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Reminds me of this essay: http://www.maa.org/devlin/LockhartsLament.pdf

"A Mathematician's Lament", an article that's been making the rounds among mathematicians since 2002 (but was only published in 2008), expresses some similar views, and is also a good read.

I've seen the following link in many a Slashdot thread before, but it certainly bears repeating here: "A Mathematician's Lament" by Paul Lockhart It's mostly known as an insightful critique of what's wrong with K-12 math education, but I've always liked it as an explanation of why people who enjoy math do it in the first place: it's satisfying in an artistic way. I think it would be great if more students saw math as something worth doing for its own sake, like art or athletics, and hey, it lets you do science and engineering too.

In fact, this summary sounds similar enough to "Lament" that I wouldn't be surprised if this Dr. Lewis was inspired by and/or cited it. But this is Slashdot, so I'll let someone else check that out.

Arithmetic is math in the same way that paint by numbers is fine art.
This explains it pretty well:

http://www.maa.org/devlin/LockhartsLament.pdf

don't think anyone is arguing to try to teach the WHOLE domain of one field that way. We're talking about the _basics_.

What are the basics? Addition? Subtraction? Multiplication? Can we teach those by rote? (and at some point multiplication tables need to be memorized) Math is a layering of abstraction upon abstraction so which layer gets to be called 'basic'. The layer where you don't even have the tools to communicate concepts effectively? Or maybe Algebra gets to be 'the basics' that we try to help kids 'discover'. What about properties of operations (associative/commutative) how do you get kids to discover all of those in time to actually finish an algebra sequence? Or do we need to try and get everyone to discover what the abstract concept of zero means? How do you pick what the basics are, and how do you handle the general symbolic language and communication skills to get to that point? It seems a fairly arbitrary line to be drawn. Everyone learns differently, and learning methods change as language grasp and symbol usage develop.

The whole 'teach math discovery' idea strikes me as one of these: http://developers.slashdot.org/story/10/12/06/0124241/I-Just-Need-a-Programmer
Just another idea that is less than useless without an implementation, and the implementation details are friggin' hard with tens of thousands of caveats, corner cases, exceptions and risk. see: http://en.wikipedia.org/wiki/New_Math where math teaching reform was tried and failed.

What is taught for today's Math is a total joke - kids aren't taught to think, just to mindless follow some "arcane formula". e.g. "Two weeks of content are stretched to semester length by masturbatory definitional runarounds."

This isn't a concept/discovery problem in the context of the current discussion, it's a pacing problem and a consequence of putting vastly different types of learners all in the same room and moving at the pace of the lowest common denominator. This is a common complaint of mine but doesn't seem to fit into the current question 'teaching discovery'. Regardless of what teaching method you're using, go too fast and you lose the people that need extra attention, too slow and you lose the ones that don't.

EVERYONE should read these two papers.

* A Mathematician's Lament http://www.maa.org/devlin/LockhartsLament.pdf

* The Underground History of American Education http://www.johntaylorgatto.com/chapters/index.htm

I'll take a look at those papers later as they appear fairly long and involved.

> Rediscovering something can be really cool on a one off basis, but there isn't time to do that for the entire body of knowledge nor should we try.

I don't think anyone is arguing to try to teach the WHOLE domain of one field that way. We're talking about the _basics_. What is taught for today's Math is a total joke - kids aren't taught to think, just to mindless follow some "arcane formula". e.g. "Two weeks of content are stretched to semester length by masturbatory definitional runarounds." EVERYONE should read these two papers.

* A Mathematician's Lament
  http://www.maa.org/devlin/LockhartsLament.pdf

* The Underground History of American Education
  http://www.johntaylorgatto.com/chapters/index.htm

Kids are taught to solve stupid problems like robots. That's not Math at all. Math is about creating purely imaginary constructs, asking questions about them, and figuring out how to answer those questions. It's both creative, logical, and engaging. Judging by the reasoning abilities (or lack thereof) of 99.9999% of people I encounter, the world needs lots and lots more Math--real Math. See "A Mathematician's Lament".

you need to read A Mathematician's Lament

See A Mathematician's Lament, by Paul Lockhart. At least follow that link, even if you ignore the rest of what I write.

