Medical researcher discovers integration, gets 75 citations | Hacker News Reader

Medical researcher discovers integration, gets 75 citations

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319 pointsrobertk120 comments

The author calls out med students for approaching physics through rote memorization. It reminds me of an experience my older brother and I had with a doctor friend.

Our friend, an OB/GYN, mentioned how hard her work is, because "the average baby is born at 3am."

We laughed, but then my brother asked, "What does 'average' mean when you have a 24-hour clock? It must mean the modal time or something like that."

I contributed that this is an issue in defining average wind directions, as well. The basic problem is that if you record times on a 0-24 hour scale, or wind directions on a 0-360 degree scale, and then naively average the numbers, you get meaningless results (for example, 180 degrees if the wind steadily rotates through every point of the compass).

A quick glance at our doctor friend showed she had checked out of the conversation entirely. Possibly she just felt slighted that we were not bowing down in awe at the terrible hours she keeps. But my main impression was that she lives in a world where one receives a piece of information, notes it, and stores it away. And when repeating that received information, one's listeners duly note and store it away.

Chasing down the source of the information, calling it into question, relating it to other things in the world-- these just weren't things she seemed to find pleasurable.

Unless you're House, apparently. I've always wondered how accurate that show really is...

http://www.politedissent.com/house_pd.html

Now you will know: http://www.politedissent.com/house_pd.html

The charitable interpretation (for your OB friend) is that she was not speaking literally, and got bored when you started perseverating on her hyperbole. The more likely explanation is that your analysis is indeed correct.

I'd say the more likely case is that she wasn't speaking literally. Doctors are usually trying to explain things to people who aren't going to know what modal means. Couple that with the fact that most doctors know just enough statistics to get by, and "the most common time for a baby to be born is 3am" gets translated to "the average baby is born at 3am".

The bored look was probably just her rolling her eyes.

"Doctors are usually trying to explain things to people who aren't going to know what modal means."

I talk to doctors quite often lately, with a daughter on the way and all, and the first few times I felt a bit miffed at what I took for her talking down to us. When it got to an absurd level with some nurses (who explained things like how to add several numbers by lining them up, putting a line underneath with a plus sign next to it, and then using a calculator to find the result (true story)), I thought about it some more and it must be because they need to target the lowest common denominator. Which I guess is someone with an iq of 85 or so, as people lower would get special counseling I think.

I've tried to find effective methods to communicate to people that they can skip some of the 'duh' parts, but that's not easy. Just saying 'listen I'm no dumb' or even worse, 'hi I'm <name> and I'm a <name profession that requires university degree>' makes you look arrogant and will antagonize people, and they might not dumb it down on purpose anyway, so they might not have a way of not dumbing it down, either. Usually after a few talks people pick up the vibe on how fast you understand things and what you already know, but when you have many different contacts with various people it often not even comes to that point.

Anyway sorry for the OT ;)

My wife just had the same experience and I likened it to me phoning a tech support line. Although it's frustrating they're not insulting your intelligence, they're probably just as sad as you are that they have to break it down to that level for most people.

And, as someone with minor experience on the other side of tech support, you can't really afford to believe someone when they say they know what they're doing, they're quite possibly lying. A great tip my colleague mentioned from his days on tech support: "Never ask someone to check if it's plugged in. They'll just get offended, assume it's plugged in without checking and tell you it is. Instead tell them that dust gets into the plugs sometimes so take it out, blow on it and put it back in. When they're doing that they discover it wasn't plugged in, and replace it, usually without bothering to tell you why it magically starts working again. Must be that pesky dust!"

Yeah I think it's the same, you get to deal with all sorts of folk. My father in law is a doctor but he started out as a pathologist, as he always says - 'at least I didn't have to deal with all those sick people' ;)

And sometimes we aren't as intelligent as we think we are.

On the phone with my home DSL service provider tech support, I was sure that the modem had been fried in an electrical storm (and, in fact, it had been). But they made me go through the standard script of stuff to check first, starting with unplugging the modem from the phone-line jack and plugging it back in. I did so, killing the conversation with tech support, as the phone was plugged into the modem...

