S2Focus

At <a href="http://www.theologyonline.com/vbulletin/forumdisplay.php?s=&forumid=7" target="_blank">this link </a>, I have attempted to engage a creationist in a somewhat technical (in a very arm-waving sort of way) discussion about Dembski's mis-use of the NFL algorithm in "No Free Lunch". The results are predictably amusing! Follow the link and go to the "no free lunch" thread.

I'm posting there as "caerbannog".

(Heads up to mathematicians here: I'm engaging in what an old math professor of mine liked to call "arm waving". But hopefully it's arm-waving that makes a bit of sense!)

[ June 24, 2002: Message edited by: S2Focus ]</p>

CardinalMan

Perhaps you already know this S2Focus, but there are some mathematical theorems (not just thought experiments) that suggest very strongly that virtually every continuous function fails to have a derivative at each point of its domain. Are you familiar with the concept of Baire category? In any metric space, you can define the concept of a meager set, which is a rough notion of how topologically "large" the set is. It turns out that in the metric space of continuous functions on [0,1], the set of all functions which posess a derivative at some point is meager, and hence is extremely small in this sense.

There are also rather natural examples of continuous functions which fail to have a derivative at every point, such as those that arise in the mathematical study of Brownian motion (although I know less about this field).

If you already knew all this, I'm sorry to bore you. If you don't, and have any questions, let me know.

CardinalMan

Daydreamer

Man, Bob B is one of the most dense debaters I've ever seen. I shudder to think about his skill as a moderator.

HRG

A nowhere differentiable function has no place in the natural sciences. It would be as nonsensical as a device which measured whether a certain distance was rational or irrational when expressed in centimeters.

Generically, small changes in the parameters mean small changes in the time evolution over a sufficiently small interval of time.

But I guess that bob b just doesn't want to get your point. Apparently he wants you to write down the fitness function of E. coli before he will debate the applicability of NFL to it

Regards,
HRG.

CardinalMan

Perhaps I'm misunderstanding you, but isn't this a description of some sort of continuity rather than differentiability?

Although I agree that most of the strange functions concocted by mathematicians will probably never have a place in the natural sciences, how do you feel about studies of Brownian motion? From what I understand (I do not know all that much about research in probability), the best mathematical models of Brownian motion involve continuous nowhere-differentiable functions.

CardinalMan

Camaban

it aint pretty.

Though, on the debating side of things, I'm sure that one day, he'll actually use one of the extensive lists of books that he keeps telling us to buy a copy of.

(Cold day in hell before any of my money goes towards some of those people... and the fact that there's simply zero demand for them in most of this country anyway)

HRG

Actually, I was thinking of some kind of Lipschitz condition, not just continuity. This would be sufficient to take the fitness functions out of the reach of the NFL theorem

Brownian motion may be an exception, but the (mathematical) Wiener process is only a phenomenological description which breaks down at times which are of the order of magnitude of the average time between collisions. As far as I understand it, of course!

Regards,
HRG.

[ June 25, 2002: Message edited by: HRG ]</p>

S2Focus

Heh heh....

In one of his posts, bob b had this to say:
"C, you are making one of the most basic errors that I have seen over the years made by mathematicians working under me..."


My guess is that bob b was promoted into management through a process known as <a href="http://www.giga-usa.com/gigaweb1/quotes2/quautpeterlaurencejx001.htm" target="_blank">"percussive sublimation"</a>.

My curiosity led me to poke around the web for more information about bob b; after a bit of searching, I was able to find a picture of him <a href="http://www.toonopedia.com/dilbert.jpg" target="_blank">here</a>. (He's the dude on the left.)

[ June 25, 2002: Message edited by: S2Focus ]</p>