I was taking community college courses until recently. Initially, my plan was to take the prerequisites for a computer science degree, then transfer. I found the computer related courses interesting and generally well within my abilities; in particular, I found programming courses very easy, even the ones in which I was sitting next to professional software developers who were brushing up their skills. The courses on mathematics were quite another story. In my first semester as a (returning) full time student, I found I spent over 90% of my study time on Calculus I.

What really struck me as puzzling was that on the one hand, I could not keep up with the complex transformations on the chalkboard and the homework assignments that the other students could. On the other hand, outside of that classroom, I found that the same students showed no particular intellectual strengths beyond mine; those that were in the same programming classes that I was in weren't as good as I was at programming, or even at understanding the mathematical applications of programming. The students showed no curiosity about nor enthusiasm for mathematics; for that matter, neither did the instructors. Yet I was curious and enthusiastic about mathematics. I actually have read books on algebra for pleasure.

Years ago, when I was in college for the first time, I was an English major; for years afterwards, I was astonished when I would meet former classmates who couldn't remember any of the literature we'd studied together. Now, I find that when I talk to engineers and developers, I'm astonished that many of them remember little mathematics beyond basic algebra.

I understand Lockhart's point to be that the model for teaching mathematics is at odds with the nature of mathematics; that we waste years of students' time teaching them gibberish, which they will not remember or use, while discouraging those that would actually love mathematics from actually encountering the subject. The way mathematics is taught now is something like the way Latin used to be taught: its necessity is exaggerated, those elements that are necessary are passed over quickly, and both its real utility and its intellectual appeal is buried under tons of meaningless busywork.

I can tell it's truly News for Nerds because I can barely understand what it's saying and it drops causal references to advanced mathematics

I recommend you start visiting arXiv then.

Are you suggesting the OP, a self-described interested lay person, learns or even mere follow mathematic research by reading arXiv? If so, WTF!?

arXiv is a pre-print archive of original research articles, not exactly a welcoming place for a non-mathematician (or non-subject specialist, e.g. physics, and computer science also use it). Even with an undergrad degree in mathematics, I find it a difficult (and/or useless) place to try to follow progress in the field, without the editorial assistants to filter the wheat from the chaff. And I've been reading original (first source) research papers since the mid-1990s in multiple research disciplines.

You might as well ask him to read Euclid's Elements in its original Greek. Heck, after the translation, it would be more accessible, as it is intended to be a textbook for learning.

I would rather suggest, try reading some of the mathematics journals that are intended to be more accessible, such as from MAA and AMS societies. Some are aimed at students of two-year and four-year "colleges" (aka polytechs / technical colleges and universities), while others are just interesting yet often accessible, such as Journal of Recreational Mathematics and Mathematics Magazine and online columns such as Kevin Devlin's Devlin's Angle.

In the more general sense, I would recommend popular math writers such as Ian Stewart, Simon Singh, Paul J. Nahin, the recently deceased Martin Gardner (slashdot), and many more authors that I cannot recall.

Unfortunately I can't think of any pop-math books or articles on linear algebra, in the vein of "e: The Story of a Number" (Maor), "An Imaginary Tale" (Nahin), "Flatland" (Abbott), "Flatterland" (Stwart), "A Mathematician's Apology" (Hardy), "Fermat's Last Theorm" / "Fermat's Engima" (US) (Singh), "Does God Play Dice?" (Stewart), "Chaos" (Gleick), and many others.

To wit, mathematics is I believe the only discipline where fourth year undergrad students take third or fourth year courses with "introduction" or "elementary" in their course titles. But I digress. My point is that one "problem" is that given mathematics long history, and that is has fascinated people across cultures throughout history, the subject has accumulated such a vast body of knowledge, so it is difficult to get a firm understanding on every field within mathematics. So feeling overwhelmed with all the facts and fields to learn is normal.

