Category Archives: Bad Math

Turing Crackpottery!

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One of the long-time cranks who’s commented on this blog is a bozo who goes by the name “Vorlath”. Vorlath is a hard-core Cantor crank, and so he usually shows up to rant whenever the subject of Cantor comes up. But last week, while I was busy dealing with the Scientopia site hosting trouble, a reader sent me a link to a piece Vorlath wrote about the Halting problem. Apparently, he doesn’t like that proof either.

Personally, the proof that the halting problem is unsolvable is one of my all-time favorite mathematical proofs. It’s incredibly simple – just a couple of steps. It’s very concrete – the key to the proof is a program that you can actually write, easily, in a couple of lines of code in a scripting language. And best of all, it’s incredibly profound – it proves something very similar to Gödel’s incompleteness theorem. It’s wonderful.

To show you how simple it is, I’m going to walk you through it – in all of its technical details.

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Lucky Me: the Return of John Davison to GM/BM

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Being the incredibly lucky guy that I am, I somehow managed to attract the attention of John Davison. If you don’t know John, well.. you’re lucky.

He’s a rather infamous fellow. He’s got a rather peculiar hypothesis about evolution. Basically, he claims that evolution did occur, but it was front-loaded – the path that it took was dictated ahead of time by evolution encoded into the primitive genome.

To make matters worse, his approach to debate is, generally, to shout, call people names, make vague threats, and generally piss everyone off, regardless of whether or not they agree with him. He was the first person that I ever banned back at ScienceBlogs.

And to make it even worse, the guy doesn’t understand how blogs actually work. He started one blog, made one post, and then continued to post on the blog simply by adding comments to that post. Then he threw a tantrum, deleted it, started a new one, and did exactly the same thing. It appears that his current blog (which has the incredibly pompous name “The Proceedings of the Natural History Society of South Burlington Vermont”) actually has several posts on in – the most recent one being somewhat more than two and a half years old. But he’s still posting comments on it. Hundreds and hundreds of comments, nearly all by him. It appears that he progressed from thinking that a blog post was an entire blog (and thus adding new “posts” as comments on the only existing post on the blog), to thinking that a blog post is a category (and thus adding new posts on comments on the five different posts on his blog).

He’s showed up in the comments here. Naturally, being John, he’s commenting in the wrong place. And, of course, being John, he’s throwing tantrums about how nobody is paying attention to him.

The poor guy is clearly lonely and desperate for attention.

So. His comments are here, here, and here.

Please respond to them (if you must) in the comments on this post, so that it’s easy to keep track of. I warned John privately that I’m not going to tolerate him insulting other commenters; similarly, I’d ask that anyone who responds to him do so on the content of his posts, and refrain from just throwing insults at him.

Frankly, I doubt that he’s capable of actually engaging in a civil discussion. I’d put money on it taking less than an hour from the time this post goes up until he starts insulting people. But hey, why not give him the chance to try?

So, to repeat the warning: as always, my comment policy is:

  • you’re welcome to insult me: after all, I insult people in my posts; it’s only fair that they be allowed to insult me back
  • you are not allowed to insult other commenters. You can disagree as strongly as you want – but personal insults will not be tolerated.

If you break that simple rule, you get one warning, and then you get banned. That goes for John, and that goes for anyone else commenting.

Return of the Revenge of the Return of the Compression Schmuck

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Well, folks, this one is going to be boring for most of you. But the
compression jackass, Jules “Julie-baby-dumbass” Gilbert has been repeatedly
bugging me. And today, he replied to my latest “fuck off and stop sending me
mail” with a long-winded proselytizing response in which he requested that I
be courteous and not publicize the discussion of his “work”.

Fuck that

The entire correspondence is below.

Before I get to it: the short summary of what Jules is doing
is munging a file in a way that makes it amenable to recompression. In
the classic sense, this is removing a trivial bit of information from the
file, which thus allows is to be re-compressed just a tiny bit
more.

The catch is, of course, you can’t un-compress it without re-introducing
the information that you removed. In his case, you need to repeatedly
un-compress, un-munge, un-compress, un-munge, and so on –
exactly the right number of times. From some of his emails, he
does this hundreds to thousands of times.

You can’t un-compress his stuff without knowing how many times the compressor
ran. And how many times is that? Well, gosh, to know that, you need to know
some extra information. Anyone want to take a bet on what the
relationship is between the amount of additional compression he can get, and
the number of repetitions of his system? Anyone?

Ok. On to the transcript.

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Euclid? Moron!

