goodmath

Moving on

goodmath — Mon, 02 Aug 2010 08:41:49 +0000

Moving on

Finally, at long last, I can tell you what I've been up to with finding a new home for this blog. I've created a new, community-based science blogging site, called Scientopia. With the help of many wonderful people, we're ready. We launched this morning. So to continue following GM/BM - along with the work of many other wonderful bloggers, like Scicurious, Grrlscientist, Mike Dunford, Dr. Skyskull, and lots of others, come on over to Scientopia, the new home of Good Math/Bad Math"/a>.

goodmath Mon, 08/02/2010 - 04:41

Goodbye, Scienceblogs

goodmath — Wed, 07 Jul 2010 20:01:49 +0000

Goodbye, Scienceblogs

So my decision is made. I'm closing up around here. I'm in the process of working out exactly where I'm going to go. With any luck, Seed will leave this blog here long enough for me to post an update with the new location. But I'm through with Seed and ScienceBlogs.

goodmath Wed, 07/07/2010 - 16:01

Seed, Conflicts of Interest, and Sleaze

goodmath — Tue, 06 Jul 2010 18:47:04 +0000

Seed, Conflicts of Interest, and Sleaze

As my friend Pal wrote about, Seed Media Group, the corporate overlords of the ScienceBlogs network that this blog belongs to, have apparently decided that blog space in these parts is now up for sale to advertisers.

We've been advertiser supported since I joined up with SB. I've never minded that before. Providing a platform and bandwidth takes money, which has to come from somewhere. The way that ads have been handled before has been no problem: the ads are clearly distinguished from the content. There's no way that you're going to mix up one of my posts with a paid advertisement.

Until now.

Seed has, in its corporate wisdom, decided to let Pepsico buy its way into a blog on ScienceBlogs. Pepsi writes SMG a nice check, and suddenly their content gets mixed in to the ScienceBlog RSS feeds, the ScienceBlog feed to Google News, etc., exactly the way that my blog posts do.

This is not acceptable.

For now, I'm suspending my blog for a few days. If Seed decides to back out of this spectacular stupidity, then I'll start posting here again. If not, then I'll go looking for a new home for GM/BM. The money that I've made from the ads that Seed has sold has been nice - but it's not worth my integrity.

If Blogs here are for sale, then I'm gone.

goodmath Tue, 07/06/2010 - 14:47

Searching for Topics

goodmath — Mon, 28 Jun 2010 09:02:24 +0000

Searching for Topics

As regular readers have no doubt noticed by now, posting on the blog
has been slow lately. I've been trying to come back up to speed, but so
far, that's been mainly in the form of bad math posts. I'd like to get
back to the good stuff. Unfortunately, the chaos theory stuff that I was
posting just isn't good for my schedule right now. Once you get past
the definitions of chaos, and understanding what it means, actually
analyzing chaotic systems is something that doesn't come easily to me - which
means that it takes a lot of time to put together a post. And
my work schedule right now means that I just don't have that amount of
time.

So, dear readers, what mathematical topics would you be particularly
interested in reading about? Since I'm a computer scientist, my background
obviously runs towards the discrete math side of the world - so, for the
most part, the easiest topics for me to write about are from that side. But
don't let that limit you: tell me what you want to know about, and I'll take
the suggestions into consideration, and figure out which one(s) I have the time
to study and write about.

I don't want to limit you by making suggestions. I've tried that in the past, and
the requests inevitably end up circling around the things I suggested. But I really want to
know just what you want to know more about. So - fire away!

goodmath Mon, 06/28/2010 - 05:02

Saturday Recipe: Ginger Scallion Sauce

goodmath — Sat, 26 Jun 2010 15:19:41 +0000

Saturday Recipe: Ginger Scallion Sauce

Today's recipe is something I made this week for the first time, and trying
it was like a revelation. It's simple to make, it's got an absolutely
spectacularly wonderful flavor - light and fresh - and it's incredibly
versatile. It's damned near perfect. It's scallion ginger sauce, and once you
try it, it will become a staple. To quote David Chang, whose cookbook
I learned this from: if you've got ginger scallion sauce in the fridge, you'll
never be hungry.

There are two main variations of this: there's a cooked version, and a raw version. Mine is the raw version. I love the freshness of flavor, and while cooking it will intensify some of the flavors, it will also detract from that delightful freshness.

Ingredients

Fresh ginger - roughly one inch, peeled.
A bunch of fresh scallions.
A teaspoon, give or take, of coarse salt.
1 tablespoon of soy sauce.
1 tablespoon rice vinegar.
1/4 cup oil - peanut oil, canola oil, or something
other neutral oil.
A dash of sesame oil.

