Deconstructing Dembski (2005)

Introduction

In his 2005 paper Specification: the pattern that signifies intelligence, William Dembski tries to give a rigorous definition to his concept of Complex Specified Information (CSI). This paper has numerous problems, the most painful of which is repeated equivocation of terms, making it very difficult to read. Once I got past the equivocation, I discovered basic errors in how probabilities are calculated and interpreted. One error in particular is very hard to swallow, and anyone with a basic understanding of probability should know better. Dembski has a master’s degree in statistics and a PhD in mathematics, therefore it is reasonable to think he knows better. How could he be so wrong?

Here's the spoiler, in case you don't care to read the whole post:

• The concept of CSI in Dembski (2005) is based on a meaningless number, which is interpreted as probability even though it is not. As a consequence, CSI cannot have the meaning and interpretation stated. Dembski's math is wrong.

More after the fold ...

Rock Paper Scissors SPOCK Lizard

Sorry Sheldon, but it should be 

Rock Paper Scissors Spock Lizard,

NOT 

Rock Paper Scissors Lizard Spock.

Here is Sheldon Cooper explaining the game:

In the original Rochambeau we have the simple rules:

Rock crushes Scissors
Scissors cut Paper
Paper covers Rock

Which we can represent as:

Rock < Paper < Scissors < Rock

where greater-than "<" represents the win/lose relationship

loser < winner

and Rock is repeated to complete the circular relationship. 

If we call this game "Rock Paper Scissors Spock Lizard" then we can write the rules like this:

Rock < Paper < Scissors < Spock < Lizard < Rock < Paper

now with Rock and Paper repeated (or just understand that it "wraps around"), and the additional rule that any sequence of three (with wrapping) is also a rule.

Rock Paper Scissors
Paper Scissors Spock
Scissors Spock Lizard
Spock Lizard Rock
Lizard Rock Paper

And now the rules are the same as the name of the game.

Image source: Hollywood Nuts!

The Creationist 419 Scam

You would think that outrageous claims are so likely to be rejected that the person making the claim would just give up and go away. For an example of this you might check out this Sensuous Curmudgeon post "ICR: Plants Are Not Alive". The Institute for Creation Research claims that because plants do not move and do not have blood, they are not alive, and they justify this based on the Old Testament and a some quadruple backwards spinning logical somersaults that would make Gabby Douglas gawk. There are plenty of other examples, but I won't belabor the point. As my buddies at The Sensuous Curmudgeon often note, the scammers* have to know they have no scientific standing, but they do it anyway. WHY?

Consider a known scam that everyone can agree is a scam; one that is no farther away than your email SPAM folder. Microsoft scientist Cormac Herley has a paper out:

 "Why do Nigerian Scammers
Say They are from Nigeria?" (pdf) 

Edit: Original link seems broken. Try this instead.

... dissecting the mathematics of the Nigerian 419 scam. The Wall Street Journal Online has a less technical summary, see "Why We Should Scam the Scammers".

Here is a brief quote from Herley, with my emphasis added:

"... Far-fetched tales of West African riches strike most as comical. Our analysis suggests that is an advantage to the attacker, not a disadvantage. Since his attack has a low density of victims the Nigerian scammer has an over-riding need to reduce false positives. By sending an email that repels all but the most gullible the scammer gets the most promising marks to self-select, and tilts the true to false positive ratio in his favor."

 Here is Herley again, later on:

"Since gullibility is unobservable, the best strategy is to get those who possess this quality to self-identify. An email with tales of fabulous amounts of money and West African corruption will strike all but the most gullible as bizarre. It will be recognized and ignored by anyone who has been using the Internet long enough to have seen it several times.  [ ... ]  It won’t be pursued by anyone who consults sensible family or fiends, or who reads any of the advice banks and money transfer agencies make available. Those who remain are the scammers ideal targets."

It's brilliant actually. Finding people susceptible to a scam is hard, but weeding out those least susceptible is as easy as concocting a lame story. The more outrageous the tale, the less likely it is to attract those who can see through it, leaving those who are mostly likely to be successfully fleeced by the scammer.

There's is a shorter summary, and an older one; Abraham Lincoln put it like this, "You can fool some of the people all of the time, and all of the people some of the time, but you can not fool all of the people all of the time."



The scammers know that most people will apply some amount of logic and reason and reject the obviously incorrect, and this is what they want. They want to weed out the majority who will never buy into the scam, and speak to the few they might fool. When the scammer is the ICR and the marks falls for the false dichotomy that religious belief must overrule scientific knowledge, the scam is particularly insidious.

