Skip
# Back to self-school

Hmmm. 2X+1=5 means X=2. Is that harder to understand than "what number when doubled and then incremented by one becomes five?"

Centuries of progress in mathematical notation rolling back.

posted by twoleftfeet at 9:11 PM on September 4, 2009

I'm sure that this is very difficult for you to relate to, but I genuinely do find the wordy one easier to understand. I don't for a second believe that it is actually a

High school mathematics was a bizarre exercise for me. I got through it (even did pretty well at it) by constantly translating mathematical notation into words in my head. I was fine with the conceptual stuff that other kids sometimes got stuck on, but something as simple as

2 X 8x = 32

would just signal a reactionary revolt in my head:

It's silly and hopelessly clunky in comparison to the elegant conciseness of the notation above, I know, but it got me through highschool.

So yeah: I would

posted by Rumpled at 1:45 AM on September 5, 2009 [10 favorites]

On the other hand, mathematical

And in all its objectiveness, mathematics is an incredibly subjective sport. I think most people hijack and reshape parts of their thinking process to understand mathematics. It can be words, or an abstract sense of relationships, or pictures, or cartoons.

What I mean is that I do math in my head. Now I don't use mathematical symbols up there when I'm doing math, I translate everything into a visually spatial-ish gumbo. A mathematician I know actually thinks in mathematical notation. This wouldn't work for me.

How you do mathematics is very personal and subjective. How we understand mathematics is very personal and subjective. Mathematics itself is very rigid and objective, and we need all the help we can get to understand and do math. And so I think that presenting mathematics

posted by krilli at 5:58 AM on September 5, 2009 [1 favorite]

That's just what we want you to think.

posted by madcaptenor at 6:35 AM on September 5, 2009 [1 favorite]

Hip.

posted by joe lisboa at 11:55 AM on September 5, 2009 [7 favorites]

I prefer to think of it as "decades of poor mathematical instruction having its gaps filled in."

posted by Amanojaku at 12:16 PM on September 5, 2009

Conflicted—both positive

posted by Crabby Appleton at 12:39 PM on September 5, 2009 [7 favorites]

Well, "the language instinct" is fairly orthogonal to the question of connectionism, especially as an introduction to linguistics/cognitive science, and even presents a toy neural network example at one point. You have to be really anti-Pinker (and there are such people) to not see the value of that book in a self-education type of context. In any case, that particular faculty member isn't a connectionist (she studies language acquisition, spatial language, & Williams syndrome using a range of methods). I think the instantiation of connectionism in the department is actually quite unusual, and these days doesn't really fit at all with the way connectionist modeling plays out in psychology.

posted by advil at 1:55 PM on September 5, 2009

posted by krilli at 1:56 PM on September 5, 2009

You could well be right. The wikipedia page would seem to indicate that most dyscalculics have more troublesome symptoms than I do -- difficulty reading time, for instance, and trouble distinguishing left and right -- but I could well possess a very mild form of it.

Knowing this doesn't do much, though: there's no verified treatment.

I guess it's neat that it has a name.

(And it does potentially make the honours I won in highschool maths kiiiinda heroic. ^_^)

posted by Rumpled at 8:41 PM on September 5, 2009

Post

# Back to self-school

September 4, 2009 7:30 PM Subscribe

The autodidact course catalog. Twenty-two professors at Johns Hopkins propose reading lists for courses of self-study, from "Society Can Be Dangerous To Your Health" to "Higher Mathematics in Nouns and Verbs" to "Biochemistry and Human Evolution (with Rather a Lot about Mitochondria.)" If you're not going back to school this week, why not take on one of these syllabi instead?

madcaptenor: the target audience thinks that it is mostly meaningless symbols, more or less random hieroglyphics that only those who have drank the blood of a virgin during a lunar eclipse and sold their soul to the great Erdos can read. They see symbols and single letter variable names and their eyes glaze over and they lose all mental functioning out of a visceral fear of all things algorithmic. So they like the idea of math that is explained in nouns and verbs instead.