My wife is an MD/PhD, and I'm almost a PhD (molecular biology/bioinformatics), so I completely get what you're talking about. It is almost a night and day difference when talking to doctors. When they find out what you know, you can then have a much higher level conversation about things. For example, with our kids' pediatrician, there is no need to pitch vaccines. The only question is what shot are they getting today?

It's even funnier with our dog's vet. He started bringing out journal articles to explain stuff once.

So, yeah, it can be a bit of a give and take to figure out what level the conversation can take place at, but once you're there, you can be far more productive. I find that's it's easier to just say, "I'm a scientist/programmer/whatever, so I get it...". Unfortunately, this type of problem arises anytime you have a highly skilled person trying to explain something to a novice, doctors don't have a monopoly on this.

The other thing to remember is that sometimes they are just following policy and covering themselves legally by explaining something stupid.

Yes, and obviously I condensed the anecdote. Some aspects of the situation warranted charity (for example, we'd all traveled a long way to be there). Other aspects of her personality point to a basic lack of interest in anything outside her areas of expertise.

And obviously it's just an anecdote-- my friend doesn't represent all doctors. Nor am I detailing her many excellent qualities (she truly cares about her patients and those around her).

I'm in medical school and took absolutely no offense; your storytelling was quite reasonable.

Or she knew that the term "average" can just as validly refer to the mode as the mean, and was bored by the whole exercise.

I believe a sizeable proportion of HN users would benefit from reading these two articles by Philip Guo. I know I did.

Geek behaviors present during conversations

http://www.stanford.edu/~pgbovine/geek-behaviors.htm

Social tips for geeks

http://www.stanford.edu/~pgbovine/social-tips-for-geeks.htm

I like the intention of the second one but it felt too prescriptive for my purposes. I've had decent success trying to learn to better empathize genuinely.

Practice with public speaking and corporate politics and influencing are doing a lot to help me better understand how to befriend and relate to people that don't share my interests. It was initially surprising for me to be one of the geekier people in a building that is ostensibly full of IT workers.

Things that work for me: Toastmasters, Dale Carnegie books, Rands in Repose (blog and/or books), regional sports blogs.

Correct. I could have written "bored by the whole exercise" rather than saying she had "checked out of the conversation".

To recap-- my brother said, literally, one sentence. I added one more sentence, relating the question to another field of study. Our friend was instantly, irremediably, and unabashedly bored.

From which I concluded that she took little pleasure in exploring any aspect of the statement she herself had introduced.

That she was "bored" by the exercise doesn't necessarily mean that she doesn't share you and your brother's bold, hard-driving, searingly intense curiosity about the world, and the nature of our ability to infer knowledge about it.

It might, instead, have had something do with the fact that the point you guys were trying to make was rather trivial.

Or that disecting a joke ruins it?

Exactly. Nobody cares if the exact details aren't 100% correct in a non-technical discussion. Suppose I begin recounting a blog entry which describes an odd situation. I may not remember all the details right, but I certainly have the gist of it and can convey that. There is no point in someone stepping in and saying, "you know, it was actually in Des Moines, not Dallas," if the city is entirely irrelevant to actual content of the post.

What is the group supposed to do with that statement? Someone has to segue back to the original topic, while someone else just lost face. Most people will just either ignore the correction entirely, or just drop the topic altogether.

It’s actually quite possible to define quantities like mean and variance on a circular dimension like hours or angles, with definitions analogous to the conventional ones on the reals; it just takes a bit of mathematical cleverness. (The general field is sometimes called “circular statistics”, and for the mean specifically, Wikipedia has an article here http://en.wikipedia.org/wiki/Mean_of_circular_quantities)

That the two of you ignored your friend’s point and started talking about mathematics instead could be insulting† and she was may have been quite justifiably annoyed. Interpreting that annoyance as evidence that doctors are uncritical/uncurious/uncreative is pretty narrow-minded, IMO.§

† depending on your existing relationship and usual interactions.

