Weinersmith’s Book Club #6
Nov 10 – Songs of the Doomed (Thompson)
Review: Enjoyable prose because it’s Thompson, but I usually feel like Thompson’s stories are more entertaining than enlightening. He was part of a culture that seemed to consider chaos objectively desirable, which I’m sympathetically opposed to.
Nov 10 – Epigenetics (Francis)
Review: Not great. Some interesting stuff, but alternatingly too in depth or too shallow. Also, a remarkably amount of discussion of Jose Canseco’s shrunken balls (seriously).
Nov 11 – Hallucination (Sacks)
Review: Fun stories by Oliver Sacks. As always, a bit overwrought, a bit redundant with his other books, and thoroughly enjoyable, a bit like an old uncle who’s gotten very good at telling his great stories.
Nov 13 – Caliban’s War (Corey)
Review: Written by my friends, so NO REVIEW FOR YOU INTERNET.
Nov 15 – Singularity Rising (Miller)
Review: Written by someone I know, so NO REVIEW FOR YOU INTERNET.
Nov 16 – Climax of an Empire (Morris)
Review: Very long, but very good. Morris is probably a bit rosey on the old empire for most people, but he’s open about this, and does a lot of work to present what was bad as well.
Nov 18 – The 39 Steps (Buchan)
Review: Corny mystery, but its oldness makes it a bit more fun. Evil Germans and a man tailed by a “monoplane.” Solid.
Nov 20 – Light Verse from the Floating World (Uedo, ed.)
Review: Lovely Senryu, which we would recognize is haiku about mundane topics. Kelly and I read this together.
Nov 23 – An Anthropologist on Mars (Sacks)
Review: More good Sacks.
Nov 24 – Long After Midnight (Bradbury)
Review: Ech. I love Bradbury, but when he’s not great, he’s the height of cornball. This was largely a collection of the latter.
Nov 25 – A Leg to Stand On (Sacks)
Review: Yet more good Sacks.
Nov 25 – A Manual for Living (Epictetus)
Review: Very quotable, but it’s no Marcus Aurelius, and a bit too far toward the nihilistic end of stoicism for my taste.
Nov 26 – Starburst (Pohl)
Review: An interesting book, though it has the sci fi author’s frequent flaw of worship for technocrats. Also, it’s dystopic visions for the future seem out of date these days.
The Higgs Field Fallacy
A little while ago, I did a comic in which the joke was a lady saying something like “if you don’t agree that math is gender neutral, you will be!” while brandishing a knife. Interestingly, this got some trans advocacy groups AND some mens’ rights groups mad. For the sake of this argument, I’m more concerned with the latter.
The claim being made was that the joke mocked genital mutilation. I suppose this is, strictly speaking, the truth. The joke is that this lady will cut your dick off for reasons that are amusing because of a pun on “neutral.” I can’t deny that it’s a joke that involves the idea of cutting someone’s dick off, but I don’t agree that this is necessarily a serious matter. I was trying to figure out the exact reasoning, when I happened to come across a passage in a book of funny etymology stories.
The story was about military K rations. More interesting to me than the etymology was a joke from the author, who presumably spent some time in the military. The joke went something like this: “K rations served the dual purpose of feeding soldiers and making them angry enough to kill.”
That is, of course, a joke about killing a fellow human being. I think I can safely say I’d rather have my dick cut off than be killed, which suggests to me that one is more serious than the other. Yet this joke is considered so tame that it appears in a cute illustrated book with the unintimidating title “Who Put the Butter in Butterfly?” So, I’m assuming that most people would not take it as advocating or trivializing murder.
And then I realized what the problem was. We’re really talking about a particular straw man argument, in which a statement intended as a joke is taken to be serious. Because something that is light is made out to be massive, I thought it might be funny to call it “the Higgs field fallacy,” since the Higgs field gives rise to mass. It’s possible it already has a name, in which case forgive me.
The essence is this: Sometimes jokes are meant to be serious and sometimes they are not. This is the advantage and disadvantage of being a comedian – you can choose whether your past statements are serious or not (and so can other people). We sometimes assume that all statements carry weight, when in fact many really, truly, seriously don’t. When your parents taught you to play Hangman, for example, I’m guessing neither of you felt like you were mocking capital punishment.
It is perhaps unfortunate that communication is imprecise, resulting in light things seeming heavy to one person and vice versa. However, this is a condition of signal transmission in this universe, so there’s not much sense in fretting over it.
