Now I know how Hercules must have felt. Like the mythical hydra, you slap down one relativity denialist, and two more pop up in his place. In my case, one appeared as a comment on my blog (filtered as spam – I have a wise filter), and another appeared as spam email in my work mailbox. I haven’t looked at the latter one yet, and will post on it later, if entertaining enough, but let’s take a look at our commenter, John Ryskamp (after the fold; it’s loooooong)…

Well, according to your definition, Einstein would not be a “good scientist.” I don’t think you understand the mathematical point of view Einstein used in constructing the relativity of simultaneity. Doubtless you have heard of his notion of “practical geometry,” but I don’t think you understand anything about natural mathematics, of which it is an expression. If you want to understand that better, you should read P. Maddy, Naturalism in Mathematics.

Natural mathematicians do not believe that logical content in argumentation is possible. They believe any attempt to achieve it ends in paradox. This is an extremely old view, going back to Artistotle’s concern with Zeno’s “paradox.”

I use quotes because all paradoxes are constantly criticized as to whether they have any logical content. That is, they seem to be compelling, but is the compulsion we feel actually an artifact of the way they are constructed, or are the misgivings they convey actually the product of internal consistency in their terms?

In any event, natural mathematicians feel that in order to avoid paradox, it is necessary to arbitrarily insert in every argument the idea that mathematics is an inherent human function. This avoids paradox, at the cost of logical content. That’s the way they feel.

Einstein felt the same way. He got a megadose of natural mathematics from Poincare’s Science and Hypothesis, although natural mathematics is so much a part of western intellectual life that it seems only to have confirmed his predisposition, gathered from his whole educational experience on this subject.

You are vain and ignorant, like all physicists. You want to think that relativity is an internally consistent argument. You want to think that you would never sign off on any point of view as stupid as natural mathematics, because you insist on a standard of internal consistency in your arguments. You think that Einstein is like you, that surely he strove for internal consistency in his argument.

You are wrong. Einstein was a natural mathematician, and he made sure that relativity followed the natural mathematics line. The only question has been: where did he do it? At what precise stage of the argument did he introduce natural mathematics into relativity, thereby depriving it of logical content?

He did it when he introduced the concept of “natural” coincidence, which he did implicitly in the 1905 paper. He did it explicitly, and very clearly, in the train experiment.

I discuss it in the paper below, which is largely about the need to go back over ones favorite 20th century theories to see if (how) natural mathematics is used in them. Your understanding of Einstein is poor, and you are not careful with your terms. Try disciplining your mind.

By the way, if you don’t like “natural” coincidence, don’t argue with me. Argue with Einstein. He put it there. And if you argue that relativity has logical content, don’t argue with me. Argued with Einstein–he’s the one who felt that arguments could not have logical content.

And by the way, if you want to read scathing critiques of Poincare’s understanding of set theory (contemporary debates about Cantorian set theory led him to write Science and Hypothesis), read Grattan-Guinness’ book The Search for Mathematical Roots, and Garciadiego’s Bertrand Russell and the Origins of the Set-theoretic ‘paradoxes.’

In short, you are out of touch. Don’t comment more on relativity until you have educated yourself–you just sound silly.

(I’ll put all of Ryskamp’s quotes in blue, to distinguish them from others.) What to say about this? There’s so much ‘nincompoopery’ here (I think I like that term more than ‘crackpottery’) that one scarcely knows where to begin. As this comment appeared in my relativity denialist critique post, and the arguments seem spiritually related to the nincompoop in that article, I can only assume that this is a fellow traveler if not an acolyte of that author. Ryskamp, however, has even less substance in his comments than Darrell Williams, because there’s hardly anything present here other than semantic quibbling. Let’s take a look at some of the highlights:

Well, according to your definition, Einstein would not be a “good scientist.” I don’t think you understand the mathematical point of view Einstein used in constructing the relativity of simultaneity. Doubtless you have heard of his notion of “practical geometry,” but I don’t think you understand anything about natural mathematics, of which it is an expression. If you want to understand that better, you should read P. Maddy, Naturalism in Mathematics.

Natural mathematicians do not believe that logical content in argumentation is possible. They believe any attempt to achieve it ends in paradox. This is an extremely old view, going back to Artistotle’s concern with Zeno’s “paradox.”

