Uncertainty Principle: Intrinsic Property or Measurement Effect?

At last night's Saint Louis Skeptics in the Pub, the conversation came---as it always must---to physics. Saint Gasoline and unBeguiled wanted to know whether the position-momentum uncertainty principle is a real property of a quantum particle, or simply a limitation of our ability to measure both the position and momentum of quantum particles. I guess, even more strongly than "they wanted to know," they were arguing for the latter, more intuitive answer.

As an example of the kind of thinking they argued for, take this quote from the Wikipedia article on the uncertainty principle:

Heisenberg's microscope
One way in which Heisenberg originally argued for the uncertainty principle is by using an imaginary microscope as a measuring device. He imagines an experimenter trying to measure the position and momentum of an electron by shooting a photon at it.
If the photon has a short wavelength, and therefore a large momentum, the position can be measured accurately. But the photon scatters in a random direction, transferring a large and uncertain amount of momentum to the electron. If the photon has a long wavelength and low momentum, the collision doesn't disturb the electron's momentum very much, but the scattering will reveal its position only vaguely.
If a large aperture is used for the microscope, the electron's location can be well resolved (see Rayleigh criterion); but by the principle of conservation of momentum, the transverse momentum of the incoming photon and hence the new momentum of the electron resolves poorly. If a small aperture is used, the accuracy of the two resolutions is the other way around.
The trade-offs imply that no matter what photon wavelength and aperture size are used, the product of the uncertainty in measured position and measured momentum is greater than or equal to a lower bound, which is up to a small numerical factor equal to Planck's constant.

Now, I don't think this thinking is exactly wrong. I mean, if one constructed this experiment I don't doubt that it would validate the results predicted by the uncertainty principle. However, I think the model behind it is flawed. What we imagine in this gedankenexperiment is a little ball that is the electron being hit by a little ball that is the photon and the two bouncing off each other.

What this sort of explanation ignores is the fact that matter behaves as a wave.

I may need to do some argumentation to convince you (specifically Dustin) that matter waves aren't just a mathematical convenience for calculations but are, in fact, the actual nature of matter. If I need to do that, I'll do it later. Today is not the day to explain matter waves. Here, though, is a very quick argument: we know ordinary waves (water, sound, etc.) do certain things like reflection and refraction and interference and whatever. Some of those things are done only by waves and nothing else. We see quantum particles doing those same things. Here's a handy chart.

So let's simply accept for now that electrons are, in almost all circumstances, wavelike. I think we all have heard many times that quantum particles are both particulate and wavelike at times, and might take it for granted. We sort of skip over the fact that electrons are waves without really understanding what that implies, so let's investigate. This will involve a little math, but stick with me. It shouldn't be that bad.



Let us assume the electron has as its wavefunction pretty much the simplest wave you can get, a sine wave. This is a periodic function, which means that if you are at any point and you move some special distance away, everything about the function will look the same. This distance is called the wavelength, denoted by lambda. There is a relationship between wavelength and momentum called the de Broglie relation, which says momentum is equal to Planck's constant divided by wavelength.

p = \frac{h}{\lambda}

So for an electron with a sine wavefunction, we know it has a definite momentum.

What about position? To find the position of the electron, we need to square the wavefunction and integrate it over all space. (Don't worry, I won't make you sit through that.) When we do that with a sine, the result we get is meaningless. It says there is a smeared out probability to find the electron everywhere, and no place is more probable than any other. Thus there is no helpful position information we can get out of this wavefunction.

This is all summarized nicely in this picture I stole.

To make some kind of meaningful statement about position, then, the electron can't be in a state with a wavefunction that is just a sine wave. What we can do is make a "wave packet" by adding together a few different sine waves. If we pick the wavelengths and amplitudes properly, we should be able to get a decently localized position. However, by adding together different sine waves we have introduced more than one wavelength. With more than one wavelength we don't know exactly what the momentum is. Again, I stole a picture.

Now, looking over this example I gave, is this a measurement effect? Most emphatically NO. If you know the momentum exactly, it is not the case that you just can't measure the position, but the idea of position doesn't even make sense. Look back at that youtube video I posted. That is a wave with a well-defined wavelength, and therefore a well-defined momentum. I ask you: where is that wave? Is that wave in a particular place? At a particular position? No it is not. The wave is spread out over all space. If the wave had a less-precise momentum, as in perhaps there are several waves of different wavelength added together, we would see waves only in some constrained area and there would be no waves outside that area. In that case, it is meaningful to say that the wave is in a particular place, because it is localized to an area.