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A coworker of mine at Google sent me a link this morning to an interesting piece of crackpottery: a guy who calls himself “the Soldier of the Truth” who claims to have proved Euclid’s parallel postulate; and that therefore, all of non-Euclidean geometry, and anything in the realms of math and science that in any way rely on non-Euclidean stuff, is therefore incorrect and must be discarded. This would include, among numerous other things, all of relativity.

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Revenge of the Return of the Compression Idiot

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Do I really need to go through this again? Argh!

As long-time readers will remember, a while back, I had an encounter with
a crackpot named Jules Gilbert who claimed to be able to cyclically compress
files. That is, he could take a particular input file, compress it, do
something to it, and then compress it again, making it smaller. He claimed to
be able to do this for any input.

And to make it more annoying, his claim to be able to do this brilliant
magical cyclical compression was attached to an obnoxious christian “I want to
save you soul” rant, where he effectively offered to share the profits from
this brilliant invention with me, if I’d only give him the chance to tell me
about Jesus.

I tried to get rid of the schmuck. I asked him to leave me alone politely.
Then I asked him to leave me alone not-so politely. Then I asked him to
leave me alone very, very rudely. Then I publicly mocked him on this blog.
After the last, he finally seemed to take the hint and go away.

Unfortunately, good things often don’t last. And yesterday, I received
another new message from him, bragging about the results of his uber-magical
compression system. He has now perfected it to the point where he can take
any input file, and compress it down to about 50K:

I am now compressing single bit as:

I use C code to pack up one bit to a byte and call bzip2’s compress
buffer.

I print the result and compute the size.

(I did this for both gzip and bzip2.) Gzip didn’t compress; it gave
me back about 6.25, but I needed at least 8.0.

And bzip2 gave it to me. About 8.2 and higher. (This is with no
actual I/O, just buffer to buffer.)

This was with random data. At least that’s what people call it.
Bzip2 data. (It looks pretty random to me.)

I expect to show up at a friend’s house and show him the system on
Monday. THIS IS NOT A COMPLETE SYSTEM, but it’s not just research
either. The input was randomly chosen (not by me, by a C function,)
and the program has been arranged to simply open another file when a
current file is exhausted.

Every input file has been compressed once with bzip2. Each input file
is at least 5k bytes and was chosen with the intent to represent all
popular OS’s somewhat equally.

This program is easily able to process MN’s 415k file. And since it
uses 256 byte blocks, I can bring it down to about 50k (number
demonstrated in testing.) Another way to say this is that (with this
program,) all files greater than about 50k can be made that small.

This is the simplist system I have ever made that uses my “modern”

techniques (I mean, not my LSQ ideas of a decade ago.) i started
coding it this morning, to see if a certain idea worked…

I’m trying to drop bzip but it’s pretty good! I’m also trying to
modulate my input to it, in order to obtain a gain from the pattern
recognition (the BWT may not be an actual FFT but it’s a similar
idea.) If I can do this I will keep it.

If all this is greek to you, here’s the thing: Just about every other
computer scientist in the whole wide world believes this is
impossible. Why is this valuable? Because it means that all files
and messages can be compressed in while in transit to, say, 50k —
probably much less. (Or while sitting on a CD-ROM or DVD.)

I love that line in there: “Just about every other computer scientist in
the whole wide world believes this is impossible”.

Jules, baby, belief has nothing to do with it.

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Metaphorical Crankery: a bad metaphor is like a steaming pile of …

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So, another bit of Cantor stuff. This time, it really isn’t Cantor
crankery, so much as it is just Cantor muddling. The post
that provoked this is not, I think, crankery of any kind – but it
demonstrates a common problem that drives me crazy; to steal a nifty phrase
from youaredumb.net, people who can’t count to meta-three really shouldn’t try
to use metaphors.

The problem is: You use a metaphor to describe some concept. The metaphor
isn’t the thing you describe – it’s just a tool that you use. But
someone takes the metaphor, and runs with it, making arguments that are built
entirely on metaphor, but which bear no relation to the real underlying
concept. And they believe that whatever conclusions they draw from the
metaphor must, therefore, apply to the original concept.

In the context of Cantor, I’ve seen this a lot of times. The post that
inspired me to write this isn’t, I think, really making this mistake. I think
that the author is actually trying to argue that this is a lousy metaphor to
use for Cantor, and proposing an alternative. But I’ve seen exactly this
reasoning used, many times, by Cantor cranks as a purported disproof. The
cranky claim is: Cantor’s proof is wrong, because it cheats.

