Statistics Saturday: Some Shapes Which You Ought Not Use As Dinner Plates For Your Trendy Restaurant

  • Triangle-base pyramids
  • Whole spheres
  • Saddle curves
  • Vertical walls
  • Great Stellated Dodecahedrons (unless you are serving a food that can be usefully jabbed on spikes, such as pancakes or lumps of cheese ripped out of a whole)
  • Square-base pyramids
  • Sierpiński sieves (that triangle-with-interior-triangles cut out thing, as while it’s a great shape it actually has no surface area, so it can only hold food by way of surface tension)
  • Bipyramids
  • Doughnut-shaped toruses (unless it is an edible container, like those soup-in-a-loaf meals, itself containing many small doughnuts within, in which case I would like to invest in your restaurant)
  • The Great Rhombicosidodecahedron not because no food could be placed atop it but because when word gets out you have Great Rhombicosidodecahedrons in your restaurant the health department will begin an inquiry which will ultimately clear you but which will generate needless amounts of bad press in the meanwhile.

Another Blog, Meanwhile Index

The Another Blog, Meanwhile index rose two points on reports that someone saw a pair of mice snuggled up against each other sleeping and one opened its eye just enough to yawn and doesn’t that sound adorable? We thought it was adorable.


Caption This: Ray Walston Doing Things

Before we get to the main stuff. My mathematics blog? I had a couple more comic strips to talk about yesterday. Yes, one of them is Barney Google. I think you might enjoy it anyway. A lot of cartoonists did jokes about gambling last week, for some reason. Now:

Ray Walston pours a drink from a pyramidal glass into a shorter square-cylinder glass.
In this thrilling episode of Star Trek: Voyager, Ray Walston acts all cranky and asks why he has to talk to Neelix. I’m guessing.

Ray Walston Character: “Humans. Humans think of themselves as the supreme beings of their universe, the masters of their destiny — if not now, then at least, as beings who will be someday masters of their destiny. And yet as you explore the universe, its great potentials, its vast failures, its diversity of form and thought and expression, you come to a realization. The fatal flaw of the species, my friends, one I imagine that will never be overcome, is that humans are quite mediocre at discerning whether very different shapes enclose approximately equal volumes.”

Go ahead, top me with a better caption. I can take it, I’ll pretend.

The Big Picture

We’ve started looking at maybe buying a new TV. Our current TV is working fine, which has been part of the problem, since it’s your old-fashioned standard-definition tube-model TV screen hewn by Alan B DuMont himself from his shadowy hidden laboratory deep in the highlands of North Jersey. It was a fine TV in its time, and it’s clearly determined to outlast the entropic heat-death of the universe, but it’s starting to get annoying watching TV shows that assume screens are wider, like they are anymore. The Daily Show is pretty good about not putting stuff outside the bounds of the standard-definition screen, but it’s getting tiresome to guess what’s happening on the missing edges of Cona O’Brie.

The obvious change in TV technology since our old set was made has been the size, of course. There’s now no way to buy a TV set smaller than a tennis court in area, which will demand we rearrange the living room so it fits. We might have to have a carpenter come in and take out the stairwell, and just get to our bedroom by way of a rope ladder, trampoline, or perhaps a very patient giraffe (possibly mechanized). On the bright side modern TVs are only half as thick as other units of the same model, so if we buy a flatscreen we’ll be able to slip it in-between the wall and the paint on the wall.

The other thing is that shapes have changed. Picture-tube TVs all had that slight outward curve made. That curve was great as you could just place a large enough number of picture tubes near one another and automatically form a ball of television sets thirty feet across, allowing anyone to create an art installation about the disposability of modern pop culture whenever they wanted. But then they started making screens flat, so that every TV show you looked at seemed to be weirdly impacted in the middle, like someone had smooshed Bob Barker right in the belly. They’ve fixed that now, by finding a pre-smooshed host for The Pric Is Righ, and I suppose they’ve worked out what to do for other shows too.

And now the stores have innovative new shapes, too. The big one at the store last week was screens curled inward, giving us the experience of watching a couple seconds of a waterfall then a roller coaster then fireworks then the Grand Canyon while staring at the inside of a bowl. I guess that’s got advantages in how it makes the picture look curled inwards, and how the eyes of the Best Buy sales associates follow you wherever you go until in a fit of shyness you curl up behind the bin of $4.99 games for the Wii.