Now that I put a name to the fallacy, I can think of lots of instances where I’ve come across it. It’s a great debate tactic, because in casual language we often laugh at the dreadful. But, if you’re in a debate, and someone does this, all you have to do is keep a serious face and say “Well, I’m glad you feel you can laugh about it.”
What’s particularly strange is how often we invoke this fallacy on public officials. When a public official uses a non-PC term we’ve used or heard a thousand times in private company, we get mad. Or if a public figure makes an offensive joke we’ve told or laughed at a thousand times, we call him an asshole. Why? Well, our jokes are massless. To theirs, we give a Higgs field.
A Favorite Chesterton Quote
Nicely threads the needle, as he often does. This is from “What I Saw in America”
Travel ought to combine amusement with instruction; but most travellers are so much amused that they refuse to be instructed. I do not blame them for being amused; it is perfectly natural to be amused at a Dutchman for being Dutch or a Chinaman for being Chinese. Where they are wrong is that they take their own amusement seriously.
PS: Yes, I’m well aware he was an anti-evolutionist! But, also a great writer. C’est la vie.
Three Original Senryu
(ref)
“Monogamy gene?
How’s junior’s genome have it
If yours and mine don’t?”
“Kilt your son,” He says.
“Are you completely insane?”
He glowers at Abe.
“Why do Bobby’s pants
Smell like old lady?” asks Mom.
“And where’s my lotion?”
An Old Joke
Dork that I am, I was enjoying an excellent book on senryu today, called “Light Verse from the Floating World.” The short version of senryu is that they’re haikus as we in the west think of them, but are closer to observational humor than lofty poetry.
Anyway, I happened on an interesting one just now. A few of you may know this modern joke: “How does every racist joke start? With a look over your shoulder.”
Well, here I am reading a book of 18th century Japanese poetry, when I find this similar one. First, I’ll put it in Japanese for those who read Japanese (I do not), then in English.
subete onna
to iu mono to
sokora wo mi
“All women…”
he begins, and then
glances around.
Ha! It’s the exact same joke, though shifted from race to gender.
End of the Science Posts
After giving it a lot of thought, I’ve decided to indefinitely stop with the sciencing blogs. There are a number of small reasons, but the main one is this: I just don’t have the time.
The big appeal to me of studying science is “horizontal knowledge.” That is, there is some knowledge that is vast, but doesn’t build upon itself (literature, for example, generally speaking), which you might call “vertical knowledge.” Horizontal knowledge is when you must have one floor of the edifice to climb to the next. Logic, math, and most of the sciences work this way.
I like to think it’s good to have both. As you may guess from the last post, I feel I’m doing relatively well on the vertical end. But, it’s been slow going on the horizontal end, largely because, well… teaching is hard. Understanding is hard enough. Trying to find the right words, the right analogies, the right thought modes, is even harder. It’s especially hard when I understand a concept very well. That to me is the real art of teaching – understanding something well while remembering why it was that you didn’t always understand it well.
But, I want to move faster. Some rough estimation I did tells me I could be learning at least three or four times more quickly if I weren’t obligated to transcribe what I’ve learned. Although I’ve been really happy to have people say that I helped them learn, I believe it’s probably a better use of my time to give myself the best possible education I can, then use my larger channels (comics, books, etc.) to distribute the information.
Additionally, hell, a lot of people are doing this a lot better. Khan Academy, Code Academy, Coursera, OpenCourseWare, BetterExplained, and many more. These people are dedicated teachers and damn good at it. Although I enjoy explaining things to people, I don’t consider teaching a calling. It’s fun, but I don’t get out of bed in the morning for it. Other people do. There might be a few people who want to learn from me, but there is nobody who needs to learn from me.
I want to thank everyone who read along with me, especially those of you who offered corrections and insight. Some of you follow me on twitter, and I will no doubt be abusing your kindness as I continue my self-education.
So, with some regret, I’ll be stopping with the formal regular science blogs as of now. I’ll only be posting new stuff when I have some particular insight or excitement about a topic. I hope this’ll free me up to spend more time on science and more time on my other backburner projects. I’ll make sure to keep you all in the loop.
<3
Zach
Weinersmith’s Book Club Part 5
Wow. It’s been over a year since the last one of these. I got an email request to do another, so here we are. I’ve read a good number of books since then, so I don’t have time to properly review all. So, I’ll be using the following system:
1/5: Avoid
2/5: Not good
3/5: Read if you’re into the subject matter or genre
4/5: Definitely read
5/5: Cherish that shit
NC: No comment because it was written by a friend (or acquaintance or friend of a friend or relative or anyone else who’d make it awkward) and I don’t want to go down that road.
