Zalman Shmotkin is not a Mathematician

I just got the following email from Rabbi Zalman Shmotkin

Dear Friend,

Real quick:

What do 191 people in Mozambique, 334 in Bahrain and 4,719 in Japan have in common?

Simple.

They all joined more than one million unique individuals, each of whom who gleaned advice or received inspiration, meaning, community and much more, during this past week at Chabad.org…!

Were he a mathematician, he would have referred to the "more than one million distinct individuals." In mathematics, when you say there is a unique object having a certain property, it means there is only one object with that property. Obviously, there is not a unique person having the property of having visited chabad.org. If you want to assert that n objects have a certain property, and you want to make clear that you didn't count any of those objects twice, you'd say "there are n distinct...."

Consider the statment, "There is one person responsible for cleaning the house for Pesach, the housewife." This statement does not exclude the possibility that the housewife shares the responsibility with someone else. A better way to say it would be "There is a unique person...."

Consider the statement, "There are two people who are responsible for cleaning the house for Pesach: the housewife and the cleaning lady." This statement does not (explicitly) exclude the possibility that the housewife and the cleaning lady are the same person. A better way to say this would be "There are two distinct people...."

כפרות טויגט אויף כפרות

Can you imagine a ritual that would stimulate repentance less effectively than kappores? I suppose I could--if I expended great effort.

Atheist by De Morgan's Law

There are different versions of De Morgan's law, but the basic idea is as follows:

Suppose A, B, and C stand for propositions. If it's not the case that A is true and B is true and C is true, then it is the case that either A is false, or B is false, or C is false.

To believe in standard Orthodox Judaism, you need to believe in a whole bunch of propositions: god exists, created the world, and spoke to the Israelites on Mt. Sinai; the Talmud reflects what god told Moses; etc.

By De Morgan's law, standard Orthodox Judaism would be false if only one of those propositions were false. So it's much easier for me to be right than y'all to be right.

What is Modern Chabad?

I have recently had the opportunity to observe Modern Lubavitchers in their natural habitat. At first I was appalled by their flagrant disregard of traditional Lubavitcher scruples. The men touch their beards and wear jeans. On Shabbos they're all in cuff links and ties (although they all wear white shirts). The women show much too much elbow, knee, and tichel. Why, even the rabbi's own daughter wears short sleeves, despite her old age of four!

But then I started thinking, af dem hut men gehorevet in Tomchei Temimim? Are clothes and hair all that distinguishes these creatures from their forebears? Here are some more subtle irregularities I have found:

ML men rarely pray with a minyan.
ML men are comfortable praying hatless, jacketless, and in pajamas.
ML families might use the same countertops and tables for both milchigs and fleishigs.
ML households buy whatever meat the kosher store sells.
ML couples vacation in Los Vegas.
When MLs invite friends for Shabbos meals, they use cloth napkins, napkin rings, chargers, and would never serve gefilte fish.
At said Shabbos meals, topics of conversation may include sports, movies, TV (presumably watched on computer screens), and prostate exams.
Many MLs use a non-Alter-Rebbe's eruv on Shabbos.

(Note: These conclusions are based on studying an extremely small sample of the ML population.)

Clearly, among the local population an insidious rot has crept into even the most deeply held of our sacred principles. On the other hand I have noticed that at the kindergarden graduation of a school at which many ML children are educated, the Rebbeim dramatically eclipsed God. So maybe these people can still claim to be Lubavitchers.

Oh yeah, there's also the small issue of stealing a rich synagogue. But that's neither here nor there.

Searching for Truth

Today I visited the following six Crown-Heights stores looking for frozen 6-inch pie shells: Kahan's Superette, Benz's, Albany Bake Shoppe, Koshertown, Empire Kosher, and Kol Tov. Two of the stores did not carry this item. The other four all carried the same brand, namely Unger's (in packages of four). Yet, they each charged different amounts. The respective prices were, $4.19, $4.09, $3.99, and $2.99.

Can you guess which stores carried it and at which prices?

The prize for the correct guesser is a six-inch sweet-potato pie.

Formerly Frum Peeps: Know Your Limits

Those who think they're going to save the world by attending The internet is NOT your problem to protest the big anti-Internet asifa, should first read the wisdom of Shulem Deen and Ushi Katz.