Of course, if you look at Cantor’s proof as a mathematical construct, it’s
a perfectly valid, logical, and even beautiful proof by contradiction. There’s
no cheating. So where do the “cheat” claims come from?

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The Unfalsifiable Theory Of Everything from viXra

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Today is another bit of rubbish from viXra! In the comment thread from the last post, someone (I presume the author of this paper) challenged me to address this. And it’s such a perfect example of one of my mantras that I can’t resist.

What’s the first rule of GM/BM? The worst math is no math.

And what a whopping example of that we have here. It’s titled “Spacetime Deformation Theory”, by one Jacek Safuta. I’ll quote the abstract in its entirety, to give you the flavor.

The spacetime deformations theory unifies general relativity with quantum mechanics i.e. unifies all interactions, answers the questions: why particles have mass and what they are, answers the question: what is energy, unifies force fields and matter, implies new theories like spacetime deformations evolution.

This is a theory of principle (universal theory delivering description of nature) and not constructive theory (describing particular phenomenon using specific equations).

The theory is falsifiable, background independent (space has no fixed geometry), not generating singularities or boundaries.

This is hard to believe but a belief has nothing to with it. The real intellectual challenge is to falsify the theory.

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Gravity, Shmavity. It's the heat, dammit!

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Sorry for the ridiculously slow pace around here lately; I’ve been ridiculously busy. I’m changing projects at work; it’s the end of the school year for my kids; and I’m getting close to the end-game for my book. Between all of those, I just haven’t had much time for blogging lately.

Anyway… I came across this lovely gem, and I couldn’t resist commenting on it. (Before I get to it, I have to point out that it’s on “viXra.org”. viXra is “ViXra.org is an e-print archive set up as an alternative to the popular arXiv.org service owned by Cornell University. It has been founded by scientists who find they are unable to submit their articles to arXiv.org because of Cornell University’s policy of endorsements and moderation designed to filter out e-prints that they consider inappropriate.”. In other words, it’s a site for cranks who can’t even post their stuff on arXiv. Considering some of the dreck that’s been posted an arXiv, that’s pretty damned sad.)

In my experience, when crackpots look at physics, they go after one of two things. Either they pick some piece of modern physics that makes them uncomfortable – like relativity or quantum mechanics – and they try to force some argument that their discomfort with it must mean that it’s wrong. The other big one is free energy – whether it’s perpetual motion, or vacuum energy, or browns gas – the crackpots claim that they’ve found some wonderful magical process that defies the laws of thermodynamics in order to make limitless free energy. The cranks rarely (not never, but rarely) go after the kinds of physics that we experience every day.

Well, this is something different. This guy basically wants to claim that gravity doesn’t really exist. And along the way, he claims to have solved the problems of dark matter and dark energy. See, we’ve all got it totally wrong about gravity! Gravity isn’t a force where matter attracts other matter. It’s a force where warm things attract other warm things! Gravity is actually a force created when things radiate heat.

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Big Number Bogosity from a Christian College Kid

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I know that I just posted a link to a stupid religious argument, but I was sent a link to another one, which I can’t resist mocking.

As I’ve written about quite often, we humans really stink at understanding big numbers, and how things scale. This is an example of that. We’ve got a jerk who’s about to graduate from a dinky christian college, who believes that there must be something special about the moral atmosphere at his college, because in his four years at the school, there hasn’t been a single murder.

Yeah, seriously. He really believes that his school is special, because it’s gone four whole years without a murder:

Considering that the USA Today calculated 857 college student deaths from 2000 to 2005, how does one school manage to escape unscathed? It’s certainly not chance or luck. For Patrick Henry College, it’s in our Christian culture.

Critics mock us for our strict rules – like no dancing or drinking on campus, no members of the opposite sex permitted in your dorm room, nightly curfew hours – and the lack of a social atmosphere it creates. We have been the subject of books (God’s Harvard), television shows, op-eds, and countless blogs who rant against our brand of overbearing right-wing Christianity that poisons society’s freedom.

Yet, what is the cost of students being able to “express” themselves? Is that freedom worth the cost of drunk driving deaths, drug related violence, and love affairs turned fatal?

There were 857 college student deaths in the five-year period from 2000 to 2005! Therefore, any college where there weren’t any murders in that period must be something really special. That christian culture must be making a really big difference, right?

Well, no.

According to Google Answers, the US Census Department reports that there are 2363 four year colleges in the US. So, assuming the widest possible distribution of student deaths, there were 1506 colleges with no student deaths in a five-year period. Or, put another way, more than 60% of colleges in the US went that five-year period without any violent student deaths.