§ obviously I wasn’t there and don’t know your friend, so can’t really judge. YMMV

Of course you can average times of day, as well as wind directions. Express them as vectors on a 2-D plane, then separately average the components in each dimension. Although this is somewhat obvious in the case of wind measurements, it works for times of day as well if you think of them as points on a 24-hour clock face.

Your medical friend was not checked out. She was busy stifling impolite laughter at your unfamiliarity with Cartesian coordinate systems.

For time, what would then be the average of let's say 3 and 9 o'clock? Center of the clock I presume, but what does that mean in terms of time? Or would you then need to define the average of several points in time as a non-point in time?

0 o'clock could be interpreted as 12 o'clock too.

The GP explicitly specified a 24-hour clock face, plus even on a 12-hour clock the question would remain.

Hand waving: I'm guessing that you could make a new vector from the average x and the average y. The direction would indicate the average time, and the length would indicate the certainty, so a length of zero would mean total uncertainty.

That's pretty much exactly right - the variance of the von mises distribution is essentially the length of the average vector.

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

You'd have to talk about a time vector, with your case being the zero-length vector, or "no preference". Then a vector with a longer extent would indicate a "strong preference". Something like the standard deviation or something in a linear measure, I guess.

For 24-hours clock you should have said 6 and 18 hours.

How embarrassing - I initially had written a paragraph here pointing out how wrong you are and I was just seconds away from posting it before realizing you're right ;)

So yes you're right, to be consistent with the article and my reply elsewhere in this thread it should've been that. Luckily it seems that most posters managed to derive the underlying question from the circumstances ;)

You can do that for wind, but what does it mean?

An equally valid measure for wind would be to take the absolutes, and average their squares. That'll give you a measure of the average energy in the wind.

It means the average direction of the wind, which is an important factor in many places.

Of course this might need to be combined with an average windspeed to get a better picture of what the wind in a certain location is really like.

Why don't we just look at the distribution in the first place? Make a nice circle chart for all wind vectors and color it according to probability.

That may be a decent "hack" approach, but more generally you should use distributions meant to operate on circles, eg. von Mises (analagous to Gaussians): http://en.wikipedia.org/wiki/Von_Mises_distribution

Chasing down the source of the information, calling it into question, relating it to other things in the world-- these just weren't things she seemed to find pleasurable.

Do you really want your doctor to be that sort of person? Do you want the person treating your kid for rickets to stand up and challenge the establishment and test a new hypothesis on the disease?

I don't know about you, but I'd prefer it if the medical researchers did the challenging, questioning and validating, and the practicing doctors (in general) went with the established knowledge. In my opinion practice and research (of most any subject) are fundamentally divided, and so long as a person can maintain perspective I think no worse of them for preferring one side to the other.

>Do you really want your doctor to be that sort of person?

Are you joking? Abso-fucking-lutely I do.

Hell, I want everyone to be that sort of person. I contend that it is simply impossible for a person without those qualities to ever progress beyond 'adequate' at any task which is more than mechanical repetition of simple tasks.

Second this. Especially in medicine; not to go tl;dr on everybody again about my son's kidney disease, but our search through seven nephrologists stopped when we finally found one capable of looking at his case in a non-recipe-based manner.

Or the doctor was splitting the clock in half hour chunks (or similar). "born at 3am" probably means "born between 2:45am and 3:15am". If a baby was born at 3:02am, the next day they will say "I got no sleep, a baby was born at 3am last night!".

How did this get voted for?

The doctor is far more knowledgeable about a VERY complex engineering system (the female reproductive system) than you or your brother are ever likely to be in any sphere of knowledge. She probably hadn't, as you put it, checked out, she was just being polite and waiting for you to stop babbling pedantic trivia. Perhaps amusing herself by wondering if you might have Aspergers.

Your final 'impression' of her thought processes is banal and insulting. And people wonder why geeks don't have girlfriends.