Have the OTD rabble rousers forgotten how frum people think? Sure, the secular press will love to write about them and their I-grew-up-in-a-cult horror stories, but the frummies they're trying to enlighten will never in a million years listen to them.

I wish I knew how to use a slide rule

From Wikipedia:

Compared to the portable electronic digital calculators that were introduced in the early 1970s, slide rules had various advantages and disadvantages.

Advantages

• The spatial, manual operation of slide rules cultivates in the user an intuition for numerical relationships and scale that people who have used only digital calculators often lack.^[21] Since users must explicitly note the order of magnitude at each step in order to interpret the results, they are less likely to make extreme calculation errors; users are forced to use common sense and an understanding of the subject as they calculate. Since order of magnitude gets the greatest prominence when using a slide rule, and precision is limited only to the few digits that are normally useful, users are less likely to make errors of false precision.
• When performing a sequence of multiplications or divisions by the same number, the answer can often be determined by merely glancing at the slide rule without any manipulation. This can be especially useful when calculating percentages (e.g. for test scores) or when comparing prices (e.g. in dollars per kilogram). Multiple speed-time-distance calculations can be performed hands-free at a glance with a slide rule.
• Other useful constants such as pounds to kilograms can be easily marked on the rule and used directly in calculations.
• A slide rule does not depend on electricity or batteries.
• The principle of operation of a slide rule can be demonstrated with a pair of hand-made paper scales.
• A slide rule displays all the terms of a calculation along with the result. This eliminates uncertainty about what calculation was actually performed.
• A slide rule is physically more durable than an electronic calculator and is impervious to moisture and immersion in water.

The professor who taught me physics was from the slide-rule generation. He could do calculations like sin(4)/1.76 in his head.

Not Only Sarabonne has Roommates

My roommate: You know how people should really celebrate Easter? By dressing up as zombies. Doesn't Easter commemorate Jesus' becoming a zombie? What do bunnies have to do with it?
Me: Well, you know that the Easter bunny developed out of earlier, pagan traditions.
Roommate: Yeah, I know. Hey. I knew some Christians who wouldn't celebrate Halloween, because they say it's devil worship. They should make up for it by dressing up on Easter.
Me: What about the girls who want to dress slutty? Oh, I know! They can dress like Mary Magdalene.
Roommate: Yep, the only Biblically sanctioned costumes are zombies and Mary Magdalene.
Me: Well, the zombies in the Bible don't try to eat people's brains.
Roommate: The Christians are the zombies! They eat Jesus' flesh and blood.
Me: Right! That's why they're called born-again. Baptism symbolizes dying in the water and emerging reborn--as a Jesus-eating zombie.
Roommate: Totally. We've just figured out what Christianity is really all about. We should make sure our message gets out before Easter.

It's my blog, and I'll cry if I want to...

...and I'll recommend books that no one will ever read.

There's this perennial discussion whether math is "real" or not. My personal opinion is that it isn't. Are you "really" out when you get hit with a ball in dodge ball? Does something about you change when you get hit? Not really. If the recess bell rang right then, your outness and your friends' inness, would suddenly disappear. The property of "being in" or "being out" exists only within the game. So you're "really" out as much as the game is real, which I don't think is a whole lot.

Math is the same way. Is it a "real" truth that every odd-dimensional square matrix with real entries has at least one real eigenvalue, but some even-dimensional square matrices with real entries have no real eigenvalues? Well, it's a real truth in this game of mathematics.

Why are dodge-ball properties less real than say biological properties or physical properties? A wise man once said, "Reality is that which does not go away when when you stop believing in it." If we stopped believing in physics or biology, they would still exist. Nobody would know about their existence, just like nobody knew their existence for thousands of years before science came around. Dodge ball, on the other hand, exists only as long as we believe in it.

And math is the same.

If my blog had any readers other than those who have heard this lecture from me before, they would doubtlessly be clamoring, "What do you mean? Two and two would still be four, even if nobody knew it!"

To which I respond, would the polynomials still form a ring if nobody knew it? Would Gaussian integers still have unique factorizations (up to multiplication by a unit) if nobody knew it? Would "P implies Q" be equivalent to "not P or Q" if nobody knew it? Would e^(ix)=cos(x)+isin(x) if nobody knew about it? More simply, would (-2)*(-2) still equal positive four if nobody knew it?

