Three Dollar Quill

One thing I want to look at about Terrence Howard's beliefs is the way that many of them didn't form in a vacuum. Aside from some annoyingly common beliefs, he also, let's say, "cites", previous works of pseudoscience by other people, as well as fringe or niche areas of mathematics that he frankly does no favors by mentioning.

Hold on, before I get into that, let's take a moment to think about "citation". Terrence Howard's book, apparently called One Times One Equals Two has a strange layout, and there are multiple versions available.

I was previously working from a version I downloaded from a now-defunct Flat Earth website (which is amusing, because he explicitly believes in a spherical Earth with atmosphere fading into vacuum), which uses various pictographs on the title page, and has the mirror image of the title page as the back cover. The version I'll be mostly using this month has an abstract wash of color for the title page, with a flower in the upper middle, and a symbol in the lower middle. Each version has an end page with a date, and the Wash Of Color version has a later date (September 23, 2020) than the Pictograph version (May 19, 2019).

The pages are numbered starting from 1 on the title page. Most pages have a pair of columns that look like pages, but the page number is outside and between the columns. There is little enough on a given page that it should usually suffice to simply cite by page number.

With all that said, let's see what jumps out at me.

Hmm. I've actually got some mathematical ideas from looking at this. Probably not novel, and I know of some prior art that's pretty close. On page 15, Terrence makes some comments about the act of multiplying 1 by 1, which are entirely fatuous in the context of standard mathematical abstractions. Talking about how the 1's are things that have to be conserved. I thought to myself, having apparently not gotten this out of my system yesterday/two months ago,

"Oh, come on. If you do nothing, and then you do nothing again, then overall you did nothing. ... If you do nothing for a minute, and then do nothing for a minute again, then you did nothing, but. But it took two minutes. Which we don't care about. But what if we did?"

Suppose we have a magma, and we pick out a set of generators, which need not be minimal or finite, and to each generator in the set we assign a cost. (For reasons of elegance, the identity element, if any, should have a cost of zero unless there's a specific reason to give it a higher cost.) When we apply the monoid operation to two elements with associated costs, we add the costs together, to produce the cost associated with the result. We can divide all possible (element, cost) pairs into equivalence classes based on the element, and take the one with the smallest cost in a given class as representative. Fans of recreational mathematics will recognize this as one way of thinking about "God's number", an idea that I imagine will sound interesting to Terrence until he realizes how much it has to do with cubes.

I can imagine various variants of this idea, such as using sets of generators instead of numeric costs, associating each generator to the set containing only itself, using set union instead of addition, and creating a function from each element to the subset of the power set of generators associated with it. The other thing that comes to mind is to look for a semiring that would do something interesting if you took the direct product with the tropical semiring. Actually, semirings in general look neat. I should mess around with them.

Anyway, let's see if anything else jumps out at me.

The next thing I ended up looking into has a lot more to dig into, and I'll see what I can find out about it later. Basically, I got to page 32, where he reproduces Walter Russell's goofy circle element chart, and I decided to look into it some. I took a look at The Universal One, and I have to say, these takes on Mendeleev's 1904 revision of the periodic table are fascinating, and not in a good way.

Before the discovery of the noble gasses, elements were grouped into "octaves" of seven each, with the idea that the elements regularly cycle through different properties as atomic weight increases. This concept informed the development of the periodic table; at one point, the groups of the periodic table corresponded to the different members of the octave, with an additional group for the "triad" that separated some pairs of octaves, and was seen to mediate between them. When the noble gasses were discovered, they were originally put on the left, with a gap in the group following every period that ended in a triad. The resulting jagged chart looks strange to us now, but the main concern at the time was, like, copper shouldn't be classified as an alkali metal, right? Like, that just doesn't make sense.

Anyway, Walter Russell, writing presumably sometime after 1920, criticized the 1904 revision, which, like, could he have done a later one instead? I get that he didn't have a search engine... Anyway, he declared that there were "missing" noble gasses (which would presumably go somewhere between group 8 and group 10 in the modern table), but also that various elements were in the wrong place. He disagreed with the existence of Group VIII (groups 8 to 10 today), but some of his other decisions were... confusing, from a modern perspective. He takes no issue with the equivalent of the first three periods (understandable, as they fit with the octave concept that he's trying to revive), and then he gets partway through the fourth period, gives his blessing to scandium (modern group 3) as being in group III (which until then had corresponded to modern group 13), and then highlights everything from titanium to germanium as out-of-place, including gallium, which would actually make sense to go under boron and aluminum. He does generally keep up this pattern, so I guess he's being consistent...

He also calls out large gaps in the lower rows. Uh, yeah, Walter, that's because those elements hadn't been discovered yet. What were they supposed to put in those spots? (Putting aside that the lower periods were doubled up, and the lanthanoids and actinoids hadn't been separated out properly.) Basically, this chart had problems, but it got important things right, and Walter Russell seems to have had an amazing instinct for getting those categories exactly backwards.

Reading the chapters around that caption for context, I can see a lot of the buzzwords that Terrence tends to pull out.

Anyway, I'll see where my interest takes me next. For now, if I don't get ready for bed, I will regret it.

Good night.