Tag: math

Science Journalism Marches On

The claim that bacteria in the human body outnumber human cells by an order of magnitude or so has become a popular observation among Science Fans. A 2008 article in the ghastly New York Times states:

The bacterial cells also outnumber human cells by 10 to 1, meaning that if cells could vote, people would be a minority in their own body.

This is misleading. A single bacterium masses something on the order of 10-13 – 10-12 grams, while a human body cell is in the neighborhood of 10-9g — 1,000 to 10,000 times larger. By weight, bacteria therefore compose somewhere between 1% and 0.1% of you, depending mainly on how recently you went to the restroom. Thus, the Important and Popular Fact presented in the NYT and other sources is technically true*, in the sense that Vin Diesel is outnumbered by a small bag of crickets.

*: The claim also skips over the fact that the largest fraction of the bacterial population in question consists of symbiotes, which could be designated honorary human cells under the mitochondrial grandfather clause, but that’s a whole other post.

Local and Global and the Terrible Telescope, Part 1

In the comment thread for my previous post, I remarked that

I don’t know of a good theory that bridges the chasm between individual justice (where I think free association is an important fundamental right) and global justice (universal behaviors like [modes of systemic oppression]). I don’t pretend to have one.

What I’d like to do in this series is try to convince you that you probably don’t have one either.

  • Local and Global • William Lane Craig is Terrible • Kant is Also Terrible
  • the Repugnant Conclusion is Neither • Telescoping Considered Harmful
  • You Are Not God, You’re Not Even President of the Galaxy
  •  The Can’tegorical Imperative • Further Reading

1. Local and Global

One hard lesson every student of advanced mathematics learns is that a construction that seems easy and obvious locally–for instance, in a small region of a space–can be very difficult, or outright impossible, to make meaningful globally–eg, over the whole space.

For example, think about the direction ‘North’.  Which way is north? Wherever you happen to be reading this, you probably know already; if you don’t, your phone can probably tell you. ‘North’ is an easy local concept–we can all check which way north lies. We can find ‘north’, no matter where we go. Right?

Wrong.

Continue reading “Local and Global and the Terrible Telescope, Part 1”

Geometry is Heroic

Why study Euclid?

Euclid’s geometry shows you that you, personally, can know truth without taking anything on faith.

You don’t have to believe Euclid, you just have to walk the same road that Euclid and millions of others have walked, and see what’s there: truth that’s available to everyone, that doesn’t rely on faith, popular consensus, or opinion. The truth found in geometry is not an expression of power relations; it was constructed by people of many cultures but isn’t “socially constructed”. It is not moral, it does not demand obedience, it does not yield to hegemony, it does not submit to authority. You can only attain it by your own efforts, but you can still communicate it and share it with others.

Knowing this kind of truth, and knowing that you can know this kind of truth, is a power that can be gained no other way.

The Mark of an Ergodic Crab

I. Chasing ergodic crabs

Yes! Ergodicity is interesting and very useful. At least in statistics. Don’t ask me what physicists do with the thing though. Those guys are crazy. The problem with ergodicity is that it’s pretty complicated. Go ahead, take a look at the Wikipedia page, I’ll wait a minute.

…

…

Ok, good. The math geniuses are gone now. You know the type – they can look at some math they’ve never seen before and understand it in minutes. Right now they’re busy proving theorems about ergodic flows on n-dimensional locally non-Hausdorff manifolds. And twitching at that last sentence. You and me? We’re going to learn about ergodicity with a pretty crabby extended metaphor.

Continue reading “The Mark of an Ergodic Crab”

Gödel for Dummies

Gödel’s theorems say something important about the limits of mathematical proof.

Proofs in mathematics are (among other things) arguments. A typical mathematical argument may not be “inside” the universe it’s saying something about. The Pythagorean theorem is a statement about the geometry of triangles, but it’s hard to make a proof of it using nothing but points and lines in a plane! For instance, Euclid’s own proof (per Wikipedia) starts like this:

  1. Let ACB be a right-angled triangle with right angle CAB.
  2. On each of the sides BC, AB, and CA, squares are drawn, CBDE, BAGF, and ACIH, in that order. The construction of squares requires the immediately preceding theorems in Euclid, and depends upon the parallel postulate.[13]
  3. From A, draw a line parallel to BD and CE. It will perpendicularly intersect BC and DE at K and L, respectively…

The proof uses words, symbols and other tools that aren’t points and lines in a plane. Euclid’s proof thus is about geometry but isn’t inside geometry.

How does this apply to logic? Logic is (among other things) the mathematics of arguments. It’s reasonable to wonder if proofs about logic fit inside logic! More precisely, given a particular system of logic S, we can ask what S can and can’t say about itself.

Continue reading “Gödel for Dummies”

Ice Under the Bridge

The BBC is renowned worldwide for the high quality of its journalism. Take this article from 2005:

A thirsty thief is being blamed for downing a bottle of water, valued at £42,500, at a literary festival.

The two-litre clear plastic bottle containing melted ice from the Antarctic was devised to highlight global warming by artist Wayne Hill…

Its value was worked out by the artist from the damage worldwide of the entire ice sheet melting – he estimates between £6 trillion and £9 trillion – and the relative amount of damage from two litres of water.

Hmm. Something seems off about those numbers. Let’s check them!

Continue reading “Ice Under the Bridge”