I can tell it's truly News for Nerds because I can barely understand what it's saying and it drops causal references to advanced mathematics

I recommend you start visiting arXiv then.

Are you suggesting the OP, a self-described interested lay person, learns or even mere follow mathematic research by reading arXiv? If so, WTF!?

arXiv is a pre-print archive of original research articles, not exactly a welcoming place for a non-mathematician (or non-subject specialist, e.g. physics, and computer science also use it). Even with an undergrad degree in mathematics, I find it a difficult (and/or useless) place to try to follow progress in the field, without the editorial assistants to filter the wheat from the chaff. And I've been reading original (first source) research papers since the mid-1990s in multiple research disciplines.

You might as well ask him to read Euclid's Elements in its original Greek. Heck, after the translation, it would be more accessible, as it is intended to be a textbook for learning.

I would rather suggest, try reading some of the mathematics journals that are intended to be more accessible, such as from MAA and AMS societies. Some are aimed at students of two-year and four-year "colleges" (aka polytechs / technical colleges and universities), while others are just interesting yet often accessible, such as Journal of Recreational Mathematics and Mathematics Magazine and online columns such as Kevin Devlin's Devlin's Angle.

In the more general sense, I would recommend popular math writers such as Ian Stewart, Simon Singh, Paul J. Nahin, the recently deceased Martin Gardner (slashdot), and many more authors that I cannot recall.

Unfortunately I can't think of any pop-math books or articles on linear algebra, in the vein of "e: The Story of a Number" (Maor), "An Imaginary Tale" (Nahin), "Flatland" (Abbott), "Flatterland" (Stwart), "A Mathematician's Apology" (Hardy), "Fermat's Last Theorm" / "Fermat's Engima" (US) (Singh), "Does God Play Dice?" (Stewart), "Chaos" (Gleick), and many others.

To wit, mathematics is I believe the only discipline where fourth year undergrad students take third or fourth year courses with "introduction" or "elementary" in their course titles. But I digress. My point is that one "problem" is that given mathematics long history, and that is has fascinated people across cultures throughout history, the subject has accumulated such a vast body of knowledge, so it is difficult to get a firm understanding on every field within mathematics. So feeling overwhelmed with all the facts and fields to learn is normal.

I can tell it's truly News for Nerds because I can barely understand what it's saying and it drops causal references to advanced mathematics

I recommend you start visiting arXiv then.

Are you suggesting the OP, a self-described interested lay person, learns or even mere follow mathematic research by reading arXiv? If so, WTF!?

arXiv is a pre-print archive of original research articles, not exactly a welcoming place for a non-mathematician (or non-subject specialist, e.g. physics, and computer science also use it). Even with an undergrad degree in mathematics, I find it a difficult (and/or useless) place to try to follow progress in the field, without the editorial assistants to filter the wheat from the chaff. And I've been reading original (first source) research papers since the mid-1990s in multiple research disciplines.

You might as well ask him to read Euclid's Elements in its original Greek. Heck, after the translation, it would be more accessible, as it is intended to be a textbook for learning.

I would rather suggest, try reading some of the mathematics journals that are intended to be more accessible, such as from MAA and AMS societies. Some are aimed at students of two-year and four-year "colleges" (aka polytechs / technical colleges and universities), while others are just interesting yet often accessible, such as Journal of Recreational Mathematics and Mathematics Magazine and online columns such as Kevin Devlin's Devlin's Angle.

In the more general sense, I would recommend popular math writers such as Ian Stewart, Simon Singh, Paul J. Nahin, the recently deceased Martin Gardner (slashdot), and many more authors that I cannot recall.

Unfortunately I can't think of any pop-math books or articles on linear algebra, in the vein of "e: The Story of a Number" (Maor), "An Imaginary Tale" (Nahin), "Flatland" (Abbott), "Flatterland" (Stwart), "A Mathematician's Apology" (Hardy), "Fermat's Last Theorm" / "Fermat's Engima" (US) (Singh), "Does God Play Dice?" (Stewart), "Chaos" (Gleick), and many others.