NR: I don’t feel I remember this book well enough to judge. That said, if that’s the case it may be a reflection on book quality.
NW: No way, I refuse to rate a classic like this. You should read it.
July 7 – Malcolm X: A Life of Reinvention (Marable): NR
July 8 – Just Six Numbers (Rees) 3/5
July 9 – Pale Blue Dot (Sagan) 5/5
July 10 – Marie (Haggard) 3/5
July 12 – The Disappearing Spoon (Kean) 4/5
July 13 – Politics (Aristotle) NW
July 17 – Fairy and Folktales of the Irish Peasanty (Yeats) 5/5
July 18 – Eiffel’s Tower 4/5
July 27 – The Rational Optimist (Ridley) 4/5
July 29 – Polio: An American Story (Oshinksy) 4/5
July 30 – Child of Storm (Haggard) 3/5
Aug 1 – Mooonwalking with Einstein (Foer) 3/5
Aug 2 – Preferred Risk (Pohl/Del Ray) 2/5
Aug 3 – History of Western Philosophy (Russell) NW
Aug 4 – 1864: Lincoln at the Gates of History (Flood) 3/5
Aug 8 – Fiasco (Lem) 4/5
Aug 9 – A Plum in Your Mouth (Taylor) 4/5
Aug 10 – The Matisse Stories (Byatt) NR
Aug 12 – Ghengis Khan (Lamb) NR
Aug 15 – Game of Thrones 1 (Martin) NC
Aug 17 – Buddha (Armstrong) 3/5
Aug 19 – Life and Times of the Thunderbolt Kid (Bryson) 5/5
Aug 19 – Not Forgotten (Oliver) 3/5
Aug 20 – The Opposite of Fate (Tan) 1/5
Aug 20 – The Midas Plague (Pohl) 1/5
Aug 21 – Tarzan of the Apes (Burroughs) 2/5
Aug 23 – Wolfbane (Pohl) 2/5
Aug 30 – Rudyard Kipling to Rider Haggard (Ed. Cohen) 3/5 (Personal 4/5, but it’s pretty fucking obscure)
Aug 31 – Winner Take Nothing (Hemingway) 3/5
Sep 1 – Kabloona (de Poncins) 5/5
Sept 2 – Chitty Chitty Bang Bang (Fleming) 5/5
Sept 5 – Growing Up Bin Laden (Sasson) 2/5
Sept 8 – Crime and Punishment (Dostoevsky) NW
Sept 9 – Everything is Obvious Once You Know the Answer (Watts) 3/5
Sept 12 – Nichomachean Ethics (Aristotle) NW
Sept 14 – The Sky is Not the Limit (Tyson) NC
Sept 17 – 1920: The Year of 6 Presidents (Petrusa) 3/5
Sept 18 – America 1908 (Rasenberger) NR
Sept 18 – Pythias (Pohl) – Short Story 2/5
Sept 23 – Leviathan Wakes (Corey) NC
Sept 24 – The Professor and the Madman (Winchester) 4/5
Sept 26 – Moll Flanders (Defoe) NW
Sept 27 – Ghost in the Wires (Mitnick) 3/5
Sept 27 – The Hated (Pohl) – Short Story 2/5
Sept 27 – The Tunnel Under the World (Pohl) – Short Story 2/5
Sept 28 – The Garden of Eden (Hemingway) 4/5
Oct 3 – On China (Kissinger) 3/5
Oct 10 – Acting White: The Ironic Legacy of Desegregation 4/5
Oct 11 – J Robert Oppenheimer: Shatterer of Worlds (Blythe) 3/5
Oct 25 – Nature via Nurture (Ridley) 3/5
Oct 26 – The Futures (Lambert) 3/5
Oct 26 – A Plague of Pythons (Pohl) 2/5
Oct 28 – Newton and the Counterfeiter (Levenson) 2/5
Nov 2 – The Confessions of St. Augustine NW
Nov 5 – The Other Brain (Fields) 5/5
Nov 6 – The Space Trilogy 2 (CS Lewis) 2/5
Nov 8 – The Day of the Boomer Dukes (Pohl) 1/5
