Content-Type: text/shitpost

The antelope, so called because of its propensity for jumping in front of people. (“Lope” is akin to “leap”.) And the anteater, an insectivore that consumes its prey from the front, whereas the postater always approaches them from the back.

Jeff Boes points out this piece of uncannily apropos news: Dems demand info on acting attorney general’s “masculine toilet” scam.

And it's also World Toilet Day.

Hmmmmm.

OR SUFFER THE UNSPEAKABLE CONSEQUENCES

Incidentally, Harris’ The Natural System of Colours has more than one plate. In addition to the one depicting the “prismatic” colors, starting from the primaries red, yellow, and blue, and showing how they mix to form the secondaries orange, green, and purple, he has a second plate that starts with the secondaries and mixes them to form tertiaries.

Harris names the tertiaries “olave” (orange-green), “slate” (green-purple), and “bronn” (purple-orange). I think “olave” and “bronn” are just alternate spellings of “olive” and “brown” but it is after midnight and I do not want to go downstairs to get out the Big Dictionary.

Wikipedia asserts that the terms “citron”, “slate”, and “russet” have since become common, and attributes them to George Field's Chromatography (1835). Field actually calls them “citrine”, “olive”, and “russet”.

Here is a page from Moses Harris’ extremely influential book The Natural System of Colours, published around 1760. This image is widely reproduced and you may have seen it before:

(This particular image is from a copy of the second edition of 1811, and as you can see it has suffered significant damage.)

I have wondered about this for decades now: Why is the label for yellow written backwards?

More progress on counting paths on octahedra! Suppose you want to know how many paths of length !!n!! there are between two opposite vertices of an octahedron.

It turns out that it is the same as the number of ways to take !!n!! terms, each of which is either !!\pm1!! or !!\pm2!!, and add them up to get an odd multiple of 3. (Order matters.)

For example, there are 8 paths of length 3, which correspond to !!1+1+1, -1+2+2, 2-1+2, 2+2-1,!! and their negatives.

That actually seems like an improvement because it seems like counting those sequences will be a straightforward application of generating functions.

Note to self: On the octahedron, we don't have !!xy=yx!!, but we do have !!xyx=yxy!!.

This is a consequence of !!x^2=1!! and !!(xy)^3=1!!.

Your original idea labeled the endpoints of the edges instead of the edges themselves. Putting the same label at each endpoint means that !!x^2=1!! for all !!x!!. Maybe you don't need this. Or what if we go partway in this direction and label the endpoints !!x!! and !!x^{-1}!!?

Your original idea was to think of the dodecahedron as a Cayley graph, but then you didn't really follow this up. Go back and think about Cayley graphs more carefully.

In the tetrahedron, each face is a product !!abc!! in some order, so at every starting point !!xyz=1!! whenever !!x,y,!! and !!z!! are all different. In the cube the corresponding property for faces is !!xyxy=1!!. The coloring of the dodecahedron that you're using has no such good property. Can you find one that does? This would probably require that you use five labels.

The fact that you found a labeling of the tetrahedron and cube where label order didn't matter is an expression of some fact about the symmetry of the polyhedron itself that you aren't looking at directly. What's really going on there?

It's obvious why this labeling exists for the cube (and for the !!n!!-cube generally). But why does it exist for the tetrahedron? What's going on there?

According to the National Conference of State Legislatures, 24 states legally decide the outcome of tied legislative elections by drawing straws or flipping coins.

(“Mississippi state election settled by 'drawing straws'”)

The 1978 film All You Need is Cash:

John Lennon loved the film and refused to return the videotape and soundtrack he was given for approval.

Alcohol was strictly forbidden during rehearsals and recording, so the cast fortified themselves with milk. The milk in turn was fortified with brandy.

(The Goon Show)

Everyone types git vommit at some point, it's not worth mentioning.