Or, let’s try looking at it another way. According to the census, there are 15.9 million people currently enrolled in college. The school that, according to the author, is so remarkable for going without any murders in the last four years? It has 325 students. Not 325 per class – 325 total.

In other words, among a group making up less than 2/1000ths of one percent of the college population, there were no murders. Assuming that the distribution of violent deaths is perfectly uniform (which it obviously isn’t; but let’s just keep things simple), given that there were 857 violent deaths in the student population as a whole, how many violent deaths would you expect among the student body at his dinky christian college?

That would be a big, fat zero.

The fact that there were no violent deaths at his school isn’t remarkable, not at all. But to a twit who’s incapable of actually understanding what numbers mean, that’s not the conclusion to be drawn. It’s also not that the violent death among college students is actually remarkably rare. Nor is it that most college students will go through college without any violent deaths on campus. No – according to a twit, with 857 violent campus deaths over five years, the only reasonable conclusion is that there must be something special about the ridiculous religious rules at his college that prevented the great rampaging plague of violence from touching the students at his school.

I actually spent five years as an undergraduate at Rutgers University in NJ. During that time, there were no violent student deaths. (There was one death by alchohol poisoning; and there was one drunk driving accident that killed four students.) But zero violent deaths. Gosh, Rutgers must have been an absolutely amazingly moral university! And gosh, we had all of those horrible sinful things, like dancing, and co-ed dorms! How did we manage to go all that time with no violence?

It must have been the prayers of the very nice Rabbi at the Chabad house on campus. Yeah, that must be it! Couldn’t just be random chance, right?

Ok, now let me stop being quite so pettily snide for a moment.

What’s going on here is really simple. We hear a whole lot about violence on campus. And when you hear about eight-hundred and some-odd violent deaths on campus, it sounds like a lot. So, intuitively, it sure seems like there must be a whole lot of violence on campus, and it must be really common. So if you can go through your whole time in college without having any violence occur on campus, it seems like it must be unusual.

That’s because, as usual, we really suck at understanding big numbers and scale. 800 sounds like a lot. The idea that there are nearly sixteen million college students is just not something that we understand on an intuitive level. The idea that nearly a thousand deaths could be a tiny drop in the bucket – that it really amounts to just one death per 100,000 students per year – it just doesn’t make sense to us. A number like 800 is, just barely, intuitively meaningful to us. One million isn’t. Fifteen million isn’t. And a ratio with a number that we can’t really grasp intuitively on the bottom? That’s not going to be meaningful either.

Bozo-boy is making an extremely common mistake. He’s just simply failing to comprehend how numbers scale; he’s not understanding what big numbers really mean.

The Danger When You Don't Know What You Don't Know

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A little bit of knowledge is a dangerous thing.

There’s no shortage of stupidity in the world. And, alas, it comes in many, many different kinds. Among the ones that bug me, pretty much the worst is the stupidity that comes from believing that you know something that you don’t.

This is particularly dangerous for people like me, who write blogs like this one where we try to explain math and science to non-mathemicians/non-scientists. Part of what we do, when we’re writing our blogs, is try to take complicated ideas, and explain them in ways that make them at least somewhat comprehensible to non-experts.

There are, arising from this, two dangers that face a math or science blogger.

  1. There is the danger of screwing up ourselves. I’ve demonstrated this plenty of times. I’m not an expert in all of the things that I’ve tried to write about, and I’ve made some pretty glaring errors. I do my best to acknowledge and correct those errors, but it’s all too easy to deceive myself into thinking that I understand something better than I actually do. I’m embarrassed every time that I do that.
  2. There is the danger of doing a good enough job that our readers believe that they really understand something on the basis of our incomplete explanation. When you’re writing for a popular audience, you don’t generally get into every detail of the subject. You do your best to just find a way of explaining it in a way that gives people some intuitive handle on the idea. It’s not perfect, but that’s life. I’ve read a couple of books on relativity, and I don’t pretend to really fully understand it. I can’t quite wrap my head around all of the math. That’s after reading several entire books aimed at a popular audience. Even at that length, you can’t explain all of the details if you’re writing for non-experts. And if you can’t do it in a three-hundred page book, then you certainly can’t do it in a single blog post! But sometimes, a reader will see a simplified popular explanation, and believe that because they understand that, that they’ve gotten the whole thing. In my experience, relativity is one of the most common examples of this phenomenon.

Todays post is an example of how terribly wrong you can go by taking an intuitive explanation of something, believing that you understand the whole thing from that intuitive explanation, and running with it, headfirst, right into a brick wall.

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