Herley suggests a response to the 419 scams, to counter-SPAM the scammers with automated responses, false positives that waste time and money and take the profit out of the scam. This would be harder to apply to Creationist scammers, requiring a large number of people (or automated facsimiles) to "Go Poe" and troll the Creationists where they live. That doesn't sound like fun, and it doesn't strike me as ethical. Still, the suggestion has been made before.

* I'd like to make distinction between those who hold to Creationist belief and those those making claims in support of Creation science. The former may hold a sincere belief, but the latter are deliberately lying in an attempt to undermine science and science education.

How to tell the difference between a theoretical statistician and an applied statistician

How to tell the difference between a theoretical statistician and an applied statistician?

A theoretical statistician knows all about measure theory but has never seen a measurement whereas the actual use of measure theory by the applied statistician is a set of measure zero.

--- Stephen Senn

Found on Statistical Modeling, Causal Inference, and Social Science

The Real Secret of the Super Rich?

I found an interesting series of blog articles, starting here:

The Real Secret of the Super Rich

What caught my interest isn't so much that this reveals any surprising secrets, but that it is a reasonable mathematical analysis of the value of education and ability explained in simple terms. Simplified, but it makes a good point all the same.

I am less certain about the author's holistic politics, which are also interesting. However, I don't really have the time or energy right now to evaluate this properly. I do see a certain appeal in his mathematical approach to politics, but I remain skeptical that this approach can't be manipulated to fit specific goals, rather than the math driving the policy.

Arthur Benjamin and Mathemagic!

Celebrity for the math-geek, and some good advice for students (quoting from memory):

Arthur Benjamin: "The number of math courses you take in college is the single best predictor of your future income."

Steven Colbert has an answer for that too, but he always has an answer*.

The Colbert Report	Mon - Thurs 11:30pm / 10:30c
Arthur Benjamin
www.colbertnation.com
Colbert Report Full Episodes Political Humor Economy

* Always, except maybe for that time when Jane Fonda was on the show. ;-)

Depressing News for Grad Students

From Discoblog:

Alien Math Shows Why Grad Student Doesn’t Have a Girlfriend

 PS: This is old news to most grad students.

Diesel Exhaust is a Weighty Matter

Scientific American has this online article -

Idle Moments Turn into Tons of Air Pollutants at Schools

- the point of which is to point out the enormous amounts of pollutants produced by idling truck engines, and that New York City has a law regarding this that really ought to be enforced. I have little doubt that this really is a significant source of pollutions, but this statement made me raise my eyebrows:

"Idling buses, cars and trucks may not seem like a big deal, but in New York City they spew out as much pollution as nine million diesel trucks driving from the Bronx to Staten Island, according to the Environmental Defense Fund. That’s roughly 130,000 tons of carbon dioxide, 940 tons of nitrogen oxide, 24 tons of soot particles, and 6,400 tons of carbon monoxide each year"

Can that be right? That's a lot of trucks making the trip. I'm a statistician, and I wonder about such things like the accuracy of statistics like this. Watching TV on a Friday night, I started doing so some Googling and back-of-the-envelope calculations during the commercials.

The claim of the article: 130,000 + 940 + 24 + 6,400 = 137364 of pollutants released each year, that's 274,728,000 pounds. The distance between the Bronx and Staten Island is 33.9 miles (so says Google Maps), and in 9 million trips that works out to 305,100,000 miles. 274,728,000 pounds divided by 305,100,000 miles is 0.9 pounds of pollutants per mile.

The Economy of Diesel trucks: The average big diesel truck pulling a load gets about 5.5 miles per gallon of fuel (so says Wiki Answers), or 0.182 gallons of diesel per mile. Diesel weighs about 7.2 pounds per gallon (in cold weather yet, so says faqs.org), so 0.182 gallons/mile times 7.2 lbs/gallon is about 1.31 pounds of diesel per mile driven.

Now 0.9 lbs/mile of pollutants divided by 1.31 ponds per mile of diesel work out to 0.6873, or about 70% of the total mass of the diesel fuel converted to pollution. At this point, I ran into difficulty finding a source for the actual composition of diesel exhaust. 70% might be reasonable; after all, the mass of the fuel has to go somewhere.

But wait, I've made a mistake - most of the 130,000 tons of carbon dioxide is oxygen, without looking up the molecular weights of carbon and oxygen, AT LEAST two-thirds of that mass is coming from the atmosphere and not the diesel fuel. 70% now seems more reasonable.

