## Thursday, April 5, 2012

### Proof That There is 0% Chance that Gene Callahan Will Have a Logical Thought

Oh boy, the comments continue to poor in on my post with regard to the Gene Callahan statement. Callahan, himself, has stepped in screaming
Absolutely incredible, folks! I did not invent this example: it is absolutely standard probability theory. Go ask any math PhD. I think next I will post, "The square root of two is an irrational number," and then wait for the stampede of lemmings to arrive here declaring "Callahan has just shown his Keynesian irrationality."
Which now forces me to prove that there is 0% chance  for Callahan to have a logical thought. Let's go back to Callahan's original statement:
"There's a 0% chance that X will happen."
Most people interpret that to be equivalent to, "X will never happen."
But that isn't so. An example: If one were to toss an infinitely fine-pointed dart at the real number line and hit a spot between 0 and 1, for any particular number in that range, there is a 0% chance you will hit it. But you *will* have hit *some* number, so even though there was a zero percent probability that number would be hit, it was hit.
Now, when most people hear that "There's a 0% chance that X will happen." in a dart throwing contest (using darts in this example as Callahan does), people are assuming we are discussing a dart that has some physical substance to it, to be thrown at some real target. Since at this point, Callahan has not added the non-common way of thinking about the situation in terms of an "infinite dart". Now, it is perfectly legitimate to construct any type of thought experiment you want, but this has zero to do with Callahan's original statement. As David Gordon points out Callahan's first sentence is ambiguous.

He is saying, "Ha, ha most people aren't as smart as I am because they think  0% chance means something will never happen". But "most people" are correct using every day non-infinite concepts. When Callahan introduces an "infinitely fine-pointed dart", he introduces a factor not considered in everyday use of the term probability.  The people are right and Callahan is wrong and I can prove this by using Callahan's infinite concept and proving that he has 0% chance of coming up with a logical thought.

Let us examine Callahan's thinking process along a timeline divided up into an infinite number of points (slyly slipping in the concept of infinite as does Callahan in his dart argument). Now, we all know that a thought takes time to develop, so that at any point on Callahan's infinite timeline it is impossible for him to have a logical thought. The chance is 0%.

Now, this is nutty and has nothing to do with reality, since we  generally do not consider thoughts at a point on an infinite timeline, but neither do we consider infinite darts. But on second thought, as I assemble a number of my infinite fractions of thought, I see something unique happens with Callahan logical thought, his logical thought here over time in this discussion does intersect with his infinite thoughts at 0%.

1. Why is there this heated divide among Austrian economist these days and what the heck for?

1. As far as I know, Gene doesn't really consider himself an economist (I could be wrong). Which, considering that his focus is primarily philosophy, that makes sense. However, I think the biggest divide comes from the fact that Gene isn't a libertarian and often makes rather scornful comments regarding libertarian philosophy. It is true that I don't know the whole story, so there could be some personal reasons, as well.

Personally, I am an Austro-libertarian of the Rothbardian variety, so it goes without saying that I often disagree with Gene. However, he hasn't given me good reason to hate him... Yet!

2. Joe, I was writing a long response answering this, but you hit the good points.

I'll add to this by saying that I agree with your "scornful comments" bit. Personally, I'll say that I've found that Callahan comments live on a continuum that spans from snarky to douche. So to that, I say, "who's to blame if you get stung after kicking a hornets' nest; the hornets for building the nest or you for kicking it?" It's not a rationale, but are you surprised?

3. So if GC is not a libertarian he believes in what? The same worn out and tired left-right paradigm? Authoritarianism?

4. It was much better if this offensive way of interacting would stop. I really despise to read "oh this stupid statists" as well as "oh this stupid libertarians/rothbardians"... It makes no one looks good. But every side justifies his offensive statements with the offensive statements of the others.

It's like with violence, once started it feeds itself...

@Bob Wenzel

Wasn't it better and more professional if you keep your criticism more toned down and merely factual regardless of what Callahan, Krugman or whoever says?

