Sunday, August 22, 2010


Zeno and Proof Surrogate

Zeno, a mathematics educator (unlike Baby Huey and others members of PZ's Sierra College audience, I know the difference between a mathematician and a mathematics educator), claimed the following on his blog:

"Today we all know that the original Obama stimulus was too small. (Paul Krugman warned us at the top of his lungs, but most of us ignored him at our continuing peril.)"

As well as:

"There are two reasons for that which most sane people are able to identify: (1) the stimulus package wasn't big enough (and Paul Krugman warned us, too!)"

The fact of the matter, however, is that we all do not know that the stimulus was too small and there are plenty of sane economists who doubt it was even a good idea.

Economists Want Policy Makers to Back Off Now

Stimulus Skeptics

Fiscal policy and the burden of proof

Is Joe Biden disingenuous or misinformed?



Saturday, August 21, 2010


Today's Spiritual Thought Courtesy of Mormon Apostle Jedediah M. Grant

"I would ask you if Jehovah has not in all ages tried His people by the power of Lucifer and his associates; and on the other hand, has He not tried them and proved them by His Prophets? Did the Lord actually want Abraham to kill Isaac? Did the Prophet Joseph want every man's wife he asked for? He did not, but in that thing was the grand thread of the Priesthood developed. The grand object in view was to try the people of God, to see what was in them. If such a man of God should come to me and say, 'I want your gold and silver, or your wives,' I should say, 'Here they are, I wish I had more to give you, take all I have got.' A man who has got the Spirit of God, and the light of eternity in him, has no trouble about such matters."--Elder Jedediah M. Grant, "The Power of God and the Power of Satan" (Journal of Discourses vol. 2)

How marvelous! "Praise to the man who communed with Jehovah!" Holy Joe didn't want every man's wife he asked for, just some of them!

(Like a stopped clock, "Betty Bowers" is correct every once in a while, and she was right when she said, "Being lectured on what constitutes a traditional marriage by a Mormon is a bit like being scolded for loitering by a crack whore.")

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The casuistry of the man who would be Archon of California

"What Judge Walker's ruling means is you can sponsor a proposition, direct it, research it, work for it, raise $40 million for it, get it on a ballot, successfully campaign for it and then have no ability to defend it independently in court," said Dale Carpenter, a University of Minnesota constitutional law professor who supports same-sex marriage. "And then a judge maybe let you be the sole defender in a full-blown trial and then says, 'by the way, you never can defend this.' It just seems very unlikely to me the higher courts will buy that."

(Excerpted from here.)

The casuistry of Vaughn Walker, who fancies himself Archon of my home state, could not be more transparent. He allowed these people to defend Prop 8 but claims they don't have standing for an appeal. Granted, they did a lousy job of defending Prop 8 but the idea that SSM is mandated by the Constitution is so ludicrous that I sympathize with Cooper's claim that Prop 8 needed no defense. Archon Walker should have dismissed it; instead, he placed his seer stone in a hat* with a copy of the Constitution and located a "right" to SSM to the left of the emanation of the penumbra, written in invisible ink.

Over at Volokh Conspiracy, Orin Kerr asked SSM advocates when the Constitution began to require it. I love that question because SSM advocates come off as vapid no matter how they answer it. If they say it always has (or date it to the ratification of the 14th or some other amendment) then one can reply, "So, you know the Constitution better than the people who wrote and amended it?" If they give a recent date one can attack the legitimacy of judges conjuring "rights" out of thin air. For that, I don't think one can do better than Byron White's dissent in Moore v. City of East Cleveland:

The Judiciary, including this Court, is the most vulnerable and comes nearest to illegitimacy when it deals with judge-made constitutional law having little or no cognizable roots in the language or even the design of the Constitution. Realizing that the present construction of the Due Process Clause represents a major judicial gloss on its terms, as well as on the anticipation of the Framers, and that much of the underpinning for the broad, substantive application of the Clause disappeared in the conflict between the Executive and the Judiciary in the 1930's and 1940's, the Court should be extremely reluctant to breathe still further substantive content into the Due Process Clause so as to strike down legislation adopted by a State or city to promote its welfare. Whenever the Judiciary does so, it unavoidably preempts for itself another part of the governance of the country without express constitutional authority.