There is another possible error, which I don't know how to resolve. In my reading I discovered (lost the link, sorry) that idling diesel engines are relatively clean, but produce heavy pollution when under a load (you see this on the road all the time). Therefore the number of idling vehicles must be really huge to make of this difference. This is also quite possible; NYC is a BIG place, but the article does not offer any information about how many vehicles this might be.

I would assume that if NYC has a law that trucks should not idle for more than a minute, there must be some good evidence somewhere to back this up. The original claim seems to come from the Environmental Defense Fund, but I'm too tired for more digging tonight. This has been an interesting bit of fact checking, except that I ran into a wall with limited knowledge of chemistry. Maybe I should ask a Chemist?

[UPDATE, 11/01/2009]
I received this response to my question at About.Chemistry, Sean writes:

the average chemical formula for diesel is C12H23. with that said, the mass of a carbon atom is 12.01 g, and hydrogen is 1.008. so, mathematically, diesel has the molecular weight, on average of 167.304 grams per mole of fuel.
the weight of the oxygen atom is 15.99g (mostly rounded to 16g), so carbon dioxide is 44.01 grams per mole.
in general, this relates to something of the sort:
2 moles of C12H23 +  O2 gas in excess -makes-> 12moles CO2+ 12moles CO+ 23moles H2O. as the formula for the burning of the diesel, if it was a very complete and clean reaction, however, we all know that's never the case. ;.;
as for the 130,000 tons of CO2, that comes to

 117 934 016 200g of CO2

and of that gram mass, 27% is carbon, while 73% is oxygen. that's what...
31842184374 grams of carbon and 86091831826 grams of oxygen.
however, diesel is more of a blend of things and not just the carbon and hydrogen, which pretty much takes all that I have written and makes it almost useless. In my research, though, I've seen more about the fact that sulfur is present in the fuel than the carbon emissions, as that will inhibit the use of catalytic filters to scrub the exhaust clean, as in most vehicles.
also, in response to your lost link, I dug this up
http://busbuilding.com/bus-conversion/diesel-engine-idling-from-an-authority-detroit-diesel/
which says that idling is bad for diesel because it produces more exhaust via incomplete combustion.
anywho, I'm not too advanced in chemistry, so forgive me if I supplied you with random nonsense, I was trying to think of a way to equate the mass of fuel to pollutants produced, but as I can't find an exact formula for what the reactions are this is the best I think I can do. I'm hoping someone else can chime in from here and make more sense of things, and of anything, I wish you luck with your search.

Thanks Sean!

After some more digging I turned up an abstract and a paper on wind tunnel experiments (Part 1, Part 2) that are related, but none seem to be the origin of the original statistics. I might have more luck searching from work tomorrow.
-- OR --
I could ask the author of the SciAm article, Mr Brett Israel. Would that make it too easy?

[Further update 12/09/2009]
I never heard back from the author and I've pretty much given up. Sean's comment about catalytic converters is something else I had not thought of that might affect the results. So many windmills to tilt at, and so little time.

Chicks Dig Math

Chicks Dig Math!!!

But not these chicks ... sorry ... not these ladies ... well ... maybe they do. It's hard to say.

[image http://www.kismetgirls.com/]


Now THESE chicks really do dig math, and you can read about the innate mathematical ability of chicks at 90Beats. Sorry, make that 80Beats. Hey ... I was within 10 ...


[image Livingromcom]





But as long as I am confusing subjects, how about more chicks women and math?


[image Eat.Sleep.Geek]




and more

[image GaySocialites]










and more.

[image CPBN]

New Math

Freakonomics already linked to this site, so they can probably handle the extra bump on traffic that my posting the link will add: New Math by Craig Damrauer.




More to see at New Math.

The Rodriguez File, Revisited

I find myself short of time and ideas tonight, so I shall regale you with past exploits.

I encountered The Rodriguez File one day at Improbable Research, where I was intrigued by the question ...

"I would like to explore the statistical chances of getting such a line".

The straight line being the arrangement of words to the right such that 5 or 6 spaces line up to form a line.

So I took a stab at the problem, and Kees (duck researcher extraordinaire) choose to post it for the world to see:
The Rodriguez File (part 2).

However, I was not satidfied with that effort, and made a second attempt, which appears here:
The Rodriguez File (part 3).


Then someone asked the question a different way, and I had yet another go at it:
The Rodriguez File (part 4).

It's good to be a statistician. We get to consider all kinds of strange and interesting questions.

Financial Morons

What wrong with this chart? Mark CC rants at Good Math, Bad Math.