But just now I asked it to git re-arse master.

    data Narf a = Narf (Narf a) deriving (Eq, Show)

One kinda funny thing about this type is that it does actually contain a (countably) infinite family of values. But there's no way to tell any of them from any of the others.

    narfn 0 = undefined
    narfn n = Narf $ narfn (n - 1)

The deriving Eq is a strikingly empty promise.

Last time I looked to see if Spotify had George Crumb's Vox Balaenae, it didn't, but now it does.

Yay.

Mmm, they now have Harry Partch also.

Considering the dodecahedron as a graph with 20 vertices and 30 edges, it's not hard to find a hamiltonian cycle on the dodecahedron. This is a path along the edges of the dodecahedron from vertex to vertex that visits each vertex exactly once and returns to its starting point.

Such a path tontains 20 of the 30 edges, and it turns out that one can color the 30 edges in three colors so that the union of the edges in any two of the three colors forms a hamiltonian cycle.

Or, put another way, the double dodecahedron graph, with 20 vertices and 60 edges, is a union of three 20-cycles.

    -- Haskell

    data Narf a = Narf (Narf a) deriving (Eq, Show)

    narf = Narf narf

Today I'm thinking about the function $$\sin\bigl(2^x\bigr)$$

which I don't remember having considered before.

Another local delicacy is “scrapple” of which I am very fond. It has an undeservedly sketchy reputation. Many years ago Conrad Heiney described it memorably (if not accurately) as what you get when you throw a grenade into a barnyard.

For the record then: scrapple is primarily corn meal or other flour that has been boiled in meat broth. The meat broth may contain small bits of meat. The boiled mush is put into a loaf pan and left to firm up. None of this is very different from polenta, a similar Italian dish that enjoys a better reputation.

The loaf is then sliced, and the slices are fried until they are brown and crisp. This too is often done with polenta.

The batteries have a rated capacity of 235 mAh at a voltage of 2–3V. This works out to over 400 calories. If such a battery were to release its stored energy all at once in an enclosed space, I see no reason why it could not start a fire. If three were kept together, a sudden failure of one battery could trigger a similar failure of the others, with potentially serious consequences.

To my amazement, I find that I am actually considering that I buy a six-pack of batteries for $12.98 instead of two four-packs for $11.96.

It happens that we need exactly five. The extras will sit around uselessly and must be disposed of sooner or later. Lithium batteries are potentially dangerous. They are hazardous waste and cannot simply be thrown in the trash. If I buy a 6-pack, I will have only one-third as much hazardous waste to deal with; perhaps that is worth paying an extra dollar?

In !!n!! dimensions, in general, there are only three regular polyhedra. (For !!n=2,3,4!! there are more, but these are the only exceptions.) One of these is the !!n!!-simplex, which is the !!n!!-dimensional analogue of the triangle and the tetrahedron. It's natural to denote this as !!S_n!!.

And, happily, the symmetry group of !!S_n!! is !!S_n!!.

Come to think of it, nobody ever uses “horizontal” to mean “pertaining to the horizon” and I think hardly anyone would understand it if used that way. But it's a bit different case since “horizontal” actually means something that resembles the horizon, which stands as the prototype of a horizontal object.

Is it common to use the word “vertical” to mean “pertaining to vertices”? Or is that just confusing?

I think that's the sense in which it's used in vertical angles, but I remember I did find that confusing.

This useful guide to what parts are best eating.

If you're looking for a motto, try:

No situation is so bad that it can't be made worse by panicking.

It's worked well for me.

• Never use a ten-point scale where a five-point scale will do

• Never use a five-point scale where a three-point scale will do

• And don't use a three-point scale if a thumbs up – thumbs down is good enough

Git's fun because every problem is a puzzle, and every puzzle can be solved with ingenuity, but none of the puzzles are too easy.