If we accept that matter actually has wave properties (and this is well-established both theoretically and experimentally, but perhaps that's a topic for another day), the uncertainly between position and momentum comes as an immediate consequence. By virtue of how position and momentum are defined, they are not completely compatible. This incompatibility has nothing to do with what you can measure. It has to do, as I outlined here, with what the concepts of position and momentum mean when applied to waves.

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What's Wrong About Physics Today? All of It!

Via my new favorite website, crank.net, I've found a treasure trove of physics denial. Typically we'll see relativity denial or abuse of quantum mechanics to serve whatever ideology you choose. But unless one is going for Neal Adams level crankery, one keeps the denial to a few topics.

Not this guy.

For pretty much any physics concept a layperson would know, and a lot they wouldn't, this guy has a refutation. He covers all the common ones, of course. Relativity, quantum mechanics, the big bang, etc.

But we also see a few surprises. For instance, the author attempts to explain away Maxwell's equations, lasers, the Boltzmann distribution, even energy conservation. How does he do? Well, since the site is too long for an exhaustive analysis, I'll pick apart a few examples.

Curved Space: The concept of a 'curved space', which is essential for present cosmological models, is logically flawed because space can only be defined by the distance between two objects, which is however by definition always given by a straight line.

Ah, circular reasoning at its best. Why can't curved space exist? Because distances between objects are straight lines. Why are distances between objects straight lines? Because space is flat, not curved.

The shortest distances between objects—geodesics—are straight lines only in Euclidean geometry. Since we can measure that the shortest path for light is not a straight line when passing a massive object, we know that matter curves space.

Gravitation: Modern theories of gravitation assume that the gravitational force between two masses is not an instantaneous interaction but is communicated by field quanta (gravitons) moving with the speed of light. However, this model can be shown to result in different forces in different inertial systems and contradicts therefore the definition of a force. [Emphasis mine]

Sorry, guy. You need to show your work.

Schrödinger Equation: Present day Quantum Theory has been developed from the original observation that radiation emitted by an atom appears in the form of discrete spectral lines. The Schrodinger Equation could reproduce this theoretically by postulating a wave equation for the atom which yields only certain energy values as a solution. The associated wave functions are continuous functions in space and therewith do not allow to exactly specify the location of atomic electrons. This has led to the interpretation that electrons as such do not exist as localized particles within the atom but only as some diffuse 'cloud' or even only as mathematical objects. This assumption however is an unallowed generalization of the Schrodinger Equation which strictly makes sense only if applied to radiative transitions. The actual (classical) location of the electron is completely unrelated to the wave functions of the radiative states (apart from a statistical connection) and any non-radiative physical effects (e.g. elastic atomic collisions) can therefore be calculated by the principles of classical physics without any logical contradictions.

Many of the wider applications of the Schrödinger Equation are therefore completely unfounded and inadequate.

Never mind that quantum mechanics as formulated by the Schrödinger equation accurately predicts the results of experiments. Never mind that the classical picture of the electron doesn't, and in fact quantum mechanics solved outstanding problems in the classical model. Never you mind those things, because they're not allowed.

In fact, while the Schrödinger equation was written to reproduce the spectral emissions of hydrogen, it can be applied to innumerable systems. And why shouldn't it? It's a differential equation that describes how a quantum system evolves in time and space. One supplies a few parameters of the problem at hand and—ideally—solves for the behavior at all future times. It would be really strange if a completely different differential equation were required for every different situation. It's not inconceivable, though. Know how we tell? Experiments, that's how. And quantum mechanics, through the Schrödinger equation, is great at predicting the outcome of experiments.

How well did he do? I'm not impressed. Obviously he fails as a scientist because he substitutes (crappy) argument for evidence. But he does pretty well as a crank; he's very ambitious to say the least.

However, I've given you merely a slice of what's contained within. I encourage you to go to the site. Perhaps you'll find something I missed that makes all his arguments hang together.

