## My Favorite Strange Number: Ω (classic repost)

I'm away on vacation this week, taking my kids to Disney World. Since I'm not likely to
have time to write while I'm away, I'm taking the opportunity to re-run an old classic series
of posts on numbers, which were first posted in the summer of 2006. These posts are mildly
revised.

Ω is my own personal favorite transcendental number. Ω isn't really a specific number, but rather a family of related numbers with bizarre properties. It's the one real transcendental number that I know of that comes from the theory of computation, that is important, and that expresses meaningful fundamental mathematical properties. It's also deeply non-computable; meaning that not only is it non-computable, but even computing meta-information about it is non-computable. And yet, it's almost computable. It's just all around awfully cool.

## Continued Fractions (classic repost)

I'm away on vacation this week, taking my kids to Disney World. Since I'm not likely to have time to write while I'm away, I'm taking the opportunity to re-run an old classic series of posts on numbers, which were first posted in the summer of 2006. These posts are mildly revised.

One of the annoying things about how we write numbers is the fact that we generally write things one of two ways: as fractions, or as decimals.

You might want to ask, "Why is that annoying?" (And in fact, that's what I want you to ask, or else there's no point in my writing the rest of this!)

It's annoying because both fractions and decimals can both only describe rational numbers - that is, numbers that are a perfect ratio of two integers. The problem with that is that most numbers aren't rational. Our standard notations are incapable of representing the precise values of the overwhelming majority of numbers!

But it's even more annoying than that: if you use decimals, then there are lots of rational numbers that you can't represent exactly (i.e., 1/3); and if you use fractions, then it's hard to express the idea that the fraction isn't exact. (How do you write π as a fraction? 22/7 is a standard fractional approximation, but how do you say π, which is almost 22/7?)

So what do we do?

## Idiotic Gitt: AiG and Bad Information Theory (classic repost)

I'm away on vacation this week, taking my kids to Disney World. Since I'm not likely to have time to write while I'm away, I'm taking the opportunity to re-run some old classic posts which were first posted in the summer of 2006. These posts are mildly revised.

Back when I first wrote this post, I was taking a break from some puzzling debugging.
Since I was already a bit frazzled, and I felt like I needed some comic relief, I decided to
hit one of my favorite comedy sites, Answers in Genesis. I can pretty much always find
something sufficiently stupid to amuse me on their site. On that fateful day, I came across a
gem called Information, science and biology", by the all too appropriately named
"Werner Gitt". It's yet another attempt by a creationist twit to find some way to use
information theory to prove that life must have been created by god.

This article really interested me in the bad-math way, because I'm a big fan of information theory. I don't pretend to be anything close to an expert in it, but I'm
fascinated by it. I've read several texts on it, taken one course in grad school, and had the incredible good fortune of getting to know Greg Chaitin, one of the co-inventors of algorithmic information theory. Basically, it's safe to say that I know enough about
information theory to get myself into trouble.

Unlike admission above, it looks like the Gitt hasn't actually read any real
information theory much less understood it. All that he's done is heard Dembski presenting
one of his wretched mischaracterizations, and then regurgitated and expanded upon them.
Dembski was bad enough; building on an incomplete understanding of Dembski's misrepresentations, misunderstandings, and outright and errors produces a result
that is just astonishingly ridiculous. It's actually a splendid example of my mantra on this blog: "the worst math is no math"; the entire article pretends to be doing math - but it's actual mathematical content is nil. Still, to the day of this repost, I continue
to see references to this article as "Gitt's math" or "Gitt's proof".

## e: the Unnatural Natural Number (classic repost)

I'm away on vacation this week, taking my kids to Disney World. Since I'm not likely to
have time to write while I'm away, I'm taking the opportunity to re-run an old classic series
of posts on numbers, which were first posted in the summer of 2006. These posts are mildly
revised.

Anyway. Todays number is e, aka Euler's constant, aka the natural log base. e is a very odd number, but very fundamental. It shows up constantly, in all sorts of strange places where you wouldn't expect it.

## Roman Numerals and Arithmetic

. I'm away on vacation this week, taking my kids to Disney World. Since I'm not likely to
have time to write while I'm away, I'm taking the opportunity to re-run an old classic series
of posts on numbers, which were first posted in the summer of 2006. These posts are mildly
revised.

I've always been perplexed by roman numerals.

First of all, they're just weird. Why would anyone come up with something so strange as a
way of writing numbers?

And second, given that they're so damned weird, hard to read, hard to work with, why do
we still use them for so many things today?

## i: the Imaginary Number (classic repost)

I'm away on vacation this week, taking my kids to Disney World. Since I'm not likely to
have time to write while I'm away, I'm taking the opportunity to re-run an old classic series
of posts on numbers, which were first posted in the summer of 2006. These posts are mildly
revised.

After the amazing response to my post about ze ro, I thought I'd do one about something
that's fascinated me for a long time: the number i, the square root of -1. Where'd
this strange thing come from? Is it real (not in the sense of real numbers, but in the sense
of representing something real and meaningful)? What's it good for?

## Zero (classic repost)

This post originally came about as a result of the first time I participated in a DonorsChoose fundraiser. I offered to write articles on requested topics for anyone who donated above a certain amount. I only had one taker, who asked for an article about zero. I was initially a bit taken aback by the request - what could I write about zero? This article which resulted from it ended up turning out to be one of the all-time reader-favorites for this blog!

