The Geekoff Intensifies

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Orac is refusing to surrender and acknowledge the obvious fact that he simple *is not* as much of a geek as I am. So I am obligated to point out several further facts in my attempt to make him surrender the crown of geekiness.
———-
First: compare our professsions. Orac is a cancer surgeon: a person whose professional life is dedicated to *saving peoples lives*. There are people living today who would be dead but for the efforts of Orac. It is an honorable profession, deserving of nothing but respect.
In contrast, I am a software engineering researcher; aka a professional computer geek. I spend my life designing and writing software (most of which will never be used) for other people to use to write software.
———–
Back in high school, I spent most of a year saving up money to buy a super-cool pocket calculator that was programmable in Basic. Then after I got it and used it for a while, I decided to switch. To a slide-rule.
Because it’s *faster*.
I still own a [K&E log-log duplex decitrig slide rule.][sliderule] (And know how to use *all* of the scales.) It’s a beauty. I look forward to teaching my children to use it. (Using a slide-rule gives you a tactile sense of how a lot of things fit together in simple math.) Here’s a pic I found of the same model that I have:
0098-ke4181-3-01-front-left.jpg
Mine’s a lot more beaten up than this one; it’s thoroughly yellowed up the full length; the view slide is a bit scraped up and missing the top-left screw. But it’s still in great working condition.
————–
Let us, for a moment, consider my name. Mark Chu-Carroll. Where do you suppose “Chu-Carroll” came from?
Obviously, it’s a combination of the last names of me and my wife before we got married. But why “Chu-Carroll” rather than “Carroll-Chu”? Is it for aesthetics? No. The real reason is *far* geekier than anything like mere aesthetics.
No. The real reason why we chose “Chu-Carroll” is… Bibliographies.
When we were married, my wife had more publications than I did. And so we decided to use “Chu-Carroll” so that people doing literature searches for *her* name would be more likely to find her papers, because “Jennifer Chu-Carroll” would appear immediately after “Jennifer Chu” in any bibliographic listing likely to contain her work; whereas “Jennifer Carroll-Chu” would be separated by some distance, and would be more likely to be missed.
So my last name was chosen based on how it would be alphabetized in bibliographies.
————————
Let’s take a look at genetics for a moment. My parents recently went on vacation, and brought back gifts for my children. One of the gifts was a set of pens with their names on them. Give a new pen and a stack of paper to a three year old boy, and what do you *think* that he would do?
*My* three-year-old son took the pen apart. He’d never seen a “click” pen before, and he wanted to know how it worked.
[sliderule]: http://sliderule.ozmanor.com/rules/sr-0098-ke4181-3-01.html

Shapes, Boundaries, and Interiors

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When we talk about topology, in general, the way we talk about it is in terms of *shapes*: geometric objects and spaces, surfaces, bodies that enclose things, etc. We talk about the topology of a *torus*, or a *coffee mug*, or a *sphere*.
But the topology we’ve talked about so far doesn’t talk about shapes or surfaces. It talks about open sets and closed sets, about neighborhoods, even about filters; but we haven’t touched on how this relates to our *intuitive* notion of shape.
Today, we’ll make a start on the idea of surface and shape by defining what *interior* and *boundary* mean in a topological space.

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Friday Random Ten: The "What a Geek" Edition

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Haven’t done one of these in a while. In light of the “Geek-off” this week, I made a playlist out of what I think of as my “geekier” music, and let ITunes assemble a random list from that playlist.
1. **Elizabeth and the Catapult, “Waiting for the Kill”**. E&tC is a NYC band that plays what they call “baroque pop”; pop music, with heavy jazz and classical influence. I heard them interviewed on the local NPR station, and immediately grabbed their first album – isn’t just an EP, but it’s fantastic. This is the best track.
2. **Flook, “The Tortoise and the Hare”**. The worlds greatest trad Irish flute-based band. Flook is really unbelievable: so full of energy, it’s impossible to *not* like them.
3. **Frank Zappa, “Drowning Witch”**. Old stuff from Zappa; incredibly goofy, and yet pretty darn cool musically.
4. **Genesis, “Here Comes the Supernatural Anaesthetist”**. A very strange track off of Genesis’ masterpiece from their Peter Gabriel days, “The Lamb Lays Down on Broadway”.
5. **Gordian Knot, “Komm Susser Tod, Kom Sel’ge”**. Bach, performed on the electric touch bass guitar.
6. **Mogwai, “Acid Food”**. Another one of those “Post-Rock Ensembles” that I’m so fascinated by. Mogwai is simply amazing; a bit more loud than the Clogs or the Dirty Three, but brilliant.
7. **Moxy Fruvous, “King of Spain”**. My wife’s favorite MF song. MF is a Canadian band that specializes in goofy a-capella. “Once I was the king of spain, Now I eat humble pie, I’m telling you I was the king of the Spain, Now I vaccum the turf at Skydome”.
8. **Steve Reich & Maya Beiser, “Cello Counterpoint”**. An amazing composition by Steve Reich. It’s all performed by Maya Beiser on cello – there are *16* tracks of Maya, all overlaid. Unbelievable. She performs it live with a recording of 15 of them, and plays the 16th live.
9. **Thinking Plague, “Blown Apart”**. Another post-rock ensemble. By far the strangest of the PREs that I listen to. Thinking Plague often goes totally atonal; and even when they don’t, they have a strange sound. One fascinating thing about them is that the vocalist treats her voice as just another instrument in the band. She’s in no way a “lead vocalist” like you’d find in a traditional band; she’s just another instrument in the mix. Her voice is as likely to be part of the background rhythm supporting the guitarist as it is to be singing a melody.
10. **Philip Glass, “Train 1” from “Einstein on the Beach”**. A small piece of Glass’s strange but brilliant opera. The opera is about four hours long, with no intermission. This section is formed from arpeggios played by saxaphone and keyboard, plus a chorus singing a pulsing counterpoint. Other parts of the opera consist of the voices chanting numbers. It’s strange, and not the easiest thing to listen to, but it’s worth it.