To wit, mathematics is I believe the only discipline where fourth year undergrad students take third or fourth year courses with "introduction" or "elementary" in their course titles. But I digress. My point is that one "problem" is that given mathematics long history, and that is has fascinated people across cultures throughout history, the subject has accumulated such a vast body of knowledge, so it is difficult to get a firm understanding on every field within mathematics. So feeling overwhelmed with all the facts and fields to learn is normal.

We only know how to calculate it in binary (or any base that is a power of 2). You can't convert to decimal without know all the rest of the digits.

Parent is correct, digits of pi can be calculated independently in base 2, 4, 8, 16 or 2^n since the 1990s. So, it is possible to calculate the 2,000,000,000,000,000th number of pi without calculating the digits before that one. Now, if we want to calculate the digit in decimal (or converse the binary digit to decimal), we need to calculate all of the two-quadrillion digits. Knowing this digit is in itself not very interesting.

Familial searches from a DNA database the size of the one in California are very, very likely to produce false positives. For example, a study of the Arizona CODIS database carried out in 2005 showed that approximately 1 in every 228 profiles in the database matched another profile in the database at nine or more loci, that approximately 1 in every 1,489 profiles matched at 10 loci, 1 in 16,374 profiles matched at 11 loci, and 1 in 32,747 matched at 12 loci. http://www.maa.org/devlin/devlin_10_06.html

With California currently having the third largest DNA database in the world, the odds of ANY new genetic evidence matching on a cold search is way too likely.

I think this applies.. http://www.maa.org/devlin/LockhartsLament.pdf

OK, try this way then: the ratio of Tuesdays to all possible days is what matters. I.e. the probability that both boys meet the critera is much smaller (i.e. both born on Tuesday).

There are two extremes for this sort of problem:

1) You know one is a boy, but you have no information to say which. Then the probability the other is a boy is 1/3. (This is counter intuitive, but Devlin explains it well).

2) You know the youngest is a boy. Then the probability the oldest is a boy is 1/2.

When you have an extra piece of information, the chance that it might apply to both children affects the overall probability, and you get a value between 1/3 and 1/2. The day of the week is unlikely to be the same for both (ignoring twins), so it's close to 1/2.

Only if you use the Devlin's logic in the story where the every possible combination is:

boy - boy
boy - girl
girl - boy
girl - girl

You are putting extra weight on the "boy - girl" combination. There are really only three possible solutions:

boy - boy
girl - girl
boy - girl (or girl - boy if you prefer...)

By pointing out one boy you know it's not a "girl - girl" outcome so that leaves you with two options:

boy - boy
boy - girl

> and had no need to remember the conversion when they learned it in science class.

That's because they teach a crappy remembrance system...

Compare and contrast to the SIMPLE way that you can do in your head:

miles -> km: x*2*2*2*2/10
i.e. 60 miles = 60*2*2*2*2/10 = 120*2*2*2/10 = 240*2*2/10 = 480*2/10 = 960/10 = 96 km

km -> miles: x/50 + x/10
i.e. 100 km = 100/2 + 100/10 = 50+10 = 60 miles

--
Why Math just isn't taught properly anymore.. A Mathematician's Lament

This thread is a good example of how our generation was taught math wrong. I'm talking about the +5 responders, not the people in the article. Most people in this discussion are saying that the number of votes needed is 137.33 based on multiplying 206 by 2/3. The fact that all of the upvoted responders used arithmetic belies the failure of our math education system. Arithmetic has its place, but not here. This is a simple number problem. 2/3 is twice 1/3, so the number of yea votes must be twice the number of nay votes. Obviously the vote failed because 136 is less than twice 70. Using arithmetic is unnecessary and overly complicates the issue. We don't need any discussion about repeating digits or order of operations. I think Lockhart said it best.

Lockhart, famous for his critique on “mathematics” “A Mathematician’s lament” is currently writing a book, to teach math the way it’s supposed to be taught.
I decided to wait for it, since all the other stuff on the market is the same retarded backwards-“teaching” shit, with the same stupid “learning rules by heart”.