The book Negative Math: How Mathematical Rules Can be Positively Bent, by Alberto A. Martínez, discusses this question at length. His answer is pretty much "No." Supposedly his book uses only basic algebra and a minimum of mathematical symbols and is easily accessible to people with rudimentary mathematical knowledge. I read it. I enjoyed it. It opened my eyes. But I don't think anyone reading this blog would enjoy it. So instead of telling you all to read it, I'll just tell you one of the central points of the book: If we wanted to, we could have made the rules of mathematics different than they are. Very different. It would have made math more suitable for some purposes and less suitable for others. Our current version is pretty damn good, and we should have no regrets. But things could have been very different.

To make matters worse, I believe City College's copy of this book is missing, even though the catalog keeps on telling me to "check [the] shelf." So I can't even get my mathematically inclined friends to read the book. Yes, life is tough.

Science: It Works Bitches

Non-Yiddish speakers, a large proportion of my blog's readership, are often told anecdotes and then told to minimize their enjoyment because the punchline "sounds better in Yiddish." They are often then subjected to gratuitous incoherent funfering.

Well today I will present to you all an anecdote which I heard in Yiddish whose punchline works much better in English! Joy!

A yeshiva boy and a heretic were once chatting about all sorts of abstract, metaphysical phenomena. The heretic was getting fed up with the yeshiva boy's thickheadness and interrupted him with a question
Heretic: What do horses eat?
Bochur: Hay
H: And what do they excrete?
B: Horse drek
H: What do cows eat?
B: Hay
H: And what do they excrete?
B: Big, flat cowpies
H: What do goats eat?
B: Hay
H: And what do they excrete?
B: Little ballies of goat drek
H: They all eat the same hay, yet the excrete such different drek! Why is that?
B: (shrugs shoulders ignorantly)
H: Well if you don't know shit, then why do you think you know about heaven?

OK. I'll admit it. The version I originally heard had the roles of the heretic and the bochur reversed. But seriously, don't you think this version makes much more sense? There's no way for an old-school yeshiva bochur to find out about animal digestive systems. But a heretic could just go to his friend the biologist, who is statistically likely to be a heretic himself, and find out why different animals make different kinds of poop.

I also lied when I said that the punchline is better in English. Sure "you don't know shit" has a double meaning in English, which it doesn't have in Yiddish. But what I translated as "you think you know about heaven" was originally something about "krichen in himmel." The verb "krichen" literally means "to crawl." But in English you can't say "Why are you crawling in heaven?" So I had to use the lame-sounding "why do you think you know about heaven." I'm sorry. This post did end with me harping about Yiddish words which cannot be accurately translated. I'm sorry.

Memories of Times Ago / Stirring the Strings of my Soul

Way back in my youth, in shiur Aleph mesivta, we learned Kuntres Uma'ayan with our not-so-venerated teacher, whom we called Larry. How exactly he got the nickname Larry was shrouded in the mysterious mists of ancient mesivta folklore. (Bochurim graduate after only three years, so folklore ages quickly there.) Anyhow, Larry would often show up late. I and one of my tablemates made up the following two songs about Larry's tardiness, which I happened to remember while showering this morning. (OK. I admit. I showered this afternoon.)

TTTO: "Always Late," from Shmuel Kunda's "The Magic Yarmulke"
Lyrics: Based on actual words said despairingly by my chavrusa early one morning
Kuntres Uma'ayan
Don't know what's flying
My notes are falling all over the floor
Ma'amer Zayin
Bechinas Acharayim
As Larry turns over in bed with a snore
Always late
Always late
Shiur Aleph they just hate
That Larry's always late

My tablemate and fellow songwriter wanted it to be "Shuir Aleph appreciates / That Larry's always late." But I thought my version fit better with the original song. Plus Shuir Aleph isn't a bunch of lowlifes who appreciate not having to learn. We are mature young men who just hate when our teacher doesn't show up.

The next song is titled "Ain't Gonna Miss Larry's Shiur." It parodies a song made by (or about?) Tiferes Bochurim titled "Ain't Gonna Miss Rabbi Lipskier's Shiur," which itself was a parody of "Ain't Gonna Work on Saturday." The Tiferes version featured such lyrical gems as "We drink ginger keil" and "We sleep on the bunk / To get closer to Havaya." I don't remember any more of it. Nor do I remember all of our version. With apologies to my past self and my tablemate, I will trascribe this song as best I can.