Pathological Programming: The Worlds Smallest Programming Language

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For todays dose of pathological programming, we’re going to hit the worlds simplest language. A Turing-complete programming language with exactly *two* characters, no variables, and no numbers. It’s called [Iota][iota]. And rather than bothering with the rather annoying Iota compiler, we’ll just use an even more twisted language called [Lazy-K][lazyk], which can run Iota programs, Unlambda programs, as well as its own syntax.
[unlambda]: http://scienceblogs.com/goodmath/2006/08/friday_pathological_programmin_3.php
[lazyk]: http://esoteric.sange.fi/essie2/download/lazy-k/
[Iota]: http://ling.ucsd.edu/~barker/Iota/

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Neighborhoods (Updated)

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The past couple of posts on continuity and homeomorphism actually glossed over one really important point. I’m actually surprised no one called me on it; either you guys have learned to trust me, or else no one is reading this.
What I skimmed past is what a *neighborhood* is. The intuition for a
neighborhood is based on metric spaces: in a metric space, the neighborhood of a
point p is the points that are *close to* p, where close to is defined in terms of the distance metric. But not all topological spaces are metric spaces. So what’s a neighborhood in a non-metric topological space?

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Obnoxious Answers to Obnoxious Questions

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A few of my recent posts here appear to have struck some nerves, and I’ve been
getting lots of annoying email containing the same questions, over and over again. So rather than reply individually, I’m going to answer them here in the hope that either (a) people will see the answers before send the question to me, and therefore not bother me; or (b) conclude that I’m an obnoxious asshole who isn’t worth the trouble of writining to, and therefore not bother me. I suspect that (b) is more likely than (a), but hey, whatever works.
Answers beneath the fold.

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Topological Equivalence: Introducing Homeomorphisms

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With continuity under our belts (albeit with some bumps along the way), we can look at something that many people consider *the* central concept of topology: homeomorphisms.
A homeomorphism is what defines the topological concept of *equivalence*. Remember the clay mug/torus metaphor from from my introduction: in topology, two topological spaces are equivalent if they can be bent, stretched, smushed, twisted, or glued to form the same shape *without* tearing.
The rest is beneath the fold.

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Back to Topology: Continuity (CORRECTED)