In a similar thread on Slashdot, someone posted a link to A Mathematician's Lament, by Paul Lockhart, which I found persuasive and very moving.

I'm in a position similar to that of the original poster. I've gone back to school, after years of low-paid jobs, hoping to work towards a CS degree. I had to admit I wouldn't be able to do it -- I've found the programming and networking courses very easy, but the calculus courses I took required ten times as much study as everything else put together, and I was still doing poorly.

Yet, outside the formal coursework, I found calculus very interesting. I kept getting the sense that the course material was all but irrelevant to the subject itself. In fact, the texts go to great length to avoid discussing subjects, particularly the concept of the infinitesimal, that have some problematic aspects, but happen to be critical to the discovery and development of calculus, and are much more intuitively clear. Annoyingly, the textbook I was using kept saying that Leibnizian notation (dx/dy) was "suggestive," but never explained how or why. It was like watching a movie from the '50s, in which the characters are talking about sex, but so indirectly that it's hard to understand what they're saying.

My hope, at this point, is that I can learn enough of mathematical reasoning on my own, without going to through the pointless drudgery of math courses, to be an effective programmer.

"I think you hit it spot on, it's not the curriculum, it's how they make it as boring as possible. I didn't enjoy math until I was actually out of public school and did that in my private life. When I picked up a Dover math book and learned the mysteries of such things as mathematical abstraction, that was exciting. At least more than learning maths verboten with no end goal in sight.

Another thing is the lack of math history being taught. Yes 1+0=1. But why? Where did zero come from? Where did numerals come from? Why was Algebra invented and where did it come from? What use is it? What about geometry? Who was Euclid? I could go on and on with fascinating topics related to math. These things are rarely answered. It's all about teaching you to understand one function, one algorithm, one technique, etc. Never to understand _why_. It downright sucks, they take all the fun out of a spectacular field. Thanks to their "teaching" me, I thought math had no room for expansion. Boy was I wrong. It's an abstract fun house where you can do whatever you dream up. To a kid, that itself should be reason enough to love any math. "

Ok, it's like this. I graduated from High school in 1972 (yup, I'm that old).

I flunked Algebra I in a flaming pile of poo. My teacher, a rookie, stunk. I did not apply myself. Second time around I worked at it, and my teacher made sure I did. My first year teacher left the school. Not blaming her singly, but I might have had a shot if I had a marginally more involved teacher.

Geometry I LOVE to this day. I would teach high school geometry if it weren't for the students. Unless I get this feeling that I can be the sort of teacher that can break through and motivate the kids to love it as much as I do. If I sit still for a moment, that feeling goes away, as it should - I am not gifted. Still.....

Algebra II was awful, but I got through.

That's 4 years of maths. No calc/trig for me. I am greatly diminished by that, and if I go back to school I will take the maths just because.

Now, how to teach math? I memorized multiplication tables up to 12x12. I've played cribbage since I can remember. Since before I was 5, for sure. I used to drive my teachers crazy counting by 15s. to this day, I I see 8 & 7, 6 & 9, etc at '15'. I can add a column of figures in my head almost as fast as I can with a calculator until I get into 5 and 6 digit strings. But I have to exercise that skill. I'm not as good as I used to be.

Where did I learn that 'zero' was a concept? Actually, in World History class. I think this was an Arab invention, but I would not have been taught that the Japanese or Chinese knew of it. In fact, in World History, I learned that much science and math was developed and greatly explored by Arab scholars. Even in the 70s, our teacher lamented that the Arab world had, in his words, 'squandered their legacy and lost their great opportunity'. I'm not sure if that's a nice thing to say, but I learned more about math history in history class than I did in math class.

But I took music appreciation for an easy credit. Wrong. Music history was taught there, and a little bit of music math.

Read Lockhart's Lament for an insight into how popular methods of teaching mathematics in American public schools is possibly destroying any hope for generations. He has an interesting point; if we taught music the way we teach math, musicians would probably never make any music.

