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The tattoo includes the patient's signature. This part has been blurred out in the picture. Complete text of letter to the New England Journal of Medicine
Sentences I wasn't expecting to read today:
The majority concluded that it was not, and that the hapless author of the drawing should not be subjected to probation and “work crew”. One of the three judges dissented, claiming among other things that the image constituted “a sexually explicit image of a minor”. Often when I read court opinions, both sides seem to have reasonable arguments. This time I think the dissenter is confused, and perhaps doesn't understand Snapchat. (The judges couldn't see the actual picture; it had expired.) The Colorado Supreme Court declined to hear the appeal.
In a recent article, I mentioned a proposal of Bjarne Stroustrup to allow overloading of whitepsace in C++. I did not read it closely, as the content seemed in offensively poor taste. Gareth McCaughan gently pointed out that the proposal's date is April Fool's Day, and then, when I missed what he was getting at, he pointed it out less gently. I admit, I was completely taken in. The humor here was definitely too subtle for me. The proposal was not far enough out of character. If Edsger Dijkstra or Joe Armstrong had published this proposal, I would have known right away it was a joke. If Larry Wall had, I would have had to read it twice and even then I would not be sure. If Hannibal Lecter claims to have eaten a baby, your first thought is not to check if it is April 1. It is a thin hope, but at least now I can look forward to the possibility that Stroustrup might someday announce that C++ itself had been a similar joke.
I like doing code reviews. Usually when I'm reading someone else's code, my persistent confusion is a liability. In code reviews, every mystery becomes something to put into the report! Instead of just being baffled, I can write down “I was baffled, please fix this”.
Thinking on convicted rapist Canaan Banana, I wondered if this description was misleading. It seems to imply that Banana was convicted of rape, which I think is not the case. He was actually convicted of sodomy in connection with the rapes. However, one could argue that
and therefore he is a convicted rapist. This is slightly misleading, but in this case only slightly. But suppose the guy had been acquitted of both rape and sodomy, and then later in a completely unrelated matter, had been convicted of embezzlement? (Or littering?) “Convicted rapist” would seem to be substantively misleading. Probably some linguist has done their doctoral thesis on this topic. Maybe more than one.
Omar Antolín Camarena and Dfan Schmidt almost simultaneously wrote to
point out that in some restricted circumstances, the Julia
programming language uses abutment for
multiplication. If v is a variable and n is a literal integer
constant, you can write nv to mean n × v. For example, M. Camarena and M. Schmidt's messages were sent barely two minutes apart:
Second prize is a set of steak knives, Dan.
Yesterday I wrote a post that used the word “abutment” seven times. I love this word, and I don't get as many opportunities as I would like. My love of this word goes back to 1991, when I received email from my (then) girlfriend, who was in graduate school studying urban planning. It said, in part:
And so the abutting doo-flotchy entered my vocabulary permanently. Google searching for “low level light area” finds exactly one relevant document, clearly a copy of a portion of some zoning code. I could find no direct internal evidence of when or where it was from. But it does mention “Ord. No. 361-03”, presumably a municipal ordinance, and this I could identify; it is indeed a Denver ordinance, passed in May 2003; the floor space bonus for abutting doo-flotchies persisted at least that long. Research is a thousand times easier than it was thirty years ago. Truly, we are living in an age of marvels, and the Internet is one of the chief marvels. I hope I never start taking this for granted.
Today's email contains a 419 scam that is interesting in a couple of ways.
A few days ago I mused:
Gentle Readers wrote in with examples.