*This was originally posted to a forum populated by former Mormons.


My response to Jerry Coyne re: mathematics

On his blog, Jerry Coyne, who is supposed to be a famous evolutionary biologist, wrote the following in response to an article by Karl Gibberson titled Mathematics and the Religious Impulse:

Mathematics is, of course, a logical system invented by humans, and so has to “work”. One could equally well ask, “Why does logic work?” But if Giberson is asking, “Why does math help us understand the world?”, that seems equivalent to asking “Why does nature obey laws?” One answer is that if it didn’t, we wouldn’t be here to ask the question. But maybe I’m missing something. Yet consider this: if nature didn‘t obey laws, would we see that as evidence for no God? Of course not! In fact, the temporary and local suspension of physical law is precisely what a miracle consists of, and miracles, of course, are evidence for God. So when physical laws are obeyed, God’s working, and when they’re broken, God’s working too. Perhaps there’s some intermediate degree of lawlessness that would convince the faithful that there is no God?

My response:

Professor Coyne,

I have no doubt that you are a giant among fruit fly ejaculate researchers but you are an ignoramus concerning mathematics (and other subjects, from what I’ve observed.) Humans did not “invent” mathematics. Not even Euler, Cauchy, Gauss, or the other greats of mathematics could have “invented” the fabulous results of complex analysis. And abstract algebra was advanced without any application in mind but it turned out to be crucial for physics.

But don’t let any of that stop you from babbling about subjects you know nothing about or spinning just so yarns.



Sunday, February 14, 2010


Dunning–Kruger Award goes to FrankT

Over at Pharyngula, a pseudointellectual with "just enough of learning to misquote," FrankT, attempted to criticize Gödel's Ontological Argument, a feat which is manifestly above his intellectual (I use the word loosely in reference to him) pay grade. I have copied the cognitively-impaired poser's comments and interspersed my responses below.

There are five axioms to it, and I will bold the ones that are bullshit:

1. A quality can be uniquely positive or negative.
(fails even a cursory Buddhist or Aristotelian analysis, but moving on)

This is a textbook example of pseudoargumentation. Moreover, it is positive or non-positive. Apparently, FrankT is unaware of the concept of zero.

2. If a quality is uniquely positive, then the qualities implied by having that quality are positive.
(I think this one slides, because it's basically definitional, not that it matters because I cannot name a single uniquely positive trait)

FrankT's inability to "name a single uniquely positive trait" is not my problem, nor is it Kurt Gödel's.

3. If two qualities are positive, both qualities together are positive.
(while I like "delicious" things and "intelligent" things, I would prefer that intelligent things not be delicious)

This is just as vapid a response as the tea "counterexample" offered by a guy at the Sierra Q&A. To quote Christopher Small:

In ordinary language, we might be inclined to say that one thing is greater than another if
the former has some positive attribute that the latter lacks. We might disagree with each
other as to the ranking of things or objects according to their value, but we must inevitably
make such judgements, whether we regard them as objective or not. In view of the
ambiguity of such concepts, it is important to understand what Gödel meant by a positive
attribute. In his own words he said that the operator Pos could be interpreted in a
moral-aesthetic sense, or in the sense of pure attribution. The concept of a predicate
being positive in a moral or aesthetic sense, provides no difficulty, at least initially.
Clearly, if Fx means that x is beautiful, we would be willing to accept that F is positive
in an aesthetic sense, even if we disagree in our judgements about beauty. If Fx means
that x is virtuous, we might grant the same, even if we have no idea what virtue is. But
what is meant by “pure attribution?” By “pure attribution,” Gödel states that we are to
understand that a predicate attributes some quality to an individual, and that the quality
contains no element of “privation.”

"Deliciousness" is not a positive property in either sense. Thus, FrankT's "counterexample" falls apart.