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Physical Theory of Subjective Mental States... or Not

Today I'll be reviewing "Towards a Physical Theory of Subjective Mental States" by Sean Lee. This marks my first entry on a physics journal article. ...You can stop cheering now. I've been looking for something I can post to use the BPR3 icon and, sadly, this isn't it. As you may have noticed from the above link, I found it on arXiv, so it doesn't satisfy the "peer-reviewed" criterion of the BPR3. And, even though I said it's a physics article, it doesn't really have anything to do with... well, let me not get ahead of myself.

The paper has been submitted to the physics-meets-philosophy journal Foundations of Physics. I don't know if this article will actually appear in the journal, as I am not sure what sorts of articles they take. I do have a new respect for the editor, Gerardus 't Hooft, based on this quote from the journal's homepage:

We receive numerous submissions from people who venture to attack the most basic premises of theories such as Special Relativity, but instead only succeed in displaying a lack of professional insight in how a physical theory is constructed. I suspect that some of these people may have been working somewhere in an attic, deprived from daylight for decades, determined only to reemerge with a Theory of Everything in their hands.

Scathing.

Anyway, "Towards a Physical Theory..." begins by introducing the hard problem of consciousness. In short, neuroscientists can, in principle, explain all the steps involved in the process of a stimulus to a person (say, a rock falling on one's foot) causing a response (for instance, jumping up and down, yelping) using nothing but physical interactions (neurons relay pain signals, we rub the area to stimulate non-pain receptors, we jump to shift weight to the other foot, etc.). I don't mean to say that they can explain every step now, but extrapolating into the future, it is reasonable to say they will be able to in the future. However, they cannot yet, and may never be able to, explain why we feel something (i.e. why the rock hurts one's foot). Currently we cannot explain first-person subjective experiences. Or, at least, that's what Sean Lee claims (not that I'm challenging that claim, I just haven't checked it out thoroughly). The activity of the brain is necessary and sufficient to cause mental phenomena, but we're not sure how "Neural Correlates of Consciousness," as they are called, produce subjective experiences.

In order to probe the barrier between the brain states and the mental states, Sean defines a mapping.

Within the context of a physical science, [the assumption that subjective states correlate to physical states] translates into requiring an unambiguous mapping M between whatever is identified as the space of physical states P with whatever is identified as the space of subjective states Q. We'll call this rather underappreciated assumption the mapping principle
M: Q→P

What is this mapping? What are the details? Lee doesn't seem to care much.

That is, the mere claim that subjectivity is at least correlated with physical states implies the existence of a well-defined mapping between the two.

In fact, Lee not only doesn't care what M is, he doesn't care about P either. P can be whatever you want, just some sort of physical description of the brain's state. With infinite precision.

States in P would [in a classical theory] be given by the distributions, momenta, and valences of all semi-classical atoms within and near the organism (by the generally presumed chain of supervenience, this entails all the understood rules of thermodynamics, chemistry, biochemistry, cell biology and the like). ...in principle a purely quantum mechanical description of the physical state should be at least equally valid (if not manifestly illuminating). In this case P might be considered to be a space of state vectors |Ψ>, or perhaps alternatively, a relevant subset of measured observables {O₁, O₂,... O_N}.

This sounds to me, if not an actual violation of the uncertainty principle, at least absurdly impractical. Knowing the state of every cell in the brain is completely implausible; knowing the position and momentum of each atom in any one cell is literally impossible. Trying to combine the two is simply laughable. It doesn't matter to Lee that these ps within space P can never be found, only that they are in principle mappable to the real numbers. Whatever. Moving right along.

The real problem for this paper (as if knowing complete information about the brain wasn't problem enough) is trying to find q, a subjective state within space Q of subjective states. You see, there's nothing we can measure to find q. After all, anything that can be measured is physical, thus those measurements provide information about p, the physical state. So how do we get information about q?

The inherently private nature of subjectivity forces us to accept that any operationally meaningful coding must be done by the experiencing subject. [emphasis original]

Wait, what?

Thus we come to the uncomfortable first conclusion that any meaningful operational definition that might rise to the standard of a science of subjectivity can only be given for a very limited number of subjects; namely for those that are willing and able to communicate with scientists!

No, you don't really mean—

In the case of subjectivity, however, the only relevant, operationally definable data that is accessible are from subjects possessing high-level language skills that are communicable to scientists.

Yes, Sean has done it. His method of "measuring" the mental state is to ask someone what their mental state is. He's pushed this completely out of the realm of any kind of scientific rigor and into anecdoteland. It gets better, though.

