Fake Moon Landings Revealed" site.  It's well worth a visit.

it's gravity, Jim, but not as we know it

I’ve just finished Angry Birds * Space (which everyone seems to call Angry Birds in Spaaaace, of course), released March 2012.  So that didn’t last long, either.

This time, the birds and pigs are fighting it out in space, and the birds have rocket drives.  There’s gravity in some places (near planets), and not in other places (not near planets). Only it’s not as simple as that. The existence of a gravitational field is shown by a red disc centred on the planet. Inside the disc there’s gravity, with the force directed towards the centre (I can’t tell if it’s 1/r^2 or constant on my little tiny phone screen); outside there’s no gravity. Gravity just switches on when an object enters the disc. Real gravity in space doesn’t work like that, of course.

Outside the disc, in the no-gravity regions, things travel in straight lines. So far, so good, maybe. But they gradually drift to a halt. No gravity, okay, but friction?? (Which is why the birds' rocket drives are on all the time.)  Real gravity in space doesn’t work like that, of course.

Also, there are some “black holes”: nothing visible at the centre of the gravity field, but stuff does get broken up if it goes there. There are also, confusingly, sometimes large planets with no gravity field at all, that act as hard (but massless!) obstacles. (Cases with invisible gravitating black holes plus visible gravity-free planets are particularly … interesting.)

There are two new birds: a light blue "ice cube" bird which freezes stuff, making it easier to break later, and a purple ("Lazer") bird that boosts in the direction of your tap (instead of the yellow Lazer bird that boosts along its tangent when you tap).

It's a Small World

The planets are very small – Clanger-esque, or even “Little Prince”-like.  In order to erect buildings on these small spheres, there are often large flat platforms. Sometimes this can lead to an almost square planet. Even with these platforms, gravity still points to the centre of the planet, so there is a small resultant force along the direction of the platform. I was delighted to notice, when an ice block was at the end of a platform, it slid towards the centre, overshot, then slid back: simple harmonic motion in action. Yay!

Square planets!

I did this time go for a perfect three stars on all levels.  That’s because the alternate-physics is fun, and three stars often required an interesting solution exploiting the possibilities, especially where planets are so close their gravity-discs overlap. Fortunately there is a helpful little "preview orbit" dotted line, that gives a partial clue to the final trajectory.  (The "Golden Eggsteroid" extra levels are great little spoofs on Space Invaders and the like.)

So, I’m just back from the Science Fiction Eastercon, where I was telling a friend that I’d nearly finished Angry Birds Space. So that’s all three done! (Vanilla, Seasons, Space) There’s also Rio, he said.

AAARGH! WHY DID YOU TELL ME THAT!

I’m now on Rio level four, collecting golden bananas…

learning from the worst

I'm not the best presenter in the world, but do I try not to make the most obvious of mistakes. Sometimes it's easier to learn what not to do from the worst (since you are not distracted by actually listening to the talk) than learn what to do from the best.

So, don't do this:

Chair: Our next speaker is Alex Umlaut from Olympus Mons University, with a talk on “non-isotropically depolarised orthophasic omicron graticules”.

AU: Good afternoon. My name is Alex Umlaut. I am from Olympus Mons University. My talk is titled non-isotropically depolarised orthophasic omicron graticules.

Here is the outline of my talk.

First, I will give this outline of my talk.

Then I will spend most of the talk on background material that you already know.  There will be lots of detailed equations in a small typeface that I will flash on the screen, but I will tell you that you don’t need to read them.  I will use lots of needless animations that will make you feel seasick.

When I get the five minute warning from the Chair, I will realise that I am running out of time, and will race over all the new and interesting parts, and completely skip 10 slides.

At the one minute warning, I will tell the Chair that I am on my last slide, but it will have 20 different reveals on it, and I will go well over time.

Finally, I will end with my conclusions.  I will mumble off into silence, so that you will not be sure that my talk has actually finished.

Here is the background to my work. You don’t need to read these equations. …

Audience: Zzzz…

The Puppet of Dorian Gray

Puppet Cliff Richard

I was reminded of this by Jo Walton’s marvellous Oscar! post, and in particular her inspired casting of Cliff Richard as "Dorian Grey".

Several years ago we worked out just why Cliff Richard, the “Peter Pan of Pop”, doesn’t age.  Made back in 1966, the film Thunderbirds are Go included a sequence with Cliff Richard and the Shadows, played, of course, by puppets.

To the right we see what the Thunderbirds puppet of Cliff Richard looked like in 1966.

Today, stored in Cliff Richard’s attic, that puppet is now terribly wizened and aged.