posted by idiopath at 7:54 PM on September 4, 2009 [7 favorites]

posted by idiopath at 7:54 PM on September 4, 2009 [7 favorites]

Mostly I feel overwhelmed (I probably am more of a state school autodidact), but I'll add a number of these books to my someday list.

posted by Edward L at 8:14 PM on September 4, 2009 [1 favorite]

posted by Edward L at 8:14 PM on September 4, 2009 [1 favorite]

idiopath, eloquently put. as a person for whom math is a square peg to the round hole of my mind, I instantly thought, regarding that course, "ooh ooh I could totally learn math if it were in words!!"

great post!! maybe it is back to school time :)

posted by supermedusa at 8:27 PM on September 4, 2009 [2 favorites]

great post!! maybe it is back to school time :)

posted by supermedusa at 8:27 PM on September 4, 2009 [2 favorites]

It's pretty lightweight stuff.

posted by neuron at 8:47 PM on September 4, 2009 [2 favorites]

posted by neuron at 8:47 PM on September 4, 2009 [2 favorites]

Most salient line of the piece:

posted by njbradburn at 8:51 PM on September 4, 2009

*The systematic didacting of oneself—it’s not a verb, but it ought to be—requires printed text bound between boards. Twitter, Facebook, Wikipedia, or an iSquint will not suffice.*Good post, and I accept the challenge.posted by njbradburn at 8:51 PM on September 4, 2009

*"ooh ooh I could totally learn math if it were in words!!"*

Hmmm. 2X+1=5 means X=2. Is that harder to understand than "what number when doubled and then incremented by one becomes five?"

Centuries of progress in mathematical notation rolling back.

posted by twoleftfeet at 9:11 PM on September 4, 2009

Mathematics is just a very precise language for expressing certain abstract concepts. Trying to use another language (except maybe German, or something else designed for computers) is just using the wrong tool for the job.

posted by phrontist at 9:38 PM on September 4, 2009 [1 favorite]

posted by phrontist at 9:38 PM on September 4, 2009 [1 favorite]

This is awesome. Thanks a lot.

For anyone else interested in reading lists within certain academic areas go check out Cosma Shalizi's Notebooks, which I believe has been mentioned in here before in a FPP.

Also, for the maths crowd check out the Khan Academy and PatrickJMT on Youtube. I got through first year uni single & multi-variable calculus with those videos. They explain things in five minutes that take a lecturer an hour.

posted by ollyollyoxenfree at 10:16 PM on September 4, 2009 [12 favorites]

For anyone else interested in reading lists within certain academic areas go check out Cosma Shalizi's Notebooks, which I believe has been mentioned in here before in a FPP.

Also, for the maths crowd check out the Khan Academy and PatrickJMT on Youtube. I got through first year uni single & multi-variable calculus with those videos. They explain things in five minutes that take a lecturer an hour.

posted by ollyollyoxenfree at 10:16 PM on September 4, 2009 [12 favorites]

doesn't a course, even if it is just a reading list, contradict the idea of Autodidacticism?

posted by trev at 10:24 PM on September 4, 2009

posted by trev at 10:24 PM on September 4, 2009

Regarding the math notation thing, I was hoping that my florid and overblown language would convey the fact that I was using hyperbole for emphasis, an example of the sort of thing that makes perfect sense to a linguistic sensibility and is less understandable to a more literal and rigorous mathematical way of thinking. I will try to be less poetic when addressing things mathematical in the future.

