In which I get dirty with $latex \LaTeX$
In which I post mathematical poetry
In which I point out pi day
Happy Pi Day!
I've just posted the following to this article about the tendency in the UK to see being bad at Maths (and Science) as a mark of pride.
It really annoys me every time a presenter on the news 'jokes' that they can't do maths or science. Melvyn Bragg on the usually excellent "in our time" is another. If you can't do it, then research your topic - or at least stay quiet!
I grew up with Johnny Ball. I really miss him on TV - he was enthusiastic and willing to find out about things which he didn't know about. Today's "science" shows are more about blowing things up in the microwave, or the caravan (yes, Braniac, that means you).
An honourable exception is discovery's mythbusters (UK site) - they don't always get the scientific terms right (misusing terms like force, pressure etc, the narrator in the UK is especially guilty of this) - but they have the sense of the scientific method, and of exploration.
I really like the idea. Each week, wannabe Johnny's would present a piece about some aspect of science. It'd need to be fun, accessible, as well as being good science. The panel would consist of, a non-scientist, a scientist (not Adam Hart-Davies!) and the 'Lloyd-Webber figure' - Johnny Ball himself.
Each week, Graham Norton would tell the contenders 'You could be Johnny'.
The theme tune would end with Jack Nicholson bursting through a door saying "Here's Johnny!"
The public would vote (usually on style over substance) and there'd be a 'present-off' between the two who had the lowest public vote, they'd explain some particularly gnarly bit of science or maths. Johnny would save one of them.
I could be a getting a little flippant here, but I'm deadly serious about the issue at hand. Personally, I think some sort of contest might be a lot of fun, as well as helping to increase interest in science and maths. It could work, couldn't it?
I... I will derive... find the derivative of x, position, with respect to time. It's as easy as can be, just find dx/dt.... I will derive!
A maths geek parody to the music of Gloria Gaynor. What's not to like?
Nicked wholesale from DoctorVee ... Whilst I do think the card might have been designed better, it speaks volumes that people are too stupid to understand this even when it is explained (e.g. specify 'colder' rather than make it numerical - or have an example such as '-8 is lower than -7)
The rest of this post is nicked:
Apologies. My first post back after a wee break does not involve much input on my part. I usually reserve these kinds of items for the linklog. But there is a quote that I just have highlight here because it makes me want to run along the ceiling in sheer frustration at the human race.
A LOTTERY scratchcard has been withdrawn from sale by Camelot - because players couldn’t understand it…
To qualify for a prize, users had to scratch away a window to reveal a temperature lower than the figure displayed on each card. As the game had a winter theme, the temperature was usually below freezing.
Tina Farrell, from Levenshulme, called Camelot after failing to win with several cards.
The 23-year-old, who said she had left school without a maths GCSE, said: “On one of my cards it said I had to find temperatures lower than -8. The numbers I uncovered were -6 and -7 so I thought I had won, and so did the woman in the shop. But when she scanned the card the machine said I hadn’t.
“I phoned Camelot and they fobbed me off with some story that -6 is higher - not lower - than -8 but I’m not having it.
“I think Camelot are giving people the wrong impression - the card doesn’t say to look for a colder or warmer temperature, it says to look for a higher or lower number. Six is a lower number than 8. Imagine how many people have been misled.”
HOLY SHIT! This is how bad standards of numeracy have become. Unbelievable.
Incidentally, my time off this blog was due to the fact that I was being educated. A certain Tina Farrell might have benefited from it more.
It is the fact that this person just couldn’t resist blaming someone else for the problem. There is not the slightest hint of her taking any personal responsibility. Even worse is the fact that Camelot have actually caved in, which will vindicate this stance in her mind.
....the sheer bloody-mindedness that illustrates a mentality along the lines of “well, if the laws of arithmetic don’t agree with my own intuition, then I’m going to bloody well complain until they fix it”. It’s not ignorance or stupidity that’s the real problem here, but the stubborn self-conviction that goes with it - the inability or unwillingness for people to ever now say “I don’t understand” or “I don’t know”.
