12 recent entriesThe road to epsilon-zero: Productive programs and well-founded ordersThere are two kinds of theoremsThe road to epsilon-zero: Coin-moving games with no coinsSeven books I keep close because I love themThe road to epsilon-zero: Infinite Nim as a coin-moving game“Steph Curry: fluke or breakthrough” ten years laterThe road to epsilon-zero: Nim always ends, even with infinite ordinalsThe road to epsilon-zero: ordinals as nim-heapsStarting to understand epsilon-zeroIt’s our language now!I owe my life to a 1913 road rage incidentDeciphering basmala
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Seven books I keep close because I love themThe bookshelf by my elbow, the one that I can reach without getting
up, has seven books on it, not necessarily the ones I look in the
most, but the ones whose emanations I most hope will infuse me as I
write.Roget’s Thesaurus (4th edition)The one I actually refer to most often is the Harper and RowRoget’s
Thesaurus. I thought I had acquired this in my teens, but the note
on the flyleaf says 1989.This is the fourth edition. I was very excited to get the eighth
edition, which I thought I might like better, and for some time I kept
them next to each other so that I could look up the same things in
both, and compare. my conclusion was that while the eighth edition
had more stuff in it, it wasn’t stuff I needed. And it is really fat.
So I have retired it to a farther shelf and will eventually get rid of
it.The thesaurus is a book that is widely misunderstood. It is not, as many people mockingly
imagine, just a compendium of synonyms, and its correct and intended
use isnotto replace common words with more impressive-sounding
ones. just as the correct use of a screwdriver is not to scrape the
veneer off of an expensive cabinet.“Thesaurus” means “storehouse” or “treasure room”. Roget’s idea,
similar to that of John Wilkins before him, was to classify everything
in the world into a hierarchy, in this case a hierarchy with a
thousand divisions. At the top level the divisions are grouped into
“Abstract concepts”, “Space”, “Physics”, “Matter”, “Sensation” and so
on. Then under “abstract concepts” there are subclasses, of which
subclass VI is “Time”, subdivided into five smaller sections:A. Absolute timeB. Relative timeC. Time with reference to ageD. Time with reference to seasonE. Recurrent timeAt the next level down, section (1)(VI)(B) is divided into:§116. Priority§117. Posteriority§118. Simultaneity§119. The Past§120. The Present§121. The FutureRoget’s idea is that if you are thinking or writing about time, and
specifically about how it goes by, you will leaf through those
sections for inspiration, not to find a more pompous way of expressing
something you have already written, but to refine your own idea of
what it is you wanted to express.Perhaps you are trying to say that one event followed immediately
after another. You might look at “§117 posteriority (later time)”
which mentions “ensue”, “consequence”, “aftermath”, and “subsequent” —
not synonyms, but related aspects of similar concepts, worth more or
less consideration depending on what you are trying to emphasize.
§117 will also suggest common phrases like “step into the shoes of” —
not a synonym by any means, but a related idea. This isprobablynot
what you wanted in this case, but it in another it might be just the
thing, and in any case it might give you a bright idea.If nothing in section 117 seems suitable, it is right next to Ҥ116
priority”, and you might discover that instead of saying that the
second event followed immediately after the first, you would rather
say that the first immediately preceded the second. Or perhaps you
realize, looking at “§118 Simultaneity”, that what youreallywant
to say is that the two event werenot quite simultaneous. Or
perhaps, finding your way to “§131 Earliness” and “§132 Lateness” you
realize that your meaning would be more clearly expressed if you said
that the second event was a little tardy, or that the first event was
premature.Looking through the index for “immediately” you will see that the
index distinguishes several senses of “immediate”: are you trying to
suggest instantaneity, or continuity, or haste, or promptness, or
punctuality? And in this way the book helps you refine your understanding of
what you were trying to say.One can use the thesaurus for more concrete tasks. Perhaps I am
trying to remember a word, but I can’t quite put my finger on it. I
know it it isnot“coexisting”, but is something like it. I can
look up “coexisting” in the index, and it will take me to “§118
Simultaneity” where I find “contemporaneous”… aha, that’s what I was
looking for! The really important thing about the thesaurus is this
large-scale organizing principle, which puts related ideas near one
another.Note that none of this works for someone who doesn’t know what the
words actually mean. All that person can do with the thesaurus is to
replace one wrong word with another one, more or less at random.