You can still say "average" (mean) for distributions over cycles (eg. on circles, von Mises distributions are analogous to Gaussians).

von Mises on Wikipedia: http://en.wikipedia.org/wiki/Von_Mises_distribution

I'd laugh a lot harder when people struggle for days and then reach a half-assed piece of some algorithm that's completely well know if I hadn't been there a dozen times myself.

Programmers are especially vulnerable to this. Who hasn't made a 4 page case statement when 3 lines of recursion would have done it, especially when starting out? Then again, I've never named my case statements after myself.

No matter how brilliant one is, its ridiculously hard to know what you don't know. In fact, sometimes being very advanced in one field makes it doubly hard to think of in one you're poor in.

Sure, it's completely fair. We all reinvent the wheel sometimes.

That hilarious part is that this paper was published in a peer-reviewed journal---and none of the reviewers realized that he'd rediscovered some 17th century math.

"One could not be a successful scientist without realizing that, in contrast to the popular conception supported by newspapers and mothers of scientists, a goodly number of scientists are not only narrow-minded and dull, but also just stupid." — James D. Watson

To be fair, James D. Watson is a bit of a jerk who delights in calling other people stupid. Usually winning a Nobel Prize tends to make people more charitable, since they no longer need to prove themselves to anybody... apparently it didn't work for Watson.

I wouldn't recommend following Watson's advice on the correct attitude to your fellow man.

For further information, see http://en.wikipedia.org/wiki/James_D._Watson and scroll down to "Controversies".

I would speculate that the reason it didn't work for Watson is the unacknowledged use of Rosalind Franklin's data, with the resulting belief by many that Watson couldn't have done it on his own. The fact that Rosalind died in part due to radiation absorbed during collecting that data adds to the controversy.

Here is a piece of interesting trivia about that. Rosalind Franklin was a true expert on x-ray diffraction. However there are 230 possible space groups. (See http://en.wikipedia.org/wiki/Space_group for more on that.) The x-ray diffraction pattern you see depends on the space group, and so one of the first step is to go through all of the possibilities and identify which one you have, and only then can you really start figuring out what you have. Rosalind Franklin knew about all of them. But by luck Watson's PhD thesis had been on a protein with the exact same set of symmetries that DNA has. As a result he was in a much better position than she to interpret her data.

Yes, Watson is a known jerk who got hit badly by age. That doesn't mean he's wrong when he claims most scientists are stupid. They are.

And furthermore it came as news enough to other researchers that the paper got cited many times.

But rediscovering some old math doesn't make it that bad. I've rediscovered old math before, and it was something that mathematicians around me thought was interesting because they hadn't seen it before either. What makes this particularly egregious is that everyone involved theoretically took a course that not only described this exact technique, but which described an even better one! (Simpson's rule.)

> 4 page case statement when 3 lines of recursion would have done it

I just so happen to be starting out. Do you mean generating cases like "prefix-[i+1]” ?

No, lookup the the "switch" statement, depending on what language you are learning it may not support it directly. http://en.wikipedia.org/wiki/Switch_statement

Got it now, thank you!

I hear that. I once spent the better part of a day reinventing ActiveRecord's serialize class method (with tests!) only to be told by a friend that I had, uh, reinvented an existing method.

I can't imagine spending months on a peer-reviewed paper accomplishing the same amount of nothing. That would be disheartening to say the least.

I would concur, but this is rediscovering a basic mathematical tool that I was taught in a normal math class at high school. Embarrassing.

> Then again, I've never named my case statements after myself.

I bet you created a half-assed linked-list implementation and prefixed the class name with your initial, though ;)

Ooh spooky close. I was 14. I though I'd invented a whole new kind of array. I dubbed them k_arrays (for kickass arrays of course.)

When I was 15 I took my first real programming course. Soon I was a bit sadder and much wiser. Fortunately, it was just part of the cirriculum. I managed to learn the lesson without ever displaying my shocking ignorance and bringing shame to my family for generations. (not to mention completeling the homework implementing a simple linked list with much speed)

The really sad part is, despite all my enthusiasm, it never once occured to me to link them in both directions to enable bi-directional traversal. Half-assed indeed.