And then there's my niece, teaching third grade in Arizona. She's teaching her kids 'series and parallel circuits' and 'vertex edge graphs' to satisfy the standardised testing here. What? circuits? No Ohm's law fo these kids, just circuits. And vertex edge graphs? I dunno about those, and don't care. third graders? Are they deliberately trying to make these kids allergic to maths?

What a mess.

A Mathematicians Lament. I really wish more teachers would read this essay.

SIAM (Society for Industrial and Applied Mathematics) has several special interest groups related to computing/programming problems. The other major math and stat groups have excellent articles on computing problems from time to time as well like the AMS, MAA, or AMSTAT, but SIAM probably provides the most of these groups and a lot of coverage that compliments IEEE and ACM. Also depending on if you're working in a specific industry or if you're furthering your studies in a graduate program there may be other professional societies that deal with informatics or computational issues related to that focus.

I second that, I would even add that God must have F fingers.

Proof: if you want to know the n-th number of pi, you have to calculate all numbers up to n-1 to calculate n. However, in binary, octal, hexadecimal and any base 2^n you can calculate that number independently. So, to know the last "3" of "3.141592653" we need to calculate all numbers before. To know the last "0" of "3.243F6A8885A308D313198A2E0" we do not have to calculate all numbers before it. As we see here, God of course has his shortcuts to omnipotency. So, he has 2^n fingers. The actual number of his fingers must be close to ours, since we were created to his semblance. Having less fingers than us would make him less perfect (a god without thumbs would be plainly absurd), so he must have F.

Obviously, you can't teach Mathematics through a video game. You can, however, clarify some of the more obscure portions of Mathematics through demonstration, and video games are an excellent way to demonstrate.

Not that monstrosity that they call mathematics (and which really has not much to do with it), that's right.
But real mathematics.. I think Paul Lockhart would strongly disagree. :)

Lockhart's paper was referenced March 2008 on the monthly Mathematical Association of America (MAA) online column of Keith Devlin, here

it's a thought-provoking essay, by someone with the credentials to be taken seriously. Nice to see it finally being slashdotted :)

Lockhart in his Lament indicates that the process of discovery is the real heart of mathematics. In that case, reading original works that presumably showcase that process is vital, especially for those just starting out in the field.

Ideally, though, you'd read them with updated notation.

29th/Nov?

Wow - that's my birthday as well. Cool coincidence.

Not really.

With the LaTeXDoc plugin for mediawiki you can edit the entire latex document in a wikipage, then press a link to create the PDF. You can include graphics and other external documents as in standard LaTeX by adding an extra line that tells the wiki to include these files. You can read an article about this system in the MAA Focus (PDF) .

I suggest A Mathematician's Lament also known as "Lockhart's Lament", it was written by Paul Lockhart in 2002. It is a relatively short read and I consider it absolutely essential for anyone in mathematics, but especially the ones who dream of being teachers.

All voting systems are mathematically flawed. It's a mathematical property and can't be avoided. (check Election Math as a reference).

This game series has kept me busy for nearly a year now.

No fancy graphics here; it's pure turn-based puzzle, kind of a mix of Nethack and Gauntlet. Everything from horde monster fights to door-lock puzzles to old classic riddles.

A kind review: http://www.maa.org/editorial/mathgames/mathgames_06_13_05.html

There's an interesting essay by Keith Devlin on the sad state of math education in the US. http://www.maa.org/devlin/LockhartsLament.pdf

Also: http://www.maa.org/devlin/

There's an interesting essay by Keith Devlin on the sad state of math education in the US. http://www.maa.org/devlin/LockhartsLament.pdf

Also: http://www.maa.org/devlin/

I looked at the sample questions, and I have to recommend that math teachers learn English before teaching math.

It reminds me of Lockhart's Lament. We're teaching math wrong. Highly recommended reading:

http://www.maa.org/devlin/LockhartsLament.pdf

Check out WikiBooks. They aren't quite there yet, but some of their stuff is quite good - and being a wiki, your inputs are encouraged.