4. All properties are uniquely positive or negative and not both.
(this one is just actually laughable, so whatever)

Yet another textbook example of pseudoargumentation from intellectually-bankrupt FrankT. Moreover, as I noted above, it is positive or non-positive. Apparently, FrankT is unaware of the concept of zero.

5. Existence is a quality that is positive.
(existing would seem to have an overall degree of positiveness equal to the overall positiveness of the thing that either did or did not exist. Something baleful like a werewolf would be more negative if it existed than if it did not exist, while something awesome like the invisible pink unicorn would be more positive if it existed. And of course, something completely inconsequential like the celestial teapot would be just as meaningless if it existed as if it didn't)

Necessary existence is a positive, you damn moron. Gödel's Ontological Argument employs modal logic.

So basically it's really easy to refute, because all of the premises are wrong. Furthermore, there is a core problem with the logic, which is that just because an infinite series summation of positive traits would, given those premises, sum to the existence of an all powerful all whatever god-thing, doesn't mean that such an infinite series ever actually starts.

Achilles catches the tortoise, because Zeno's paradox is answered by Leibnitz and Newton and the infinite series of half distances does complete and total up to a whole. But Achilles does not catch every tortoise, he just catches the ones he chases. He has to start a series before he can finish it. And there is no reason to believe that anything ever started amassing an infinite series of all possible positive traits, even if there was such a thing.

Now, the Ontological Argument goes that basically by imagining the collection of all possible positive traits that you have in fact started that process - that your very own hubris is Achilles and that when you catch the tortoise it will be an omnipotent god. That is a level of solipsism and hubris that defies ready comprehension. But you can see why it might have appealed to St. Anselm, Leibnitz, and Kurt Gödel. Because they were all whack jobs who spent all their time thinking about infinity.


The fact that the Ontological argument is a total failure has little to do with the fact that it uses modalities. It's that both the premises and the logical chain after it are wrong. Perfectly valid attacks against it include attacking virtually any of the premises. But also the fact that infinite series summation just doesn't work that way. Convergent series reach conclusion and give real answers. But divergent ones don't. In the real universe there are no infinitely large rocks, infinitely large amounts of energy, infinitely large spaces, or infinitely powerful forces. Everything, even amongst the really stupidly large things, is finite.

So if someone has a series that includes infinite power or infinite anything else, then that series by definition never completes. So since it never finishes acquiring all the traits, there's no reason to believe it ever acquires "existence" either.

This is the most moronic part of an exceedingly moronic screed. So moronic, in fact, that it is not even wrong. (Yet, FrankT was still able to hoodwink a number of dupes over at Pharyngula, which speaks volumes.) First of all, Anselm, Leibniz, and Gödel were great thinkers, not "whack jobs," and it is offensive to see them labeled as such by FrankT, a noxious mediocrity. Moreover, an "infinite series summation" doesn't enter into it. Axiom 3 (as listed by FrankT, which follows the presentation on wikipedia) simply states that if p1, p2, ..., pn are positive then the collection, i.e.,
p1 AND p2...AND pn is positive. There is no infinite sum here.

Now, if we were talking about probability (we're not) and we looked at the probability of p1 AND p2 ... AND pn, i.e., the intersection (for the sake of argument treating the pk's as events, which they aren't), then we would have an infinite product of probabilities as n approached infinity provided the pk's were independent (again, treating the pk's as events, which is not the case). Even that stretch does not give an infinite sum, though. To arrive at an infinite sum, you would have to look at the probability of p1 OR p2...OR pn, i.e., the union of the pk's, which would be an infinite sum of probabilities as n approached infinity provided the pk's were mutually exclusive.

However, we are not dealing with probability and even if we were, the closest analog is an infinite product, not an infinite sum. (Incidentally, both the infinite product and the infinite sum I mentioned would fall in the interval [0, 1]). How this brain-dead pharyngulite came to associate Gödel's Ontological Argument with an "infinite series summation" is beyond me.

Incidentally, for those readers who do not know the difference between independent and mutually exclusive events, I recommend the following video I posted to youtube a couple of years ago.