What is this ‘natural mathematics’ that Ryskamp is talking about? I confess that the term is not one I’ve had to deal with in nearly twenty years of physics education and research. A quick Google search turns up that the term is used most commonly in teaching: mathematics is best taught by instructing children by using ‘natural’ problems, not abstract mathematical ones. I’m guessing that’s not the one we’re supposed to be interested in! Almost every other reference to ‘natural mathematics’ is written by John Ryskamp, himself. There is a wikipedia entry, but it is poorly referenced and probably written by Ryskamp as well. Let’s stick with Ryskamp’s official definition:

Natural mathematicians do not believe that logical content in argumentation is possible. They believe any attempt to achieve it ends in paradox.

This seems very similar to the line of our previous denialist, who basically suggests that mathematics can never be used to deduce anything about the physical world. Just like our previous denialist, this demonstrates a complete lack of understanding of how science is done.  He harps upon ‘internal consistency’ in science again and again… but ‘internal consistency’ is hardly the most important part of a physical theory! Quantum mechanics as initially developed was a mishmash of poorly defined terms such as ‘observer’ that still confound the study to this day. But, and all of the physicists can say this part together with me: It works perfectly well anyway! The most important part of a physical theory is not internal consistency, but coming up with a model that accurately represents the physical world and properly predicts its features.

Special relativity is one of those happy theories that is the whole package: it matches experiment perfectly and a simple description that to this day is apparently free of any real logical flaws or paradoxes. If we find a true problem with relativity theory, we’ll actually be happy: we’ll come up with a new theory that encompasses the old and fixes the new. That’s what we call science.

Note the word ‘believe’ in the definition above. ‘Natural mathematics’ is a polemical position, not an objective fact. Ryskamp doesn’t believe in internal consistency, so we shouldn’t either. Hardly a convincing argument.

You think that Einstein is like you, that surely he strove for internal consistency in his argument. You are wrong. Einstein was a natural mathematician, and he made sure that relativity followed the natural mathematics line.

Let me just say this: Nice strategy, Ryskamp, hiding behind a dead guy. Quite frankly, I don’t worship the words of Einstein just because Einstein said them. That’s called an argument from authority, and isn’t a particularly strong one in science. Again, and I’m getting tired of having to say this, what matters is that the postulates are reasonable, the mathematics correct, and the experiments validate all of it. It’s a little odd for someone who is criticizing special relativity to use the words of its creator to both support and refute his position. “Einstein is wrong, but Einstein agreed with me.”

You are vain and ignorant, like all physicists. You want to think that relativity is an internally consistent argument. You want to think that you would never sign off on any point of view as stupid as natural mathematics, because you insist on a standard of internal consistency in your arguments.

Ah, now we’re getting to the real crackpottery! Ryskamp knows better than all physicists (and apparently most mathematicians). His argument against me now boils down to, “You’re a stupid-head!” As far as believing that relativity is internally consistent, see above: as far as I can tell, it works just fine, and so I’ll believe that until I see proof otherwise. Am I vain? If I am vain in my scientific attitudes, it’s a vanity that comes not from my achievements alone, but that I’m standing at the end of a long line of very, very smart scientists whose work backs up my own views and investigations.

Your understanding of Einstein is poor, and you are not careful with your terms. Try disciplining your mind. By the way, if you don’t like “natural” coincidence, don’t argue with me. Argue with Einstein. He put it there. And if you argue that relativity has logical content, don’t argue with me. Argued with Einstein–he’s the one who felt that arguments could not have logical content.

I’ll get right on that ‘mind disciplining’ thing. But what is this statement that Einstein put “natural” coincidence “there”? Well, I Googled his paper to see if I could dredge more understanding of his vague statements (more about that Googling in a moment), and I found the following:

Consider this passage from Lawson’s accurate translation of Einstein’s Relativity:

Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative. When we say that the lightning strokes A and B are simultaneous with respect to be embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length AB of the embankment. But the events A and B also correspond to positions A and B on the train. Let M1 be the mid-point of the distance AB on the traveling train. Just when the flashes (as judged from the embankment) of lightning occur, this point M1 naturally coincides with the point M but it moves…with the velocity…of the train.