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*(Note: in the original version of this, I made an absolutely **huge** error. One of my faults in discussing topology is scrambling when to use forward functions, and when to use inverse functions. Continuity is dependent on properties defined in terms of the *inverse* of the function; I originally wrote it in the other direction. Thanks to commenter Dave Glasser for pointing out my error. I’ll try to be more careful in the future!)*
Since I’m back, it’s time to get back to topology!
I’m going to spend a bit more time talking about what continuity means; it’s a really important concept in topology, and I don’t think I did a particularly good job at explaining it in my first attempt.
Continuity is a concept of a certain kind of *smoothness*. In non-topological mathematics, we define continuity with a very straightforward algebraic idea of smoothness. A standard intuitive definition of a *continuous function* in algebra is “a function whose graph can be drawn without lifting your pencil”. The topological idea of continuity is very much the same kind of thing – but since a topological space is just a set with some additional structure, the definition of continuity has to be generalized to the structure of topologies.
The closest we can get to the algebraic intuition is to talk about *neighborhoods*. We’ll define them more precisely in a moment, but first we’ll just talk intuitively. Neighborhoods only exist in topological metric spaces, since they end up being defined in terms of distance; but they’ll give us the intuition that we can build on.
Let’s look at two topological spaces, **S** and **T**, and a function f : **S** → **T** (that is, a function from *points* in **S** to *points* in **T**). What does it mean for f to be continuous? What does *smoothness* mean in this context?
Suppose we’ve got a point, *s* ∈ **S**. Then f(*s*) ∈ **T**. If f is continuous, then for any point p in **T** *close to f(s)*, f-1(p) will be *close to* *s*. What does close to mean? Pick any distance – any *neighborhood* N(f(s)) in **T** – no matter how small; there will be a corresponding neighborhood of M(*s*) around s in **S** so that for all points p in N(f(s)), f-1 will be in M(*s*). If that’s a bit hard to follow, a diagram might help:
continuity.jpg
To be a bit more precise: let’s define a neighborhood. A neighborhood N(p) of a point p is a set of points that are *close to* p. We’ll leave the precise definition of *close to* open, but you can think of it as being within a real-number distance in a metric space. (*close to* for the sake of continuity is definable for any topological space, but it can be a strange concept of close to.)
The function f is continuous if and only if for all points f(s) ∈ **T**, for all neighborhoods N(f(s)) of f(s), there is some neighborhood M(s) in **S** so that f(M(s)) ⊆ N(f(s)). Note that this is for *all* neighborhoods of *all* points in **T** mapped to by f – so no matter how small you shrink the neighborhood around f(s), the property holds – and it implies that as the neighborhood in **T** shrinks, so does the corresponding neighborhood in **S**, until you reach the single points f(s) and s.
Why does this imply *smoothness*? It means that you can’t find a set of points in the range of f in **T** that are close together, but that weren’t close together in **S** before being mapped by f. f won’t put things together that weren’t together originally. And it won’t pull things apart that weren’t
close together originally. *(This paragraph was corrected to be more clear based on comments from Daniel Martin.)*
For a neat exercise: go back to the category theory articles, where we defined *initial* and *final* objects in a category. There are corresponding notions of *initial* and *final* topologies in a topological space for a set. The definitions are basically the same as in category theory – the arrows from the initial object are the *continuous functions* from the topological space, etc.