And it’s not only scratchcards that this problem surrounds - virtually every major issue today, from the Iraq war to global warming to immigration, is characterised by people (on both sides) who will never even entertain the possibility they might be wrong, let alone admit to it. In the good old days stuck-in-the-mud irrationality and delusion was usually rooted in ideology or religion (”if Lenin/Smith/Jesus says so, it must be right”), but they are by and large absence from most aspects of modern life - which has created a vacuum into which some weird, fucked-up cult personality of the self (”if I say so, it must be right”) has entered. Add to that a culture where any grievance, no matter how petty, must always be redressed or avenged and it creates a terrifying vision of the future.
The classic 19th century novella, which discusses the mysteries of the mythic 'third dimension' to a two dimensional viewer, Flatland, has been made into a movie. This is something I'd like to see, but it requires transatlantic shipping. If only I'd have spotted it a couple of weeks ago!
Ian Stewart wrote a sequel to Flatland, called Flatterland. In which we learn that A. Square was called Albert. Albert's descendant, Victoria Line, meets up with another creature who shows her the wonders of more than just the third dimension....
I drew another fractal today, the Koch Curve (click on the graphic for full size). The Menger Sponge took more time, and by rights I should be more satisfied with it, but the Koch curve is somehow nicer to me, it's simply elegant.
The curve is formed by starting with a line, and in the centre third, creating an equilateral triangle. This is repeated for every one of the four lines we now have, and so on.
The fractal dimension is around 1.26, this is because to make curve we have had to use four smaller copies, each is a third the linear dimension. I.e. To increase the size 3 times we need four copies.
3dimension=4, so dimension=ln(4)/ln(3).
Like the Menger Sponge I drew the koch curve freehand.
It was just one of several sketches I drew today. Of the 'arty' ones, I'm quite pleased with the water.
This is a close up of the sketch in my moleskine (click on the picture to enlarge) which shows a Menger sponge. A Menger sponge is a fractal shape, and so an accurate rendition is not possible. I've gone to 'level 4', with 'level 1' as a cube.
To make a Menger sponge, start with a cube, and make a square tunnel through each side. Each face is 8/9th the area it started with. This can be thought of as eight squares in a ring. In the centre of each of these squares, remove another square tunnel. Wash, rinse, repeat.
When taken to infinity, we end up with a very holey solid. It has a fractional dimension, it's a fractal.
It actually has a dimension of 2.72683. What's this mean? Well, imagine a line, double it in size. It gets twice as big. I.e. you need two original lines to make the new one. That's a change of 21. I.e. this has one dimension.
Take a square, double it in size, it's area increases four times. I.e. you need four original squares to make the new one. That's a change of 22. I.e. this has two dimensions.
Take a square, double it in size, it's volume increases eight times. I.e. you need eight original cubes to make the new one. That's a change of That's 23. I.e. this has three dimensions.
Now, to make a larger menger sponge, we need to increase it in linear size three times. That's not a problem, with cubes we'd need 33 cubes (27 cubes), the dimension is still 3.
With menger sponges we'd need 8 for the top and bottom layer, and 4 for the inner layer, so that's 20 smaller spongers to make one larger sponge.
This means that 20=3dimension, so ln(20)=dimension*ln(3)
In turn this means that the dimension of the sponge is ln(20)/ln(3) or approximately 2.72683. It's more solid that a flat surface, e.g. paper, but less solid than a solid, e.g. a cube.
These are a series of geometric shapes, the idea was to give practice with shading and hatching. At the top left are a series of hatching practices, followed by a sphere (not too hot), some cones (I like), a cube, a cube done with a putty eraser, a menger sponge, a möbius strip and some hatched cones.
I can imagine coming back to this sort of idea regularly as my skills improve.
As usual with these pictures, clicking on the picture will often get a more detailed image.