Sound and Fury

All SI prefixes that are positive powers of 10^3 end in an “a” except “kilo-” I propose we change it to “kila-” because it won’t really make a difference to how people talk; a kilagram and a kilogram would be pronounced similarly by most people. What about people talking about “a kilo of rice” or whatever? Well, “kilo” can be adopted as a non-SI measure of weight much like “pound” or “ounce.”

Similarly, all SI prefixes that are positive powers of 10^-3 (or negative powers of 10^3) end in an “o” except “milli-” We should change that to “millo-” again with little or no need to alter how we talk.

Surely the Système International d’Unités is all about consistency. This is a a huge oversight on their part. Also, having a kilo, or kilagram, in Paris which is what we use to define what a kg is is quite unsatisfactory. If you want to know how long a second is, you look it up on wikipedia:

the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

You can get an atom of caesium 133 and do it yourself. With that measurement in place you can find out how long a metre is:

The metre is the length of the path travelled by light in vacuum during a time interval of ¹⁄_299,792,458 of a second. It follows that the speed of light in vacuum is exactly 299,792,458 metres per second.

You can procure a light source and a vacuum and find out how big a metre is.

But the kilagram, not so. If you want to know how big a kilo is, you have to go to Paris and weigh something against the International Prototype Kilogram. And while we’re at it, why does the SI unit have a prefix. That’s annoying too! I’m glad there are at least proposed future definitions. I don’t know if I’ve got my physics all backwards here, but here is perhaps another approach: Define a kilagram to be the mass a proton has when accelerated to speed X. Since distance and time are both well defined without recourse to an artefact like the IPK, this would put the kilo on the same level as them. This is an impractical definition, but no more impractical than counting osscilations in a caesium atom to measure a second or the proposed “counting atoms of carbon” approach to defining the kilagram.

Here’s a good quiz question: what do Liberia, Myanmar and the US have in common? They are the only 3 countries that have not adopted SI units as their primary method of measurement.

How cool is it that I can copy/paste text from wikipedia into wordpress and all the links automagically still work. That is really neat. Is that wordpress’ doing? Or wikipedia’s? Or firefox’s? Or Ubuntu’s? Whoever is responsible, you are now my heroes!

So apparently, science and maths exams are harder than arts subjects. Someone has done some research into differences between exam grades in science and arts subjects and found that “There were “substantial differences in the average grades achieved by the same or comparable candidates”.” This is really silly research. First, the average mark isn’t a very good indicator of the difficulty of the exam. Obviously, the difficulty of the exam contributes to the grades achieved, but the quality of teaching and probably several other factors also have an important effect. Secondly, I bet they found that the standard deviation in science subjects was much bigger too. It’s possible to do exceptionally well on more objective topics like chemistry and also exceptionally poorly. In, say, English the difference between a very good paper’s mark and a rather poor exam script will probably be smaller. And is a direct comparison of the type being made here even legitimate? “Easier” and “harder” are surely subjective and dependent on the individual pupils. Some people (myself included) found maths and science subjects at school to be fairly easy but struggled more with “soft” arts subjects. And the flipside is also true, some people who are gifted linguists for example might struggle with maths. So science and maths exams are harder for whom? I don’t think that comparing average grades across subjects and across pupils gives you any kind of meaningful conclusions.

The lower grades in science subjects is at least in part due to the dearth of properly qualified science teachers. As I said above, the quality of a teacher has a big impact on how well the students do in exams. And then there’s all the noise about dumbing down of exams; “maths exams are too easy” and so on. So what should we believe? Those who set the syllabus have the unenviable task of pushing the gifted kids, without leaving those who are struggling behind. But I think they should ignore all this noise in newspapers demanding easier/harder exams.

So here are some more iconic pictures.

Today’s Guardian had a cool little special section about CERN. It is available here. I now have a false colour bubble chamber image as my desktop background. So the LHC hasn’t blown us all up yet, which is nice. If it ever does, I might feel the tiniest bit responsible, since I’m signed up to the LHC BOINC project…

In other news, the nine-point circle is my favourite fact about triangles. I will try and mention it and its relation to incircles and excircles in my dissertation. Hopefully with gratuitous use of diagrams drawn in Kig. If I can be bothered to learn how to get pictures to work in LaTeX… Another thing I’d like to do is learn how to write chapters as separate files and include them in some master file. For 15,000 words it’s hardly worth it, but it’ll be useful for next year. I’d also like to change the default font to Gentium, for no other reason than to make a move away from default LaTeX formatting…

So I looked into it and Topology and sigma-algebra are distinct things. Apparently a sigma-algebra need only be closed under countable intersection, whereas a topology requires arbitrary intersections to be included. Also topologies won’t necessarily be closed under complement, whereas sigma-algebras will be. But the smallest sigma-algebra containing some topolgy is called the “Borel sigma-algebra.” So that’s that all cleared up…

I took out a book on Euclidean geometry today written by none other than Charles L. Dodgson; better known as Lewis Carroll. Cool huh? And what is more, it’s written as a dialogue! I also recently managed to find Alfred Renyi’s Dialogues on Mathematics. So I’m pleased with both of them.

What with various talks and my being quite lazy I haven’t really managed to get a whole lot done today. And I’m to a conference tomorrow. So this week has been a bit of a write-off really. The real proper work on my dissertation kicks off on Monday. Hoorah!