Besides these inverted-bowl shapes there’s exciting new concepts in solid geometry coming, such as the saddle-curve hyperboloid which wowed people at the Consumer Electronics Show. It expertly suggested the experience of horse-riding, what with how as you get closer to the screen it looms higher and higher over you, until you get right up close to it, at which point the it bites your hair, covers your head an inch deep in horse boogers, and stomps on your foot, which any horse-expert person like my sister will tell you is a show that the horse likes you and it’s all your fault anyway. I didn’t even know my sister watched that much TV, what with her horse-experting to do. Anyway, television boogers clean up easily, but cleaning them off leaves you open to charges you’re one of those people who announces “I never watch television” every four minutes, even to empty rooms.

Personally, I think the most exciting new TV shape is one that projects the image onto the contact surface formed in the tangent space M \times \textbf{R}^{2n+1} so that for any fiber bundle \alpha you can find a sympletic coordinate pair perfectly matching, say, the statistical entropy to the chemical potentials of the system. I think most of you agree with my assessment because you’re hoping if you nod vigorously enough I’ll stop talking what might be mathematics or physics or possibly some conspiracy theory linking Nikolai Tesla to the Knights Templar and go on to literally any other topic at all. (Hi, LFFL!)

Anyway, this is all very thrilling stuff and it makes me figure that I should go back to watching narrower programs on the old TV set.

Statistics Saturday: Counting On The Splendid Bowl

If current trends continue, then in the year … … there will have been as many Splendid Bowls as there are or were:
2020 Faces and vertices of the medial rhombic triacontahedron
2026 Days in January and February (non-bissextile years)
2026 Minimum number of games in the National Hockey League postseason (per rules in effect for 2015)
2027 Days in January and February (leap years)
2028 Counties in New York State
2031 Years between a Punxsutawney, Pennsylvania groundhog’s first being recorded to predict the weather and the predictive groundhog’s receiving the name “Phil” [1]
2034 Secretaries of State of the United States (as of 2015)
2044 Inches of height of Michael Jordan
2048 Games in a regular National Basketball Association season (as of 2015)
2049 Episodes of the original Star Trek
2054 International Astronomical Union-recognized constellations
2071 Maximum number of games in the National Hockey League postseason (per rules in effect for 2015)
2173 Recipients of the Nobel Prize in Physiology or Medicine (as of January 2015)
2331 Days in the year
2686 Species of Pokemon revealed as of 2015
9886 Elements of the sporadic Mathieu group M11

1: Wikipedia’s description is very breezy and chatty, causing me to doubt that the topic has been the subject of credible historical inquiry.

Statistics Saturday: A List Of Some Things Which Look Considerably More Dignified If Depicted Wearing Glasses

  1. Dogs
  2. Statues
  3. Rabbits
  4. Eggs
  5. Dragons
  6. Instructors
  7. Robots (the good kind)
  8. Trees
  9. Small rocks
  10. Squirrels
  11. Teeth
  12. Robots (the morally ambiguous kind)
  13. Ducks
  14. Dodecahedrons

Note: I mean eyeglasses. Drinking glasses is a completely different thing.

Explaining The Angles

I’ve been working on a biography of Donald Coxeter, one of the most important geometers of the 20th century. I mean reading it, since the hard work of writing it was already done by someone else (Siobhan Roberts), and the even harder work of being an important geometer of the 20th century was done by another person entirely (Donald Coxeter). Mine is really the easiest part except for the people who aren’t reading it, who can do that anytime and from anywhere. Anyway, I’d run across some of his work in references to H M S Coxeter, and a careful examination of the first paragraph pointed out that “Donald” is not one of the leading names with an initial H, M, or S.

Anyway, Roberts explains that Donald’s parents wanted to call him Donald, and they did, but “the birth certificate recorded his first name officially as MacDonald, after his father’s father”. Fine and/or dandy. His mother added “Scott” to honor another relative, and a godparent suggested that he should have his father’s name of Harold, too, and that’s why he was Harold Scott MacDonald Coxeter.

And I just admire how very much that looks as if it explained the situation.

