“Spiders Aren’t Animals!” Well, Actually….

spider 240px-Kaldari_Phidippus_audax_01

Over the years, literally hundreds of people have told me that spiders are not animals. This seems to happen the majority of the times that the topic of spiders comes up in conversation.  When I reply that spiders are, in fact, animals, the usual response is “Spiders are insects!” This gives me headaches, because (1) spiders aren’t insects, and (2) insects are also animals.

Spiders happen to be my favorite animal, so this is quite confusing to me. Hopefully, this screenshot from my Google-search for “animal definition” will help spread the word that spiders are, indeed, part of the animal kingdom.

animals

[Spider image from https://en.wikipedia.org/wiki/Phidippus_audax. Also, I added the red arrow and ellipse to the Google-screenshot, using MS-Paint.]

The President of the “United States or America”

I just took this screenshot of a presidential tweet. It might get edited later, but this is what it looks like right now. He literally misspelled the name of our nation. 

POTUS

Which one is it, Mr. Trump? Are we the United States, or America? 

American Fascism 2017

american-fascism

It’s easy to throw words like “fascism” around without really thinking about their definitions . . . so I looked the word up, to reexamine it. In my opinion, the “shoe fits,” as the saying goes, whether you call it “American fascism,” or simply “Trumpism.” Just look at the details of the Google-provided definition above:

  • Authoritarian? Check.
  • Nationalistic? “Make America Great Again!” “America First!”
  • Right-wing? Very much so.
  • Government? Firm control of two of three branches, at the moment.
  • Social organization? They’re working on that, in the usual “us and them” form.
  • Extreme? Almost comically so.
  • Intolerant? Vividly so.

What’s more, all of this is apparent after Donald Trump has been in office for only a week.

A Deck of Polyhedra

There are 52 rotating polyhedra below. Starting right now, 52 of anything can be called a “deck” of that thing. The derivation of this term is the the number of cards in a standard playing-card deck. The deck is the smaller “cousin” of the mole, or 6.02 x 10²³ of anything, from chemistry, as well as the “big brother” of the dozen, or twelve of anything. All three units are measures of specific quantities, and can be applied to any objects, at least in principle. One never encounters a mole of people because there aren’t that many of us, but a mole of people can still be imagined. The same thing applies to a deck of Earths.

This deck of virtual, rotating polyhedra was created using Stella 4d, a program you may purchase here. If you would like to see a larger image of any one of these polyhedra, simply click on it. 

What do you mean, you “can’t wait?” Obviously, you can!

 

you can wait

Why do people so often, and completely incorrectly, say they “can’t wait” for things? No one ever says this, it seems, unless they already are waiting for whatever they are talking about.

A seasonal example: “I can’t wait for Christmas!”

When I hear this, I generally point out to people that they are already waiting, and therefore, obviously, they can do so.

What is it with this? Why do so many people say this thing that clearly makes no sense at all?

A Plea for Consistency in the Use of Numerical Prefixes

consistency

First, let’s face facts: the numerical prefixes currently in use, in English, are a horrible mess. Most of the ones used with polyhedra, for example, such as tetra- (4) and penta- (5), are derived from Greek. For polygons, however, a four-sided figure is usually called a quadrilateral, with “quad-” derived from Latin, just as it is in “quadrillion,” or “quadruplets.” Why use two prefixes for the number four? It would be more consistent (and therefore better), since four-faced polyhedra are called tetrahedra, for four-sided polygons to be called tetragons, just as we call five-sided polygons pentagons. Consistency improves comprehension, simply by reducing the number of prefixes one needs to understand, and can therefore aid in both teaching and learning. Inconsistency, though, has the opposite effect, and that benefits no one.

The Greek-based prefix for 5, “penta-,” has a Latin-based rival, also: “quint-,” as in quintuplets, or the number quintillion. It doesn’t make sense to use two different prefixes for the same thing, for both English, and mathematics, are complicated enough without adding unnecessary complications. The necessary complications are quite enough!

My preference is for Greek-based prefixes, for two reasons: (1) more of them are in use than their Latin counterparts, and (2) the Latin-speaking Romans appropriated ideas from the ancient Greeks, not the other way around.

Even the number one is not immune from this problem. For one, we use “mono-,” “uni-,” “un-,” “uni-,” “en-, “and “hen-,” all to mean “one,” and each has at least a slightly different derivation. Examples include “monomer,” “monologue,” “unicycle,” “undecillion,” “undecagon,” “endecagon,” and “hendecagon,” the last three of which all name the same polygon. (Also, these last three prefixes are for 11, actually, formed by combining a prefix for the one with the Greek-based “deca-” prefix for ten. Combinations of prefixes will be addressed later.) I call 11-sided polygons “hendecagons,” for both prefixes in that word are derived from Greek.