E.W. Dijkstra's magnificent body of unpublished napkin notes (pardon me, ‘manuscripts’) contains a discussion of “invisible operators”. Complaining about the invisible multiplication sign, he says:
Languages that use abutment for string concatenation include SNOBOL,
REXX, and awk. Also the C preprocessor from C90 forward. I was going
to say I thought this was the only choice of concatenation operator
that was worse than overloading “It’s weird, but it works better than you'd expect” might be SNOBOL's official motto. I would like to visit the alternate universe in which SNOBOL was as influential as ALGOL 60. It might not work as well, but it would be charming. People would wear hats with antennas sticking up, and everything would be decorated with rocket fins. SNOBOL also uses abutment to indicate concatenation of patterns,
which, because of the semantics of pattern execution,
is rather like using it for execution
sequencing. That is, if Many languages, such as Haskell, use abutment as functional
application: I think Larry Wall once said that you can tell what a language thinks is
important by looking at what it uses the
I spent two hours today figuring out why the margins were chopped off
this thing I was printing. It was a long diff file, and I was trying
to print it with First I wasted a lot of time tinkering with the CUPS PPD file for the printer. It has a lot of stuff that looks like this:
and it's not real clear how these things are related or which of these 10 numbers needs to be changed. Okay, the printer was only cutting off the two short edges, not the two long ones, so we can rule out half the numbers that refer to width dimensions rather than length ones. And tinkering with the first two lines didn't change the output at all (what are they for, anyway?) so really there are only three numbers to play around with: the 36, the 783, and the 792. I messed around with those and printed 26 test pages with the same content in 26 slightly different positions, labeled each one with the magic numbers that produced it and tried to develop a theory about what the numbers actually meant. And I did develop a good model and I thought I understood more or less what they were doing, except that it didn't solve my problem because the content was somehow cut off in every single one of those 26 pages. That 26 doesn't count the three times I choked the printer by trying to supply negative values in place of the 36. One complication was that there is at least two ways for the content to be cut off. It could be cut off because CUPS thought it would be outside the printable area, and so didn't bother to render it there, or it could be cut off because it was outside the printable area, and so even though CUPS rendered it, the printer couldn't put any ink there. If the cutoff is far enough from the actual paper edge, you can be sure it was the first thing and not the second, but that is no help because what you really want to know is what is going on when the cutoff is near the edge. At last by comparing the standard system test page and the printed
output of
No, that wasn't it. That would have cut off the long sides, not the
short sides, because A4 is longer and narrower than US letter. And
anyway, I was printing on a Hewlett-Packard Deskjet D4360. And apparently
letter-size paper somehow becomes different when it is inserted into a
Hewlett-Packard Deskjet. It is no longer And that's what I did with a small but appreciable fraction of my ever-diminishing remaining lifetime.
A couple of days ago I mentioned being intrigued by the Twitter hashtag #الغيبوبه_الجماعيه that was trending last September 1. A correspondent in Egypt has provided the explanation: That day was the end of Eid al-Adha, a major Muslim feast, celebrated worldwide. My correspondent informs me that people stay up late partying and feasting and are tired out by the end.
A couple of days ago I mentioned Nicole Leffel's project to find the survey question that annoyed the most nuns in 1967. I didn't say at the time, but the most annoying question, which 3,702 out of 140,000 nuns found “too annoying to answer” was whether they agreed or disagreed with the statement:
I was not at all sure what this meant, and I imagine many readers were in the same boat. Sumana Harihareswara posted the survey to MetaFilter and in the ensuing discussion, MetaFilter user Eyebrows McGee provided a long and detailed explanation. This is a brief excerpt:
The whole explanation is much longer and very detailed. Check it out. Another user comments:
I went to have my piano lesson today with Ms. E. I've been with her for almost three years and it's a perfect professional relationship: I pay her for piano lessons and she teaches me to play the piano; we make small talk for approximately ten seconds before each lesson. Ms. E seems to be in her late twenties, and has a nose piercing and knuckle tattoos. She is in some sort of band, because sometimes she misses our lesson because the band is recording. But I don't know the name of the band or what kind of music they play. She seems very quiet and while I suppose she sometimes laughs I don't think she has done it around me. As far as I can tell, she never thinks about anything except playing the piano. I know next to nothing about Ms. E. Not even: in whose house do we have the lessons? Not hers; at one point a couple of years ago she mentioned that she lived somewhere else. Who are the other people who live in the house, whom I have seen almost every week for three years? Her family? I do not know and while I am vaguely curious I am not interested enough to ask. The two kids who have the lesson after mine arrived about ten minutes early. They are around eight or nine years old. They were not very patient while they waited for me to finish. They whispered and squabbled and then started to shove each other on the sofa. Over her shoulder, Ms. E snapped at them “knock it off!” I have never heard her raise her voice before! This is a whole new side of her that I have never seen. Certainly she has never spoken to me that way. I suspect that the kids' lesson is rather different from mine. I got a hint of this once before, when one of the other students showed up early, and Ms. E had crayons and a coloring book ready. It dawned on me then that giving piano lessons to kids is somewhat less than 100% piano and more than 0% babysitting. I really wanted to hang around and observe the kids' lesson to see what else was different and what Ms. E was like when giving it but of course I didn't suggest it. (Triple creepy!) But I still wonder what it is like and I will probably never find out.