I seriously doubt the book attempts to do away with mathematical notation altogether. What I at least

posted by idiopath at 10:39 PM on September 4, 2009 [7 favorites]

I seriously doubt the book attempts to do away with mathematical notation altogether. What I at least

*imagined*the book to be was an introduction to mathematics for people who are not fluent in the sort of literal, pedantic way of thinking which makes you good at math and bad at judging the tone of a metafilter comment.posted by idiopath at 10:39 PM on September 4, 2009 [7 favorites]

Super cool. My highly science-y college career was lacking in topics unrelated to the dispensing of drugs, and I'm a couple of months into a serious effort to educate myself on all the stuff I wish I knew about. I'll be adding to my reading list.

posted by little e at 10:50 PM on September 4, 2009

posted by little e at 10:50 PM on September 4, 2009

This feels less audodidactic, and more "dinner party conversation fodder", not that there's anything wrong with learning interesting facts — it's just that you can't apply the knowledge from reading those books.

posted by amuseDetachment at 11:39 PM on September 4, 2009 [1 favorite]

posted by amuseDetachment at 11:39 PM on September 4, 2009 [1 favorite]

Can one apply for some sort of scholarship or perhaps get a government subsidy in order to purchase the books necessary?

posted by psylosyren at 11:46 PM on September 4, 2009

posted by psylosyren at 11:46 PM on September 4, 2009

Yeah, actually now that I've given it a closer look the list has much less in common with syllabi than I'd hoped. Oh well, back to lurking around campus bookstores of colleges I don't attend!

posted by little e at 1:41 AM on September 5, 2009

posted by little e at 1:41 AM on September 5, 2009

*twoleftfeet: Hmmm. 2X+1=5 means X=2. Is that harder to understand than "what number when doubled and then incremented by one becomes five?"*

I'm sure that this is very difficult for you to relate to, but I genuinely do find the wordy one easier to understand. I don't for a second believe that it is actually a

*better*or

*more*

*efficient*way to talk about mathematics than mathematical notation -- and I'm sincerely glad that there are arithmetically-minded people who can deal with the sort of stuff I can't -- but it just isn't how my brain works.

High school mathematics was a bizarre exercise for me. I got through it (even did pretty well at it) by constantly translating mathematical notation into words in my head. I was fine with the conceptual stuff that other kids sometimes got stuck on, but something as simple as

2 X 8x = 32

would just signal a reactionary revolt in my head:

*Aaaarrghwhatthe-*that I had to work hard to quell. I would have to breathe, calm myself, and ask, "if you halve thirty-two, what do you have? Mm, okay. And if you then split it into 8 pieces? What is the size of any one of those pieces?"

It's silly and hopelessly clunky in comparison to the elegant conciseness of the notation above, I know, but it got me through highschool.

So yeah: I would

**never**espouse the rolling-back of mathematical notation in general practice, but the concept of math-in-words being available appeals very strongly to me. As strange as I'm sure it seems, we are out there -- doing small hand-gestures under the table to conceptualise how a bill should be split, or covering a textbook's graphs with our left hand so that we can focus on the excellent, clunky, wordy explanation.

posted by Rumpled at 1:45 AM on September 5, 2009 [10 favorites]

I'd like to see more of this kind of thing.

A lot of PhD programs have comprehensive exams which come with reading lists that really lay out what that particular department thinks are all the relevant readings in the field.

I really wish these would show up on the web because they would be an excellent resource.

posted by srboisvert at 1:49 AM on September 5, 2009 [2 favorites]

A lot of PhD programs have comprehensive exams which come with reading lists that really lay out what that particular department thinks are all the relevant readings in the field.

I really wish these would show up on the web because they would be an excellent resource.

posted by srboisvert at 1:49 AM on September 5, 2009 [2 favorites]

twoleftfeet: "Hmmm. 2X+1=5 means X=2. Is that harder to understand than "what number when doubled and then incremented by one becomes five?"

