Interesting Links for 5-7-2011

[andrewducker]

• EU ready to cut absurd data roaming charges
  (tags: data mobile_phones europe)
• Amazon's App Store seems to be having some pretty severe problems
  (tags: amazon android_market app_store)
• A rather deflective, but entertaining, interview with Rupert Grint
  (tags: RupertGrint HarryPotter interview)
• News Corp may face test to make sure it is a "fit-and-proper" owner of Sky
  (tags: media sky RupertMurdoch television)
• Prenatal exposure to SSRIs may modestly increase risk of autism spectrum disorders
  (tags: psychology serotonin children autism)
• MIT develop glasses that can see the emotional state of the person you're looking at.
  (tags: autism emotion empathy psychology technology)
• Positive reframing, acceptance and humor are the most effective coping strategies (now with science!)
  (tags: emotion happiness psychology)
• What happens to relationships when your partner marches to a drum of a different tempo?
  (tags: time relationships speed)
• I would like this in my garden. Very much.
  (tags: awesome ADescriptiveTagWouldSpoilTheSurprise)
• Complex numbers made straightforward
  (tags: numbers mathematics)
• How To Be An Ally to Sex Workers
  (tags: prostitution sex business society advice)
• Research that up to 72% of dietary health claims in UK newspapers lack evidence is itself unreliable
  (tags: journalism research science badscience food diet)
• Happy Fucking Fourth Of July
  (tags: usa funny)
• A good explanation of the Dilnot proposal for reforming adult social care
  (tags: society healthcare uk)
• Opera by Billy Elliot writer cancelled over gay reference
  (tags: opera lgbt children school uk)
• Iceland considers prescription-only cigarettes
  (tags: cigarettes tobacco smoking iceland)

Comments

[gonzo21.livejournal.com]

That SSRI/Autism link sounds like it needs a much bigger study done as soon as humanly possible. Because that sounds like a way more convincing theory for the rise in Autism than anything else I've heard.

And yes, the garden thing is awesome. I wonder if it is life-sized.

[andrewducker]

Yup - a bigger study is definitely needed.

(Best theory I've heard is that it's actually an increase in spotting autistic people, who used to go unnoticed a lot of the time.)

[gonzo21.livejournal.com]

I have that debate with my father quite regularly about cancer, he thinks there is a lot more cancer today and it is something in modern society causing it, but I reckon it's just because people live longer now and it gets diagnosed.

[andrewducker]

Did you know that joggers are more likely to die of cancer?

This is, of course, because the two biggest killers in old age are heart attacks and cancer, and if you reduce your chances of a heart attack then cancer is what's left!

[gonzo21.livejournal.com]

Ha, excellent. No, I did not know that.

[channelpenguin.livejournal.com]

IF, and this is in NO way proven, jogging is good for preventing heart attacks. (I won't bore you with why that might not be so...)

Incidentally, the man who is thought of as starting the jogging craze (Jim Fixx) diesd of a heart attack...

But I do take your point!

[laplor.livejournal.com]

My family has had a long-running joke that the most effective prevention for diabetes, heart attacks, and cancer is car-crashes.

[daveon.livejournal.com]

Yes. This.

[a-pawson.livejournal.com]

Ben Goldacre has now posted a reply in the comments.

[andrewducker]

Interesting. Let the battle commence!

[nancylebov.livejournal.com]

e explained

[momentsmusicaux.livejournal.com]

> Complex numbers made straightforward

That's a lousy explanation. Treating complex numbers as just an ordered pair with some wacky rules turns it into a completely arbitrary, nonsensical system.

[andrewducker]

It's the first explanation I've heard that makes any sense to me.

[momentsmusicaux.livejournal.com]

It's so bad I was wondering if it was a spoof.

[momentsmusicaux.livejournal.com]

And yes, it'll make sense to someone who already has an analytic mind. And it's how complex numbers are rigorously defined in mathematical analysis. But it's not the way to initially teach them, absolutely not.

You say to someone: "A complex number is an ordered pair of real numbers ("complex", here, just meaning "made up of more than one thing")" and they reply, 'why the fuck would you want to do that?' and 'why the stupid multiplication rule?'

[andrewducker]

Demonstrably not true, as I didn't.

[momentsmusicaux.livejournal.com]

Sorry, but it's total damn crack, I'm adamant on this.

[andrewducker]

You're entitled to be adamantly wrong as much as you like. You can even be emphatic, if you like.

[momentsmusicaux.livejournal.com]

Seriously. I spent enough time explaining maths to people at 6th form and then at uni to know what works and what will just confuse.

Want a spec to write a complex numbers implementation in a programming language? That link is just what you need. Want something for a human being? Nope.

[andrewducker]

Are you saying I'm not a human being?

[momentsmusicaux.livejournal.com]

Eliza?

[sigmonster.livejournal.com]

All abstract number systems are arbitrary and nonsensical. The real line, where the overwhelming majority of numbers cannot be accurately written down, uniquely identified or otherwise defined, is just silly.

[momentsmusicaux.livejournal.com]

Of course they can be written down. Here's one I'm going to write down now: π

;)

[sigmonster.livejournal.com]

Don't stop there! Keep on going! :-)

[spacelem.livejournal.com]

I absolutely agree. I posted a reply which I think is far easier to understand, which I'll repost here (if you don't mind).

In my opinion (and I got this mostly from studying dynamical systems and eigenvalues), the easiest way to understand complex numbers is just to say: "real numbers stretch things, imaginary numbers rotate them; let me show you an example on an argand diagram..."

Once you've got this, multiplying by 2 stretches your number twice the distance from the origin of the complex plane, multiplying by -1 is just rotating your number by a half turn (τ/2), and i is just a quarter turn (τ/4). It's then obvious that two quarter turns make a half turn, which is -1.

Complex numbers that are neither purely real nor purely imaginary are combinations of stretching and rotating. With this definition, I think it's as easy to understand imaginary numbers as it is to understand real negative numbers.

[andrewducker]

Oddly, it was seeing that explanation that made me realise that it was just two dimensions in space, and that the multiplication was just a transformation in said space.

I've never had someone try to explain them with pictures - I'd be willing to give it a go. "rotating your number by half a turn" would definitely need a picture for me to understand it if I hadn't already read the previous explanation.

[sigmonster.livejournal.com]

Personally I'd do it with pictures of the plane first, then rotation matrices (and determinants), then complex numbers as a more concise notation. If possible, get a little group theory and abstract algebra going on alongside, so that you can show that the various models of complex numbers are all homomorphic. ("...new math, new-hew-hew math, it won't do you a bit of good to review math!")

But different people find intuition in different places.

[spacelem.livejournal.com]

That was how matrices twigged for me.

I remember seeing a series of short videos about famous mathematicians (sadly I can't remember what the series was called). They discussed the real number line, how multiplying shifted you along the line, and how multiplying by -1 was rotating a half turn; you get i by only going half as far. This leaves you off the real number line, which was causing all the trouble, but adding an extra dimension made everything fall into place. Pretty graphics obviously helped.

The take home message (and it works so often that it's amazing it's not the first thing they teach you) is that imaginary numbers are just rotations (sometimes oscillations). Then it becomes obvious how they coexist with real numbers, and appear in the world around us.