Instructions

Mince the ginger. Toss the minced ginger into a food
processor.
Cut the roots off of the scallions, cut them coarsely, and
add them to the food processor.
Add the rest of the ingredients to the food processor.
Run the food processor until everything is finely ground into a
smooth sauce.

That's it. Ginger scallion sauce. Taste it - make sure it's
got enough salt. Don't add any soy sauce - just use plain salt if it
needs any.

So what can you do with it? Just about anything. A few
great ideas:

Ramen noodles. Just cook up a batch of ramen, and toss it
with a tablespoon of the sauce. You can also add some stir
fried meat and veggies to make it a bit more filling.
Grilled meats. Use a bit of the sauce as a marinade,
then grill it, and dress it with a bit of the sauce
when it's done.
Use it instead of mayo on a sandwich.
Add a bit more vinegar, and use it as a vinaigrette
over a salad.
Sautee some shrimp, and toss some ginger-scallion
sauce in just before they're done.
Get a nice whole fish, steam it cantonese style
with just a bit of salt, soy, and sake. Spoon
a bit of the sauce over it when it's done.

If you wanted to try to cooked version, you take the ginger, scallions, and salt, and puree them in the food processor. Then put them into a large pot. In a different pot, heat the oil up until it just starts to smoke, and then pour it over the ginger/scallion/salt mixture. When it cools, whisk in the rest of the ingredients.

But like I said - I think it's best to just stick with it raw.

goodmath Sat, 06/26/2010 - 11:19

The Surprises Never Eend: The Ulam Spiral of Primes

goodmath — Tue, 22 Jun 2010 09:58:52 +0000

The Surprises Never Eend: The Ulam Spiral of Primes

One of the things that's endlessly fascinating to me about math and
science is the way that, no matter how much we know, we're constantly
discovering more things that we don't know. Even in simple, fundamental
areas, there's always a surprise waiting just around the corner.

A great example of this is something called the Ulam spiral,
named after Stanislaw Ulam, who first noticed it. Take a sheet of graph paper.
Put "1" in some square. Then, spiral out from there, putting one number in
each square. Then circle each of the prime numbers. Like the following:

If you do that for a while - and zoom out, so that you can't see the numbers,
but just dots for each circled number, what you'll get will look something like
this:

That's the Ulam spiral filling a 200x200 grid. Look at how many diagonal
line segments you get! And look how many diagonal line segments occur along
the same lines! Why do the prime numbers tend to occur in clusters
along the diagonals of this spiral? I don't have a clue. Nor, to my knowledge,
does anyone else!

And it gets even a bit more surprising: you don't need to start
the spiral with one. You can start it with one hundred, or seventeen thousand. If
you draw the spiral, you'll find primes along diagonals.

Intuitions about it are almost certainly wrong. For example, when I first
thought about it, I tried to find a numerical pattern around the diagonals.
There are lots of patterns. For example, one of the simplest ones is
that an awful lot of primes occur along the set of lines
f(n) = 4n²+n+c, for a variety of values of b and c. But what does
that tell you? Alas, not much. Why do so many primes occur along
those families of lines?

You can make the effect even more prominent by making the spiral
a bit more regular. Instead of graph paper, draw an archimedean spiral - that
is, the classic circular spiral path. Each revolution around the circle, evenly
distribute the numbers up to the next perfect square. So the first spiral will have 2, 3, 4;
the next will have 5, 6, 7, 8, 9. And so on. What you'll wind up with is
called the Sack's spiral, which looks like this:

This has been cited by some religious folks as being a proof of the
existence of God. Personally, I think that that's silly; my personal
belief is that even a deity can't change the way the numbers work: the
nature of the numbers and how they behave in inescapable. Even a deity who
could create the universe couldn't make 4 a prime number.

Even just working with simple integers, and as simple a concept of
the prime numbers, there are still surprises waiting for us.

goodmath Tue, 06/22/2010 - 05:58

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

goodmath — Thu, 17 Jun 2010 11:45:15 +0000

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

So, another bit of Cantor stuff. This time, it really isn't Cantor
crankery, so much as it is just Cantor muddling. The href="http://rjlipton.wordpress.com/2010/06/11/does-cantors-diagonalization-proof-cheat/">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?

Muddled metaphors.

A common way of describing Cantor's proof is in terms of games. Suppose
I've got two players: Alice and Bob. Alice thinks of a number, and
Bob guesses. Bob wins if he guesses Alice's number.

