I’ve been getting tons of mail from people in response to the announcement of the mapping of
the E8 Lie group, asking what a Lie group is, what E8 is, and why the mapping of E8 is such a big deal?
So the Discovery Institute’s most recent addition has chosen to reply to my post about
tautologies. (Once again, I’m not linking to him; I will not willingly be a source of hits for the DI website when they’re promoting dangerous ingorance like this.) Typically, he manages to totally miss the point:
Darwinist blogger and computer scientist MarkCC (why don’t they use their real names?) called me a lot of names a couple of days ago. The most profane was that I am a ‘bastion of s***headed ignorance.’ Profanity seems to be a particular problem with the computer-math Darwinists. A dysfunctional clad, perhaps. They’re dysfunctional because, as Aristotle wrote, effective rhetoric has three characteristics: logos, ethos, and pathos. Effective rhetoric appeals to the best in reason, ethics, and emotion. When I’m called unprintable names merely for expressing my skepticism about the relevance of Darwin’s theory to the practice of medicine, I’ve already won the ‘ethos’ and ‘pathos’ skirmishes. I can concentrate on the logos.
Yes, Dr. Egnor. Let’s make sure that we focus on issues of style rather than substance. Because we both know that you have nothing to say in response to the substance of my criticism of your pigheaded ignorance.
One more bit of personal blogging, and then it’ll be back to the math. You may have noticed
that I haven’t been as active in the discussions on my posts for the last few weeks as I
would normally be. There are two reasons for that; one I’ve mentioned before – my father’s illness.
The other is actually something good.
As of today, I’m unemployed. Briefly.
After 11 years at IBM Research, I decided to change jobs. Today was my last day working for IBM. One week from monday, I’ll be starting work for Google, as a Software Engineer at their New York lab. Nothing against IBM – it was just time for a change. Over the last few weeks, the process of interviewing, and then wrapping up my work at IBM has been taking up a lot of time. Things should be nicely mellow for the next week, and then a bit crazy for a while as learn the ropes at my new job.
My fellow SBer Craig Hilberth at the Cheerful Oncologist writes about a
meta-analysis that purports to show the positive effect of intercessory prayer. Neither Craig
nor I have access to the full paper. But what we know is that the claim is that the meta-analysis
shows a result of g=-0.171, p=0.015.
This really ticks me off. Why? because g=-0.17 is not significant. Meta-analysis generally considers g=0.20 to be the minimum cutoff for statistical significance.
Briefly, what is meta-analysis? The idea of it is, suppose you’ve got a bunch of studies of the same topic. Meta-analysis lets you take data from all of the studies in the group, and attempt to combine them. What you can do is get aggregate means and standard deviations, and measures of the significance and reliability of the aggregate measures.
Meta-analysis is a useful technique, but it’s very prone to a number of errors. It’s very easy to manipulate a meta-analysis to make it say whatever you want; and even if you’re being
scrupulously honest, it’s prone to sampling bias. After all, since meta-analysis is based on
combining the results of multiple published studies, the sample is only drawn from the studies that were published. And one thing that we know is that in most fields, it’s much harder to publish negative results than positive ones. So the published data that’s used as input to meta-analysis tends to incorporate a positive bias. There are techniques to try to work around
that, but it’s hard to accurately correct for bias in data when you have no actual measurements
to tell you how biased your data os.
So getting back to the meta-analysis results that they cited, what’s g? g, also called “Hedges g”, is a measure of how much the overall data set of the combined studies differs from the individual data sets means. G is a measure of the significance
of any aggregate result from combining the studies. The idea is, you’ve got a bunch of studies, each of which has a control group and a study group. You compute aggregate mean for both the study and control groups, take the difference, and divide it by the aggregate standard deviation. That’s g. Along with G, you compute a P-value, which essentially measures the reliability of the g-figure computed from the aggregate data.
Assuming a fixed events model – that is, that the studies are essentially compatible, and all measuring the same basic events – the minimum level at which g is considered significant is |g|=0.2, with a minimum p value of 0.05.
This meta-analysis has |g|=0.17, with a p-value of 0.015. So they’re well-below the minimum level of statistical significance for a fixed events model meta-analysis, and their P-value is less than one third of the level at which a |g|=0.2 would be considered significant.