[From Good Math, Bad Math]

Law of Large Numbers is Alive and Well

I originally wrote this for the newsletter of a local statistics professional group in late August, 2002. Writing "Time to Play" reminded me of this, and after finally discovering the archived-archive where it was hiding, I have dusted it off to present as a bit of recycled writing. The only trouble was I couldn't decide which of my blogs to put it on; Science and Math, or Math and Games? Since I'm facing a bit of a time crunch this week anyway, I'll post it to both. Problem solved! (but I'll try not to make a habit of it.)

Law of Large Numbers is Alive and Well
at 2002 GENCON Games Fair

“All these people came here to play games?” said one astonished worker to another, as they walked through the midst of several thousand people at the 35th GENCON Games Fair, all busily rolling dice or shuffling cards for a dazzling variety of games. I almost trailed them to see if I could overhear more comments, but I needed to get back to my own session. However, I did continue to think about this pair, and about why people like games.

My own exploration of probability began with the boardgame Risk when I was young, and soon I was writing my own simulation programs on an Apple II+. I was fascinated by the thought of enumerating all the possible outcomes and determining the best strategy for winning the game. This self-study soon expanded to include most of my favorite games, got me hooked on computers, and eventually led me to the study of statistics and a career. I still like to study my favorite games; I love to play them, disassemble the rules, study the probabilities, put them back together again, then go play some more.

Looking over the GENCON crowds gathered in the Midwest Center, I have to believe that there are lots of people out there who are quite interested in probability, and whether they know it or not, interested in statistics too. Some of the people I spoke to are very knowledgeable of the probabilities involved in a game. Furthermore, THEY THINK IT’S FUN.

Now, when was the last time your heard someone describe their college stats class as fun? How many times have you seen people get the “your-a-WHAT” look on someone’s face when you tell them of your profession? I have personally met at least half a dozen people still in statistical-shell-shock, twenty or more years after taking an intro level stats course. How many people have you met that would consider statistics to be fun?

I am very happy being a statistician, but I sometimes think that as a profession, we haven’t done a very good job of selling ourselves. Too many people have the impression that statistics has to be dull, boring, or cryptically complex. Too many people think that statistics are something they can’t understand. It doesn’t have to be that way. I think statisticians need to try harder to increase awareness of what we do, what it’s good for, and how it can be of benefit. I think it’s very important to reach out and find ways to attract new people to our profession, and to let them know that it offers excellent opportunities.

There are plenty of people who are interested. There are plenty of people who grasp the basic concepts. I know there are, because I just saw thousands of them at GENCON. All of them were shuffling cards or rolling dice, all of them putting the Law of Large Numbers to the test, and all of them loving it.

Update - Six Years Later: The need for statistics education has not gone away. There is more and more information being presented to us every day, and our ability to process all that information is limited. A working knowledge of math and statistics is a crucial skill nowadays. I don't mean that every person needs to understand high level probability theory (heck - I don't understand all that stuff - at least not very well), but I do mean that every person needs to be educated as a consumer of information. They need to know what the numbers mean, and when they don't mean anything at all. They should have a basic understanding of how numbers are presented (descriptive stats), what they represent (estimation), and how decisions are made on this basis (inference).
I should add for the benefit of students interested in math and statistics at more than a basic level; there are a lot of jobs available to you even as an undergraduate; there are a graduate statistics programs desperate for good students and willing to pay you to go to school; there is a rich field of careers in math and stats to look forward to, and finally - if you work it right - it might be a lot of fun.

Mathematics and Magicians, the Rant Continues

An old friend of mine just wrote in reply my Mathematics and Magicians post yesterday. He couldn’t post his comments directly to the blog site, so he emailed them to me. With his permission, I present it to you here in full (I did add the first two links for reference):

Hey Dan

I read one of your blog entries, and I got so worked up that I furiously banged out a reply. Then the silly thing wouldn't let me post it, probably because it was too long. So I'll just email it to you. You can ignore it or delete it or post it yourself....but at least I will have had my say! And for the record, I'm griping with the author you cite, not you...so we're on the same side.

Here's my reply to your entry "Magicians and Mathematicians":

Having worked in the financial arena for about 15 years now, I'm here to tell you that the term "human side of finance" is as big of an oxymoron as "sanitary landfill" or "military intelligence" or "compassionate conservative". If you want that touchy-feely crap, go down the hall to HR and cry them a river. The finance people have work to do, thank you very much.

All businesses which are traded in the public markets exist for one purpose: the pursuit of profit for shareholders. How the "quants" apply their profit mandate to their daily tasks is merely a matter of corporate policy. It's shockingly naive to assume that anyone in a financial capacity would ever "appreciate...the unintended consequences" of their individual actions or even give a hoot for that matter.