I just read Laplace's

That being said, some mathematicians go too far with making everything symbolic; there's a middle ground. But this really is not a sin committed by mathematicians so much as by

posted by madcaptenor at 5:28 AM on September 5, 2009 [1 favorite]

I just read Laplace's

*A Philosophical Essay on Probabilities*, which is full of stuff like that, only with more complicated mathematical expressions. It gets kind of annoying; I kept translating into modern notation. The problem with writing these things out doesn't become apparent with things like 2x+1 = 5. It's with the more complicated formulas (which might take half a line, say, in symbols, and half a page in words) that the power of notation is more obvious; you just can't hold half a page in your head at once, even if it's a very redundant half page.That being said, some mathematicians go too far with making everything symbolic; there's a middle ground. But this really is not a sin committed by mathematicians so much as by

*students*of mathematics, who have just learned the notation and are trying to use it everywhere possible.posted by madcaptenor at 5:28 AM on September 5, 2009 [1 favorite]

srboisvert: you might be able to Google for those lists. I know I've come across them by accident, and you can probably do better if you're looking for them on purpose. Those exams go by different names in different fields, so try looking for "preliminary exam, "oral exam", or "qualifying exam". Though "preliminary exam" can actually have a different meaning -- in my PhD program, in mathematics, it's an exam that one takes immediately upon entering the program to show that you've mastered the undergraduate material. And of course "oral exam" can describe any exam where you stand up in front of a bunch of people to be tested -- but for a lot of people that's the only one they ever take.

posted by madcaptenor at 5:32 AM on September 5, 2009

posted by madcaptenor at 5:32 AM on September 5, 2009

In my view, mathematics isMathematics is just a very precise language for expressing certain abstract concepts. Trying to use another language (except maybe German, or something else designed for computers) is just using the wrong tool for the job.

—phrontist

*thinking about abstract concepts*, or working with them.

On the other hand, mathematical

*notation*is a very precise language for expressing these abstract concepts, and is designed to remove any ambiguity and present very rigid definitions, to present the object of the idea while eliminating any wiggle room for subjective interpretation. It's used as a bulletproof point of reference, like a dictionary.

And in all its objectiveness, mathematics is an incredibly subjective sport. I think most people hijack and reshape parts of their thinking process to understand mathematics. It can be words, or an abstract sense of relationships, or pictures, or cartoons.

What I mean is that I do math in my head. Now I don't use mathematical symbols up there when I'm doing math, I translate everything into a visually spatial-ish gumbo. A mathematician I know actually thinks in mathematical notation. This wouldn't work for me.

How you do mathematics is very personal and subjective. How we understand mathematics is very personal and subjective. Mathematics itself is very rigid and objective, and we need all the help we can get to understand and do math. And so I think that presenting mathematics

*exclusively*in mathematical notation is a shame – a lot of people will have an unnecessarily hard time with it. Kinda like soap operas don't work that well for autistic people, and like using that alphabet stuff isn't the best way to present info to a dyslexic.

posted by krilli at 5:58 AM on September 5, 2009 [1 favorite]

*Mathematics itself is very rigid and objective*

That's just what we want you to think.

posted by madcaptenor at 6:35 AM on September 5, 2009 [1 favorite]

y = x², but how does x

posted by krilli at 6:46 AM on September 5, 2009 [2 favorites]

*feel*about that?posted by krilli at 6:46 AM on September 5, 2009 [2 favorites]

Rumpled, as your internet psychologist, I diagnose you with a mild version of dyscalculia - learning disability which affects a person's ability to understand, remember, or manipulate numbers or number facts.

posted by nooneyouknow at 8:08 AM on September 5, 2009

posted by nooneyouknow at 8:08 AM on September 5, 2009

Difference != Disability

posted by regicide is good for you at 9:07 AM on September 5, 2009

posted by regicide is good for you at 9:07 AM on September 5, 2009

If I read all these books, does that mean I get a degree from Johns Hopkins?

posted by mathlete at 9:17 AM on September 5, 2009

posted by mathlete at 9:17 AM on September 5, 2009

I'm by no means a mathematician, but from the math I've studied it's seemed to me that the standard notation which is now traditional to teach and do mathematics in is far from a single thing, far from unambiguous, far from rigidly defined, has lots of wiggle room and subjective interpretations built in. The language of math is like English, only, if anything, even more bastardized and corrupt. It's a creole of several different systems developed by brilliant, idiosyncratic individuals and made into a brittle but hard canon by everyone else. Even the numeration system is borrowed, second, third, fourth hand and has been reshaped, by centuries (even millenia) of use, like a stone in weather. The subject matter of math is all patterns and relationships and the notation used to express them is the least important thing about them. It seems to me that we cling to it like desperate, shipwrecked sailors to that oddly shaped rock, in a storm.