I was in the mikveh at seven thirty-eight
I thought that I would get it, for coming in so late
But I when I got to Mesivta
Boy, was I surprised
Larry hasn't shown up; it's already eight oh-five!
Oh!
Ain't gonna miss Larry's shiur
Ain't gonna miss Larry's shiur
Ain't gonna miss Larry's shiur
Why?
Because he never shows up.

Thank Zeus I'm American

A few months ago, you made a loan to a student on Vittana. Guess what? We've got great news.

EDUCATION CHANGES EVERYTHING Hi e, A few months ago, you made a loan on Vittana to Khoirul Anam, a student in Indonesia who wanted to study Mechanical Engineering. Guess what? Khoirul just made his first repayment! As one of his lenders, we wanted you to be the first to know. In total, this month you've received $1.05 in repayments from 1 student . Every month from now until they're repaid, you'll receive an email from Vittana notifying you of any repayments you've received. One of the most powerful aspects about Vittana is that students repay the loans you've made, enabling you to multiply the impact of the same money over and over again. If you have a minute, we'd love if you helped another student. Right now, hundreds of young people need loans on Vittana, in countries from Jordan to Bolivia to Ghana. They want to be chefs, nurses, teachers and much more. Click here to see all Vittana students. http://www.vittana.org/students Thank you for being a part of Vittana's mission and education around the world. Sincerely, The Vittana Team P.S. As always, if you have any questions or comments, please don't hesitate to get in touch with us. You can find us at community.vittana.org. Your Impact 1 Students Funded $25 Loans Made $2,816 Lifetime Student Impact

"Only the educated are free." -- Epictetus (55 AD - 135 AD)

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When I started reading this email, I thought they'd tell me that the entire $25 had been repaid. Silly me. $1.05 a month is a lot. I should just leave my scholarship-sponsored apartment and go to my government-sponsored school and learn something.

You Know You're a Math Major When...

...the left column is unintelligible, but the right column is crystal clear.

This reminds me of a joke:

A mathematician and an engineer attend a lecture by a physicist. The topic concerns Kulza-Klein theories involving physical processes that occur inspaces with dimensions of 9, 12 and even higher. The mathematician is sitting, clearly enjoying the lecture, while the engineer is frowning and looking generally confused and puzzled. By the end the engineer has a terrible headache. At the end, the mathematician comments about the wonderful lecture.

The engineer says "How do you understand this stuff?"
Mathematician: "I just visualize the process."
Engineer: "How can you visualize something that occurs in 9-dimensional space?"
Mathematician: "Easy, first visualize it in N-dimensional space, then let N go to 9."

Meshichist Anthem

Yellow flags are in the house tonight
Everybody just have a good time
Emunah pshuta'll make you lose your mind
Everybody just have a good time

Yellow flags are in the house tonight
Everybody just have a good time
Emunah pshuta'll make you lose your mind
We just wanna see you... wave that
 .
 .
 .
 Every day I'm shuckling...

And People Claim that Chabad is not Idolatry.

Hmph.

This goes through my head every time I ride the subway.

(source)
Becomes a DIGITAL SUBSCRIBER. Visitors get 20 free articles a month. Subscribers get unlimited access
--New York Times ad of which I could not find a picture online and whose text I may not recall with complete accuracy.

It appeared that there had even been demonstrations to thank Big Brother for raising the chocolate ration to twenty grams a week. And only yesterday, [Winston] reflected, it had been announced that the ration was to be reduced to twenty grams a week.
--George Orwell, 1984 (source)

The Saddest Six-Word Story Ever Told: A Contest

In the comments, share the saddest story you can tell using six words or fewer. After a few days, I'll tell you a super-sad six-word story my sister-in-law told me over Pesach. We can vote on whose story is the saddest.

Mathematically Proven Fact: Accelerate While Turning

Today I was chit chatting with my mentor about curvature and other differential-geometry-related shtuff, when she told me a most surprising fact. Unfortunately I can not explain it without relying on abstract mathematical concepts, because I myself can only understand it in those terms. It's really counterintuitive. Imagine you're driving on an exit ramp (or any any curved road for that matter). You want your acceleration vectors to point towards where you want your car to go, which in this case would be centripetally, towards the center of the circle in which you're driving. If you speed up, the acceleration vector gets longer, and pushes you more strongly to the center. If you decelerate, however, your acceleration vectors point backwards, away from where you want to go, so your car starts to skid. Of course it's good to slow down before making a turn. But once you start turning, you want to speed up. I'm talking nonsense? Well, that's what SHE said.