Ah memories - I 'invented' a fully recursive compression algorithm when I was 14. Oddly enough it didn't work nearly so well in code as it did in my head, and the impossibility of successfully extracting an infinite variety of information from a few bytes didn't cross my mind :-)

No matter how brilliant one is, its ridiculously hard to know what you don't know.

This cannot be overstated. And when ego is the cause...oy vey! I believe that one of the greatest intellectual challenges to overcome when one over identifies as being "brilliant" is the, oft youthful, focus on pedantry. How embarrassingly ironic to display one's ignorance as a result of flaunting one's intellect. As a recovering pendant well in to those years that separate true youth from "decidedly middle-aged" let me sincerely recommend to some of our (mostly) younger members that they put down the Bertrand Russell long enough to pick up some William Blake.

  When used properly, I have found that one of the most powerful phrases I can use to build confidence, trust, and credibility with a client is "I don't know."

I'm a doctor who majored in physics, and I agree with this post. Watching these folks come up with formulas in physiology was excruciating. People get their names on things that physicists wouldn't even bother noticing as something other than a single step in a derivation. Hacker News and Python have been come my group therapy and secret addiction, respectively.

Just to be clear, and this might be tangential, but she is not a physician - I think she is a dietitian. I think its a fallacy to assume that only physicians publish in medical journals and there is a negligible link between over-the-top premeds and this article.

Mary M. Tai

www.ajcn.org/cgi/reprint/54/5/783.pdf

http://journals.lww.com/topicsinclinicalnutrition/Citation/1...

I can't access the article, so I can't make any comment on the actual methods, but I think it seems a little presumptuous to flippantly make broad strokes about a paper from a different field solely by looking at the abstract.

He does make a good point about overeager premeds (and for good reason), but this post seems to be more airing out grievences and stereotypes than an argument about education or differences between diciplines.

We found the same link... and you're correct, she isn't a physician.

In the Topics in Clinical Nutrition 1992 paper, she is listed as having an MS and an EdD. So, it's safe to say that she probably didn't realize that she was describing integration.

The entire post had a "I'm smarter than you" chip on your shoulder type of vibe.

It should also be noted that this paper had a number of letters to the editor about it, so in this case, I'd say that the process works (even if it got by the editors).

http://www.ncbi.nlm.nih.gov/pubmed/8137688

I agree that it seemed to have this "I'm smarter than you" vibe, but the only reason I half-agreed is that I feel like it takes some nerve to try to name your discovery after yourself. It wouldn't be so bad if she called it the "curve-approximation method" or something like that; but coming up with something and deciding to name it after yourself feels kind of presumptuous and not exceptionally helpful to boot. (As far as I know, most concepts and ideas named after people weren't self-named; Dijkstra, arrogant as he was, published "A note on two problems in connexion with graphs," and never mentioned "Dijkstra's algorithm.")

Everything in medicine is named with arbitrary names of discoverers and so on. That's why you have to be good at rote memorization to get through med school - you can't even communicate with your colleagues otherwise.

This is a fundamental cultural difference between medicine and engineering.

For my next New England Journal paper, I'm going to use a random number generator to simulate whether conditional, probabilistic health outcomes occurred or not.

I'll cycle through this thousands of times to obtain stable estimates, and then call this the Monte Carbocation method.

good luck with that.

Incidentally, you'll also be able to use this technique to determine the area under a curve! Let's patent it together and get rich!

Let's trademark it and copyright it, too!

Now we just need to find a coder to implement our great idea.

No, it should be the "Las Vegas method"

That name is already taken.

Here's another paper: http://www.ncbi.nlm.nih.gov/pubmed/7677819

"Tal's Formula is the Trapezoidal Rule"

A rebuttal doesn't get much blunter than that.