Nov 8 – Beyond Good and Evil (Nietzche) NW
Nov 10 – Snowcrash (Stephenson) 3/5
Nov 12 – Nonsense on Stilts (Pigliucci) NC
Nov 15 – Aeneid (Virgil) NW
Nov 16 – Plain Tales from the Hills (Kipling) 4/5
Nov 18 – American Gods (Gaiman) NC
Nov 21 – The Bell Jar (Plath) 5/5
Nov 22 – Hiroshima (Hersey) 5/5
Nov 30 – 1493 (Man) NR
Nov 30 – Farmer in the Sky (Heinlein) 4/5
Dec 7 – Caesar – Life of a Colossus (Goldsworthy) 4/5
Dec 9 – She and Allan (Haggard) 3/5
Dec 11 – Steve Jobs (Isaacson) 4/5
Dec 11 – White Man’s Burden (Easterly) 5/5
Dec 12 – Sex at Dawn (Ryan and Jetha) 3/5
Dec 16 – The Black Arrow (Stevenson) 2/5
Dec 19 – Truman (McCullough) 4/5
Dec 22 – Keynes-Hayek (Wapshott) 3/5
Dec 23 – Nothing to Envy (Demick) 3/5
Dec 24 – Uranium (Zoellner) 3/5
Dec 28 – The Rise of Theodore Roosevelt (Morris) 5/5
Dec 31 – Theodore Rex (Morris) 5/5
Dec 31 – Consider the Lobster (Wallace) 4/5
Jan 4 – Colonel Roosevelt (Morris) 5/5
Jan 7 – Thus Spoke Zarathustra (Nietzche) NW
Jan 10 – Foundation and Empire (Asimov) 2/5
Jan 10 – Autobiography of Charles Darwin NW
Jan 12 – Dracula (Stoker) NW
Jan 15 – The Long Dark Teatime of the Soul (Adams) 3/5
(Move to Alabama)
The Quest for Cosmic Justice (Sowell) 3/5
The Most Powerful Idea in the World (Rosen) 5/5
Cleopatra (Grant) 4/5
Jan 31 The Iliad (Homer) NW
Feb 7 – The Everlasting Man (Chesterton) NW
Feb 9 – Coolidge – An American Enigma (Sobel) 3/5
Feb 10 – Eternity Soup (Critser) NC
Feb 13 – A Universe from Nothing (Krauss) 3/5
Feb 15 – Broom of the System (Wallace) 3/5
Feb 15 – Gateway (Pohl) 5/5
Feb 17 – Age of Wonder (Holmes) 4/5
Feb 17 – John Carter of Mars 1 (Burroughs) 2/5
Feb 17 – Tom Sawyer Abroad (Twain) 5/5
Feb 17 – Bad Astronomy (Plait) NC
Feb 19 – Shadow of the Hegemon (Card) 3/5
Feb 20 – The Sword in the Stone (White) 5/5
Feb 26 – Storm of Steel (Junger) 4/5
Feb 27 – Intellectuals and Society (Sowell) 2/5
Feb 28 – Fatal Journey (Mancall) NR
March 1 – Dialogues (Plato) NW
March 1 – The Sixth Column (Heinlein) 3/5
March 7 – The Witch in the Wood (White) 5/5
March 7 – The Poison Belt (Doyle) 3/5
March 9 – The Ego Tunnel (Metzinger) 4/5
March 9 – The Color Purple (Walker) 5/5
March 11 – Polk (Borneman) 4/5
March 13 – Madison’s Metronome (Weiner, Greg) NC
March 13 – Man Plus (Pohl) 3/5
March 23 – Heart of the World (Haggard) 3/5
(ECCC Prep, forgot to record dates…)
Armageddon Science (Clegg) 2/5
Hedy’s Folly (Rhodes) 4/5
The Ill-Made Knight (White) 6/5 (JESUS, what a good book)
April 4 – The Last Days of Ptolemy Grey (Mosley) 3/5
April 5 – One Flew Over the Cuckoo’s Nest (Kesey) 4/5
April 7 – Faster (Gleick) 3/5
April 8 – The Prince and the Pauper (Twain) 4/5
April 10 – Incognito (Eagleman) 3/5
April 13 – The One Percent Doctrine (Susskind) 3/5
April 14 – Last Chance to See (Adams) 2/5 (though charming!)