To understand this, do the following experiment:
Take a deep breath.
Pretend you're in a car.
You're driving down the highway.
You approach a curve in the road.
You head straight into the curve.
Oh no! You're going to fast! You gently push the break.
Visualize it.
What do you feel happening?
I feel the tail of car swerving off the road.

Now let's try this again.
Pretend you're in a car.
You're driving down the highway.
You approach a curve in the road.
You head straight into the curve.
As you start curving, you press the accelerator.
Visualize it.
What do you feel happening?
I feel the car griping the road.

These thought experiments are really worthless. It's possible that the reason I connect decelerating with losing control is because I usually slow down only if I'm going too fast to begin with. And I connect accelerating with control because I usually accelerate only if I started off at a slow enough speed. It's a shame she didn't tell me about this when I met with her last Wednesday. That way I could have experimented when I drove to Pittsburgh last Thrusday. All my passengers were screaming that I drive too fast. Wouldn't they love it if I told them that taking curves fast is safer? And then proceeded to demonstrate it experimentally?

But the bottom line is: you should definitely slow down before the curve. And if you are pulled over for speeding through a curve, explain to the cop that if you would have slowed down, you would have skidded off the road. Then pull out a pad and draw the acceleration vectors. The cop should excuse you, because math never lies.

I'm Proud to be an American / At Least Phelps is Free

Isn't it neat that the John Galliano thing happened within a few days of the Snyder v. Phelps verdict? Where would you rather be? In France where you can be locked up for calling someone a fucking kike, or the U.S.A., where you you can tell grieving parents that god hates them and their recently killed son is in Hell.

I choose the latter. I'm proud of my right to be rude. The First Amendment tells us, "You guys are big boys and girls. As long as nobody is physically hurting anyone else, I trust you to fight it out between yourselves."

But even in America, Land of the Free and Home of the KKK, people on their own are forcing this you-can't-offend-anybody pussiness on others. Recently an anti-abortion group put up an ad drawing attention to the prevalence of abortion among Niggers (Yes! This is America! That word is still legal!)

You don't like it? Big deal. Pro-abortion people are never going to like anti-abortion ads. I don't like HSBC's ads where they misuse numbers and quote irrelevant statistics (There are more vineyards in Turkey than in South Africa. Bank with HSBC). I'm also offended with those gruesome ads trying to get you not to drink soda. But I don't make a fuss. I just try to ignore them. We are adults. Part of life is getting offended. Deal with.

But apparently I'm wrong. Apparently it's an outrage that anyone ever needs to endure offence related to race (or sexual orientation, to a lesser extent). The mother of the girl in picture is "furious," "devastated," and wants an apology. Well lady, when you took your kid to the stock-photo studio, you signed away your rights to the picture. Too bad. Honor your agreement, and live with it. This ad is just pointing out a fact, that lots of Black fetueses are aborted. No, Daily News, they are not comparing abortion to genocide. (Seriously, where did the Daily News see anything about genocide?) They are pointing out a statistical fact in a provocative way. Isn't that standard for advertising?

Together with the right to free speech comes the possibility of getting offended. Live with it.

Dammed Lies and Statistics, or, Context, Context, Context

"1 MILLION WORKERS. 90 MILLION iPHONES. 17 SUICIDES" screams the front cover of this month's Wired Turns out that there's this huge company called Foxconn that produces some huge chunk of the world's electronics. And 17 of their employees committed suicide. Now we're supposed to feel guilty that our insatiable desire for electronics drove them to death. There's only one problem with this story. Foxconn has one million employees. Seventeen out of a million is actually quite small. American college students are four times more likely to commit suicide. The non-sensational fact is that Foxconn is a better place to work than other Chinese factories (which is not saying much). Sure, some of the things which make Foxconn a better place to work were done in response to the public outcry caused by the suicides. But even before the suicides, it was better than the other factories. So leave Foxconn alone, and let them rake in the cash in peace.

The morals of this story are:
Without context, numbers mean nothing.
People do not know what a million is.