This weekend we were discussing the strange locution
or
The word “over” here means “the field of scalars of this vector space is…”. It would be less obscure to say “this is a vector space with real scalars” or “a general vector space with scalars from field F”. I don't know why we use the word “over”. Most “over” in mathematics suggests some sort of spatial intuition, or else refers to a particular notation in which something is over something else on the printed page. This is certainly not the second of these and I don't think it is the first either. Vector spaces have a very strong geometric flavor, but the scalars are not independent and they are certainly not under the rest of the space. I thought about it more and I think I remembered the first time I heard "X over Y" to describe a vector space. I was puzzled, but I don't think I was puzzled because of the spatial language. It was because the example was “a basis for the reals over the rationals”. I think there is no way anyone could understand what this means unless they had already heard “over” used this way or unless they were already familiar with the bizarre mathematical object being described. The real numbers can be considered as a vector space where the scalars are rationals, easy enough, but then if you want the vector space to have a basis you have to go to mathematical la-la land to find it. Aha, I thought of another use of “over”: we can sum over the terms of a series or over the values of an index set; similarly in computer programming we loop over the elements of an array or we map over a sequence.
Everyone seems to agree on what constitutes a good french fried potato: it should be crisp and golden-brown on the outside, soft and fluffy inside. But most of the fried potatoes I get in restaurants are pretty terrible, pale yellow, soggy and mealy. I don't understand it. Everyone agrees on the criteria for a good fry, so why do all these restaurants serve fries that they know nobody will like? And then people eat them. Wouldn't some restaurant figure out that they could make more money by serving better fries? Or maybe customers would complain more? “Hey, do you call this limp wad of starch a french fry? Everyone knows fries are supposed to be crisp and golden-brown!“ It's not hard to make a good fry. He's the secret technique:
<sarcasm>Tricky, huh?</sarcasm> Cooking good fries is not hard. You just have to be a little bit patient. It is very easy to take them out too soon, and very difficult to take them out too late. Just leave them alone and do something else for a while. If you do take them out too soon, it's easy to fix an underdone fry. Put it back in. The fries are happy to be fried twice. Some people even say they are best that way. I suspect those people would be just as happy if the fry were left in twice as long to begin with, but whatever. After a lifetime of getting soggy fries, I discovered that in most restaurants you can get much better fries by ordering them “well-done”. Sometimes they come out soggy and yellow anyway, but you can send them back: “I ordered these well-done!” Let's all create a better world by demanding better fried potatoes.