Yesterday’s Guardian had some maths puzzles from Key Stage 2, 3 and GCSE level. I was pleased to note I could manage them all except number 12. At least, that’s what I thought. For example number 8. The puzzle goes like this:

Look at these diagrams:

Diagram A {1,2,3,4} 10

Diagram B {2,3,4,5} 16

Diagram C {3,4,5,6} 18

Which one is the odd one out? Explain why.

The first four numbers there are arranged clockwise around the last number. Surely the answer is that in A and C, the outside numbers add up to the middle number. So B is the odd one out. The answer given says that “There isn’t one answer for this but you must be able to justify your answer” Fair enough. But I think my answer is one of the most obvious, so why don’t they list it in the “for example…” The ones they list are the following: “A has no numbers greater than 10, the other two do; if you add the numbers on the left hand side [that'll be the first and fourth of my lists] then double them, you should get the middle number but in B you don’t; it is only on C that two outside numbers, 3 and 6, multiply to make the middle number.” These all seem way more convoluted than my fairly elegant solution.

But it gets sillier. One of the puzzles (Number 11) doesn’t even have a solution. It is undetermined by the information given. So it’s one of those things where the numbers in the row below add up to the number in the row above. It is a triangle, three circles on the bottom, two above them and one above that. Only two entries are filled in. A little reflection will show that no two entries can determine the whole answer. Here is what the puzzle looked like, I have added letters to the empty squares to make it easy to talk about.

So the two numbers simply do not determine anything about the solution. D will have to be greater or equal to 8.2 + 5.1, A and B have to add up to 8.2 (therefore have to be less than 8.2) and C has to be at least 5.1. We are still miles from a solution. I ended up putting 8.2 in A, 0 in B. C and D were then fixed (5.1 and 13.3 respectively) But the rather arbitrary solution they give is 4.2, 4, 9.1 and 17.3 for A-D respectively. That is crazy! Where did those numbers come from?

These two questions would have bugged me loads in the exam. Maths (at school at least) is about getting THE solution. If any number of solutions are possible, isn’t this just going to trip kids up?

Incidentally, I’ve been thinking about the relationship between a sigma-algebra and a topology. Both are kinds of structure you can impose on a set X and are subsets of X’s power set. Maybe tomorrow when I’m in a LaTeX mood, I’ll write my tentative conclusions here…

From now on, if I can’t think of a title for my posts, they will all be Futurama references. Until I run out of them (in, like, 400,000 posts time) when I shall move on to Kung Pow, then Commando and so on, in that fashion.

So I went to Rock am Ring at the weekend. I got rained on and sunburned. I also saw lots of bands and so on.

My new favourite thing is the Burnt Pancake Problem because bacteria are better than computers at solving it. Also because both Bill Gates and David X. Cohen have written about it. Incidentally, if computing the nth digit of pi P or NP hard? Apparently there is an algorithm which allows you to compute digit n without having computed all lower digits. That is pretty cool.

The English language is full of stupid phrases that annoy me. For example “Subject to availability.” What does that mean? How could anything fail to be subject to availability? Surely this isn’t the kind of caveat that is really necessary.

Another one is “due to planned maintenance works.” Why the hell should I care whether the works are planned or not? If I wasn’t aware of them and the works and they disrupt my journey, I take absolutely no consolation from the fact that the works were planned. I recently saw a sign saying “Changing room on tuesday due to emergency maintenance works.” Again, I don’t care how much planning is behind the current or near-future inconvenience.

“If you’d just like to…” This annoys me too. “If you’d just like to take a seat here…” or “If you’d just like to put your card there…” First of all, it’s not a proper sentence. And secondly, it is useless verbiage. It’s simply a way for someone to tell you to do something while still sounding polite. I can imagine a mugger going “If you’d just like to hand over your wallet and phone, then I won’t kill you.” Perhaps you wouldn’t feel quite as “mugged” because of that supercillious politeness. And in fact, the mugger at least finished the damn sentence properly!

I bought some juggling balls online on Tuesday. They arrived today in the most unnecessarily oversized bag I’ve ever seen. They were in this paper bag like thing which could have held a package three or four times bigger at least. It was weird. Now, I could have chosen to spend an extra £4 for next day delivery. That would have meant that my order would have arrived a whole day earlier. I can’t imagine being in a situation where I am in such desperate need for juggling balls that I pay for that kind of extra. If I really really desperately needed to juggle as soon as possible, I’d buy some oranges and juggle with them. It would probably cost me less that the extra postage would.

Also, I would really like to juggle with raw eggs. If only I could find some excuse to do so…

Given a circle, what’s the best way to find it’s centre? Is it true that the midpoint of every chord of a circle goes through the centre of that circle? How would you prove that? I’m sure it would only take a minute to show if I could be bothered (and if it is true, obviously).

I’m glad to see that none of the restrictive amendments to the Human Fertilisation and Embryology Bill got through the free votes over the past few days.

I just found a great way to end my essay on Galileo. It’s a shame I still need to write another 1000 words, because coming up with such a great conclusion makes me feel I’ve finished. I really am running low on stuff to say now. Essay fatigue has really set in.

Also I am physically exhausted because I went to the gym yesterday and foolishly agreed to go through my friend’s gym routine. It was a bit much for me. However, it was good to do some exercise.

8 days to go until essay deadline frees me from this niggling feeling I should be working harder. At least for a while. Until I begin to feel I should start working on my dissertation.