I think Bob Murphy does an amazing job in criticizing thoroughly while still being respectful.

Maybe you should go and watch a Basketball game with Gene once. If I got it right, you both are fans of it ;)

5. "I don't know the whole story, so there could be some personal reasons, as well."

Yes, maybe there was even a girl involved... They really can mess things up among men!

At the girls: No offense meant. Its (usually) not your fault ;)

6. Mike,

Gene used to be a libertarian at one point. Today it is difficult to classify him completely into one category, because while he leans more old-conservative, I have seen him agree with some on the left at times (though, not often). I think that if you read some Oakeshott you will get a clearer picture as to Gene's political ideology.

As for me, I get along with Gene even though we rarely agree (esp. politics). The simple fact is that I will be cool with anybody no matter what they believe, so long as their beliefs don't affect me directly and they show some level of decency and respect. Also, while I don't know him personally (I only know him from our email/online correspondence), he was the only guy that offered any help when I was in a time of need. For that he has my respect.

7. "keep your criticism more toned down"

Well, then that just wouldn't be Bob anymore... It just isn't Bob's style. There is a reason that people come to this site, and it isn't to see Bob turn into Mother Teresa (RIP).

One of the things that I truly love and appreciate about Bob Wenzel is that he is his own man and he simply does not give a shit what anybody else thinks. It also helps that I agree with him about 90% of the time, with the other 10% usually comprising a difference of opinion regarding the particulars. You can ask pretty much all of the heavy hitters in the Austro-libertarian community if they like Bob and they will all say yes (even those who've gone toe to toe with him). I think part of the reason is that he is willing to stick his neck out and say the things that they are either too afraid to say, or just haven't had the insight to take notice of. Is he always right? No. But, at least he isn't a pussy.

In the event of a zombie apocalypse, I'd be willing to bet that not only would Bob make it through, but he'd figure out a way to profit from it. LOL

You only get one go at this thing called life and once that minute is gone, it's gone. Bob is one of the few people that REALLY understands that.

8. Hey Joe,

I am not criticizing that he makes bold clear statements (it's great that he doesn't hide behind platitudes that later on always can be interpreted either way), I am just saying it gets too personal at times that's all.

All in all I really like his blog and his work!

Regards

9. skylien, no problemo.

JFF, gracias. Now, if I can only find a way to monetize my comments. Hmm....

2. I'd like to thank Gene for giving me something to think about on my 1 hour drive home: heuristic devices.
Here's another riddle: What chance does an infinite snowball have in hell?

3. It seems Gene is a "look at me, I am a contrarian for contrarian sake" academic who uses slight of hand, obfuscation gimmicks to garner attention.

1. This is not a contrarian point: it is absolutely standard probability theory.

4. If I threw an infinitely fine-pointed dart into Gene's right eye, what is the probability that he would cease this inane argument?

5. The point of the "infinitely fine pointed dart" would pass easily through the vast emptiness between the subatomic particles comprising the atoms that make up the number line. The finite girth of the shaft of the "infinitely fine pointed dart" would ultimately lodge between two real numbers, having struck neither of them directly.

That was easy!

1. It would be impossible for the dart to be lodged between two real numbers. There is no space between real numbers. Any two real numbers, no matter how close together they are, have an infinite number of real numbers between them.

6. Have you seen Cowen's latest nonsense? Maybe it was meant for April 1st.

7. Gene Callahan wrote a fantastic book on introductory austrian economics called Economics for Real People. Why is there this fight amongst two Austrians then? Did Gene Callahan completely changed his mind and changed to become a keynesian or a monetarist? What's the beef between Wenzel and Callahan?

1. For the record, I do not believe I have ever met Gene Callahan. I don't know him personally. I have never read any of his books, but he does post on Austrian/libertarian blogs, where I have taken notice of his comments and, now, occasionally visit his blog. From time to time he has made some truly off the wall comments, which I consider "teaching moments".