Pathetic Statistics from HIV/AIDS Denialists

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While I was on vacation, I got some email from Chris Noble pointing me towards a discussion with some thoroughly innumerate HIV-AIDS denialists. It’s really quite shocking what passes for a reasonable argument among true believers.
The initial stupid statement is from one of Duesberg’s papers, [AIDS Acquired by Drug Consumption and Other Noncontagious Risk Factors][duesberg], and it’s quite a whopper. During a discussion of the infection rates shown by HIV tests of military recruits, he says:
>(a) “AIDS tests” from applicants to the U.S. Army and the U.S. Job
>Corps indicate that between 0.03% (Burke et al.,1990) and 0.3% (St
>Louis et al.,1991) of the 17- to 19-year-old applicants are HIV-infected
>but healthy. Since there are about 90 million Americans under the age
>of 20, there must be between 27,000 and 270,000(0.03%-0.3% of 90
>million) HIV carriers. In Central Africa there are even more, since 1-2%
>of healthy children are HIV-positive (Quinn et al.,1986).
>
>Most, if not all, of these adolescents must have acquired HIV from
>perinatal infection for the following reasons: sexual transmission of
>HIV depends on an average of 1000 sexual contacts, and only 1in 250
>Americans carries HIV (Table 1). Thus, all positive teenagers would
>have had to achieve an absurd 1000 contacts with a positive partner, or
>an even more absurd 250,000 sexual contacts with random Americans
>to acquire HIV by sexual transmission. It follows that probably all of
>the healthy adolescent HIV carriers were perinatally infected, as for
>example the 22-year-old Kimberly Bergalis (Section 3.5.16).
Now, I would think that *anyone* who reads an allegedly scientific paper like this would be capable of seeing the spectacular stupidity in this quotation. But for the sake of pedantry, I’ll explain it using small words.
If the odds of, say, winning the lottery are 1 in 1 million, that does *not* mean that if I won the lottery, that means I must have played it one million times. Nor does it mean that the average lottery winner played the lottery one million times. It means that out of every one million times *anyone* plays the lottery, *one* person will be expected to win.
To jump that back to Duesberg, what he’s saying is: if the transmission rate of HIV/AIDS is 1 in 1000, then the average infected person would need to have had sex with an infected partner 1000 times.
Nope, that’s not how math works. Not even close.
Suppose we have 1000 people who are infected with HIV, and who are having unprotected sex. *If* we follow Duesberg’s lead, and assume that the transmission rate is a constant 0.1%, then what we would expect is that if each of those 1000 people had sex with one partner one time, we would see one new infected individual – and that individual would have had unprotected sex with the infected partner only one time.
This isn’t rocket science folks. This is damned simple, high-school level statistics.
Where things get even sadder is looking at the discussion that followed when Chris posted something similar to the above explanation. Some of the ridiculous contortions that people go through in order to avoid admitting that the great Peter Duesberg said something stupid is just astounding. For example, consider [this][truthseeker] from a poster calling himself “Truthseeker”:
>If Duesberg had said that, he would indeed be foolish. The foolishness,
>however, is yours, since you misintepret his reasoning. He said, as you note
>
>>Most, if not all, of these adolescents must have acquired HIV from perinatal
>>infection for the following reasons: sexual transmission of HIV depends on an
>>average of 1000 sexual contacts, and only 1 in 250 Americans carries HIV
>>(Table 1). Thus, all positive teenagers would have had to achieve an absurd
>>1000 contacts with a positive partner, or an even more absurd 250,000 sexual
>>contacts with random Americans to acquire HIV by sexual transmission.
>
>This states the average transmission requires 1000 contacts, not every
>transmission. With such a low transmission rate and with so few Americans
>positive – you have to engage with 250 partners on average to get an average
>certainty of 100% for transmission, if the transmission rate was 1. Since it is
>1 in 1000, the number you have to get through on average is 250,000. Some might
>do it immediately, some might fail entirely even at 250,000. But the average
>indicates that all positive teenagers would have had to get through on average
>250,000 partner-bouts.
Truthseeker is making exactly the same mistake as Duesberg. The difference is that he’s just had it explained to him using a simple metaphor, and he’s trying to spin a way around the fact that *Duesberg screwed up*.
But it gets even worse. A poster named Claus responded with [this][claus] indignant response to Chris’s use of a metaphor about plane crashes:
>CN,
>
>You would fare so much better if you could just stay with the science
>points and refrain from your ad Duesbergs for more than 2 sentences at
>a time. You know there’s a proverb where I come from that says ‘thief thinks
>every man steals’. I’ve never seen anybody persisting the way you do in
>calling other people ‘liars’, ‘dishonest’ and the likes in spite of the
>fact that the only one shown to be repeatedly and wilfully dishonest
>here is you.
>
>Unlike yourself Duesberg doesn’t deal with matters on a case-by-case only basis
>in order to illustrate his statistical points. precisely as TS says, this shows
>that you’re the one who’s not doing the statistics, only the misleading.
>
>In statistics, for an illustration to have any meaning, one must assume that
>it’s representative of an in the context significant statistical average no?
>Or perphaps in CN’s estimed opinion statistics is all about that once in a
>while when somebody does win in the lottery?
Gotta interject here… Yeah, statistics *is* about that once in a while when someone wins the lottery, or when someone catches HIV, or when someone dies in a plane crash. It’s about measuring things by looking at aggregate numbers for a population. *Any* unlikely event follows the same pattern, whether it’s catching HIV, winning the lottery, or dying in a plane crash, and that’s one of the things that statistics is specifically designed to talk about: that fundamental probabilistic pattern.
>But never mind we’ll let CN have the point; the case in question was that odd
>one out, and Duesberg was guilty of the gambler’s fallacy. ok? You scored one
>on Duesberg, happy now? Good. So here’s the real statistical point abstracted,
>if you will, from the whole that’s made up by all single cases, then applied to
>the single case in question:
>
>>Thus, all positive teenagers would have had to achieve an absurd 1000 contacts
>>with a positive partner, or an even more absurd 250,000 sexual contacts with
>>random Americans to acquire HIV by sexual transmission.
>
>This is the statistical truth, which is what everybody but CN is interested in.
Nope, this is *not* statistical truth. This is an elementary statistical error which even a moron should be able to recognize.
>Reminder: Whenever somebody shows a pattern of pedantically reverting to single
>cases and/or persons, insisting on interpreting them out of all context, it’s
>because they want to divert your attention from real issues and blind you to
>the overall picture.
Reminder: whenever someone shows a pattern of pedantically reverting to a single statistic, insisting on interpreting it in an entirely invalid context, it’s because they want to divert your attention from real issues and blind you to the overall picture.
The 250,000 average sexual contacts is a classic big-numbers thing: it’s so valuable to be able to come up with an absurd number that people will immediately reject, and assign it to your opponents argument. They *can’t* let this go, no matter how stupid it is, no matter how obviously wrong. Because it’s so important to them to be able to say “According to *their own statistics*, the HIV believers are saying that the average teenage army recruit has had sex 250,000 times!”. As long as they can keep up the *pretense* of a debate around the validity of that statistic, they can keep on using it. So no matter how stupid, they’ll keep defending the line.
[duesberg]: www.duesberg.com/papers/1992%20HIVAIDS.pdf
[truthseeker]: http://www.newaidsreview.org/posts/1155530746.shtml#1487
[claus]: http://www.newaidsreview.org/posts/1155530746.shtml#1496