With cheap laptops/ebook readers on the horizon, and projects like WikiBooks / Project Gutenberg I am hopeful that we are only a few years from prolific material availability.

Also, slightly off topic - but since you mentioned schools I'd like to refer you to Lockhart's Lament. Do we even really need text books?

More really good demoes are compiled at my maa.org article, 64K or less. http://www.maa.org/editorial/mathgames/mathgames_08_16_04.html The main demoscene sites are better though: http://www.scene.org/ and http://www.pouet.net/ . One of my own recent favorites is a 4K demo, synchroplastikum http://www.pouet.net/prod.php?which=20967

I term this reverse confirmation bias: if many people have tried and failed, it must be impossible.

But what credit is there to that? Many were the claims to transmute lead into gold. What proved impossible by chemical means was by no means impossible within the framework of the right technology. I think you need to study the "Four Colour Corollary". This theorem states that the truth or falsity of the theorem is entirely independent of the number of bozos who publish unfounded and incorrect speculations disguised as purported proofs. Furthermore, we still don't have a proof that could possibly have been discovered before the computer era, so the deck was stacked towards impossible ... until it wasn't.

The same thing happened within the field of AI. This still annoys me. A lot of grand claims were put forward in the 1960s, and it all fell far short of what was promised. Nevertheless, there has been an unbroken stream of solid and important results, if not yet worth writing home about. Weren't the smart people silently expecting it to play out this way all along?

I feel the statistical results are the most important:
http://www.ucl.ac.uk/media/library/robotillusions

And there recent is progress even in the long discredited field of automatic proof:
http://www.maa.org/devlin/devlin_01_05.html

Guess what? Computers are now checking computerized proofs. Does this series converge, or not?

As for this new blood test, the human genome was sequenced a scant seven years ago, the explosive shock wave of proteomics is expanding almost at the limiting wave velocity, and we are now beginning to disentagle some of the fundamental neurochemistry involved. If there are any correlates in the blood whatsoever, it would be shocking to not find them at the present time, or in very short order.

Concerning percentage prediction rates, have we learned nothing? If you have a population of size N which you wish to classify into two distinct groups, given prior p and (1-p), the information required to achieve this is N * H(p), using Shannon's information measure. If this test provides any additional information beyond the prior, one can formally determine the ratio of the unknown information this test provides. If the test is worthless, the ratio will be zero. If the test is perfect, the ratio will be one. If the ratio comes out negative, you just assume the water goes the other direction (by metaphor with electrochemistry), and substitute the absolute value.

The interesting term is the cross entropy between what the experts can determine and what this test can determine. If the cross entropy is 100%, then either test gets you to exactly the same place, and it will probable come down to a matter of economics, which the cheaper approach prevailing. If the cross entropy is significantly less than 100%, then one will likely employ both tests, possibly using the cheaper test to screen the more expensive test, depending on tolerance rates for false negatives and false positives.

Given that they have included 18 elements in this test given a small positive sample size (they don't state their negative sample size), it's almost certain that some of these 18 factors are bogus, and will be eliminated as the sample size increases. If this test is bogus, the factors remaining will dwindle to zero, as the predictive rate also dwindles to nothingness. If the test is fundamentally predictive (to some ratio of the information content) as the bogus factors are pared out, the predictive ratio will likely improve by some marginal amount, maybe enough to be worth doing, maybe not.

In the 1970s one could make easy sport of predicting that any given claimant of the "four colour proof" was wrong and pat yourself on the back for an unbroken chain of confirmations. Great work: you've managed to predict that the world is full of de

http://en.wikipedia.org/wiki/Ivars_Peterson>Ivars Peterson is a mathematics writer who writes entertaining books that explain concepts clearly.

His homepage is here and an archive of his "Math Trek" articles can be found here.

Just a few days ago there as brief thread on alt.tv.wonder-years about the math stuff that Danica McKellar did, and then someone came up with a link about the process of naming theorems, where the author cites the "Chayes-McKellar-Winn theorem".

