Three Dollar Quill

Oh boy. I've gotten to page 39, so Terrence is mixing it up a little. Not content with being wrong about arithmetic, physics, chemistry, and probably other things I've forgotten, he branches out into saying incoherent things about English grammar. This sort of ties in with a general theme in his work, where he tries to define the behavior of reality in terms of (his understanding of) the English language. Like, "multiplication, which by definition means, 'To make greater.'" on page 24. On page 39, he says that "In long form writing it is expressed as follows 'One time(s) ␍ One.'" I don't think I've ever seen that, and then he tries to argue that the (optional according to him?) s makes it a plural. There are actually so many different things wrong with this that I'm having trouble deciding how many there are. One is that the word being used for the multiplication operation doesn't have anything that could be a plural marker in other languages, like Spanish "por". This segues into another related issue, which is that we can just as easily say "one by one" in English. However, it's important to note that mathematical terminology can sometimes be a fraught area when it comes to grammar. In English, numbers go before adjectives, but mathematical expressions are used as arguments to verbs, so they ought to be nouns. And the usage of "by" and "divided by" seems to indicate that mathematical operations are prepositions, but we understand indicating addition with "and", and when it comes to indicating more advanced operations, it's often the case that they come after the number, like "squared" or "factorial". These could be sort for "the square of" and "the factorial of", but the abbreviation scheme isn't consistent: consider how "the square root of" becomes "root" before the number. To say nothing of "sine squared", in which "squared" now comes before the number, or is it after "sine"? Despite the weird number of things going on, this all works well enough, as a means of communication, and not some kind of magical language to bind the nature of reality.

I mean, ultimately, nobody is reading this looking for a proper debunking, because I'm pretty sure nobody else really believes what Terrence is saying.

This book had an editor?

Truly, a deeper mystery than any question Terrence raised on purpose.

But enough snark, let's see if I can find anything interesting.

Again, if we are discussing Light and the unquestionable constant of the speed of light, a measurement that we are told is unchanging. Light is believed to travel faster than most things within our 3-D Universe. Due to the seemingly instantaneous transference of information across the electrified Universe as observed in Birkeland Currents, we know that electricity is not limited to the speed of Light, it is much faster. Yet, Light a radiative product of a magnetic interaction isn’t doing so bad coming in a close second. Remember, Radiant Light moves in the opposite direction of Electricity and Light’s centrifugal expansion is at a higher ratio than the centripetal contraction of Electricity, which leaves behind the effects of gravity, as a by product!

This was kicked off by him recounting one of his elementary school teacher's presumably increasingly desperate attempts to get him to do multiplication properly. (I mean, the way he tells it, I can't figure out where she was going with it.) There's a lot there, and I'm fairly confident that none of it came into play at the time. Let's try to salvage some points of legitimate interest from all of this gawking:

• I kind of glazed over a bunch of pages where Terrence was talking about, like, Einstein, and Superman, and Pythagoras, and stuff. Does he explain anywhere what he means by "Radiant Light"?
• What are Birkeland Currents? Who claims that they exhibit ftl effects?

Let's see:

• That is, in fact, the only time he uses the word "Radiant" in One Times One Equals Two, so I'm just going to ignore it for now.
• Birkeland currents are a geomagnetic phenomenon that, among other things, cause the aurorae. It has been hypothesized that a similar phenomenon could be responsible for the periodic radiation patterns of particular stars, through the creation of waves that "move faster than light" without carrying information or particles.

Let me break out of the list to try to explain. Imagine you have a very powerful laser pointer, and you're standing at the center of a cylindrical room ten light-minutes in radius. (Please ignore the material engineering issues inherent in this hypothetical.) You turn on the laser pointer, and set it horizontally. Twenty minutes pass, and the dot appears. (It is a very powerful laser pointer.) Over the course of the next minute, you rotate it through three quarters of a circle, hold for ten seconds, then turn it off.

For twenty more minutes, nothing happens to the dot. Then, it starts moving steadily across the wall, somewhat slower than the second hand of a clock, but seemingly moving over forty times the speed of light! A minute passes, and the dot sheds its impossible speed just as easily as it picked it up, then, ten seconds later, finally disappears.

The key reason this is not a problem for our current understanding of physics is that being next to the dot at one moment gives you no information about the pace where the dot just was previously; it's all completely different light.

Anyway, let's give it another shot. Maybe this time I'll have the patience to wait for him to quote or namedrop someone.

Aww yeah, "NJ Wildberger" (51). This is now a Norman Wildberger discussion blog. I will still quickly explain what Terrence is getting wrong here. Wildberger is a finitist; among other things, he doesn't feel that it makes sense to talk about irrational numbers, where part of his concern is the lack of an exact decimal representation. Terrence brings up the square root of two here, and I feel the only way to do justice to Wildberger here is to enumerate the three different viewpoints in play here:

• Most mathematicians consider the square root of two to be an irrational number.
• Wildberger accepts at least one proof that there is no rational number whose square is exactly two.
• Terrence categorically rejects all proofs that there is no rational number whose square is exactly two.

In my capacity as a CS (Computer Sicko), I have a lot of interest in Wildberger's work in finitist mathematics, and I'd like to be better read in that area than I currently am. This is because it's helpful when a computational procedure terminates in a finite (ideally small) number of steps, and provides an accurate answer. This opinion needs to be qualified with the caveat that although I think of these as practical concerns, I haven't actually written code based on Wildberger's work, so I can't honestly say that my motivations here are, as yet, anything other than aesthetic.

With that said, the idea of developing a discrete geometry, as I understand Wildberger has done, is neat, in the same way that I was saying that semirings look neat. At the same time, I'm not interested in restricting myself to finite mathematics, and I'm now remembering my attempts to work with Dafny. Perhaps I'll look into that again later.

Anyway, I think I'm done for tonight.

Good night.