And while Kurt Gödel ended his life of starvation because he was mortally afraid of being poisoned and would not eat unless his wife prechewed his food to assure him that it had not been poisoned, he was very good at thinking about infinity when he wasn't waiting for his wife to get out of the hospital so that he could eat again.


Which is why I was so surprised that our creationist friend stood up and said that his best argument for a god was Gödel's ontological proof. Because that one is a set of magic words written by a crazy man after he started wasting away into madness. That's like saying that your best argument for something is the last mad scratchings of Dr. Herbert West.

This is a low-blow but one I would associate with a mind of FrankT's caliber. Not only that, but it competes with his "infinite series" nonsense on the scale of utter stupidity. Kurt Gödel formulated his ontological argument long before he started suffering from paranoia and even if that were not the case, there is no reason to believe it would have adversely affected his mathematical work. The fact of the matter is that Gödel was far, far more intelligent and competent in his final days than FrankT could ever hope to be on his best day.

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Sunday, January 31, 2010


Stirring the hornet's nest part II

In response to bogus claims from the audience that Gödel's Ontological Argument is circular, I articulated the most basic form a premise would take in modal logic (related to the topic at hand), i.e., if God exists, then he exists necessarily. The audience, in unison, shouting back "IF God exists..." to which I replied, "YES IF, that's the form mathematical arguments take. In mathematics we define an object and then seek to prove it exists." I was trying to show them that a premise of the form "If P then necessarily P" is legitimate and not "circular." The following is excerpted from this article:

"If God exists, then it is necessary that he exists."

In this example, "necessary" has narrow scope, that is, its scope is restricted to the proposition's consequent, rather than the whole proposition. The proposition claims that if God does in fact exist, then His existence is a necessary one. This is a special claim about God which is not true of other things; for instance, it is thankfully not the case that if Osama bin Laden exists then he necessarily exists. If the scope of the modality were broad, then the proposition would say that it is necessarily the case that if God exists then He exists. While this is true, it is true of everything including Osama bin Laden.

In these two examples it is clear what the scope of the modality is, but in other sentences it is not clear whether the modality has a broad or narrow scope. The modal scope fallacy occurs when this amphiboly is exploited.

The audience was hopeless, however, and accused me of being an obtuse creationist. I refer the interested reader to my previous comments on Dawkins' fan club, wherein I combat similar inanity. Also, I refer the interested reader here for what a mathematician (i.e., "Tarski") who publishes research and does not accept Gödel's Ontological Argument wrote in response to an pretentious atheist who was similarly clueless in asserting that the argument is transparently circular.

"Tarski" in brief:

There is a difference between saying that Gödel just simplemindedly begged the question and recognizing that not only do we usually take truths in axiomatic system to be based on the assumed truth of the axioms, it is also the case that the ontology of the entities derived in existential proofs must lean on the ontology of the axioms in some way also; but this seems tricky to me.

This type of thing does not interfere with the work of (most) mathematicians and scientists.

To be continued...

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Stirring the hornet's nest part I

The question I posed to PZ was:

"In your own words, your contributions to science are piddling. [Those are your words, not mine. I just happen to agree with them.] To that I would add that your arguments against God are just as risible as those of Dawkins and the other occupants of the new atheist clown car. Given that, why should anyone who is not already one of your chamchas pay attention to you as opposed to others who are far more accomplished and rational?"

(I added the bracketed part upon hearing a feral growl from the audience.)

PZ responded by trying to dismiss me as a creationist. Now, I don't mind being labeled a creationist, provided it is understood that I accept that the age of the earth is measured in billions of years and that I am not solicitous about the historicity of anyone before Abraham. However, my question/challenge to PZ had nothing to do with creationism, except in the broadest sense of someone who thinks God created life (somehow). I interjected that my question had nothing to do with creationism and PZ replied that his talk was about creationism. (Except the last slide was about atheism, not creationism, and that was the slide to which I was responding.) PZ then claimed I used a creationist tactic by quote-mining him in that I did not include his caveat about most (all?) individual scientific contributions being piddling. (I'll let the reader judge whether I quote-mined PZ.)