If Alice is restricted to a finite set of integers, then Bob will
win in a bounded set of guesses. For example, if Alice is only allowed
to pick numbers between 1 and 20, then Bob is going to win within 20 guesses.

If Alice is restricted to natural numbers, then Bob will win - but it
could take an arbitrarily long time. The number of steps until he wins is
finite, but unbounded. His strategy is simple: guess 0. If that's not it, guess 1. If
that's not it, guess 2. And so on. Eventually, he'll win. And, in fact, after
each unsuccessful guess, Bob's guess is closer to Alice's number.

If Alice can use integers, then it gets harder for Bob - but it doesn't
really change much. Still, in a finite but unbounded number of guesses, Bob
will get Alice's number and win. Now, the "closer every guess" doesn't really
apply any more - but something very close does: there are no steps where Bob
gets further away from the absolute value of Alice's number; and
every two steps, he's guaranteed to get closer to the absolute value of
Alice's number.

We can make it harder for Bob - by saying that Alice can pick any
fraction. Now Bob's strategy gets much harder. He needs to work out a system
to guess all the rationals. He can do that. But now the properties about
getting closer to Alice's number no longer apply. He's no longer doing things
in an order where his value is converging on Alice's number. But still, after
a finite number of steps, he'll get it.

Finally, we could let Alice pick any real number. And now,
the rules change: for any strategy that Bob picks for going through the
real numbers, Alice can find a number that Bob won't even guess.

There's a fundamental asymmetry there. In all of the other versions of the
game, Alice had to pick her number first, and then Bob would try to guess it. Now,
Alice doesn't pick her number until after Bob starts guessing - and she
only picks her number after knowing Bob's strategy. So Alice is cheating.

The game metaphor demonstrates the basic idea of Cantor's theorem. The
naturals, integers, and rationals are all infinite sets, but they're all
countable. In the game setting, even if Alice knows Bob's strategy,
she can't pick a number from any of those sets which Bob won't guess
eventually. But with the real numbers, she can - because there's something
fundamentally different about the real numbers.

Of course, if it's a game, and the only way that Alice can win is
by knowing exactly what Bob is going to do - by knowing his complete
strategy from now to infinity - then the only way that Alice can win is
by cheating. In a game, if you get to know your opponent's moves in advance,
and you get to plan your moves in perfect anticipation of every
move that they're going to make --- you get to change your move
in reaction to their move, but they don't get to respond likewise
to your moves --- that is, by definition, cheating. You've got an unfair
advantage. Bob has to pick his strategy in advance and tell it to Alice, and
then Alice can use that to pick her moves in a way that guarantees that
Bob will lose.

The problem with this metaphor is that Cantor's proof isn't a
game. There are no players. No one wins, and no one loses. The
whole concept of fairness makes no sense in the context of Cantor's
proof. It makes sense in the metaphor used to explain Cantor's
proof. But the metaphor isn't the proof. A proof isn't a competition.
It doesn't have to be fair; it only has to be correct.
The fact that what Cantor's proof does would be cheating if it were a game
is completely irrelevant.

This kind of nonsense doesn't just happen in Cantor crankery. You see the
same problem constantly, in almost any kind of discussion which uses
metaphors. There are chemistry cranks who take the metaphor of an electron
orbiting an atomic nucleus like a planet orbits a sun, and use it to create
some of the most insane arguments. (The most extreme example of this in my
experience was a guy back on usenet, who called himself Ludwig von Ludvig,
then Ludwig Plutonium, and then href="http://www.iw.net/~a_plutonium/">Archimedes Plutonium. He went
beyond the simple orbit stuff, and looked at diagrams in physics books of
"electron clouds" around a nucleus. Since in the books, those clouds are made
of dots, he decided that the electrons were really made up of a cloud of dots
around the nucleus, and that our universe was actually a plutonium atom, where
the dots in the picture were actually galaxies.) There are physics bozos who
do things like worry about the semi-dead cats. There are politicians who worry
about new world orders, because of a stupid flowery metaphorical phrase that
someone used in a speech 20 years ago.

It's amazing. But there's really no limit to how incredibly, astonishingly
stupid people can be. And the idea of an imperfect metaphor is, apparently,
much too complicated for an awful lot of people.

goodmath Thu, 06/17/2010 - 07:45

The Unfalsifiable Theory Of Everything from viXra

goodmath — Fri, 11 Jun 2010 12:29:53 +0000

The Unfalsifiable Theory Of Everything from viXra

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.