Cool book I'm reading right now: The Book of Numbers by John Conway and Richard Guy.

posted by wobh at 9:33 AM on September 5, 2009 [1 favorite]

Cool book I'm reading right now: The Book of Numbers by John Conway and Richard Guy.

posted by wobh at 9:33 AM on September 5, 2009 [1 favorite]

Upon reading this list I was very pleasantly surprised to see one of my colleagues represented, especially seeing as we're a really small department. I guess it's a small world too!

posted by ob at 9:46 AM on September 5, 2009

posted by ob at 9:46 AM on September 5, 2009

Neat. To my surprise, I see I had more than a few of them as professors when I was at Hopkins.

My favorite physics professor was definitely Adam Falk (Einstein Just Shakes His Head: Readings in Quantum Physics). As you'd expect, I had him for my two quantum classes, which he taugh with great clarity. If you ever get your hands on the after-semester professor reviews, you'd see nothing but praise for him. And if you look at his blurb carefully, notice that he's a dean as well as a professor. He was teaching a course (well!), running a office, and had a graduate student!

Also, I'm a little surprised to see so much Pinker on the cognitive science list. The courses I took (admittedly few) had a strong connectionist bent.

posted by keenduck at 10:22 AM on September 5, 2009

My favorite physics professor was definitely Adam Falk (Einstein Just Shakes His Head: Readings in Quantum Physics). As you'd expect, I had him for my two quantum classes, which he taugh with great clarity. If you ever get your hands on the after-semester professor reviews, you'd see nothing but praise for him. And if you look at his blurb carefully, notice that he's a dean as well as a professor. He was teaching a course (well!), running a office, and had a graduate student!

Also, I'm a little surprised to see so much Pinker on the cognitive science list. The courses I took (admittedly few) had a strong connectionist bent.

posted by keenduck at 10:22 AM on September 5, 2009

This makes me wish that MetaFilter University had actually happened.

posted by lazaruslong at 11:29 AM on September 5, 2009

posted by lazaruslong at 11:29 AM on September 5, 2009

*y = x², but how does x feel about that?*

Hip.

posted by joe lisboa at 11:55 AM on September 5, 2009 [7 favorites]

*Centuries of progress in mathematical notation rolling back.*

I prefer to think of it as "decades of poor mathematical instruction having its gaps filled in."

posted by Amanojaku at 12:16 PM on September 5, 2009

*y = x², but how does x feel about that?*

Conflicted—both positive

*and*negative.

posted by Crabby Appleton at 12:39 PM on September 5, 2009 [7 favorites]

*Also, I'm a little surprised to see so much Pinker on the cognitive science list. The courses I took (admittedly few) had a strong connectionist bent.*

Well, "the language instinct" is fairly orthogonal to the question of connectionism, especially as an introduction to linguistics/cognitive science, and even presents a toy neural network example at one point. You have to be really anti-Pinker (and there are such people) to not see the value of that book in a self-education type of context. In any case, that particular faculty member isn't a connectionist (she studies language acquisition, spatial language, & Williams syndrome using a range of methods). I think the instantiation of connectionism in the department is actually quite unusual, and these days doesn't really fit at all with the way connectionist modeling plays out in psychology.

posted by advil at 1:55 PM on September 5, 2009

Wow. That isy = x², but how does xfeelabout that?Hip.

