I don’t remember where I found this, but it’s really amazing. The 2005
conference on electron/ion microscopy gave awards for the best bizarre or art-like images produced using electron or ion microscopy. The images range from beautiful,
like the C60 crystalline lattice to the right, to extremely bizzare like the nano-meter scale toilet image to the left.
Since the friday pathological programming died out, I’ve been looking for something else to
do for special friday posts. A while back, I posted a bunch of recipes for a mutant meme, and
it seemed a lot of people really liked it. So I’ve decided to do an off-topic friday thing: friday random recipes.
For today, a special chinese dish: braised salmon in meat sauce. This dish would traditionally
be done using pork for the meat in the sauce, but since I don’t eat pork, I use ground chicken thighs. Whatever meet you use, you need to make sure it’s not too lean – the sauce does need a bit of fat in it; not a huge amount, but in needs some. Ground chicken breasts are too dry. I like to do this with wild alaskan salmon. If you don’t like or can’t get salmon, it would work with other strong-flavored firm fish – this would probably be very good using swordfish, or mahi-mahi.
There’s a kind of graph which is very commonly used by people like me for analysis applications, called a lattice. A lattice is a graph with special properties that make it
extremely useful for representing information in an analysis system.
Both in comments, and via email, I’ve received numerous requests to take a look at
the work of Dembski and Marks, published through Professor Marks’s website. The site is
called the “Evolutionary Informatics Laboratory”. Before getting to the paper, it’s worth
taking just a moment to understand its provenance – there’s something deeply fishy about
the “laboratory” that published this work. It’s not a lab – it’s a website; it was funded
under very peculiar circumstances, and hired Dembski as a “post-doc”, despite his being a full-time professor at a different university. Marks claims that his work for
the EIL is all done on his own time, and has nothing to do with his faculty position at the university. It’s all quite bizarre. For details, see here.
On to the work. Marks and Dembski have submitted three papers. They’re all
in a very similar vein (as one would expect for three papers written in a short period
of time by collaborators – there’s nothing at all peculiar about the similarity). The
basic idea behind all of them is to look at search in the context of evolutionary
algorithms, and to analyze it using an information theoretic approach. I’ve
picked out the first one listed on their site: Conservation of Information in Search: Measuring the Cost of Success
Last time, I showed a way of using a graph to model a particular kind of puzzle via
a search graph. Games and puzzles provide a lot of examples of how we can use graphs
to model problems. Another example of this is the most basic state-space search that we do in computer science problems.
Much to my professional shame, PZ recently pointed out David Plaisted, a Computer Science professor at
the University of North Carolina, who has an anti-evolution screed on his university
website. Worse, it’s typical creationist drivel, which anyone with half a brain should know is utter
rubbish. But worst of all, this computer scientist’s article is chock full of bad math. And it’s
deliberately bad math: this guy works in automated theorem proving and rewrite systems – there’s no way
that he doesn’t know what utter drivel his article is.
Via Atrios, I found this article at the American Prospect, which demonstrates an example of a very
common and very serious math error that’s constantly made in the media: unit errors. If you want to
compare two numbers, you need to make sure that they’re actually numbers that can be compared. You can’t meaningfully compare height in inches to height in centimeters; you can’t compare income in dollars
to income in Euro’s – to do a meaningful comparison, you need to convert to a common unit.
The specific error pointed out the by Prospect was in the New York Times. The Times published an article discussing politics and economics in Germany. They make some silly arguments about how the Germans don’t like goverment economic reforms because they’re all a bunch of lazy socialists who like to have the government take care of them. In support of that, they compare the
unemployment rate of Germany to the unemployment rate in the US. And that’s where they make their
error: the unemployment rates that they compare don’t measure the same thing. It’s a slightly
subtle kind of units problem – but it is a units problem.
The German government reports official unemployment numbers using a unit which is “percentage of
employable people with full-time employment”. By contrast, the US government reports official unemployment numbers in units of “percentage of people eligible to work with any employment”. In the German figures, if you work a part time job 20 hours per week, you’re considered unemployed. In the US, if you work a part time job 20 hours per week, you’re considered employed. A huge portion of the “unemployed” Germans would be considered employed in the US; or put the other way, a large number of people who are considered employed in the US because they’re working part time jobs would be considered unemployed
in Germany because they don’t have full-time jobs.