Julie Moronuki asked why left adjoints are left and right ones are right, and I had to admit that I always get them mixed up also. My grasp of spatial relations is excellent, but I often get handedness backwards. As a kid I learned left-hand from right-hand quite late, and depended for a long time on the trick of holding up my hands to see which one looked like the letter “L”. On one memorable occasion my sister was driving and I was navigating, and I told her to turn left at the next traffic light. As she began to turn, I got very agitated. “No, left! Turn left! … sorry, I meant right.” I hadn't mixed up the route. I knew which way I wanted her to turn, and it was the correct turn, but I used the wrong word for it. Strangely, I have never had any trouble with clockwise and counter-clockwise. For many years I was not always sure which one would turn the water on and turn the water off, but I could remember that counter-clockwise is for un-screwing a screw, and I would picture the faucet mechanism in my mind and imagine the screw and the washer moving upward up to let the water in, so I always got that right. I couldn't help Julie with the left and right adjoints. I said:
Near my house is the “Garden Court Eatery”, a typical neighborhood deli / beer store / convenience market. I have passed by it dozens of times, but I never realized before that its sign is perplexing. If you were running a neighborhood deli, what three things would you put on your sign? “Beer”, certainly, people always want beer. That would be my first pick too. “Breakfast” also seems like a good choice. It might not be obvious to prospective customers that the store serves hot breakfast, since many similar delis don't. But buffalo wings? Is that the thing most likely to get people into the store? More than, say, SANDWICHES? LOTTERY TICKETS? Or SNACKS, or COLD CUTS? Okay, you could argue that people will already realize this is a deli and will assume that those things are available, whereas the mention of buffalo wings is genuinely informative. But there are so many other things that would be equally informative. Why is BUFFALO WINGS the most important item? There must be a story here, if only a small one. In former times the sign was even more perplexing. Instead of BUFFALO WINGS it emphasized “DUNGEONESS CRAB”.
Today in the “I wish I had thought of that” department, Nicole Leffel has analyzed the results of a 1967 survey that was given to 140,000 American women in Catholic ministry to find the question that the subjects found the most annoying! I love this. I didn't realize before that answering this question was on my must-do list, but now that I know I can cross it off, because M. Leffel has already taken care of it for me. Thank you! what’s the most annoying question to ask a nun* in 1967?
Katara and I were talking about something she didn't want to do and we conclueded that there was no way around it; she would have to do it. “Oh well,” I said. “At least it'll build character.” “Shut up,” replied Katara. “Hey, don't you tell me to shut up!” “You said that if you ever say that something builds character, it's parody, and I'm allowed to tell you to shut up.” I thought about this. “Yeah, that does sound like something I would say.”
Sometimes I like to go to the Twitter page that shows the currently-popular hashtags and see what they are about. Today, I learned, the Brits are discussing the new national budget proposal. The most intriguing ones are often in Arabic. For example, today we have 92,000 tweets about “#زد_رصيدك51 ” whatever that is. Google Translate glosses it as “# Z_Rassick 51” which leaves me no better off than before. One memorable example was “#الغيبوبه_الجماعيه” that was usually accompanied by various cartoon images of people collapsing into bed, or propping open their tired eyes with toothpicks, or the like. Google translated it as “coma collective”. I never did find out what this was about. The world is a lot bigger and even more interesting than I imagine, and it's fun to get these glimpses of some of the details. This is my first attempt at a blog post with both left-to-right and right-to-left text. I had a lot of trouble typing it.
A couple of months ago I listened to Alanis Morisette's Jagged Little Pill for the first time; I mostly missed it when it came out. I liked it a lot. Wikipedia says, of the album:
and of course the songs people mostly remember from it are the screeching angry ones like “You Oughta Know”. But another song, “Head Over Feet” has made a strong impression on me for the opposite reason. It is one of the most optimistic, positive songs I have ever heard. It is from the point of view of a person who is in the middle of their first successful relationship:
I often don't notice lyrics, and when I do notice them I often regret it. These lyrics are evocative and draw a picture of the two people. The narrator's new partner treats them nicely and loves them even though that is not always easy to do. I had been led to believe this album would be one-dimensional, but it is not.