Effective tool use requires skill and training, and careful thought.An online version would be more convenient, but again, it wouldn’t
have the same stuff and I am very attached to the one I have.My banishment of the 8th edition left a lot of space on the shelf,
some of which I have filled with an anthology of the prose of Sir
Thomas Browne. I think this will be healthful and inspiring for me,
especially if I remember to take it up and thumb through it from time
to time.The Prose of Sir Thomas BrowneOne recurring theme on this blog since the very earliest days has
been the writers of the English Baroque period. In 2008 I wrote:[Browne] is witty, and learned, and wise, and humane, and to read
his books is to feel that you are in the company of this witty,
learned, wise, humane man, one of the best men that the English
Renaissance has to offer, and that you are profiting thereby.His work was also a favorite of Jorge Luis Borges’, in case you
consider that a recommendation.Browne has shown up here a number of times, although not so much as he
should have, because I started the blog the yearafterI was on my
big Thomas Browne kick. One reason I have put this book next to my
elbow is that I hope it will spark a new Browne kick. (I wrote in
2006 “I’m sure I will return someday”, and it is long past time for
that return.)My favorite book by Browne is hisPseudodoxia Epidemica, which is a compilation of
stuff that people in 1646 believed that Browne thought was probably
wrong.I wrote about that in some detailin 2008 although
I didn’t get around to publishing it until 2020. And somehow the
other three articles I was writing about this have never seen the
light of day. One is about his discussion of whether John the Baptist
actually ate locusts or whether they were locustbeansor something
else. Browne is firmly on the side of it being actual locusts, as am
I. My unpublished article says:Chester Brown’sversion of the gospels makes it
clear that John was a crazy old
bug-gobbler.Panels fromYummy Fur#17, page 15, byChester Brown.Also Sir Thomas comes up in connection with whether snails have eyes
in their horns — a rare example where he was wrong, and for a dumb
reason:If we concede they have two eyes, we must alse grant, they have no
lesse than four… And therefore if they have two eyes, they have also
four, which will be monstrous, and beyond the affirmation of any.Browne seems to be noping out of the very idea of four-eyed snails,
and therefore that they must have none at all. In a later edition of
the book, he changed his mind, which is to his credit.He had a thoughtful and well-informed opinion about whether
Pythagoras forbade his followers from eating beans, supposedly because
he thought they contained the souls of the dead. (Browne says the
former is true, but not the latter.)I have trouble connecting with the thinkers of the Middle Ages. Their
thinking seems to me to be frightened, so overcautious, so cramped and
circumscribed, I can’t read it without sadness for the way that
medieval Christianity strangled the human spirit for so long. But in
the early Renaissance there is a flowering of a joyfully brave
willingness to try to understand the world, and to follow any inquiry,
no matter how extravagant or ridiculous. The whole idea of God has
transformed, changed from something constricting to something
empowering. The world before belonged to God, and humans were in it
only grudgingly and on promise of good behavior. But when the
Renaissance started, the world became a beautiful gift, in which
humans had been placed to honor God by admiring and marveling at his
creation.This admiration and marvel, the willingness to follow any path to
understanding, is how I want to be about knowledge and how I hope I
am. Reading Browne, I always feel like he and I would have gotten
along well, and that that is one of the best parts of myself.Boccaccio’sDecameronThe story of theDecameronis this: It is 1348, and Florence is
devastated by Black Plague. Nothing can be done, despair is
everywhere, and there are not enough left living to bury the dead. So
ten young people, still healthy, decide to turn their backs on
suffering and quit town. They take provisions and servants, retire to
the country, and try to forget the horrors they have seen. There they
spend the time feasting, walking in the gardens, playing chess, and,
once a day, for ten days, they meet, choose a theme, and then each of
them tells a story on the theme.I explained this once to a friend who said “That sounds cool, when was
it written?” I said “In 1348!” It is one of the two great works of
classical Italian literature, the other of course being Dante. Dante
is solidly medieval, hierarchical, doctrinaire, and obsessed with a
God who is supposedly loving but doesn’t seem to know how to show it.
That was in 1308 or so, and then, only a few decades later, we have
theDecameronwhich could not be more different. It is about
people, doing people things in the real world, eating, drinking,
singing, arguing, and making love. God is present, but not
oppressive. He has sent a terrible plague for who knows what reason,
but rather than submit to it the characters of theDecamerontry to
take practical steps to make the best of it.There is a story in theDecameronfor every mood, usually more than
one. Some are sad, some romantic, some funny and salacious.