Not only does Lee remove his experiment from the realm of falsifiability, he sweeps away replication. He constructs a thought experiment in which a future scientist can induce a certain brain state in a subject, then performs the previously mentioned asking in order to collect "data" on the subjective state. However, once wouldn't be enough.

This pairing [of brain state and mental state] may be confirmed by repeatedly generating the state p₀, each time immediately afterwards asking the subject:

'Are you certain that your experience now is any different than just a moment ago?' [emphasis original]

"Yeah, doc, it's different. Now I'm annoyed with you."

The procedure he outlines here is unable to collect real non-anecdotal data in the first place, but the attempt at replication and averaging introduces a new, constantly changing stimulus to the subject. As he asks the subject more and more times if his or her mental state is exactly the same as before, the experiment will be increasingly annoying and frustrating his subjects.

Non-objective (though I guess that was implied by the name "subjective state"), non-reproducible, non-falsifiable, this scheme has absolutely nothing going for it. The subject being studied is presumably supposed to say things like, "I feel hungry. This seat is a bit uncomfortable. I just farted, so I'm smelling that. You're standing too close and I'm getting creeped out." What about the innumerable other things the subject is thinking and can't put into words? What about the lag time between thinking and speaking? What about the fact that searching around for words to describe thoughts is a thought, and one that will probably not be mentioned without infinite regress?

Most importantly of all, what if your subject is lying, or even just keeping things from you? Perhaps he or she has just been cheated on by a spouse and doesn't want to talk about it, but that thought is constantly going through his or her mind. Perhaps he or she is uncertain about the future, but doesn't want to mention it to some jerk scientist. Maybe, just maybe, your subject doesn't care about your experimental protocol and will make up any old "mental state" just to screw around with your results. For all you know every test subject could be doing that. That's because this isn't science. There is absolutely no way to accurately obtain any data. You're relying on pure anecdote.

I hope I don't sound disrespectful; I don't mean to come off that way. I applaud any effort to investigate the nature of subjectivity empirically. However, I don't think the method described in this paper is worth our time. Truth be told, I don't think there is a method in this paper, just a collection of musings on what such a method might possibly look like. But I guess that's what I get for trawling arXiv for any paper that floats my way.

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Self Contradictions from Sal Cordova

After a nice vacation, creationist Sal Cordova has posted a few new articles on his blog Young Cosmos. He takes ad hominem potshots at PZ Myers and writes meaningless arguments from authority (here and here). There is a little fun, though, when he waxes philosophical on a young vs. old universe and makes claims about what would prove ID true.

Sal says that in his recent modern physics class he "went through the major experiments which led to the development of modern physics." That's good; that's what a physics class should teach a student. He also says

My experience in class only reinforces the fact that the claim that “Darwin’s theory is the central theory of science” is a falsehood promoted by Darwin’s followers. It has no basis in truth.

Hmm, I don't really think he learned that in his modern physics class. I think it's much more likely that the class made zero mention of Darwin or evolution and Sal's confirmation bias twisted that actual class discussion into support of his evolution denial.

We also see that, while Sal may be a good student of science history and facts, he hasn't absorbed the methods of science

An assumption of Einstein’s relativity is that the speed of light is constant. If we accept Einstein’s theory as is, or even Maxwell’s equations as is, then the cosmos must be old and not young. Accepting an old cosmos was not a problem for me in class, because the assumption of an old cosmos is reasonable (unlike Darwin’s ridiculous idea that Darwinian processes can evolve a fish into a bird, and a cow into a whale).

I can accept old-earth ideas as a working hypothesis. However, if Einstien’s theory and Maxwell’s equations can be amended to allow temporal-spatial variations of the speed of light, then various YEC cosmologies can succeed without being inconsistent with present operational physics. I look forward to exploring the possibility of variable speed of light (VSL) and will blog on developments in VSL periodically…..

In effect, he says he'll accept scientific facts until he can get a degree, then cherry-pick evidence to support his discredited pet hypothesis. Sal presents himself as being open to whatever comes out of his "exploration," but typically people do not name their blogs after ideas that they're ambivalent towards [hint, it's named Young Cosmos].

There is more evidence of ideological bias and a blatant false dichotomy in the final paragraph.