Prefixes for the number two are also unnecessarily numerous, as well as ambiguous. “Bi-” is used in “bicycle,” “binary,” and “billion,” but that’s a horrible idea, since “bi-” is also used, in some cases, for ½. This shows up, for example, in chemistry: the bulk of a carbonic acid molecule, if fully ionized, is called the carbonate ion. However, if it is only half-ionized, it is often called the bicarbonate ion, as in sodium bicarbonate, better-known as baking soda. In chemistry, “di-” is used for two, as in carbon dioxide, a molecule containing two oxygen atoms. “Do-” and “duo-” are also both used for the number two, with the first derived from Greek, and the second from Latin. When combined with the Greek prefix for ten, to make twelve, these prefixes appear in words such as “dodecagon,” “dodecahedron,” and “duodecimal.” I find the word “duodecimal” particular irritating, for it combines Greek and Latin prefixes in a single word. If one person had deliberately designed this entire system, with the goal of causing confusion, it would have taken a lot of work to invent a system more confusing than the one we actually use.

If, for ½, we only used “bi-,” that would be nice, but that isn’t what we do. Half a circle is a semicircle, and then half a sphere is a hemisphere. Since it originates from Greek, my preference is for “hemi-.”

At least three’s prefix is usually consistent, with “tri-” being all-but-universal. The only exception I know of appears when “tri-” is combined with “deca-,” to create a prefix for thirteen, and the Greek work for “and,” which is “kai,” often appears with it, as in triskaidecaphobia, the fear of the number thirteen — in this word, “tri-” is modified to “tris-.” However, a thirteen-sided polygon is simply called a “tridecagon,” with no “s” attached to “tri-,” and the “kai” omitted.

I don’t actually care if we use “kai,” or not, in numerical prefixes, but we should pick one or the other, and stick with it. It makes no sense that a fifteen-sided polygon is usually called a “pentadecagon,” while sometimes called a “pentakaidecagon.” Why do we not simply choose just one?

Six and seven are similarly troublesome. The numbers “sextillion” and “septillion,” as well as the month of September, all use Latin-derived prefixes for these numbers. I prefer the Greek-derived prefixes used with polygons and polyhedra: “hexa-,” and “hepta-.” With eight, though, as in the case of three, English-speakers lucked out, with “octopus,” “octillion,” “octagon,” and “octahedron” all starting with the same three letters.

With nine, however, our system falls apart again. In high school, geometry students are taught the Latin-prefix-containing word “nonagon” for a nine-sided polygon, and “November” contains yet another Latin-based prefix meaning nine. (It was named the ninth month, rather than the eleventh, because the start of each new year was marked with the first day of Spring in ancient times, rather than the first day of January.) A professional mathematician, however, is more likely to call a nonagon an “enneagon,” for “ennea-” is derived from Greek, making “enneagon” consistent with its “neighbors,” the octagon and the decagon. Ten is not a problem, though, for the Greek-based “deca-” was simply appropriated by the Latin-speaking Romans, who named their tenth month December — using a prefix close enough to “deca-” that it is unlikely to cause confusion.

One numbers exceed ten, though, a new problem is encountered, in addition to the issue of whether or not we use “kai.” Numbers such as 12 and 24 require us to combine prefixes, but there is no consistency in the order in which this is done. For example, a twelve-faced polyhedron is a “dodecahedron” — using a prefix for two, followed by a prefix for ten: the smaller number, and then the larger number. We continue this practice with words such as “pentadecagon,” already described above. Then, however, we have this thing, the dual of the snub cube:

Penta Icositetra

The faces of this polyhedron are 24 pentagons, and it isn’t the only well-known polyhedron with 24 faces, so “pentagonal” is part of this polyhedron’s name, which makes sense. However, if its name followed the pattern in the paragraph above, that would make it a “pentagonal tetraicosahedron,” or perhaps a “pentagonal tetrakaiicosahedron” — the smaller “tetra-,” meaning “four,” would come before the larger “icosa,” meaning twenty. At least both these prefixes originated in the Greek language, but, for mysterious reasons, the prefixes are put in the reverse order, relative to the order used for the dodecahedron: it is called the “pentagonal icositetrahedron.” Polyhedral names are hard enough to learn without arbitrary switches between “smaller, then larger,” and its opposite, “larger, then smaller.” We should choose a method, one or the other, and then stick to it.

[Note: the rotating polyhedron above was created using Stella 4d, software you can buy, or try for free, at this website.]

In chemistry, naming-disputes (what to call a newly-synthesized element, for example) are settled by the IUPAC: the International Union of Pure and Applied Chemistry. I know of no organization with a corresponding role in the field of mathematics, but, if one were created, perhaps that would help get this mess cleaned up.