This passage is by now so familiar that we think there can be nothing new to be seen in it. But there is: it is the term, “naturally coincides.” This term (“fällt zwar…zusammen” in the German) leaps out at us because we are looking at it with twenty-first century eyes, not twentieth-century eyes; indeed, perhaps the most difficult cultural task now before us is simply to realize that we are not living in the twentieth century.
“Natural” coincidence is otherwise known as a spacetime point. Einstein has already spent twenty-odd pages of this very brief book laying out the assumptions which underlie the train experiment. He is very careful about being consistent with them, and he is a devoted and very strict Euclidean. But Einstein was not, it appears, quite careful enough. We know that he is assuming, along with Euclid, that the definition of the coincidence of two points is a point. However, we have never gotten (and never get, in any of Einstein’s writings) a definition of a “natural” coincidence of two points. This alone prevents us from going on and this argument, which defined the twentieth century, abruptly ends. We also have a problem if we try to resolve the issue ourselves. If we simply drop the term “naturally” we run into a situation in which Einstein has told us to assume two Cartesian coordinate systems, but now leaves us with one, since, following from the definition of the coincidence of two points, if two parallel coordinate systems coincide at one point, they coincide at all points and are one coordinate system, not two.We have been led to a contradiction.

This is where things get really funny! First of all, the book that he’s critiquing and semantically deconstructing is Relativity: The Special and the General Theory, subtitled, A clear explanation that anyone can understand. This is a popular book on relativity theory, which is using popular arguments to make the theory accessible to people. Criticizing Einstein for not being rigorous in such a text is as silly as criticizing me for not being rigorous when I explain my research to my grandmother. The book contains very few equations, as Einstein himself says,

The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics.

Ryskamp’s own ‘work’ on relativity is missing the same important ingredient: equations. There is no indication that he understands the mathematics or the physics involved, so why I or anyone else should take him seriously is beyond me.

Ah! But let’s look at the one, single, semantic term that riles up Ryskamp so much: ‘naturally coincides.’ Because, in this popular, nontechnical account of relativity theory, Einstein doesn’t clearly define a single term whose meaning is obvious to anyone else, Ryskamp is ready to discard the entire theory. That’s another symptom of massive crackpottery: an obsession with the meaning of words, and a generally uncharitable interpretation of their meaning. What does Einstein mean? Again, this is a nontechnical argument, meant to illustrate the relativity of simultaneity: it is not a mathematical proof! Einstein is simply saying that, according to the person standing on the embankment next to the train, the middle of the train coincides with the central point between the two lightning flashes. He’s saying that the origins of two coordinate systems coincide at a specific instant of time according to the observer on the embankment.

If we simply drop the term “naturally” we run into a situation in which Einstein has told us to assume two Cartesian coordinate systems, but now leaves us with one, since, following from the definition of the coincidence of two points, if two parallel coordinate systems coincide at one point, they coincide at all points and are one coordinate system, not two.

More semantic gobbledegook! Mathematically, I can talk about an infinite number of idealized coordinate systems which all lay precisely on top of each other. If they are stationary with respect to each other, there’s no fundamental difference between them, but I don’t have to call them the ‘same’. If those two coordinate systems are moving relative to one another, as in the train example, they are definitely not the same, even in a Newtonian sense: they will only coincide perfectly for a single instant of time, before their origins move apart from one another. In an Einsteinian sense, they don’t even coincide at that single instant of time, except at that single point.

…indeed, perhaps the most difficult cultural task now before us is simply to realize that we are not living in the twentieth century.

* snort! giggle! * So our ‘deep thinker’ has a hard time realizing he’s living in the 21st century? Okay, that’s a cheap, uncharitable shot,but it made me laugh.

Okay, so I haven’t really figured out what the hell he’s trying to get at, other than to observe that Ryskamp shows lots of signs of crackpottery. I’m going to pass this along to Good Math, Bad Math to see if MCC wants to attack his mathematical arguments further…

Let me return to my Google search. Googling ‘John Ryskamp’ didn’t provide me with any real clue of who this guy is, except for the following: a bunch of Amazon.com book reviews of other people’s books touting his odd critique of relativity (including one criticism of a book on ‘molecular evolution’ (?)) and an entire thread on physics forums devoted to talking about his massive spamming efforts! So we’ve got not only a crackpot, but a blog troll on our hands!

Let’s end with a response to his final comment:

In short, you are out of touch. Don’t comment more on relativity until you have educated yourself–you just sound silly.

Oh, noes! Hey, everybody! Some guy thinks I’m out of touch and sound silly! What should I do now that I’ve got the shame of some guy looking down on me? Will I ever work my way into some guy‘s good graces again?

Sorry; I’m going to just go on continuing to comment on relativity, just like every other physicist does. We’ll just have to stumble along blindly in the dark, doing our research, until you show us the light by using whatever the hell it is you’re talking about to demonstrate whatever the hell it’s supposed to do.