Sounds like a bunch of academic rubbish to me. It would also be foolish to subscribe to the notion that this is a relatively new phenomenon (ref. the managers with history degrees – as if to say “back in the good old days”). The Spanish conquistadors directly or indirectly caused the deaths of millions in the pursuit of profit (unbridled imperialism). The Bolsheviks made a naked power grab in the early 20th century and wreaked 70 years of financial, ecological, and social havoc, all under the pretense of making a better life for the masses (rampant socialism/communism). Wall Street capitalists speculated themselves into quite a mess in 1929 (runaway capitalism).

Greed is an intrinsic part of human nature, and unfortunately greed is also part of the group mentality of "quants" which are otherwise known as "people". It seems the article's author is the one who has lost his "human side".

P.S. I resent being identified as a mere "quant", which sounds suspiciously like “quantum”, especially since the definition of THAT word would be even more dehumanizing.

http://dictionary.reference.com/browse/quanta


Ahh........I feel better now.......so it's back to clearing general ledger errors for me!

Rick

I will have to investigate if there is a limit to comment length, but after reading Rick's reply I rather suspect that it was a hardware failure instead (his keyboard probably melted!).

Magicians and Mathematicians

[via Tao of Gaming]
Paul Wilmott writes about Magicians And Mathematicians, and I might have a bone to pick.

Quantitative finance and risk management are not just about the numbers. Numbers play a part, but so does the human side of the business. When analyzing risk it is important to be able to think creatively about scenarios. Unfortunately the training that most quants get seems to actively discourage creativity.

I certainly agree,

This is really a question about whether modern risk managers are capable of thinking beyond maths and formulas. Do they appreciate the human side of finance, the herding behaviour of people, the unintended consequences, what I think of as all the fun stuff. And this is a nice question because it very quickly sorts out different types of thinkers.

and

Once you start thinking outside the box of mathematical theories the possibilities are endless. And although a knowledge of advanced mathematics is important in modern finance I do rather miss the days when banking was populated by managers with degrees in History and who'd been leaders of the school debating team. A lot of mathematics is no substitute for a little bit of commonsense and an open mind.

How can we get quants and risk managers to think beyond the mathematics? I'm afraid I don't think we can, the way the majority of them are currently educated.

[The emphasis is mine. ]

I'm OK with the part about training the quants to understand these things, and it's somewhat criminal that they were not required to understand these things before being allowed to play in that particular sandbox, thus precipitating a financial meltdown. However, this in no way removes the problem from the "box" of mathematics. It's still math, but it has to be applied in a consistent and conservative way, and founded in a basic knowledge of the subject area. -- And now I'm going to contradict my self -- It is more than math, it is statistics. It was once suggested to me that the difference between math and statistics is the manner of application (of stats), which might fairly be described as an art. A herd of quants well versed in the application of statistics ought to have realized the most obvious error (dependencies among risks).
That there is an essential art to understanding financial markets I do not doubt. It's too bad so many people forgot, or were blinded to that fact by greed.

[UPDATE: The rant continues here!]

Secrets Revealed

GG is a spoiler! He has revealed the secret to my favorite math trick. He also has one I didn't know, and another I had seen but couldn't recall. Check them out at Skulls in the Stars.

Use this equation 0=NP(20C+B)/75

Use this equation 0=NP(20C+B)/75 to determine if the boobline is too low.

“Following her [Britney Spears] wardrobe malfunction — where she was snapped nearly popping out of a very low-cut dress at her 27th birthday bash, below — scientists, undies experts and mathematicians have been trying to figure out where the decency perimeter lies. And here we can exclusively reveal the formula to work it out.”

Ben Goldacre discusses this equation and other important mathematical findings at Bad Science.

Guitar Chords, Missing Pianos, and Math

There is a Piano in A Hard Days Night (yes, The Beatles) and Dr. Jason Brown proved it. Pick up the story at 360.

2 is 1

A discussion over at Good Math, Bad Math reminded me of this - My favorite math riddle:

Proof that 2 = 1

Start with: X = Y
multiply both sides by X: X*X = X*Y
subtract Y^2 from both sides: X^2 - Y^2 = X*Y - Y^2
do some factoring: (X+Y)*(X-Y) = Y*(X-Y)
divide both sides by (X-Y): (X+Y) = Y
substitute Y for X: (Y+Y) = Y
divide by Y and simplify: 2 = 1

There you have it, a mathematical proof that two is equal to one!