Thursday, December 07, 2006



Here's an interesting maths fallacy (and thanks to DH for pointing me to the page with it on).

Sci-Fi Stuff

I also had a nifty scientific idea this morning. I was watching Firefly (TV sci-fi series, they only ever made one series of it) yesterday. One of the odd details is that all the planets and moons are meant to be in the same stellar system, but they all look remarkably like Earth. Odd that.

Anyhow - I was wondering how one might go about getting enough light and heat from the Sun to make them warm enough for habitation, and I figured that putting a lens at the Lagrange Point could well do it. Then I realised that such a lens would need to be pretty huge - nearly planet-sized even, and so would effectively require you to demolish a planet / moon to make it.

Then I thought of an interesting way round - use a Fresnel Lens (like those magnifying sheets you can get). You'd still need a big lens, but it'd be essentially 2D rather than 3D, so would need far far far less material and at least be possible.

And finally...

It's my birthday! Woo!


lottie said...

happy birthday :-D

Anonymous said...

Happy birthday! (I love firefox screen magnification). And your fallacy is really rubbing me up the wrong way! I obviously haven't had enough tea yet this morning.

John said...

Thank you very much.

As an addendum, Fresnel lenses are of course wavelength dependent, so you'd need to make it cunningly.

Elle said...

hello to you too! happy birthday! :-) i shall tell them about that random mathematical thing in further maths tomorrow...they might appreciate it! what do you know about snells law...? lol our teacher gets excited when anyone mentions it... :-)

Anonymous said...

Happy birthday Mr. Allister!
I was wondering if you still have your review of Angels and Demons as I am doing my coursework on antimatter in sci-fi and in reality and I think the review would be a useful source for me if its ok with you.
Thanks a lot,
Phil Hall

Daniel Hill said...

Happy Birthday!

John said...

My review of angels and demons is here.

In terms of silly stuff in sci-fi with antimatter, the classic example is an early episode of Star Trek where the enterprise gets linked to the anti-enterprise. In that episode, each character has their anti-character (bad where the other is good, etc) and the universe is annihilated if they meet. But it's fine with an anti-character (made of anti-matter) on a starship made of normal matter, for example.

John said...

Oh, and the CERN page debunking the book is quite good too.

Anonymous said...

Oh dear, you're a trekkie. You've just gone down in my opinion:-(

Unknown said...

[geek mode]
I think the excuse in the Firefly universe for all the planets looking like Earth is that all the planets they visit have been terraformed to have Earth-like conditions.
[/geek mode]

Happy Birthday, by the way!

John said...

DS - Who said I'm a trekkie? ;)

I'm not a great fan of the original series at all, and the later ones are interesting far more for seeing the underlying philosophy than anything else.

Caleb - The problem is that terraforming won't affect the amount of energy coming in and unless you have a greenhouse effect way beyond that on Venus, you aren't going to be able to get very warm at all once you get too far from the Sun / star.

Sad to say, stuff like that bothers me, but I do remember it. Hence knowing details of obscure Star Trek episodes. I can only remember ones where there are mistakes that bother me.

Anonymous said...

Eureka, I see the flaw! (With a little help, though not quite the exact solution, from the internet.) I take it you've seen the standard algebraic 1=2 fallacy? The one with all the 2(a^2 - ab) malarky.

John said...

The one with dividing by zero but not calling it zero? Yes

Anonymous said...

I guess sqrt(1) = 1 and also sqrt(1) = -1 but that doesn't mean that 1 = -1.

I don't get it.

John said...

The trick is that sqrt is only a sensible function for positive real numbers.

Even once you include negatives, it should really be ± sqrt (as with quadratics at GCSE).

So 1 x 1 = 1 = -1 x -1
But you can't just do the square root to get 1 = -1.

A posher way of saying it is that sqaure roots are not distributive over multiplication with negative numbers, which invalidates the central equals sign.

But that basically means the same.