johnaspden

And thus, benefits from trade.

Ron appears to have got what he wanted, starting from a very bad position!

So, there are two ways to do things, an easy way and a hard way. Once you've done it the easy way, it's probably a lot easier to cover up the traces and make it look like you did it the hard way.

And a guy who is famous both for being incredibly clever and for being rather arrogant and insecure told all his competitors that they were incompetent if they didn't do it the hard way.

Programming is a form of mathematics. Maths papers are terse and beautiful and look as though they have sprung fully armed from the head of Zeus.

But you don't see the days of hacking through examples and crazy leaps of intuition (that are almost always wrong) in the finished paper, because the mathematician removes them from the story in order to leave an argument that is easy to verify.

I am not saying that Dijkstra couldn't do things the hard way. I would be amazed if his best stuff was done the hard way.

If we had infinite energy we could make more aluminium.

Is it perhaps the same difference as between "I am English" and "I am an Englishman"?

Presumably you'd need to be a true bilingual to tell if they feel the same, and even then, your thought processes aren't going to be the same as either type of monolingual.

I think interesting rather than weird. According to Galton at least, people like you are much more common amongst scientists than people like me. Thank you very much for your comment. I was hoping that people would give me answers like this when I posted the link.

Cool article, thanks! I particularly like the bit at the end, which reminds me of the fact that I can no longer code without syntax highlighting.

I've no idea what your mental whiteboard must feel like, but I imagine it's very useful. I find a whiteboard to draw graphs (networks) on really helps me to think, and it looks like you don't need one!

There's a second half being written which will do symbolic differentiation, and maybe a few small macros. This is supposed to be a gentle introduction for non-lispers and I seriously think this will be enough for two hours.

But I'm writing something more devious just in case.

Any sufficiently advanced technology is indistinguishable from magic. I do know how it works. I've done my meta-circular interpreters.

I also know there's an abs function. There's a sqrt function too. That's not really the point of the thing.

And I am never going to believe that (+ (* x x) (* y y)) is clearer than xx + yy, even though I do realise that that's only because those rules were drummed into me at school.

More exotic examples of operator precedence, yes, I agree.

Cool, thanks!

Because 'don't be evil' is one thing (a good thing).

But here they seem to be going for 'do the right thing', which is a whole different plan.

This will cost them, at least short term. That's part of what 'the right thing' means.

Originally they said they believed that collaborating would do more good than not doing.

Now they are saying that they no longer believe that, and will no longer collaborate.

I am sceptical, but I still applaud it.

We can be cynical too. Let us show them that those sort of actions are appreciated.

For instance, their share price is falling. Let those who are keen on real altruism buy shares to drive it back up.

Perhaps we can create a climate where good corporate behaviour is actually profitable, and where corporations and governments fear to be caught in the act of evil.

Firefox, same problem on that page, changing encoding solves it.

I stopped reading this half way down. Is there anything in the article except blether?

The first half seemed to be saying 'Drugs companies do tests against placebos. Merck is short of drugs.' Can someone who took the trouble to plough through it summarise the second half?

The slacker view:

http://johnlawrenceaspden.blogspot.com/2009/11/horror-of-pro...

I wrote this article after people had a go at me for teaching kids to program. The first half doesn't sound like you, so skim it, but the second half might be relevant. Start at the bit where it says "A well paid job that you don't enjoy is a curse".

You certainly need to be paid by the hour. The problem at the moment is that you're ripping yourself off.

Sometimes people ask me to work 80 hour weeks, but they only do it if it's really critical, and I never feel ripped off by it.

Mostly they're happy with about 35, since they know as well as I do that any more than that on a regular basis and I'm not going to be too productive.

Upvoted for "The Machine Stops". What vision from 1908! I notice that it's copyright EMF 1947. Any idea what that means? There's something about 'dying in France' that made me think of the Great War.

Thank you so much for that and for your previous post. Exactly what I wanted.

That makes me feel really sad. My epiphany was your iron curtain coming down.

I can see how. In fact I had the same reaction initially (and my parents are graduates, but they don't know the first thing about maths, so they were no help to me either).

I have no idea why I wrote the program to plot a circle that made it obvious what sin and cos were.

In fact I think I might have misremembered my own story. I had a ZX81 first, and I don't think that had a circle function, so it may be that the ZX81 manual explained how you could use SIN and COS to do that.

But I think we can agree that google and wikipedia are wonderful things. The upcoming generations of programmers and mathematicians are going to be Gods. How could they not be with a library like that!

Well, actually,

sudo apt-get ipython sudo apt-get install ipython ipython -pylab sudo apt-get install pylab sudo synaptic (<--used it to find pylab packages) sudo apt-get install python-matplotlib sudo apt-get install python-matplotlib-data sudo apt-get install python-matplotlib-doc ipython -pylab

And then the program works.