A couple of nights ago, Toph and her friend Albertus were going to go from our house to his. They got on their jackets and went out to the courtyard to wait for me to be ready. I put on my boots and came outside, but then realized I had left my keys behind. When I returned with the keys, about thirty seconds later, Toph and Albertus had vanished. I guessed they had wandered off to a different part of the courtyard, so I walked around hollering for them, but did not find them. Then I guessed that they were hiding as a prank, although that would have been out of character. When they turned up again a few minutes later I was beginning to be frightened and angry, and scolded them for wandering off. But what had actually happened did them credit. They had seen me come out of the house. They set off down the driveway, expecting that I would be right behind them, and did not see me go back for my keys. When they got to the next corner, they didn't see me, so they stopped to wait for me to catch up. Then when I didn't appear they concluded that something had gone wrong and came back looking for me. I like when things turn out to be better than I thought they were, especially when it turns out that everyone was doing what they should be doing. That kind of minor misunderstanding can happen to anyone at any time, and nobody is to blame. The only question is how well you handle the error condition. I think Toph and Albertus handled this one flawlessly. I apologized for scolding them and explained that it was only because I had been worried; when your kid disappears suddenly at night, it is hard not to freak out. And I told them that I thought they had done just the right thing and shown good judgment. They are good kids, mature and wise. Except for the time Albertus had cut up his hand by punching through the glass storm door, and when I asked what had happened, he demonstrated by punching it again. That was not so smart.
After my blog got some referrals from Voat last week, I looked into its history. It reminded me of a story. When Katara was in second grade, some of her age mates formed a “Stealing Club”. Katara reported this with great disgust. She found the premise contemptible. But she also pointed out “If you're going to have a stealing club, you shouldn't call it ‘Stealing Club’.” Anyway, this was on my mind because I learned that one of the
communities that reconstituted at Voat after being banned from Reddit
was
The Third Edition of the OED (not the Second) has the answer. Its earliest citation for the phrase is from 1821 (“You prudently drop that subject, as Pat says, ‘like a hot potato.’”) but for the game it only goes back to 1915. Thanks to Jesse Sheidlower for this information.
This is the most exciting thing to happen to me this month: When the rest of Philadelphia was being wired for broadband Internet, my little cluster of 46 houses was somehow skipped. We have been limping along with copper DSL for the past ten years, to everyone's frustration and especially that of my kids. Our homeowners’ association has spent the last five years nagging and chivvying the communications monopolies to honor their legal commitments and provide us with high-speed internet. Last month the phone company sent a team of workers to install conduits for our new fiber-optic cables. Today these guys are in my back yard running the cable.
What a lovely metaphor this is. So evocative! Everything about it is clear, except perhaps: why would you be holding a hot potato to begin with? Well, that's life, sometimes someone hands you a hot potato, or one drops into your lap, and then there is nothing to do but get rid of it again, as quickly as possible. For metaphors, I like thinking about what a non-native speaker would think of them. Good metaphors stick with you. When I was studying Korean, my teacher mentioned the simile “flat as a squid”. I was confused. “Flat as a squid?” I asked. We confirmed that we were both thinking the same for “squid”, and I asked “why is a squid flat?” But then the answer: the Korean phrase is alluding to a dried, pressed squid, which is a common bar snack. Aha! “Flat as a squid,” indeed. And I have never forgotten it; if anyone ever said “flat as a squid” I would think of the dried squid again. I think “hot potato” is like that. Maybe the Koreans don't say “hot potato” but they do have potatoes and it's immediately obvious that to drop something like a hot potato does not mean to drop it grudgingly and reluctantly. I don't know if Koreans ever say anything like “flat as a pancake” but they do have pancakes of many sorts and I'm sure they would understand right away. I tried to find out: does the phrase predate the game of Hot Potato, or did the phrase come after and specifically allude to the game? But none of the usual dictionaries was helpful. [ 20171120: The answer ]
Nobel-prize-winning biologist Albert Szent-Györgyi:
I felt similar disappointment in high school when my friend told me about the Schrödinger equation that perfectly describes the future of any physical system, but we can only solve it for the case of a single hydrogen atom.
There is a trope that when a thirteen year old girl has a crush on Corey Taylor, she will fill pages of her notebook with her future name “Mrs. Corey Taylor” to see how it will look. I have done this myself a couple of times. I wrote “Mark Jason Dominus, FRS.” (I recognize that this is never going to happen. Fellows are elected only from Commonwealth nations, and I am not qualified anyway. A boy can dream.)