It has nothing to do with Austrians fighting or not fighting (although I am not sure Callahan considers himself an Austrian--anymore). I call out high level confusion where I see it.

2. I am curious, Mr. Wenzel, if you would mind sharing your own view of Rothbard and Mises's theory of probability.

Both Rothbard and Mises would have scoffed at the idea of assigning a numerical probability to a singular case, like the situation Callahan proposes. They followed Richard von Mises in arguing that numerical probabilities can only be applied a posteriori to "classes" or "collectives" of events.

Am I right to assume that you don't agree with Rothbard and Mises's view of probability, since you do not criticize Callahan along the lines we would expect Rothbard or Mises to criticize him?

3. I don't think Callahan is discussing a single case here. He could just as well argue his argument with a million throws of his "infinite dart". Thus, the Richard von Mises insight wouldn't make any important point relative to Callahan's argument.

That said, I think there is very much to be said for the case versus class distinction made by Rothbard and the Mises brothers.

I note in some of the comments here, the use of the term "finite" to attack Mises and Rothbard on case/class, so there must be some argument out there against them, which I haven't seen. But just use of the tern finite suggests to me a very likely misinterpretation of case/class distinction.

4. I actually don't think that Callahan could make the same argument after tossing the dart an infinite number of times (i.e., tossing the dart to the "limit," as Richard von Mises says).

If we had a frequency distribution that included all of the past frequencies at which every number was hit after tossing the dart an infinite number of times, it seems inconceivable that every number would not be eventually be hit. At the very least, tossing an infinitely fine dart an infinite number of times at a number line with an infinite number of points would make the example even more complicated and absurd than it already is.

I guess what I was more interested to know is whether you agree more generally with the Mises brothers that it is absurd to calculate probabilities a priori. All of the comments yesterday, for example, basically took it as given that there is an "objective" a priori probability in the example of either zero or slightly more than zero.

The von Mises brothers and Rothbard, on the other hand, would say that this is absurd. One cannot even talk about numerical probability, let alone say unequivocally that some number has a probability of zero, until one has already performed the experiment and has a past frequency of occurrence in one's hands.

My own opinion is that Mises and Rothbard adopted a definition for probability that contradicts the rest of their theoretical system. They adopted the positivism-inspired definition of Richard von Mises, instead of recognizing that they ought to have defined probability subjectively. Probability, like economic value, is subjective.

http://libertarianpapers.org/articles/2009/lp-1-26.pdf

5. I said a million, not an infinite amount, which is a major difference. Don't distort my argument.

Also, it sounds to me you have a butchered view of the distinction between case and class that Rothbard and the Mises brothers were making, which, as I said, has nothing to do with Callahan's argument.

Probability is subjective? I really need to play Blackjack with you sometime.

6. I just read into page 3 of your paper that you provide the link to above, and you are using an example that is a pedestrian error about odds set by casinos at sporting events. Casino operators don't set odds based on the probabilities of who they think will win,as you state, they set odds so that the money flows are the same for both sides of the bet.

From the Sportspage

"the goal of oddsmaking for the casino oddsmakers is not to predict the outcome of a game, it is to furnish the bettors with a betting line that will split the public in two with half of the people betting one side and half on the other. ....Sportsbooks move lines to reflect betting trends to balance the betting so that the book won’t lose gobs of money on a particular game or event."

You don't even understand reality, never mind imaginary constructs around infinity.

7. You said a million, but the Richard von Mises "limit" concept that was adopted by Rothbard means a virtually infinite number of repetitions. I wanted you to consider the von Mises conception of probability.

In what way have I "butchered" the class-case distinction?

As for probability being subjective, this is pretty mainstream stuff nowadays. Nassim Taleb, for example, defends a subjective interpretation for probability. All it means is that probability is a measure of subjective belief, not some mysterious property "in" the world. This does not mean that probability is arbitrary, or that some people's odds and probabilities turn out to be more accurate than others. It just means that there is no "objective" probability out there that we can "measure."

