Thursday, January 11, 2007

Enter Night

You find yourself in a dark auditorium, lit only by the scarce light of the night sky. Pale sights in the sky, such as the Milky Way and the Andromeda galaxy, are actually visible, so you must be in a remote location, far from the influence of light pollution. In the pale light, you can't tell how full the auditorium is or recognize anyone around you.

The auditorium is completely silent, but when a figure starts to walk out on stage, it somehow becomes even more so. If silence were a zero point, this would be negative noise. The sight of the man is much the same; his visage is so dark that it passes the zero marker of luminosity and radiates darkness. The darkness does do the job of detailing him, however. Flipping the colors... is that Infophile? And is that a darkness-radiating spherical cow rolling along behind him?

Once he reaches the center of the stage, he turns to face the audience and starts to speak:

Welcome one, welcome all, to the grand opening of the Night Museum! I'm very pleased that you all *ahem* decided to attend. Don't worry if you're feeling disoriented; it's perfectly normal. You see, this museum occupies a space which obeys slightly different laws of physics than the universe you know. Fortunately, the differences won't interfere with your biological functions, so you'll be perfectly safe.

Some might describe such a different type of space as being in "Another dimension." This isn't completely accurate. All another dimension means is that there's another degree of freedom for movement. This is part of the case here, but it's best to say that this museum occupies a different location in another dimensional axis. To be exact, this axis is circular, and this museum is at a polar position to the universe you know. For the technically-minded, you might say that it--along with myself--was created entangled with Infophile and his blog.

You might wonder where the name of this museum and the name of this space come from. As for the museum's name, it's a tribute to the cult classic science-fiction/fantasy show, Night Gallery, hosted by the famed Rod Serling. Although not as popular as The Twilight Zone, Night Gallery was still an important contribution to the science-fiction/fantasy genre (plus it was more easily tributable).

The name of this space, The Night Relentless, uses its peculiar form as a tribute to Terry Pratchett's Discworld novel, The Light Fantastic. Pratchett used a method he called "Stealth Philosophy," in which he snuck philosophy into his primarily-comedic novels. In this method, he held up a distorted mirror to society, making its flaws not only stand out, but stand out comedically. I intend to use this method to an extent myself, holding up a mirror to society in order to make apparent its flaws, hopefully with a few laughs along the way.

But anyways, let's get onto the museum itself. The Night Museum is unique among museums in that it puts modern society on exhibit. The exhibits will range from showing the best humanity has to offer down to its worst. And when it comes to the worst, this museum offers something else to make it unique: We're not just about presenting it, we're about fixing it. Entire sections of the museum will be devoted to how we can fix problems that plague the world.

Today, however, I figured I'd give you a sample of something our museum will present which is on a bit more of a positive note. I have with me here my good friend, Ballzac, one of the rare species of the Spherical Cow. Say "Hello," Ballzac.

The Spherical Cow rolls around a bit so that his head--well, more of just a face, since there's no protruding head to speak of--faces the audience, and lets out a friendly "Mooo!"

The Spherical Cow is what's known as a simplifying assumption. These are tools used by scientists to make fairly accurate predictions about world, without having to perform the extremely complex math inherent in, for instance, calculating the moment of inertia or drag coefficient of an oddly-shaped body such as the normal cow.

Such assumptions may seem like they lead to worse results, but this isn't entirely fair. The truth is that in many cases if they weren't used, we wouldn't be able to get any results. We also have to be sure to remember that our results aren't expected to mesh perfectly with reality, and the only way to know exactly what will happen in any given case is to test it out experimentally.

The problem is that a technique such as this is often used as an excuse for quacks to exercise shoddy science. Simplifying assumptions are used which completely undermine the entire endeavor. For instance, take the case of one particular Creationist argument from big numbers, as previously debunked by MarkCC. Look at the following passage:


(1) we will reckon the odds of evolving a new horse species from an earlier horse species.

(2) we assume only random copying errors as the source of Darwinian variation. Any other source of variation -- transposition, e.g., -- is non-random and therefore NON-DARWINIAN.