OR SUFFER THE UNSPEAKABLE CONSEQUENCES

I am really pleased that when I decompose !!f(a, b)!! into a sum of !!f_M(a, b)!! and !!f_N(a, b)!!, where !!f_M!! is symmetric and !!f_N!! is antisymmetric, the letter “M” is actually symmetric, and the letter “N” is actually antisymmetric.

Sometimes notation works out and sometimes it doesn't, but I don't think I've ever seen it work out better than this.

A small part of Marc ten Bosch's guide to rotors and bivectors observes that:

it is possible to split a product (or any function that takes two arguments) into the sum of a part that does not change if we swap the arguments and one that does change, in the following way:

$$\begin{align} ab & =\frac12(ab+ab+ba−ba) \\&= \frac12(ab+ba)+\frac12(ab−ba)\end{align}$$

He means that in general we can decompose any !!f(a, b)!! as $$ f(a,b) = f_M(a, b) + f_N(a, b)$$

where $$\begin{align} f_M(a, b) & = \phantom{-} f_M(b, a) \\ f_N(a, b) & = - f_N(b, a) \end{align} $$

I never thought of this before. Compare Decomposing a function into even and odd parts.

Migraine, seduced by Muther Pendragon in magical disguise, was the mother of King Marthur.

This was already old when I saw first saw it, and that was in the 1980s:

    Date:     7 Apr 1977 1712-EST
    From:     Bob Chansler at CMU-10A
    Reply-To: Lord High Executier@CMU-10A
    Subject:  Re: Close, but no cigar
    To:       BRIAN.REID at CMU-10A
    CC:       chansler@CMU-10A
    Sender:   BOB.CHANSLER at CMU-10A
    Message-ID: [CMU-10A]  7 Apr 1977 17:12:49 Bob Chansler
    In-Reply-To: Your message of April 6, 1977
    My-Seq-#: 39492094
    Yr-Seq-#: 4992488
    Class:    A
    Subclass: MCMXLVII
    Author:   fred
    Typist:   fred
    Terminal: TTY88
    FE-L#:    44
    Reason:   Did Godzilla need a reason?
    Valid:    Not before 12 Apr 1977 1321Z
    Suspend:  After 19 Apr 1977 0000Z
    Spelling-errors-this-message:  0
    Spelling-errors-to-date:  23
    Weather:  Light rain, fog.
    Forcast:  Clearing by morning
    Psych-evaluation-of-sender:  slightly unstable
    Security-level:  Public
    Security-sublevel:  0
    Authority-to-send:  general
    Authority-to-rcv:  general
    #-people-in-terminal-room:  12
    XGP:      UP-cutter not working
    Ht/Wt-sender:  76/205
    Machines: M&Ms available but almond machine is empty
    M&Ms-Last-Nickel:  17
    Remailed-To: John.Zsarnay at CMU-10A
    Remailed-From: Peter.Schwarz at CMU-10A
    Remailed-Date: Saturday, 22 September 1979 0155-EDT
    Origin:  C410PS20 at CMU-10A; 22 Sep 1979 0155-EDT
    Remailed-To: Mike.Accetta at CMUA
    Remailed-From: John.Zsarnay at CMU-10A (A650JZ04)
    Remailed-Date: 22 September 1979 1615-EDT
    Origin:  A650JZ04 at CMU-10A; 22 Sep 1979 1616-EDT
    Remailed-To: Fil.Alleva at CMU-10A
    Remailed-From: Mike Accetta <Mike.Accetta at CMU-10A> (A650MA33)
    Remailed-Date: Saturday, 22 September 1979 2004-EDT
    Via:     CMU-10A; 22 Sep 1979 2006-EDT
    Remailed-To: Ken.Wertz at CMU-10B
    Remailed-From: Fil.Alleva at CMU-10B (A650FA33)
    Remailed-Date: Monday, 24 September 1979 1023-EDT
    Via:     CMU-10B; 24 Sep 1979 1025-EDT
    Remailed-To: Don.Provan at CMU-10A
    Remailed-From: Krafty Ken Wertz <Ken.Wertz at CMU-10A>
    Remailed-Date: Monday, 24 September 1979 1029-EDT
    Origin:  C425KW0F at CMU-10A; 24 Sep 1979 1036-EDT
    Remailed-To: Carolyn.Councill at CMU-10A
    Remailed-From: don.provan at CMU-10A
    Remailed-Date: Monday, 24 September 1979 1054-EDT
    Origin:  C425DP0N at CMU-10A; 24 Sep 1979 1055-EDT
    Remailed-To: Eddie.Caplan @ CMUA
    Remailed-From: Carolyn.Councill at CMU-10A (C425CC33)
    Remailed-Date: Monday, 24 September 1979 1631-EDT
    Origin:  C425CC33 at CMU-10A; 24 Sep 1979 1632-EDT
    Remailed-To: lawrence.butcher at CMU-10A
    Remailed-From: eddie caplan <EC0F at CMU-10A>
    Remailed-Date: 24 September 1979 1634-EDT
    Origin:  C425EC0F at CMU-10A; 24 Sep 1979 1635-EDT
    Remailed-To: Mike Kazar at CMU-10A, Craig Everhart at CMU-10A
    Remailed-From: Lawrence Butcher at CMU-10A (X335LB50)
    Remailed-Date: Tuesday, 25 September 1979 1811-EDT
    Origin:  X335LB50 at CMU-10A; 25 Sep 1979 1812-EDT
    Remailed-To: sipb @ mc
    Remailed-From: Mike Kazar <Mike.Kazar at CMU-10A> (C410MK50)
    Remailed-Date: Wednesday, 26 September 1979 0009-EDT