There is no "objective" probability that I will throw a 6 with my next toss of a die, for example. If you use the classical method for calculating the probability of throwing a 6 (i.e., assume equal likelihood for each side), you will say the "objective" probability is 1/6. If I use the Richard von Mises relative frequency method and actually toss this particular die a thousand times in order to calculate a probability, this number may or may not equal 1/6. Which one is the "objectively true" probability?

8. You are completely missing the point of the example. Rothbard and von Mises claim that the number itself, that is, the odd of a particular boxer winning or losing, is meaningless and absurd. I am not making a claim about the particular METHOD utilized for generating the number. They would simply say that the odd thus generated is NOT a probability.

Is that what you think?

Moreover, to consider my argument only in the light of a preliminary example, without actually reading the argument itself, is completely ridiculous.

8. Sorry, I thought you were talking about a different example from a different paper of mine. Are you seriously suggesting that the casino magically comes up with the odds to balance its sportsbook? Where do the odds come from? Do these bookies and casinos just magically pick numbers out of the sky that balance the books? There is no probability involved in balancing a sportsbook?

Who's not understanding reality now?

9. Callahan used to be a libertarian and pretended to be an austrian, then ditched that for credibility and an attempt to make money. As you can tell from his nonsense comments on blogs, he is mostly just an attention whore and drama queen. He loves to be talked about, even if he has just made a fool of himself.

10. Let me get this straight, Mr. Wenzel. Is it your position that sports odds do not accurately predict the outcome of sporting events because bookies and casinos are in the business of balancing their sportsbooks?

Allow me to point out a few things about a sportsbook. First, it is true that a bookie is in the business of trying to balance his sportsbook, but his ability to do so is predicated upon his ability to accurately generate the initial odds that will balance the bets for and against. In order to do this, he must accurately forecast what the betting public will do depending upon the odds he puts out. Sometimes he's right, and sometimes he's wrong (as were many casinos during the Super Bowl).

So, while the bookie does not personally care about the outcome of the game, he has to generate a line that DOES accurately forecast the betting public's beliefs about the outcome. His odds when he is successful, in other words, are simply a distillation of the betting public's beliefs about the outcome.

Bearing all this in mind, how can you possibly criticize what I wrote?

If that is your only justification for rejecting my argument that Austrians should define probability subjectively, and for your ad hominem, then I don't think you have any right to complain about Callahan's ability to think logically.

1. You are a master at distortion. I pointed out that in your paper (http://libertarianpapers.org/articles/2009/lp-1-26.pdf) you completely misstated what casino sports books do. Allow me to quote an erroneous paragraph from your paper:
"As is well known, however, casinos and bookies do nevertheless assign numerical odds to these singular sporting
events based upon indirect evidence (e.g., common opponents, injury reports, physical conditioning of the fighters, the fighters’ ages and weights, perceived psychological advantages and disadvantages of each fighter, venue, etc.), and their odds are astoundingly accurate most of the time. Indeed, if casinos were not able to consistently generate very accurate numerical odds for these singular events, they would very quickly find themselves bankrupt and out of

This is simply wrong. Again, casinos set odds based on getting balanced money flow on both sides of a bet--so that they don't have exposure to the outcome. It has nothing to do with their views on the outcome. Indeed, if they attempted to set odds the way you indicate they should, they would be out of business pronto.

Secondly, you completely miss my point with regard to Callahan. My charge that he can never think logically is based on his own introduction of the concept of infinity, which in these cases turns the world upside down, If you fully understood my post, you would realize that I am not saying that Callahan can't think logically, but that introducing clauses such as infinity into these arguments spins every day concepts into the opposite of what they really generally mean, and the dull will fall for it as an argument.