Actually, thanks for that, I didn't know about that stuff, and it looks really useful. If I can figure out how to get the drawings to move then it will do what I want. (to visualize the action of unitary matrices on Hilbert spaces)

But my point was that in 1982, my non-technical parents bought me a computer and then I was away. A couple of months later I had an animated model of the solar system. And I hadn't read anything except the spectrum manual (and the equivalent one for the TRS-80).

I can work out how to do the above installation for my hypothetical 12 year old son, but my poor father wouldn't have had a chance. And I suspect that the same would be true for most non-techie parents.

And how is the hypothetical son supposed to go from the pretty blue curve created by the magic plotting program to an animated solar system?

I can't see how to make the graphs move. Perhaps it can be done. Perhaps it can't and I should use SDL instead.

The point is that it is not obvious to me. Whereas the equivalent questions were obvious to a child thirty years ago.

And that will mean that we've got good darknets for real criminals to use, whilst people doing nothing wrong cover for them.

OK, to rephrase the question, what will the people accepting the jacuzzis full of money use as arguments?

So the freedom of the world now depends on the European Union, which we know is corrupt. Is there any way to buy shares in whatever method media giants use to bribe European politicians?

And China put the brakes on all innovation.

I've been going down this list, voting up things that seem interesting. And suddenly I thought "Bloody hell, I'm using my real name to criticise the government on the internet". And obviously, I've decided that I have no problem with that. But I'm a white, middle class, middle aged businessman, and a British subject rather than an American citizen. And I still thought it.

America's stupid "War on Drugs" has devastated large parts of the world. Is an equally stupid, and, more laughably, even more doomed to failure "War on Copyright" going to wreck the Internet and possibly freedom itself?

And this is Obama? Who was supposed to be the good guy?

I was in Paris for a week in Spring, and rode velibs everywhere every day.

No problems at all. Occasionally you found a knackered one, but it looked like wear and tear rather than vandalism. It's a superb idea.

As a circle expands, its area grows proportional to its circumference. The circumference is proportional to the radius.

So you're getting the area by integrating a linear thing.

Thanks! Yes, when you grow in a direction at right angles to yourself, you don't increase in magnitude. So the turning arrow is the same length at the end as it was at the beginning.

This is actually a slightly tricky point, because it requires the direction of growth to change as you grow. If you grow by a finite amount all at once, then you do get slightly longer. So you might expect an outward spiral.

But a point moving round in a circle is always moving at right angles to the radius connecting it to the centre.

And in the same way, an arrow whose tip is moving at right angles to its shaft isn't extending. If the length is changing, then the direction isn't 90 degrees.

To reason about this properly I think you need some sort of theory of infinitesimals and continuous motion.

The complex plane is the fundamental thing.

It's the only way to get to the complexes without doing anything spooky! Defining i to be "the square root of minus one" is about as sane as defining it to be the square root of the colour blue.

The first people who thought about it followed that approach, and were rightly scared stiff and confused by it. Even Euler made trivial mistakes.

Argand came up with the right way of thinking about it:

Take all the tuples (x,y). (Where x and y are just integers). Define on them addition and multiplication rules.

Oh look! There's a big system of these things, and embedded within it is a sub-system which works exactly the same as the integers and their rules.

Since they're exactly the same for all practical purposes, we may as well forget about the difference and say that we'll write (a,0) as a and (0,b) as ib, and (a,b) as a+ib

And although non of the pairs in that subsystem square to be (-1,0), also known as -1, there are two things that do! So now we know that both (0,1) and (0, -1), otherwise known as 1i and -1i, or i and -i, are square roots of -1.

No slight of hand or magical thinking necessary.

As it happens, we can do the same thing with the reals, to form something that embeds the reals. But the reals really are dark and mysterious and need to be brought about by a kind of magic.

Thanks! No, I worked it out for myself while I was thinking about what the exponential of a linear operator is. The explanation at my school was the one with Taylor Series.

By the time I got to university it was just taken as a given, so nobody explained it at all.

My explanation seems to have attracted a lot of positive votes in a few minutes. I've written a more detailed version here if anyone doesn't get it:

http://johnlawrenceaspden.blogspot.com/2009/10/ei-pi-1.html

If it gets much attention I might draw the diagrams that go with it.

I'm always bewildered how many scientific types (and even some mathematicians) find complex numbers mystical. They were originally discovered by mystic methods, but Argand showed us what was really going on, and they're no more weird than 2-dimensional vectors.

Actually a lot less weird than the Reals, which really are magical and mysterious, but which everyone seems to be quite happy with!

Imagine you're a complex number, which is just a type of 2-vector.

Exponentiation is to do with growth at a speed which is a multiple of how big you are already.

i is the multiplication which turns you through ninety degrees.

If you grow in a direction which is at right angles to yourself, you turn rather than increasing in magnitude.

Pi is how long it takes you to turn through a half circle.

So if you grow at right angles to yourself for time pi, you are pointing the opposite way.