Dioneo is exempt from following the daily theme and usually has
a story that is more or less dirty.My favorite story is probably the one about the cross-dressing English
princess, or perhaps the one about how young Caterina wanted to sleep
on the balcony so that she could hear the nightingale, which I find
very sweet. But the funniest one is about the abbess who is called
out of her cell one night to berate a nun for having her lover stay
over, and who doesn’t realize that in her hurry she has put her own
lover’s trousers on her head instead of her wimple.I have several differentDecamerons, but this copy is the Cormac Ó
Cuilleanáin translation, which has made several previous appearances
here:There’s also an unpublished blog article inviting me to look into this
passage:Messer Lotto Gualandi gave him a daughter of his, Bartolomea by name,
one of the fairest and handsomest young ladies of Pisa — although most
of the females from that benighted town look like tarantulas.The J.M. Rigg translation says “spotted lizards”. This is closer to
the original Italian, which islucertole verminare, literally small
wormy lizards.I have my doubts about the desirability of living to be a thousand
years old, but if I do decide to do it, one reason will certainly be
that I will need the time to learn Medieval Italian and translate theDecameron.From Frege to Gödel, edited by van HeijenoortThis is a collection of the most important papers in mathematical
logic from the time of Frege (who, I have written before, was
responsible for kicking the field of logic out of its medieval period
into the modern world) to Gödel (who spoiled everything).In between these van Heijenoort hits all the most important ideas,
starting with Frege’s explanation ofBegriffsschrift, which is wacky
and weird and which didn’t catch on except it kind of did and it still
underlies half of mathematical logic and which is the prototype formany of the symbols we still use. After this there is
Russell’s tragic correspondence with Frege in which he pointed out,
too late, that Frege’s foundational theory didn’t work.The book reprintsPeano’s original description of the Peano numbers, perhaps
the most successful single mathematical theory of all time.The book includes Zermelo’s proof ofZermelo’s theoremthat
every set can be well-ordered, and Ackermann’s discovery ofAckermann’s function, which demonstrated the not every
computable function is primitive recursive.The book has Russell on type theory and early work by Kolmogorov and Brouwer
on the origin of intuitionism. (Heyting is missing.)Van Heijenoort has come up here when I wanted to quote fromSchönfinkel’s paper about the SKI-calculus,Wiener’s paper inventing the ordered pair, and implicitly in
probably a dozen other math and logic articles here over the years.The book is on my shelf because I refer to it pretty often, but also
because I can usually find something interesting just by thumbing
through it. For example,these remarks by Thoralf Skolem about the futility of deriving induction from set-theoretic foundations.Bonus trivia: Van Heijenoort was the personal secretary of Leon
Trotsky, and while he was accompanying Trotsky during the latter’s
exile in Mexico, he was one of Frida Kahlo’s lovers.Orbis Sensualium Pictis(English edition), Johannes ComeniusI adore this book. My heart swells with love when I think of it.I don’t have a blog article about it and there is a story behind that.
In 2018 I went to a conference in Cleveland and my hotel was in a
building that had formerly been the Cleveland Department of Education.
It contains two big murals, one depicting “The Progress of
Education”:I planned to write a blog article about these people. It’s clear who
some of them are. For example, Moses is easy to recognize at lower
right, because of the glowing horns, and Confucius is next to him.
Some people I was familiar with once they were identified for me: the
red-haired guy second from right in the back row isFriedrich Fröbel, who I knew; his“gifts”are a forerunner
of the Montessori materials.But in doing the research I got to the bearded hat-wearing dude
topmost on the right side and completely fell off the bus, because
that is Johann Comenius who is famous because he wrote one of the most
marvelous and enchanting books I’ve ever read, theOrbis Pictus.I have to resist the temptation to say too much, becauseOrbis
Pictusderailed the article about “The Progress of Education”, it
then derailed itsownarticle which has been in progress for eight
years, and if I let it it will derail this article too, because every
time I pick upOrbis PictusI forget whatever I was doing and I am
lost in the pages with a happy and innocent smile on my face.I’m going to precommit to writing onlyoneparagraph about this
incredible book. It was the first illustrated children’s book
published in Europe, in 1658, and it was an immediate hit, being
translated from German into English the following year, then into
French, Italian, and many other languages. It swept the continent
because everyone loved it.Most of the book follows this pattern: there will be an engraved illustration,
depicting some aspect of ordinary human activity, such as (I open it
up to a random page) “Tame Foul” (that is, “fowl”):Items of interest in the engraving are annotated with numbers, and
the facing page explains the illustration, one item at a time:The Cock 1 (which croweth in a morning), hath a comb, 2.In a second column to the right of this is the same text, but in
Latin, so that while the reader is learning about tame fowl, they are
also learning Latin:Gallus1. (qui manè cantat) habetCristam, 2.The prose is limpid, gentle, pithy, and direct. It hits the important
points of interest, invites questions, and ends before anyone can get
bored. There are pages on anatomy, butchery, feasting, winemaking,
various principal virtues, family trees, cities, burials, ships,
wells, horology, amphibians.Now I will reluctantly put it down, rather than leaving this article
unfinished as I have so many before.The Bible (New International Version, large print)This of course is the cornerstone of Western culture and no
well-educated person can be without a knowledge of what is in it. It
is full of great wisdom and great stories, and also cruelty, evil
lies, and reminders that the world now is in many ways better than it
was becausepeopleare better.I would like to understand the world I live in, and there is no way to
understand 21st-century America without understanding the Bible.The NIV is not the most poetical translation, but it is clear, modern,
and accurate. (I got it on the recommendation of Sterling Hanenkampf.