The first "Assumption" isn't so much an assumption as an outline of what they're doing here, but the second one is what I want you to look at. There are many types of mutations that can occur, but they're making the unfair simplifying assumption of only looking at random copying errors. I'll let MarkCC explain what's wrong with this:

Really, there are a lot of different sources of variation/mutation. At a minimum, there are point mutations, deletions (a section getting lost while copying), insertions (something getting inserted into a sequence during copying), transpositions (something getting moved), reversals (something get flipped so it appears in the reverse order), fusions (things that were separate getting merged - e.g., chromasomes in humans vs. in chimps), and fissions (things that were a single unit getting split).

In fact, this restriction a priori makes horse evolution impossible; because the modern species of horses have different numbers of chromasomes. Since the only change he allows is point-mutation, there is no way that his strawman Darwinism can do the job. Which, of course, is the point: he wants to make it impossible.

This assumption doesn't make it simpler to find results, it makes it impossible to find results, and they use this as the base of their argument that evolution therefore must be impossible. Of course, it wouldn't be impossible at all if they didn't make this assumption.

So, how does one go about determining if a simplifying assumption is reasonable? For this, I've created the following checklist:
  1. Is there a legitimate reason to make the assumption? That is, without it, would the involved math still be reasonable?
  2. Is the assumption used in some field other than strict mathematics (in which no assumptions are allowed at all in proofs)?
  3. Is the assumption a reasonable representation of reality?
  4. Does the assumption preserve all critical, relevant portions of the situation?
If the answers to all of these questions is "Yes," then it's most likely a reasonable assumption. Let's go over a couple of cases to show how this works. First, let's take the case of assuming a Spherical Cow when determining the gravitational attraction between it and Earth:
  1. If we didn't make the spherical assumption, we would be faced with an impossible integral of determining Earth's gravitational attraction to every atom of the cow's body. Answer: Yes
  2. This is a case of physics, so Yes.
  3. Well, cow's aren't normally particularly spherical, but the important consideration here is the distance involved. Compared to the distance to the center of Earth, the size of a cow is virtually a point, so we can treat it as a point mass. Also to note: spherical mass distributions will always behave just like point masses, so on the scale we're working with, the assumption gives us a good approximation of reality. Answer: Yes.
  4. Nothing important left out, so Yes.
Looks like this is a reasonable assumption. Now, let's take the Creationist assumption of only copying errors outlined above:
  1. Without this assumption, we'd have to consider what would happen with many different types of mutations. It does drastically complicate the problem, but it might not be impossible for a good mathematician. Of course, these people aren't good mathematicians, so I'll give them some leeway and answer Yes here.
  2. Evolutionary biology, so Yes.
  3. Definitely No. This is only one of a myriad of mutations, so excepting all of those divorces this from reality.
  4. All of the other mutation types are indeed important, but particularly fission. This is the one that makes the species transition possible at all, so it definitely qualifies as critical. A resounding No here.
The last two are big No's, so this assumption most definitely isn't reasonable.

Now that you see how simplifying assumptions are useful, and how they can be abused, you should be properly armed to both use them and stop their abuse. With this, I'll conclude the introduction to the Night Museum. Please come back tomorrow, when the museum proper will open up to the public. If you wish to see this exhibit again, you'll be able to find it in the Science and Pseudoscience section, or you could simply access a recording of this presentation in the Auditorium.

Thank you, and good night.

* * * * *

Return to the Auditorium

Return to the Lobby


Thinker said...

Reading this first post, I found myself humming this, which seems appropriate:

Nighttime sharpens, heightens each sensation
Darkness stirs and wakes imagination
Silently the senses abandon their defences

Slowly, gently, night unfurls its splendour
Grasp it, sense it, tremulous and tender
Turn your face away
from the garish light of day
Turn your thoughts away from cold unfeeling light
And listen to the music of the night

Close your eyes and surrender to your darkest dreams
Purge your thoughts of the life you knew before!
Close your eyes, let your spirit start to soar
And you'll live as you've never lived before

- The Music of the Night, from Phantom at the Opera

I look forward to seeing [sic] more of the night!

Reina said...

This is great info to know.