In an employer chat channel, a co-worker once asked “if you were a supervillain, what would your power be?” I think the answer is obvious. With a name like “Dominus” it is inevitable that I would be the evil master scientist, Markus von Dominus, and regularly threaten to conquer and/or destroy the world. “Von” has been obsolete in Germany since 1919. Some people still have it as part of their surname, although it no longer has any legal significance. Some other people change their names to add it. I briefly wondered if it would be fun to change my name to “von Dominus”, but I found a list of other people who had done so and they were all pretentious jackasses. I did not want to be so obviously a pretentious jackass, so I gave up the idea.
These jokes work equally well regardless of the sex, gender, or orientation of the characters.
My grandfather told me that second one.
This math.se comment by Daniel Wainfleet offers a problem that I found fun.
M. Wainfleet quotes the author (Rouse Ball or Coxeter):
This is a very useful hint! Mouse over to view the solution: Since !!p!! and !!q!! are both odd, their mean, !!\frac12(p+q)!!, is an integer. It cannot be prime, since !!p!! and !!q!! are consecutive primes, so !!\frac12(p+q) = ab!! for some !!a!! and !!b!! each greater than 1. Then !!p+q = 2ab!!.
Yelp asks me to give restaurants a rating of between one and five stars. This suits me. People sometimes ask me to rate things on a scale of one to ten, and I never feel like my discrimination is delicate enough to warrant so many different grades. What's the difference between a 6 and a 7? I'm not sure. I have a standard system to convert my overall impression to stars. The most common rating is three stars: ☆☆★★★ “Good”
☆☆☆★★ “OK, I guess”
☆☆☆☆★ “Bad”
Yelp doesn't allow fewer than one star, which is fine with me. Going in the other direction, we have: ☆★★★★ “Excellent”
★★★★★ “Outstanding”
My impression of Yelp ratings is that this is atypical and that ratings are heavily weighted toward four and five stars, and that by giving three-star ratings to restaurants I like, I am doing them a disservice. That is unfortunate for everyone. Here are the rating distributions of a user A, on the left, and myself, on the right:
Some upward skew is to be expected. There are plenty of mediocre restaurants that I don't bother to review, but when the food is good I get excited to tell people about it. But clearly, the two of us mean something very different by five stars. When I give a restaurant five stars, you know it means I like it better than 82% of the other restaurants I've reviewed. When use A gives five stars, all you know is that it's better than the worst 30%. I've often wondered how hard it would be to weight different users’ ratings, so when user A gives out five stars two-thirds of the time, their stars are not worth as much as those of user B who awards five stars only one time in six. And conversely, user A's rating of one star seems to be more significant than mine, because a one-star restaurant is in the bottom 3% for user A, but only the bottom 10% for me.
There are red beans, pink beans, white beans, and black beans. There are, however, no blue beans. There are navy beans, but despite their name, they are not navy blue.
A user on Math.Stackexchange asks
My mathematically impeccable shitpost reply:
Do I want to suggest that there is a deep and subtle point lurking here? No, I better not push my luck. [ This stupid article now has a stupid followup. ] [ Addendum 20190526: Someone impudently downvoted this post today. Unbelievable. ]
Today, reading about the political history of Zimbabwe, I discovered that Zimbabwe's first president had the astonishing name of “Canaan Banana”. Reading the Wikipedia article to find out more, I learned:
The citations, to obituaries from The Telegraph and The Economist, check out. The Telegraph adds:
That sort of thing never works out. I suppose that if you're a politician, there's only one way to prevent people from mocking you, and that's to arrange for them to be immediately and disproportionately punished. If you can arrange that, you don't need to pass a law, and if you can't (or won't), the law is not going to help.
Even back to Fortran and Lisp, almost every programming language uses
Perhaps someone once invented a programming language that used simple abutment for multiplication, the way mathematics does? But while I know a couple of languages that use abutment to mean string concatenation, I have never seen it used for multiplication.