April 15 – God and the State (Bakunin) NC
April 16 – The Oxford Book of Ballads (1910) 5/5 (wonderful)
April 16 – Empress Orchid (Min) 3/5
April 18 – Endless Forms Most Beautiful (Carroll) 4/5
April 18 – Notes from a Small Island (Bryson) 4/5
April 19 – Sweet Thursday (Steinbeck) 5/5
April 20 – The meaning of Everything (Winchester) 4/5
April 21 – Hitchiker’s Guide to the Galaxy 5 (Adams) 2/5
April 24 – Madame Bovary (Flaubert) 5/5
April 26 – Glory (Nabokov) 4/5
April 28 – The Candle in the Wind (White) 5/5
April 29 – Money (Amis) 3/5 (though I have the strange suspicion that I just didn’t “get” this book?)
April 29 – Letter to my Daughter (Angelou) 2/5
Away for ROFLCon
May 9 – Distrust that particular flavor (Gibson) 3/5 (book of essays, some better than others)
May 9 – Judging Edward Teller (Hargittai) 4/5
May 11 – Alexander Hamilton (Chernow) 5/5
May 12 – Scourge (Tucker) 3/5
May 14 – The Fountains of Paradise (Clarke) 3/5
May 18 – The Greater Journey (McCullough) 4/5
May 20 – The Time Traveler’s Wife 2/5
May 20 – War As I knew It (Patton) NW
May 25 – The Better Angels of Our Nature (Pinker) 5/5
May 25 – Bhagavad Gita NC
May 28 – The Prisoner of Zenda (Hope) 2/5
June 2 – Wizard (Seifer) 3/5
June 3 – The Lucifer Effect (Zimbardo) 2/5
June 3 – Physarum Machines (Adamatzky) NC
June 4 – My Life and Hard Times (Thurber) 5/5
June 6 – The Reformation (Collinson) 3/5
June 6 – Burmese Days (Orwell) 3/5
June 9 – The Illustrated Man (Bradbury) 3/5
June 9 – Brief Interviews with Horrible Men (Wallace) 5/5
June 10 – The Golden Apples of the Sun (Bradbury) 3/5
June 10 – Night (Wiesel) 5/5
June 11 – Economics and Politics of Race (Sowell) 3/5
June 15 – The Beginning of Infinity (Deutsch) 3/5
Trip to Luling
June 24 – Dandelion Wine (Bradbury) 5/5
June 27 – Decoding Reality (Vedral) 2/5
June 31 – A Planet Called Treason (Card) 2/5
July 1 – Science and Religion (Russell) NW
July 2 – Eisenhower: The White House Years (Newton) 5/5
July 4 – Explorers of the Nile (Teal) 3/5
July 9 – Beyond the Blue Event Horizon (Pohl) 3/5
July 11 – The New Geography of Jobs (Moretti) 5/5
Comicon
July 20 – Cro-Magnon (Fagan) 3/5
July 20 – The Breast (Colacci) 4/5
July 21 – Economic Facts and Fallacies (Sowell) 3/5
July 22 – Charlie and the Chocolate Factory (Dahl) 5/5
July 26 – The Panic Virus (Mnookin) 3/5
July 27 – Alvin Maker (Card) 4/5
July 28 – The State of Jones (Stauffer)4/5
July 30 – Rabbit, Run (Updike) 4/5
July 31 – Abundance (Diamandis) 3/5
Aug 4 – Islands in the Stream (Hemingway) 6/5 (DAMN WHAT A BOOK!)
Aug 4 – The Forever War (Haldeman) 4/5
Aug 7 – American Lion (Meecham) 4/5
Aug 8 – The Particle at the End of the Universe (Carroll) NC
Aug 10 – Stranger in a Strange Land (Heinlein) 4/5
Aug 11 – In the Company of the Courtesan (Dunant) 3/5 (but fun!)