So – what it comes down to is, they did a meta-analysis which produced no meaningful results, and they’re trying to spin it as a “small but statistically significant result”. In other words, they’re misrepresenting their results to try to claim that they say what they wanted them to say.
For reasons that I’ll explain in another post, I don’t have a lot of time for writing a long pathological programming post, so I’m going to hit you with something short, sweet, and beautiful: binary combinatory logic.
I’ve written in the past about lambda calculus, and it’s equivalent variable-free form, the SKI combinator calculus. I’ve ever written about other combinator calculus based languages, like Unlambda and Iota.
Binary combinatory logic, aka BCL, is a language based on SKI calculus – except that it encodes the entire thing into binary. Two characters, plus two rewrite rules, and that’s it – a complete
combinator calculus based programming language.
SKI combinator calculus is a simple variable-free calculus with three constructs: S, K, and I; and I isn’t really primitive, but can be defined in terms of S and K.
So, in BCL, S is written “01”; K is written “00”. And there are two rewrite rules, which basically define “1” without a zero prefix as a a paren-like grouping construct:
So, following on unlambda’s method of handling IO, “hello world” in BCL is:
010001101000010000010110000000000101101111 000010110111110011111111011110000010011010
And here’s the really neat thing. Write an interpreter for BCL in BCL. Take the bit string that results, and convert it to a bitmap. That’s what’s over the right here. So, for example, the first line is “1111100000111001”; keep going, and you’ll find the entire BCL interpreter.
In general, I haven’t talked much about personal stuff on the blog, unless it related to
something else that I was already talking about. This post is going to be an exception to that.
There’s a bit of a scienceblogs flamewar that started up, with Rob Knop, a new SBer on one
side, and a bunch of atheistic SBers on the other. I pretty much think arguments like this are a
total waste of time: Rob isn’t going to convince PZ that he’s not a delusional idiot for being
religious; PZ isn’t going to convince Rob that he is a delusional idiot. It’s all just
ranting.
But as part of it, PZ made a statement in one of his posts that bugged me. It’s one he’s made before, and which I’m sure he’ll make again; but it’s an example of a kind of thinking that has always bothered me. The statement, from the title of his post, is “Spirituality? Another word for lies and empty noise”.
Today’s bit of basics is inspired by that bastion of shitheaded ignorance, Dr. Michael Egnor. In part of his latest screed (a podcast with Casey Luskin of the Discovery Institute), Egnor discusses antibiotic resistance, and along the way, asserts that the theory of evolution has no relevance to antibiotic resistance, because what evolution says about the subject is just
a tautology. (I’m deliberately not linking to the podcast; I will not help increase the hit-count that DI will use to promote it’s agenda of willful ignorance.)
So what is a tautology?
A tautology is a logical statement which is universally true, by nature of its fundamental structure. That is, even without knowing anything about what the statement means,
you can infer that it must be true.
In the comments to another post, Blake Stacey gave me a pointer to a really obnoxious article, called “A New Theory of the Universe”, by a Robert Lanza, published in the American Scholar. Lanza’s article is a rotten piece of new-age gibberish, with all of the usual hallmarks: lots of woo, all sorts of babble about how important consciousness is, random nonsensical babblings about quantum physics, and of course, bad math.
I’ve been getting so many requests for “basics” posts that I’m having trouble keeping up! There are so many basic things in math that non-mathematicians are confused about. I’m doing my best to keep up: if you’ve requested a “basics” topic and I haven’t gotten around to it, rest assured, I’m doing my best, and I will get to it eventually!
One of the things that multiple people have written to be about is confusion about what a mathematician means by a theory; and what the difference is between a theory and a theorem?
I’ve received a request from a long-time reader to write a basics post on modal logics. In particular, what is a modal logic, and why did Gödel believe that a proof for the existence of God was more compelling in modal logic than in standard predicate logic.
The first part is the easy one. Modal logics are logics that assign values to statements that go beyond “This statement is true” or “This statement is false”. Modal logics add the concepts of possibility and necessity. Modal logic allows statements like “It is necessary for X to be true”, “It is possible for X to be true”, etc.