—joe lisboa

*win*.

posted by krilli at 1:56 PM on September 5, 2009

For every other person of letters who desires to better their understanding of the mathematical arts, I would add

posted by ob1quixote at 3:25 PM on September 5, 2009

*How to Solve It*by George Polya to this list.posted by ob1quixote at 3:25 PM on September 5, 2009

Listen.

I'm no hater of math, but math syntax can be astonishingly obtuse and dense. Lets be honest, this is a method of expression that was designed for blackboards and rapid reiteration in an era without computers. Ease of absorption isn't even on the list of design criteria -- remember, culturally, this is a world where the more applied your field, the lower your status.

Pedagogy is an application.

Not to mention, standard mathematical syntax really has trouble encoding certain ideas at all. Consider the following -- the RC4 encryption algorithm, in pretty much all its glory:

And here's TEA, the Tiny Encryption Algorithm:

Say what you will about procedural logic, it can be remarkably straightforward.

posted by effugas at 8:30 PM on September 5, 2009 [2 favorites]

I'm no hater of math, but math syntax can be astonishingly obtuse and dense. Lets be honest, this is a method of expression that was designed for blackboards and rapid reiteration in an era without computers. Ease of absorption isn't even on the list of design criteria -- remember, culturally, this is a world where the more applied your field, the lower your status.

Pedagogy is an application.

Not to mention, standard mathematical syntax really has trouble encoding certain ideas at all. Consider the following -- the RC4 encryption algorithm, in pretty much all its glory:

for i from 0 to 255

S[i] := i

endfor

j := 0

for i from 0 to 255

j := (j + S[i] + key[i mod keylength]) mod 256

swap(&S[i],&S[j])

endfor

And here's TEA, the Tiny Encryption Algorithm:

void encrypt (uint32_t* v, uint32_t* k) {

uint32_t v0=v[0], v1=v[1], sum=0, i; /* set up */

uint32_t delta=0x9e3779b9; /* a key schedule constant */

uint32_t k0=k[0], k1=k[1], k2=k[2], k3=k[3]; /* cache key */

for (i=0; i <>>5) + k1);

v1 += ((v0<>>5) + k3);

} /* end cycle */

v[0]=v0; v[1]=v1;

}

Say what you will about procedural logic, it can be remarkably straightforward.

posted by effugas at 8:30 PM on September 5, 2009 [2 favorites]

*Rumpled, as your internet psychologist, I diagnose you with a mild version of dyscalculia - learning disability which affects a person's ability to understand, remember, or manipulate numbers or number facts.*

You could well be right. The wikipedia page would seem to indicate that most dyscalculics have more troublesome symptoms than I do -- difficulty reading time, for instance, and trouble distinguishing left and right -- but I could well possess a very mild form of it.

Knowing this doesn't do much, though: there's no verified treatment.

I guess it's neat that it has a name.

(And it does potentially make the honours I won in highschool maths kiiiinda heroic. ^_^)

posted by Rumpled at 8:41 PM on September 5, 2009

Side note:

Metafilter's XSS filter, amusingly enough, breaks C code. If you actually want to see TEA, go here:

http://en.wikipedia.org/wiki/Tiny_Encryption_Algorithm

posted by effugas at 10:09 PM on September 5, 2009

Metafilter's XSS filter, amusingly enough, breaks C code. If you actually want to see TEA, go here:

http://en.wikipedia.org/wiki/Tiny_Encryption_Algorithm

posted by effugas at 10:09 PM on September 5, 2009

i've been out of university for 2 years now.. maybe i should get back to thinking.

posted by medici00 at 9:47 AM on September 7, 2009

posted by medici00 at 9:47 AM on September 7, 2009

« Older Barack Obama, President of the Divided States of... | Gutsy Gourmet Newer »

This thread has been archived and is closed to new comments

thinkmathematical writing usually consists of?)posted by madcaptenor at 7:38 PM on September 4, 2009