Aug 14 – Moscow, December 25: 1991 (O’Clery) 4/5
Aug 14 – Tom Swift and the Electric Hydrolung (Lawrence) NW
Lost to the West (4/5
Rabbit Redux (4/5)
Old Man’s War NC
The Unbearable Lightness of Being 4/5
Away for Worldcon
Sept 7 – The Darkest Jungle (Brick) 4/5
Sept 9 – Pale Blue Dot (Sagan) 5/5
Sept 11 – The Future of Power (Nye) 3/5
Sept 14 – The Cool War (Pohl) 3/5
Sept 15 – The Snakehead (Keefe) 4/5
Sept 19 – The Life and Times of Michael K (Coetzee) 4/5
Sept 25 – Dark Sun (Rhodes) 4/5
Sept 27 – Birdsong (Faulkes) 4/5
Oct 3 – The Dictator’s Handbook (Bueno de Mesquita) 5/5
Last SMBC-T Shoot
Oct 9 – Gods Graves and Scholars (Knopf) 5/5
Oct 9 – War is a Racket (Butler) NW
NYCC
Oct 17 – Heaven’s Command (Morris) 5/5
Oct 19 – On Monsters (Asma) 4/5
Oct 21 – Something Wicked This Way Comes (Bradbury) 4/5
Oct 23 – The Drunkard’s Walk (Mlodinow) 3/5
Oct 24 – The Price of Politics (Woodward) 3/5
Oct 26 – The Acts of King Arthur and His Noble Knights (Steinbeck) 4/5
Oct 28 – The Napoleon of Notting Hill (Chesterton) 3/5
Oct 29 – Render Unto Rome (Berry) 4/5
Oct 31 – What Technology Wants (Kelly) 2/5
Nov 5 – The Information (Gleick) 4/5
Nov 6 – I Sing the Body Electric (Bradbury) 3/5 (collection, some better than others)
Nov 7 – The Star Diaries (Lem) 5/5
Nov 8 – Lincoln at Gettysburg (Wills) 4/5
Nov 8 – Thumbelina and Other Stories (Andersen) NW
Nov 9 – A Heartbreaking Work of Staggering Genius (Eggers) 5/5
Discrete! #33: Discrete Mathematics and Its Applications 2.4 Part A
2.4: Sequences and Summations
My general sense on this sections is that the real action is in problem-solving, since summations and sequences are conceptually pretty easy. So, I’m gonna be a bit breezy here and then we can get into more depth with the problem sets. If you’ve been following along with the calc posts, you’re already pretty up on this stuff.
Introduction
BOOK DEFINITION:
“A sequence is a function from a subset of the set of integers (usually te set {0,1,2,…} pr the set {1,2,3,…} to a set S. We use the notation 
to denote the image of the integer n. We call a term of the sequence.”
I think that’s pretty clear. If your sequence is then the output is just the list “2,4,6,8,10,…”
So, is basically saying “Make a list such at a at each position 1 to infinity is given by 2*(that position).”
Special Integer Sequences
Just because you recognize a pattern in a sequence doesn’t mean you know how to denote it with a pretty function like the one above. If you’re a dork, you’ve probably come across riddles about predicting the next element of a sequence.
The book gives a slightly tricky one. Conjecture a formula for {1,7,25,79,241,727,2185,6559,19681,59047}
Now, although can’t instantly say what it is, you can try some things. Is there the same difference between consecutive digits? Nope. How about a constant multiplier between digits? Nope. You step back a second, and you notice it contains prime numbers like 7 and 29. So, at the least, there’s probably some addition or subtraction. You also see that the numbers grow quickly, so we’re probably talking about some sort of exponentiation here.
After some fiddling, you’ll see that you square n then subtract 2.
Of course, there’s no one right way to do this. But, you want to get some methods of attack to be intuitive.
Summation
A summation is just a sum of the elements of a sequence over a certain interval.
is a pretty typical way to write out a summation.
The i is just the variable. The =1 just means that for the series we’re about to sum, we use {1,2,3,…}. If it’d been i=0, we’d have used {0,1,2,3…}. You could set some other starting point, but it’s fairly rare. The n at the top is where you end. So, if i=1 and n is 5, you care about the values of a at {1,2,3,4,5}.
I have to say, it always seemed to me like it’d be more clear to write something like , but perhaps there’s a good reason not to.
In any case, the idea is pretty simple. A summation is the sum of a sequence over a given interval.
The book goes on to give some examples, including a proof of the geometric series. It’s probably worth your time to go over, and I don’t really have anything to add here.
My general feeling on these things is it doesn’t help to try to memorize these things outright. You remember them if you use them regularly. In general, what’s good is to have intuition about these things. Seeing a function or list of numbers, it’s useful to be able to say “That feels exponential.” or “That feels sinusoid.”
Last, they get to infinite series. As you may know from calc, an infinite series is just the sum of an infinite sequence. If this sounds weird, remember that a lot of sequences start to get to really small numbers really quickly. For example, if the function you’re worried about is 1/x!, as the sequence gets bigger and bigger, the function’s output gets smaller than smaller. Pretty quickly, you’ve got some number right around 2.71812 or so. Often, you can get a simple formula for the sum.
Next Stop: Cardinality