Pop Quiz: Philosophers

  1. Pythagoras:
    1. I know, right?
    2. The hypotenuse squared over the sum of the sides.
    3. E = mc2.
    4. Beanfields.
  2. Descartes:
    1. Pituitary glands.
    2. God’s too nice to make mad scientists?
    3. Mornings kill people.
    4. I yam what I yam and tha’s all what I yam.
  3. Nietzsche:
    1. Oh, dear Lord.
    2. Just set that down and come back when you’re at least ten years older.
    3. Or you could start punching that book right now.
    4. Both (b) and (c).

Colorful Troubles

I don’t get invited into focus groups much, not since I explained in a slender, carefully chosen, 12,350 words how Star Trek V is much better-directed than people think. I probably had that coming. So I was thrilled when the Department of Rainbows called to have me evaluate some new meteorological products they were test-marketing. All I had to do, they explained, was watch in the early afternoon as they tried out this new rainbow concept where the colors would be there, but faint, so you’d only see them against a light cloud in the background and you’d look up and suddenly, hey, a Neapolitan cumulus was hovering there.

It transpired that come the first test period I was inside doing some emergency alphabetizing of the refrigerator, which was absolutely the top priority because I started out thinking the DVD player had a awful lot of dust on it. Fine, their phone call was forgiving, and they referred me to a pilot project in Blu-Ray dust, which is dusty with such an incredible fidelity that vinyl audiophiles swear it makes records sound more authentically dusty than actual dust can.

The second period, though, I missed because I was looking at the wrong clouds and they could not believe that I don’t know a cumulus from an altostratus. I can’t blame my parents for this; in a package of childhood documents I found the certificate from a pre-kindergarten project which showed that I memeorized every possible kind of cloud there was, including the imaginary ones, in that way that only excitable four-year-olds just learning to classify things can. In my defense, when I was a kinder, “brontostratus” was too a cloud and I can’t be blamed for missing its reclassification as “the habit of looking at the wrong month on the calendar so getting the day of the week wrong”.

The third time I missed because I was explaining to our pet rabbit that if he insisted on barking like that people were going to think I was mad. He insisted that this was my problem and if he wanted to bark he was jolly well going to bark. (I alter his words a bit; he said something more like “certainly going to bark”, but the “jolly well” seemed to fit his huffiness more.)

And the fourth time, which is entirely my fault and I can only blame myself for it, I missed because I was hard at work coming up with ways to use the word “transpire” in casual writing in ways that pedants would find acceptable.

So, Rainbows got all upset with me, and I guess they’re right to be. I don’t know how much work is involved in bringing new rainbow concepts to the test-marketing stage but I’m sure it’s something. And they did all sorts of work trying to train me, too. For example they revealed you can always tell a cumulus from an altostratus by scanning the upper right corner with a price-check laser, or by trying to play middle C and seeing what note does come out.

What I really don’t know what’s going to happen with this. I was really hoping to make a good impression and maybe get into this group I hear’s trying to refresh heptagons. They’ve been clinging to that seven-sided thing for a long while and I think we’d have to stick with that, but that “hept” thing isn’t really working. People tend to figure it’s a fake prefix because it was created by agents for the Soviet government in 1930 when the country sought ways to sneak cash out of western governments.

As such the prefix doesn’t really mean anything, but it’s caught on among people who need to group together seven things in a prefix, as soon as they think of any. I mean, you can think of groups of seven things and find them all over the place, we just do well enough calling them “the seven things” and I don’t see that changing so much, so we need to find ways to bundle seven things into smaller groups that go at the start of things, you know, like, prominent colors in a rainbow. Oh, I bet the Department of Rainbows will like it if I point that out to them.

Vim, Vigor, and That Other Thing

I’m getting back into regular exercise. I don’t want to make people envious of my physique, but in the past few years I’ve got into the best shape of my life, not counting that year in elementary school when I was a regular heptagon. When I say the best shape of my life, I mean the best shape for me, though. I have the raw athletic prowess of a tower of buckets. Given a reasonable time to warm up and stretch, I can pretty nearly successfully tip over and plummet onto the floor. Next week I’m hoping to get to tipping and plummeting onto the floor while wearing weights.