PZ then asked me which arguments for God I accepted/endorsed. I mentioned Gödel's Ontological Argument and then he adroitly turned the tables on me by asking me to defend it. Now, I was prepared to address some of PZ and others' anemic/fallacious arguments against/misrepresentations of theistic arguments but I was not prepared to defend Gödel's Ontological Argument. To adequately defend it I would needed worked out notes and access to a white board at center stage. It was essentially impossible for me to argue for it unprepared and from a seat in the audience, and I started to say as much, but I was egged on by PZ and essentially told to "put up or shut up" by a rude, corpulent chin-beard dressed in black (whose volubility was inversely proportional to his knowledge.)

Now, I'm anxious even when teaching my own class. (Although, it typically subsides as the class progresses.) However, despite my anxiety, I tried to articulate that God has every positive property necessarily and that necessary existence is a positive property.

However, at this point the audience started complaining. Zeno (a mathematics instructor at a CC in Northern CA) objected that it wasn't really a proof. I thought he was claiming that no such argument from Gödel existed, so I objected. (He later clarified that he disputed that it was a real proof, not that it existed.) Zeno and the audience made much of the fact that I described myself as a statistician, but I have a bachelors in mathematics, and even though I studied statistics in grad school, I've had graduate level mathematics courses and my advanced degree is from a mathematics department.

PZ, like his friend Dawkins, dismissed Gödel's Ontological Argument as a word game, a philosophy instructor at Sierra said "You've packed 'existence' into the very definition of God, and so your argument is circular" and some dude up front said something about thinking a certain tea was positive but that his friend did not, thereby claiming to establish the subjectivity of positivity and "refuting" the argument. This was followed up by someone in the back (sitting next to Heidi) saying "moral relativism for the win!" (The same guy also asserted that Gödel's Ontological Argument was "bullocks.")

To be continued...

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Friday, January 29, 2010


What a Long Strange Trip It Has Been...

My preliminary thoughts:

I did not expect to end up spending the night with PZ Myers. I also did not expect to be asked to defend Kurt Gödel's Ontological Argument, which I was unprepared to do. (Although, even if I were prepared, I do not think I could have done it justice as a critical respondent among an, umm, unsympathetic audience.) I give credit to PZ for unexpectedly turning the tables and essentially catching me flat-footed; it won't happen again.

Anyway, I met some nice people and I am glad I went to BJ's with the group afterward (PZ graciously invited me) because I met Mr. D, with whom I really enjoyed reminiscing about a high school where he taught and I was a student.

I will write more later.

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Wednesday, January 27, 2010


God and the fundamental physical constants

As far as I know, there is no reason to believe the values of the physical constants are necessary, in which case, we have the following likelihood ratio:

P(physical constants and the universe in which we exist|God)/P(physical constants and the universe in which we exist|no God) =

P(physical constants|God)P(the universe in which we exist|physical constants and God)/
P(physical constants|no God)P(the universe in which we exist|physical constants and no God)

Now, P(the universe in which we exist|physical constants and God)/P(the universe in which we exist|physical constants and no God) is essentially one since it does not seem likely that our universe depends on whether the physical constants we observe arose by design or not. Therefore, the likelihood ratio takes the form:

P(physical constants|God)/
P(physical constants|no God)

which I argue is large since it is easy to conceive of God wishing to create a particular universe and choosing the appropriate values of the physical constants whereas a random selection would be very unlikely to achieve the correct values.

Incidentally, I "borrowed" this argument from David Bartholomew's article, "Probability, Statistics and Theology." (Journal of the Royal Statistical Society. Vol. 151, No. 1
1988, pp. 137-178)

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Friday, December 12, 2008


More evidence that Mormonism is a fraud

As if more evidence were required.

Reassessing authorship of the Book of Mormon using delta and nearest shrunken centroid classification

I would like to perform statistical analyses on the Book of Mormon myself but I have not yet gotten around to it. Anyway, it is a good article and I recommend it.

(via Bart on Folk of the Fringe)

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