So, we've got what the author claims is a grand unification theory - the
one thing that has evaded the best minds of the last hundred years! And it's
falsifiable! Wow!

Unfortunately, as we'll see, it's not falsifiable in any
meaningful way, because it doesn't make any predictions.

One of the important qualities of a genuine scientific theory is that
it makes predictions. That is, a theory isn't a vague bundle of words; it's
something precise, which describes some aspect of reality to a sufficient
degree of details that it allows a scientist to make predictions, and then
perform a test in reality that checks whether or not the prediction is
correct. The most important property of a prediction is its potential to
be wrong. A testable theory makes a prediction which isn't guaranteed
to be correct.

As a quick aside, this is the difference between intelligent design and
evolution. ID can take any evidence, and say "That's what the
designer wanted". Mike Behe can predict that there are no "irreducibly
complex" systems. But when push comes to shove, he never defines irreducibly
complex in a testable way. He can conclude that some system is IC; but if
it's proved that it's not, that doesn't invalidate ID. It just shows that that
one system isn't IC - and he'll just wave his hands and point at another
dozen that he claims are. Even if you could get him to accept the idea that IC isn't
a proof of anything, ID remains perfectly fine: there's nothing that
can invalidate it.

Evolution is thoroughly falsifiable. It predicts, for example, that all living
things have a common ancestor. And test after test has supported that. If you can
show a single species that isn't derived from the common ancestor,
evolution goes down. If you can show a single feature of a single species that
really couldn't have been the result of evolution, then evolution goes down.

In the case of our friend Jacek, he's got a non-falsifiable "theory". It's
so woefully vague that there's nothing in the world that could possibly
falsify it. It's got plenty of problems, but due to its vagueness, any problem
that could potentially be used to falsify it can be handwaved away.

So what's his theory? Basically that everything is a distortion
of spacetime. What appears to be a particle is really just a distortion of
spacetime - a sort of pinch in the fabric of space around the location of the
point. Forces are also distortions in spacetime - they're just shaped
differently.

To quote him:

Any interaction between spacetime deformations we notice as a force: we
named them gravitational, strong and weak nuclear and electromagnetic. Any
spacetime deformation (a physical object) interacts (a force) with all other
objects (being the force itself!)

A differentiation of forces depends only on gradient and size of the
deformation subject to our detection. (see exemplary Figure 1).

Read: all
interactions (forces) are only spacetime deformations with different geometry!

So - all forces are the same deformations of spacetime. The
only distinction between the forces comes from the gradient and
size of the spatio-temporal distortion.

OK, here's one potential falsifier: he's claiming that gravity and
electromagnetic forces are exactly the same thing. Why does a magnet only
attract certain things, instead of everything? It's just a distortion
in spacetime, right? He specifically claims that the differentiation of forces
depends only on the gradient and size of the deformations. Gravity
attracts everything equally. Magnetism attracts some things, and repels
others. How can the same distortions behave so differently if they only
differ in gradient and size?

Of course, he can wiggle out of that. Throw in a couple of extra dimensions,
and claim that different dimensions distort differently. So the difference
between forces could be their size and gradients in different dimensions.
Presto! Easy.

After this, he gets to something that he seems to believe is
profound:

3.11. Finally, we can ask the question: what is pressure? And answer: it is a
spacetime deformation.

I'd love to know who asked that question? Or rather, who asked that
question without knowing the answer? Since when is the nature of
pressure a problem?

Now, we move on to the very best part. He's got an entire section
that's titled "Mathematics". It starts off with the statement:

Hooke's law in simple terms says that strain is directly proportional to stress.

Tensor expression of Hooke's Law

(The incomplete second sentence is exactly as it appears in the
paper.)

What does Hooke's law have to do with anything? He never says. The rest of
the "mathematics" section is essentially content free.

There's one drawing that is supposedly
an example of a particle in spacetime. What kind of particle? Unspecified.
What are the axes? Unspecified. What's the magnitude? Unspecified.

Then, there's a couple of bell-curves, which supposedly illustrate the
"spacetime density of nuclear matter". They're just absolutely traditional
illustratory statistical bell-curves, with no unit on the Y-axis, and the
x-axis measured in standard deviations. Standard deviations from what? He doesn't
bother to say. (In fact, in the bibliography, he credits the bell-curve
illustrations to wikipedia.)

And that's the end of the paper. That's it.