Thanks, Sterling!) In former times I had a collection of Bibles but
this is the only one that remains. I even got rid of the old King
James that belonged to my mother, since office space is precious and I have had a digital copy on
my computer since the early 1990s.I find that most of my articles mentioning the Bible are unpublished
for some reason. It comes up a bit in connection withPloni Almoni, and in passing in many other places.One of the unfinished articles is a series of notes on the theme of
Jesus’s admonition “Do not put the Lord your God to the test”
(Matthew 4:7) and its relationship to a lot of other
things like lightning rods, Christian Science (not Christian science),
how Larry Wall became a computer programmer,Pikuach nefesh, and the story of the old lady who refused
to evacuate from her house during a flood. It’ll be epic if I ever
finish it, but I probably won’t.Another incomplete one is about the incredible story of Samson and
Delilah:She asks him flat out:[Judges 16:6] Tell me the secret of your great strength, and how
you can be tied up and subdued.Instead of just telling her to fuck off, Samson
lies:[16:7] If anyone ties me with seven fresh bowstrings that
have not been dried, I’ll become as weak as any other man.The Philistines bring her bowstrings and she tries it that
night, but Samson snaps the bowstrings as easily as a piece
of string snaps when it comes close to a flame. …Then it goes as before! He tells her a different lie,
knowing full well that she will betray him, and shedoesbetray him, and he makes a fool of her again! (16:11–12)Okay, that was fun. Let’s do it again! (16:13–14)After several repetitions of this, Samson decides that being shaved,
blinded and crushed will be less exasperating than listening to any
more of Delilah’s nagging.I read once that the whole point of the book of Judges is that the
people in it are all terrible, they are all far from the path of
righteousness, and so you definitely shouldn’t act like them. I don’t
know if that interpretation is correct, but it is certainly true that
the people in it are all terrible.The Belles Heuresof Duc de BerryThis book turned up in one of my very first blog articles, onabbreviations in medieval manuscripts, although I didn’t
know it at the time. In my teens, on a visit to the Metropolitan
Museum of Art, I picked up a print of this:
The bookshelf by my elbow, the one that I can reach without getting
up, has seven books on it, not necessarily the ones I look in the
most, but the ones whose emanations I most hope will infuse me as I
write.
The one I actually refer to most often is the Harper and RowRoget’s
Thesaurus. I thought I had acquired this in my teens, but the note
on the flyleaf says 1989.
This is the fourth edition. I was very excited to get the eighth
edition, which I thought I might like better, and for some time I kept
them next to each other so that I could look up the same things in
both, and compare. my conclusion was that while the eighth edition
had more stuff in it, it wasn’t stuff I needed. And it is really fat.
So I have retired it to a farther shelf and will eventually get rid of
it.
The thesaurus is a book that is widely misunderstood. It is not, as many people mockingly
imagine, just a compendium of synonyms, and its correct and intended
use isnotto replace common words with more impressive-sounding
ones. just as the correct use of a screwdriver is not to scrape the
veneer off of an expensive cabinet.
“Thesaurus” means “storehouse” or “treasure room”. Roget’s idea,
similar to that of John Wilkins before him, was to classify everything
in the world into a hierarchy, in this case a hierarchy with a
thousand divisions. At the top level the divisions are grouped into
“Abstract concepts”, “Space”, “Physics”, “Matter”, “Sensation” and so
on. Then under “abstract concepts” there are subclasses, of which
subclass VI is “Time”, subdivided into five smaller sections:
A. Absolute timeB. Relative timeC. Time with reference to ageD. Time with reference to seasonE. Recurrent time
At the next level down, section (1)(VI)(B) is divided into:
§116. Priority§117. Posteriority§118. Simultaneity§119. The Past§120. The Present§121. The Future