I can, as a Christian, accept an old cosmos if that’s the way it really is. However, if the universe is young, and if a VSL cosmology succeeds, it will not only prove ID, but also special creation. It will also strongly suggest the Intelligent Designer is the Christian God. It will affirm the geneology of Jesus Christ in Luke chapter 3. I pray that if the Cosmos is Young, God will help the search for evidence along those lines.

Sorry, Sal. Even if there is evidence that the speed of light can change, that says zip zero zilch about ID. Any theory must stand or fall on its own merits and evidence, and ID has nothing behind it. It cannot just ride the coattails of a possible but improbable idea in an unrelated field. And under what tortured logic could a variable speed of light support the existence of a particular god? What does that have to do with the family tree of one organism out of trillions on one planet around one star out of millions in one galaxy out of billions? I think Sal has delusions of grandeur about his delusions.

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Another Post re: Sal Cordova

I really wasn't going to write about Sal Cordova's latest misunderstanding of quantum mechanics. Even though it's a long article, there didn't seem to be enough there to give me anything of substance to write about. But thanks to Blake Stacey's comment on my last post on Sal Cordova showing me that Tyler DiPietro had written a bit about the new post, I had enough to go on.

Remember this equation from before? It was never explained what any of this means. In Sal's recent article, we get something almost a little like mathematical information about the equation.

Sal writes,

That conceptual merging of all quantum systems is represented by the quantum system of the universe, or (for lack of a better term), the Universal Wave Function. Taking the Schrodinger equation and generalizing it for the entire universe, we have the universal wave function as derived by Barrow and Tipler: [picture] where the indexed Psi’s are the individual quantum systems, and the O’s are the “observations."

There is zero probability that Sal didn't just copy that out of a book. Why else would he capitalize "Universal Wave Function"? Does he know what a wave function is? Does he know what "observation" means? I sure don't, not in this context anyway.

Let's analyze this equation for a bit. Why would you multiply a wave function with this "observation"? Why sum them up? In fact, every time we see an index i we see a k, yet i and k are summed separately. Why? The product is over n, yet n only appears in the "observation." Why? What are these indices supposed to mean? What does any of this mean? Perhaps Sal should understand that math doesn't just pop out of nowhere like a child's birthday magic show: it needs to be derived. And preferably explained.

Sal then cites a respectable, peer-reviewed geocities page when he says, "Jenny Nielsen explains this beautifully in A Report on 'The Delayed Choice Experiment'.” Wait, did I say "cites"? I meant "reproduces the entire article."

For physically actualized systems, it appears then a measurement is essential for the system to be actualized.

I can only infer from this that Sal thinks before humans were around measuring everything, nothing in the universe is "actualized." When we're not looking, everything ceases to be.

For example, we see measurements defining the boundary conditions of a quantum system such as illustrated by the Nobel Prize winning experiment known as Stern Gerlach.

The Stern-Gerlach experiment has nothing to do with measurement, and everything to do with demonstrating spin. Well, I guess it does trivially have to do with measurement, as one needs to measure something to get any information from the experiment. However, I can assure you, the Stern-Gerlach experiment would run the same way whether someone was watching or not. The point of the experiment is that there is an intrinsic angular momentum to the electron and that it is quantized.

[John Barrow and Frank Tipler's book Anthropic Cosmological Principle] was hailed by the prestigious scientific journal Nature. However, in 1996, when Tipler came forward and said the “Ultimate Observer” was to be identified with the Judeo-Christian God, Tipler’s ideas were immediately ridiculed and his pay was cut.

In fact, I've found the review in question. But my university's online subscription to Nature only goes back to 01-01-87, and this article was published on 08-14-86. So close. I'll have to go to the library and track it down later.

In a comment on Tyler's article, Blake Stacey writes about a different review of Tipler.

Actually, a review of Tipler's Physics of Immortality, published in Nature, called that book "a masterpiece of pseudoscience ... the product of a fertile and creative imagination unhampered by the normal constraints of scientific and philosophical discipline". It's funny Cordova doesn't mention that review, isn't it?

So, another day, another butchering of quantum mechanics. Expect another soon enough.

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In Which I Take on a Long Commitment

Once again I come late to the party, and if you want to be well versed in this subject you might have to read all the backstory. And, to paraphrase Colin Meloy, as I tell this sorry tale / in harrowing detail / its hollowness will haunt you. Sorry about that.

Here we go. First, a little history, courtesy of Mark Chu-Carroll at Good Math, Bad Math. Sal Cordova used to blog over at the ID mecca Uncommon Descent.