11. First of all, you are simply wrong if you think the sportsbook manager does not take into account all of the various factors that I listed when they generate their odds. Everything that will affect the outcome of the fight will be considered, because the betting public takes these factors into account. It is not as though the sportsbook manager has a magic book that he can consult to determine what the line should be on any given fight. He has to forecast it based upon all of the relevant information that the public will take into account.

Second, my point in the paper is simply that sports odds are indeed accurate numerical predictions about future sporting events. You don't address this point at all. Rothbard and Mises would say that they are meaningless and absurd, but I would say that they are indeed numerical probabilities. You are strangely silent about this issue, which is the central argument in my paper!

Do you deem numerical sports odds to be probabilities, as I do, or are they meaningless and absurd as Rothbard and Mises say?

1. Well that's because I stopped reading after you wrote this on page 3:

"According to the brothers von Mises, however, the assignment of a numerical probability to a singular case such as a boxing match is totally inappropriate and meaningless. What are we to make of this? Are the numerical odds assigned by casinos and bookies to singular boxing matches (and other singular events and phenomena, like the 2008 presidential
election) absurd or meaningless, simply because they are not derived from long-run frequencies of 'collectives' or “classes,” as the von Mises brothers contend? "

You are making your case based on something casinos don't do (set probabilities). They adjust the odds for money flows. I am supposed to waste time and read further into the disaster?

2. I take it from your lack of response (again) that you do not want to go on the record as saying that the published odds and betting lines in your local paper are not numerical probabilities, as Rothbard and Mises would.

One thing I would like to know, and this question blows your whole argument apart here, is how a bookie could possibly generate the initial odds for a boxing match without predicting the event's outcome. How could the outcome of the event not be part of his model? Tell me that.

You are arguing that just because a bookie doesn't care who wins a fight that he does not generate a probability of who will win. This is a classic non sequitur.

3. Hey bud, Wenzel has you nailed. Lines move based on, as Wenzel says, money flows.

Odds also start based on expected money flows. You would have to be an idiot to start a line based on anything but money flows. If you got an active betting big city, the line is going to move against that direction, if its against a small city team with little betting action. Nothing to do with probabilities of outcome.

4. Tony, you do not understand the problem here at all. The problem is how do casinos generate the INITIAL odds to start taking bets. They can't start taking bets without an INITIAL line, so where does it come from. No one doubts that odds and lines can be adjusted AFTER they start taking bets, but where do the initial odds come from?

Quite obviously, the initial line is built, in part, on a forecast of who is going to win. Duh.

5. surprise, surprise you're both right. You come with a speculative forecast, pitch it with the odds and that will be answered with demand.

6. Exactly, Heath. Exactly.

Mr. Wenzel and Tony would have us believe, however, that the initial odds just fall out of the sky without the casino making a prediction of the outcome, and then the casino merely balances them.

I am surprised that Mr. Wenzel is unwilling to give the subjective interpretation for probability further consideration. If men like Nassim Taleb and myself are right that probability is subjective, this deals a mighty blow to economic modeling and inferential statistics as a "science." As Austrians, we would be in a very strong position from which to criticize all other empirical schools of economics.

12. "Thus, the Richard von Mises insight wouldn't make any important point relative to Callahan's argument."

yes a Wenzel/Callahan discussion jump to a Richard/Ludwig/Knight Probability discussion is a Non sequitur

that being said it is hard to read GC's post and not feel in some way -- he is backhand-hit-and-running the Austrian verbal communication probability method

or not -- I mean isn't he known for his intellectually superior tact -- ahem -- "I don’t know, Bob… when I wrote for LRC, my sarcasm etc. were all “heroic.” GC

the notion that GC is giving readers a mathematical thought experiment without agenda seems chance 0% which apparently means it could definitely happen -- oops

"Starts with an "s." s-swim, swamie, s-slippy, slappy, slimin, solmon, simin, sal, swenson, swanson? Maybe it's on the briefcase. Oh, yeah! It's right here. Samsonite! I was way off"