This morning, looking at the Washington Post, I saw the headline “Zimbabwe’s military takes control of country and detains President Mugabe in showdown over political succession”. “Wow,” I said. “Zimbabwe has had a coup.” But it seems I was mistaken. The Post reports:
A tweet from ZANU-PF, the long-time ruling party of Zimbabwe, was also eager to clear this up: This Twitter responder agrees: My favorite commentary so far has been another tweet, from ZANU-PF's youth league:
Peaceful aplomb! I have a new life goal, to conduct my affairs with peaceful aplomb. You have my word, that if I ever take control of Zimbabwe, I will do it with peaceful aplomb. Many years ago I was wandering around somewhere, maybe Fort Lauderdale, and I encountered a representative of Zendik Farm on the corner. I am a great believer in the power of Fate to lead me to things I should read, so I bought one of their zines. (Also, zines are fun.) We had a short conversation, in which the person told me about life on Zendik Farm. It sounded nice enough, if you like that kind of thing. But much too early in that conversation, without my having asked, he assured me that Zendik Farm was “not a cult”. Hmmm.
In most Slack channels, one of the permitted topics of conversation is the topic of the scope of the channel itself: it is acceptable to discuss what topics are appropriate for discussion in the channel. However, there are some abnormal channels in which discussions of channel scope are inappropriate, and should take place elsewhere. For example, consider a trivial channel Discussion of what is on-topic for abnormal channels should take place
somewhere, so one naturally wants to create a Now suppose you need to discuss whether something is on-topic for
But you definitely can't do it in (Note that there's also no real problem with Emanuel Buholzer suggests that such discussions could take place in private messages, outside of any channel. This shows that he prefers Morse-Kelley set theory to Zermelo-Frankel.
By which I think he certainly means, if the Earth explodes, the policy is worthless since it has been destroyed along with the rest of the Earth. And if your system turns out to be inconsistent, thus rendering all its theorems worthless, your consistency proof is thereby just as worthless. Why then are mathematicians even interested in consistency proofs? ZF proves that PA is consistent. But ZF would prove that PA was consistent whether or not this was actually true. I suppose it is possible that PA could be consistent but ZF could fail to prove it, so it is of some interest that this case is ruled out. Still it seems like pretty thin soup.
The Bible contains numerous references to the “ephod”. It is some sort of garment or garb, but it is not entirely clear what it was like. For example:
I suggest that the ephod was actually an iPod. The biblical evidence for this would seem to be equivocal. For example:
Presumably even in biblical times, an iPod was not made of linen. But there is an explanation: the word “ephod” could refer either to the iPod itself, or to the linen belt or sweatband to which it was attached. Clearly David was wearing some sort of sport cuff while dancing, and attached to this, or perhaps in a pocket of it, was the iPod that supplied his dance music. Whatever, I am not an expert. Biblical scholars have thousands of years of practice in explaining away minor discrepancies like this one, so I will leave it to them.
Why crows? Are they noteworthy for flying in straight lines? Why not, say, carrier pigeons, which are famous for that? (It reminds me a little of Charles Dickens’ musing on “dead as a doornail”:
“As the hawk flies” would be a funny twist on the phrase, since hawks are famous for gliding in slow lazy circles and not really going anywhere until they dive-bomb a vole. Or perhaps “as the penguin flies”. I don't know what that should mean but it can't be good.
Today I got briefly excited because I learned that there is a Vampire Flying Frog. But it turns out to be disappointing. I have no serious objections to two of the three, but the frog is not actually vampiric. Its tadpoles have two fang-like protuberances. PATHETIC! It doesn't actually fly, either, but I'll give it a pass, on the same exemption that is used by the flying fox and the flying squirrel. The flying fish has a separate exemption.
This tweet of Reid McKenzie was so inspiring that when I saw it, I stopped what I was doing and immediately set up this blog. And here we are. Thank you, M. McKenzie!
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