Not too long after that, Sal made a fairly big deal about the fact that he was returning to grad school, and had to stop blogging at UD because the dastardly darwinists would damage his academic prospects if he continued. He played the standard creationist-martyr role, poor guy, persecuted by all the horrible non-believers. Naturally, it didn't last long. He's got his own blog now, called "Young Cosmos", where he writes his usually pathetic quote-mining, plus what he calls "Advanced creation science".

Enough history. Sal wrote a post entitled "Fundamental Theorems of Intelligent Design". He proceeds to not tell the reader what these theorems are. What a letdown. He does post a few equations, however. ...or, he sort of does. I'll show you.

This is the first equation. Looks really pretty, doesn't it? Do you want to know what it means? Me too! Sal doesn't tell us diddly about what this equation means, save that it was "derived by the renowned physicists John Barrow a (sic) Frank Tipler from Schrodinger’s equation of quantum mechanics." Wow. That's sexy.

We have less information about the second equation. Sal provides a reference, saying it's on page 25 of a PDF he links. Well, there are several not-numbered equations on page 25 of that PDF with very little explanation.

The reader is left wondering what this means. Sal won't leave you hanging, though! He says, "The exploration of these fundamental theorems will take a year’s worth of blogging. They make feasible the theory of ID, and a theory of ID leads to the possiblity of theories of special creation, which make possible theories of a young cosmos."

Sal posted a second article, "Fourier Transform and Schrodinger’s Equation part I", which starts with

Various theories of Intelligent Design and Advanced Creation Science depend heavily on Schrodinger’s equation of Quantum Mechanics [as I pointed out in Fundamental Theorems of ID].

Thus it makes sense to cover a little bit about Schrodinger’s equation over several threads and hopefully after some lenghty derivations, I can connect basic physics to theories of ID and Advanced Creation Science.. To my surprise, I discovered there is a relationship of Schrodinger’s equation in physics to the Fourier Transform of math and Electrical Engineering.

I hope Sal isn't reading anything of significance into this. A lot of fields study waves, which are governed by second-order differential equations. If the solutions to these equations are periodic, Fourier series (and their associated transforms) are a great way to go. They simplify a second-order differential equation into a simple quadratic equation. So most kinds of wave motion can be made simpler by Fourier series. There is certainly nothing of cosmic significance to this, it just means Fourier came up with a great tool that a lot of people use.

A few bloggers picked up on this story, including Blake Stacey of Science After Sunclipse, Tyler DiPietro, and the aforementioned Mark Chu-Carroll. Then PZ Myers at Pharyngula passed on the links, which is where I found it all. Like I said, late to the party.

Sal's put up one more post since then, "Schrodinger vs. Darwin". As pathetic as the other two articles have been, this one takes the cake. The thesis is, in a nutshell, "Schrodinger is a real scientist and Darwin isn't because Schrodinger could do math and Darwin couldn't!" I'm not kidding.

Several ad hominems and non sequiturs follow.

Ironically the Darwinists are whining that the US is falling behind in math and engineering education and that if we don’t teach more Darwinism, the country will fail. Acually, it is apparent from Darwin’s own writings we should not follow in Darwin’s footsteps if we wish the USA to excell (sic) in math and engineering.

The nation will advance in science and engineering if more students understand the Schrodinger’s work than that of the math-challenged puppy beater, Charles Darwin…..

Wow. I'm pretty sure no one wants kids to learn evolution to be better at math. I was thinking maybe it would be about biology. Biology, as a science, doesn't always involve math. It doesn't necessarily have to. Living things are incredibly complex, so simple math can't always fit their behavior. A science doesn't have to be as mathematical as physics to make testable predictions that hold up under evidence. Biology does, ID doesn't. The end.

And as to the puppy-beating, PZ has something to say about that.

I plan to stick with this sideshow series Sal is posting. Someone has to. Hopefully he'll eventually write something that needs a physicist to take apart, rather than the collections of fallacies and quote-mines we've seen so far. And, to be completely fair, he may actually say something of scientific worth. I'll present you the evidence as it comes.

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UPDATE: More ad hominems from Sal's new post. He can't get over the fact that Darwin once said he was bad at algebra.

Also, Blake Stacey has another example from last June of Sal attributing evidence for ID to his misunderstanding of physics.

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