Or maybe not.

arbitrary doubling

One reason for the news report about temperatures (amongst other things) falling is that it has been quite warm this last week. The average daytime temperature here in the UK for March is usually about 10°C, but it has been 20°C and more.

This warmth has been the source of some irritating newspaper headlines:

The Mirror has a headline with: “temperatures soar to twice the average for March”

BBC New reports that the Daily Telegraph (which possibly should know better) says : “a barbecue weekend is in prospect, with temperatures double the usual for March.” 

No, the temperature hasn’t doubled. If it had doubled, if would be nearer 300°C!

If something doubles in size, units don’t matter. Something can double in length from 1 metre to 2 metres, or equally from 100 cm to 200 cm, or even from 3.28 feet to 6.56 feet.

0°C, 0°F and 0K are all different temperatures
(yes, there is no degree symbol when
using the absolute kelvin units)

But let’s look at changing the temperature units, say to Fahrenheit (an obsolescent temperature scale where the freezing point of water is 32°F, and the boiling point is 212°F).  10°C is 50°F, so if the doubling was real, 20°C would be 100°F. But 20°C is only 68°F (a seemingly much more modest rise!), whereas 100°F is 38°C (or nearly quadruple that 10°C, by newspaper headline “logic”!).

Things are even weirder if we used the Delisle scale (an obsolete and peculiar temperature scale where the freezing point of water is 150°D, and the boiling point is 0°D, so higher numbers are colder temperatures). 10°C is 135°D; “doubling” this gives 270°D, which is -80°C, whereas 20°C is 120°D. (Although it may seem weird for numbers to go down as temperatures go up, Delisle was not alone: this is the direction the original Celsius scale went, with freezing being 100, and boiling being 0.)

So why does doubling work for lengths, but not for temperatures? What’s different about the temperatures is that they have an arbitrary zero point. 0 metres means no length, but 0°C doesn’t mean no heat. There’s nothing special, temperature-wise, about the freezing point of water; it’s an arbitrary zero point (as evidenced by the fact that the Fahrenheit scale chooses a completely different arbitrary zero point).

To be able to do the multiplication and get a meaningful doubling, we need a true zero point for temperature, the absolute temperature, measured on the Kelvin scale (or the Rankine scale if you prefer those good old small Fahrenheit-sized degrees). There is another condition: the scale needs to be linear (rather than say logarithmic, like acidity, sound loudness, or star brightness); temperature is a linear scale, so that’s okay.  (If you want to play around with temperature scales, there’s a nice temperature units converter on the web, although it says °K, when it should be just K).

Let’s look at that doubling calculation again, now using an absolute scale. 10°C is 283K (rounded to the nearest degree, since that 10°C isn’t supposed to be very precise). Then 283K x 2 = 566K – this time, a meaningful calculation. And 566K is 293°C, which is worryingly hot for March!

The same data, graphed with
an arbitrary zero and a true zero on the y axis

This trick of an arbitrary zero leading to nonsensical comparisons like “temperatures double” is used all the time in “presentation graphics” (often in newspapers!) with misleading y axes. If the y axis doesn’t show a true zero (or worse yet, is unlabelled), then beware!



Note that we can do this kind of multiplication if we are talking about temperature differences, no matter what the scale. A rise of 20°C is twice a rise of 10°C. (A rise of 10°C is a rise of 18°F; a rise of 20°C is a rise of 36°F ). Rises work this way because a rise of 0°C, which is also a rise of 0°F, is a true zero.

However, newspapers can even mangle this! Several decades ago (although I doubt things have improved today) I saw a newspaper report that included the immortal phrase: “a rise of 1°C (33°F)”.

best April Fool evah

I was reading Jo Walton's review of the new film Oscar! over at Tor.com, thinking, this is weird, but sounds interesting.  She had me going right up to the point where we learn that Dorian Grey [sic] is played by Cliff Richard. ROFL!

The fact that it didn't strike me as at all implausible, just interesting, up until then (and then only the total perfection of that casting made me realise something was Just Not Right) demonstrates the surreal SFnal world I inhabit most of the time.

And I really want to see this film!

fallen syllepsis

A classic syllepsis, due to Dickens, is "Miss Bolo ... went straight home, in a flood of tears and a sedan-chair".  Syllepsis is a figure of speech where one word ("in" in this example) is used in two different senses simultaneously ("in a flood of tears" and "in a sedan chair").

I have a small collection of these at my website.  They are usually mildly amusing, or used for effect, resulting in a kind of mental double-take.  So I was surprised, and mildly amused, to see one today that doesn't appear to be used for these reasons:

Fresh snow and temperatures have fallen over the Cairngorms
--- BBC News, 31 March 2012

Someone must have enjoyed writing that!

And note also that, despite the date of this blog post, the original appeared yesterday.