## Friday Random Ten, December 19

1. Olivier Messiaen, "Turangalila - Symphonie: II. Chant d'amour 1": This
was an unexpected wonderful surprise. A few years ago, my older brother gave me
a book on Stockhausen, who is a fascinating guy on an intellectual level, but
whose music I find absolutely unlistenable. The book talks about Stockhausen's period studying with Messiaen. I was expecting Messiaen to be another one of "those 12-tone guys"; I've never been able to develop an ear for 12-tone. But I decided to give Messiaen
a listen, and was amazed. He's not exactly an easy listen, but it's beautiful music. It's
very dissonant, frequently atonal, and yet melodic. This section of the symphony is extremely dramatic, almost theatrical. It's really a beautiful piece of music.
2. Peter Schickele, "Funeral Oration from 'Julius Ceasar'": from the sublime to ridiculous... A doo-wop funeral oration based on Shakespeare.
3. The Tempest, "The Winning Game": What a great song! I've lately totally fallen
for "The Tempest". It's a group that started as a collaboration between Andy Tillison and Roine Stolte. They've got members from Tillison's old band (Parallel or 90 degrees),
Stolte's band (the Flower Kings), and Van Der Graff Generator. It's some of the best
neo-progressive rock you'll find anywhere. Stolte later left their band, which resulted
in a serious change in the band's sound, but both before and after Stolte, they're
an amazing group, with wonderful compositions and absolutely dazzling performances.
4. King Crimson, "Frame by Frame": One of the things that King Crimson has been
able to do is to combine some of the most far-out experimental progressive rock with
some wonderfully catchy, easy-to-listen-to pop songs. This is a great example of that;
Frame by Frame is a very catchy poppy song, and yet it's incredibly deep and complex.
5. Porcupine Tree, "Dislocated Day": some older Porcupine Tree. PT did one
really wacky album of mostly very long-form neo-progressive tapestries. This is off
of that album.
6. Marillion, "Essence": a track off of Marillion's brilliant new album. Just
7. Isis, "Holy Tears": what were the odds that I could get through a FRT
without some post-rock? Isis is a post-rock band on which leans towards the
heavy-metal end of the post-rock spectrum. They're terrific - great composition,
great performance. They do sometimes use vocals, which is fine; but a bit too
often, the vocals are distorted shrieks. This track uses a bit of that; it's OK
in moderation; in fact, I really like this track a lot. But listening to too much
Isis at a time, that use of shrieking growl vocals gets to me.
8. Bela Fleck and the Flecktones, "Misunderstood": I used to be a huge
Flecktones fan. But I despise Jeff Cofflin, the saxaphone player they added
a few years ago. I just simply cannot stand to listen to the guy - he's absolutely
awful. He's incredibly predictable - the guy's got the creativity of a
a small rock; he knows how to play at exactly one volume - too damned loud;
and he's in love with stupid gimmicks. He's playing on this track, so guess
what I think of it?
9. Tony Trischka, "Hawaii Slide-O": interesting that this came up in the shuffle
right after Bela. Tony is Bela's former banjo teacher. (I've taken lessons from Tony
as well; Tony is a great guy who's happy to give lessons to anyone who's
interested.) This track is Tony experimenting with playing slide banjo. Back when
I was taking lessons with him, I heard an early version of this track - he was
showing me what he was working on at the time, and he'd just started playing with
a slide on the banjo for the first time in years. Tony is a fabulous musician,
and I love everything on this album. (In fact, I can't think of anything Tony's done
which I haven't loved.)
10. Rachel's, "Where have all my files gone?": more post-rock, this time from the
classical end of things. Rachel's is an amazing group. This is very typical of their
sound. Very atmospheric, beautiful.

## Fitness Landscapes, Evolution, and Smuggling Information

Since my post a couple of weeks ago about NASA and the antenna evolution experiment,
I've been meaning to write a followup. In both comments and private emails, I've gotten
a number of interesting questions about the idea of fitness landscapes, and some of the things
I mentioned in brief throwaway comments. I'm finally finding the time to write about
it now.

## Once again, Egnor and Tautologies

As you've probably heard from other ScienceBlogger's, that paragon of
arrogant ignorance, Dr. Michael Egnor, is back at it again - and he's abusing
the language of logic in a way that really frustrates me. I've written
I thought I'd bump it up to the top, along with another slap aimed at Egnor.

For those who don't know, Dr. Egnor is a brain surgeon at SUNY Stonybrook - an excellent school, and Dr. Egnor is, from all information I've heard, an outstanding surgeon. In his free time, he blogs for the Discovery Institute, using his
status as an accomplished brain-surgeon to try to boost the bullshit spewing out of DI.

One of Dr. Egnor's favorite attacks in his anti-evolution screeds always makes me think of a line from one of my favorite movies: "Hello, my name is Inigo Montoya, you killed my father, prepare to die". Oops, no, not that one. (Sorry, couldn't resist.) The real line is "You keep using that word. I do not think it means what you think it means".

You see, what Egnor keeps doing, over and over again, is arguing that
evolution is just a tautology, and that therefore it's meaningless. He
defines evolution as the statement "that which survives, survives". He almost never gets through one of his posts without that accusation in one form or another: evolution is a tautology, and that implies that it's meaningless and worthless as an explanation of anything.

Leave aside for the moment the fact that he mis-states the key premise of evolution. That's a huge, obvious, and deliberate mistake, but let's just ignore it for now. Instead, I'd like to just look at the problem with his statement about tautologies. What exactly is a tautology? And does
criticizing something as "just a tautology" actually make any sense?

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