This difference in units is not an unknown or obscure fact. The Organization of Economic
Co-Operation and Development – which is as close as exists to an official authority on these kinds of
statistics – clearly documents the difference between how different governments report unemployment. They
further provide a standard measure of unemployment, which is almost the same as the US measure. (The
difference is that the US doesn’t consider you unemployed if you’re employable but not currently looking
for work; the OECD numbers consider anyone eligible for work but not working as unemployed.)
The Times cites the German rate as 9%, compared to the US rate of 5%. But that’s comparing apples to oranges. The accurate comparison, of the OECD is 6% in Germany and 5% in the US. Not nearly such a
big difference as the original article makes out.
This kind of error is very common, particularly in reporting about economics. But it’s very bad math.
In one of Jeff Shallit’s recent posts on the Panda’s Thumb, he mentioned that Tom Bethel, aside from being a creationist, was also a relativity denier. In general, relativity denial is a veritable mine of bad math. So I went looking – and found Bethel’s anti-relativity site. As I expected, we’ve got extremely silly bad math. In fact, it’s the worst kind of bad math – it’s a lack of math masquerading as being math. It’s also, sadly, full of pathetic errors.
As I’ve mentioned before, the real use of graphs is as models. Many real problems can be
described using graphs as models – that is, to translate the problem into a graph, solve some problem on the graph, and then translate the result back from the graph to the original problem. This kind of
solution is extremely common, and can come up in some unexpected places.
For example, there’s a classic chess puzzle called the Knight’s tour.
In the Knight’s tour, you have a chessboard, completely empty except for a knight on one square. You can
move the knight the way you normally can in chess, and you want to find a sequence of moves in which is
visits every square on the chessboard exactly once. There are variations of the puzzle for non-standard
chessboards – boards larger or smaller than normal, toroidal boards (where you can wrap around the left edge to the right, or the top to the botton), etc. So – given a particular board, how can you
(1) figure out if it’s possible to do a knights tour, and (2) find the sequence of moves in a tour
if one exists?
If you remember, a while back, I wrote about a British computer scientist named James Anderson, who
claimed to have solved the “problem” of “0/0” by creating a new number that he called nullity. The
creation of nullity was actually part of a larger project of his – he claims to have designed a computing
machine called the Perspex machine which is strictly more powerful that the Turing machine. If
this was true, it would mean that the Church-Turing thesis is false, overturning a huge part of the theory
of computer science.
Of course, just overturning the theory of computer science isn’t grandiose enough. He also claims that this solves the mind body problem, explains how free will works, and provides a potential
grand unified theory of physics. From Anderson’s own introduction on his website:
The Book of Paragon is a web site that offers one solution to the centuries old philosophical conundrum
of how minds relate to bodies. This site shows that the perspective simplex, or perspex, is a simple
physical thing that is both a mind and a body.The perspex can be understood in many ways. Mathematically, the perspex is a particular kind of matrix; concretely, it is simultaneously a physical shape, a physical motion, an artificial neuron, and an instruction for a machine that is more powerful than the Turing machine. In other words, a perspex is an instruction for a perspex machine that is more powerful than any theoretically possible digital computer.
The perspex machine operates in a 4D space of perspexes called perspex space. This space is related to the 4D spacetime we live in. It is claimed that the perspex machine can describe any aspect of the universe we live in, and can be built from any part of our universe. In other words, the universe can be understood as a perspex machine. And, on the materialistic assumption, our bodies and minds are physical things so they, too, can be understood as perspex machines.
This site contains mathematical formulas for the perspex machine and for properties such as feeling, consciousness, and free will. These things are described in scientific papers, books, and software that you can download and run. The site also contains news items that explain the perspex machine in a non-technical way, and it has links to old research on the perspex machine.
He also claims that the Perspex machine can prove the existence of free will, God, and original sin.
One thing you’ve got to give to Anderson – the guy’s got ambition.