For a supposed GUT, it's really missing a lot of things. For example,
it claims to explain the nature of particles - they're distortions
in spacetime. But the problem for the theory is, particles only occur
in certain, very limited forms. There are only 12 kinds of particles. If it's
all just continuous distortions in spacetime, then why aren't there a
continuum of particle sizes? Why does charge come in discrete units? Why
do electrons only exist in discrete energy levels, instead of a continuum?
The theory doesn't explain this. It seems like it predicts
a continuum of particle sizes/strengths. But we can't falsify it that
way, because it's too vague. He can wave his hands, and claim that there's
some reason for it.

He clearly states that there's no wave-particle duality: "The
wave-particle duality notion is not necessary any more as wave and particle
are the same thing. We can assume a particle to be a transverse or
longitudinal wave." And yet, there are very concrete experiments - the dual
slit experiment - that can demonstrate both non-particle wave behavior, and
non-wave particle behavior. As described, his theory can't explain that. But
we can't say that it falsifies it either, because once again, there's just not
enough precision here to say, definitively, what he means by "assume a
particle to be a transverse or longitudinal wave".

It's really quite an astonishingly bad pile of rubbish. And despite
the author protestations to the contrary, it's a perfect example of a
non-falsifiable pile of rubbish, because it lacks anything approaching the
precision or completeness that would allow it to make a falsifiable
prediction.

goodmath Fri, 06/11/2010 - 08:29

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

goodmath — Tue, 08 Jun 2010 09:47:36 +0000

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

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.

As evidence of this, the author claims to show how heating a copper sphere
changes its apparent mass! The author claims that if you put a 1068 gram
copper sphere above a 1000 watt heat element for 400 seconds will
increase its mass by 20 grams - almost two percent! And no
one has ever noticed this before!

Even better - if you put a copper hemisphere placed concave side up, below
two spheres full of ice, and you turn on a 1000W heat element for 500 seconds,
the mass will change by nearly 10 percent! And once again, no
once noticed it before our intrepid author!

Now, a sane person, looking at this, would immediately say that this
is almost certainly an error. I mean, think about what it means: you can,
using the burner on your stove, change the mass of an object by
nearly 10 percent in five minutes. Mass, which at non-relativistic
speeds is effectively constant - can be varied by a huge
amount just in your kitchen!

And yet... No one has ever noticed this before! Chemists, doing precise
measurements, have never noticed that the mass of their experimental apparatus
change when they heat them. Rockets, with precisely calculated thrusts to achieve particular
orbits, have actually changed their masses when they're heated, and no one noticed.
The space shuttle gets dramatically heavier during re-entry - and no one noticed!.

These things are obvious. The magnitude of the changes that he claims to observe are
absolutely staggering. And yet, no one else has every observed them.

So, where's the bad math? It's an issue of magnitude and scale. On the one hand, he's
producing absolutely huge numbers about how mass changes with moderate temperature
change - heating a piece of copper over your kitchen stove can produce a
ten percent change in mass! But he doesn't consider the large-scale impacts
that this would have.

He works out, based on his observation of apparent mass changes in
his copper spheres, how much heat you need to radiate to create a particular
"gravitational" force. And he then uses that to work out how much difference you
would need in the amount of heat radiated by the daylight side of the earth
versus the night side of the earth to produce the earths orbit - according
to him, it works out to about 0.08% difference. According to his computations,
8 ten-thousandths difference in the amount of heat being radiated is enough
to produce the earths orbit.

And yet - differences of similar or greater magnitude don't make a difference. He
treats the entire daylight side of the earth as being completely uniform in heat
radiation - when, in fact, it's not. The parts of the earth close to the day-night
terminator actually radiate more heat that the parts of the earth close to the night-day line.
So shouldn't the earths direction of acceleration be different because of that?

Why does the moon orbit the earth? Why doesn't it show less attraction to
the earth when it's on the dark side of the earth? Why doesn't a new moon
(where the side radiating significant amounts of heat is faced away from the
earth) have less gravitational attraction than a full moon (where the radiating face
is full towards us)?

He simply doesn't have a clue of what the numbers he's (mis-)measuring mean. So
he's drawing nonsense conclusions that make absolutely no sense. Any attempt to actually
understand the meaning of the mathematical results that he's computing would show
that they can't possibly be right. But he never does that.

Pathetic.

goodmath Tue, 06/08/2010 - 05:47

Big Number Bogosity from a Christian College Kid

goodmath — Tue, 04 May 2010 18:34:19 +0000

Big Number Bogosity from a Christian College Kid

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. href="http://thebeachnotes.blogspot.com/2010/05/tragedy-on-college-campuses.html">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.

goodmath Tue, 05/04/2010 - 14:34