Here is the link to the article: http://www.maa.org/devlin/devlin_09_05.html

Keeping any sufficiently complex code base 'clean' is like battling entropy. Eventually any code base given enough changes becomes 'messy'.

I've found the best code is planned code. Code is best, when it's created by following a methodology. It's best when the code has been written in requirements and design documents and merely typed into source code. Code is best when it's been written twice. Code is often at it's worst when it's adversely affected by scope creep, programmers stumbling over a new architecture, or poor management.

Reading code is hard. Ever try to 'debug' a mathematical proof. Sure natural language is too ambiguous for most math.* That's why logic was invented (see the chapter on Leibnitz). Going from symbolism to natural language is hard, understanding context is even harder. Just ask anyone doing research in NLP.

*I'm not a logician, but as a side note, I've always found Raymond Smullyan's books on formal logic to be the 'prettiest' math books around. He has a naturally recursive mind.

An article about the demonstrations is at
http://www.maa.org/editorial/mathgames/mathgames_0 5_02_07.html

That a dollar in nickels needs $1.88 in metal to be made is surprising.

Profit is one hard cost to stomach, isn't it. Anyway, some of us still enjoy our monthly deadtree journal, though admittedly all mine are from the MAA. There's something about rarity that makes them feel more important.

A previous Slashdot post linked to an article that listed 60 something
different SVG programs.

Vector vs Raster (at maa.org)
http://www.maa.org/editorial/mathgames/mathgames_0 8_01_05.html

Sounds like an article that trudges through SVG compliance for
all these programs is needed.

In my opinion, the seperation of science from religion is the problem. There are things that science cannot know and religion fills that gap. If people understood that science can very easily co-exist with religion, everyone would be a lot better off. When people are forced to take one over the other, then willfull ignorance becomes more prominent.

Scientists have been learning that it is absurd to believe you can know everything or quantify everything. If you don't build in the ability to deal with the unknown, then you are making a mistake. Probability Theory is quite useful these days.

This has even been shown in mathematics. If you create an axiomatic system (we'll ignore the fact that you are taking the axioms on faith), then there are still statements that you can make that cannot be shown to be true or false using the axioms you've accepted. You can either accept or reject these unknowable statements. The concept of randomness is similar (check out metamath by Chaitin. He likes exclamation points.. but his ideas are interesting.) http://www.maa.org/reviews/metamath.html

What about the uncertainty principle? What does science tell me about what will happen tomorrow? What the hell is a transcendental number? Do you ever wonder what it means to say a number exist that we can never see or understand in any real (pun?) sense? Most of mathematics is so complex I'm sure you have to simply accept it on faith, but ignoring that, there are elements of mathematics (the queen of the sciences) that even mathematicians cannot know fully. We accept the existence of things that we cannot write down or see in our heads. What does that mean?

I haven't looked at all the posts, but just in case here are some links that might be useful in your search.

http://www.ams.org/employment/
http://www.ams.org/early-careers/
http://www.maa.org/careers/index.html
http://www.ams.org/careers/
http://math.ucsd.edu/~sbuss/GradInfo/index.html
http://www.beanactuary.org/
http://www.nsa.gov/careers/index.cfm
http://www.census.gov/hrd/www/jobs/emp_opp.html

Seems this trait is shared among other artists. When researchers had random people try to duplicate Jackson Pollock's drip-style paintings which were then rated against actual Pollocks in a double-blind experiment, people vastly preferred the authentic Pollocks. Seems that there is a fractal based component to Pollock's style that is not easily replicable. Perhaps most or all great artists have a mathematical aspect to their work that is subconciously pleasing to the mind.

People, by their very nature, cannot truly produce randomness. Everything we output is laden with the associations and processes inherent in the brain. Jackson Pollack apparently painted with a certain fractal regularity that he wasn't conscious of. I imagine that Van Gough didn't intend to depict turbulence per se, he just painted that way, and others percieve the mechanics.