    I do not understand your concern about the size of message headers.

That header is 73 lines long and when I saw it, it did seem hilariously and impossibly long. Also, I believe that it was a joke, manually constructed for humorous effect. I think.

But I just selected ten email messages I received this week, all from real people, none generated automatically. The headers varied from 112 to 168 lines with a mean of 139.4.

Here's an example.

    Return-Path: <SRS0=eRb6=NB=gmail.com=xxxxxx.xxxxxx@bounce2.pobox.com>
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    Delivered-To: mjd@xxxx.plover.com
    X-Spam-Checker-Version: SpamAssassin 3.4.1 (2015-04-28) on plover.com
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        smtp.helo=mail-ot1-f53.google.com;
        x-aligned-from=fail;
        x-google-dkim=pass (2048-bit rsa key) header.d=1e100.net
        header.i=@1e100.net header.b=VnaTQExP;
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        policy.ptr=mail-ot1-f53.google.com;
        x-return-mx=pass header.domain=xxxxx.com policy.is_org=yes
        (MX Record found);
        x-return-mx=pass smtp.domain=gmail.com policy.is_org=yes
        (MX Record found);
        x-tls=pass smtp.version=TLSv1.2 smtp.cipher=ECDHE-RSA-AES128-GCM-SHA256
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    Authentication-Results: pb-mx9.pobox.com;
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          header.from=xxxxx.com;
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          smtp.helo=mail-ot1-f53.google.com;
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          policy.ptr=mail-ot1-f53.google.com;
        x-return-mx=pass header.domain=xxxxx.com policy.is_org=yes
          (MX Record found);
        x-return-mx=pass smtp.domain=gmail.com policy.is_org=yes
          (MX Record found);
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            (No client certificate requested)
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            for <mjd@plover.com>; Sun, 21 Oct 2018 10:56:14 -0400 (EDT)
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    Subject: "xxx" Xxxxxxxxxxxx Xxxxx
    To: Mark Dominus <mjd@plover.com>
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    X-Pobox-Client-Name: mail-ot1-f53.google.com
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    X-Pobox-Original-Sender: xxxxxx.xxxxxx@gmail.com

    I do not understand your concern about the size of message headers.

Holy cow. What would they have made of this in 1977, I wonder?