It's intriguing that the author's two-page rebuttal is among her 'selected publications'.

http://www.sph.unc.edu/nciph/jane_monaco_1990_1984.html

The two page rebuttal that was written by Jane Monaco is among Jane Monaco's selected publications. (You linked us to Jane Monaco's page, not Mary Tai's.)

That is what the GP thought was interesting. So do I.

I see; I misunderstood the intent of the link.

Just a guess but they only have three total so selected might mean "all" publications and even then the one you cite only has 2 authors instead of 10 and Jane's name is listed first. It's that something that is important to post graduate students?

Certainly in most scientific fields it would be unusual to be an assistant professor with a career stretching back to the early 90s and have a publication list that sparse, but I suppose things must be different in medicine?

This does happen a lot in science. Between fields and even within a field, for example a biologist discovers a handy 'new' data structure that is useful for storing DNA samples. Which is simply a basic binary tree. As the reviewers of a biology paper are usually biologists and not computer scientists, they might not notice the obvious.

Similarly, within computer science I've seen cases like this as well. A researcher in scientific visualization built an awesome visualization algorithm based on a 'new' data structure. Then it turned out this data structure was already discovered in the 90's by a theoretical computer scientist.

In neither of my cases it undermined the underlying research, it's basically just a missing reference. It's inherent in science that some things are rediscovered once in a while and it is very hard to follow articles from a completely other field.

However, something as blatant as rediscovering integration reviewers from each field should have noticed....

According to Google Scholar, it's actually been cited 137 times. Another paper published in '98, cited 499 times, reads:

The integrated area under the curve (AUC) analysis for glucose and insulin was determined according to the formula of Tai et al.

Damn.

U MAD?

Seems like a great way to both pad out your citations and troll your readers!

Peer-review failed here. It might be forgivable that a medical researcher doesn't know Calculus (maybe..), but if an article is making a mathematical claim, the journal should find appropriate reviewers. And this is not even remotely advanced math.

looking up the paper on pubmed reveals a flurry of letters to the editor published in the subsequent issue that call out the 'tai method' for what it is. i would actually bet a good number of the 70 citations that so worry 'flip tomato' are actually criticisms or commentary papers like this, as opposed to earnest citations.

I often help (good) researchers with experimental design and statistical analysis of quasi-experimental data, and it's shocking how little they understand. It pains me to think how much waste there is in science at the moment because the researchers do not have the statistical or numerical background to even know what questions are possible.

My brother is a medical researcher. Much of his work involves statistics, but he's never taken a statistics course nor read an intro book. So a lot of his results are just basic high school stats and pretty graphs, nothing deeper. It would be funny if it weren't medicine.

I'm a biochemistry grad student, and my school is just now considering offering a (bio)statistics course for the first time... But parent poster is right, chi-squared is usually as complex as it gets.

As a mathematician, I see this as a sign that my field needs an evangelist.

Can I ask you a question?

Why is rote memorization frowned upon in math?

I'm a second year math student about to enter his third year. I enter a lot of the definitions, theorems, etc. into a flash card software (Anki) for memorization. I combine this with doing tons of proofs and problems from various textbooks depending upon the course I'm studying. I would say from personal experience that rote memorization has definitely helped me: (1) understand the math better; (2) excel in exams, and; (3) able to solve extra and harder problems from books.

So I'm struggling to see why rote memorization is bad. Is not memory useful for justifying knowledge? I'm not saying memorization is the only thing. Just that it seems to build the foundation for everything else, as per Bloom's cognitive taxonomy: https://secure.wikimedia.org/wikipedia/en/wiki/Bloom%27s_Tax...

Everything I remember about maths I remember because I understood the "why" of it. The stuff I learned rote - just to pass the exams - I have long since forgotten. I'm now frustrated that I was expected to learn anything by rote, as it's all lost to the sands of time now.

Rote memorization might help you with exams and book problems, but it won't help you develop long-term mathematical problem-solving skills. If you can't explain it from first principles, you don't truly understand it.

I'm not saying that problem solving and understanding aren't important (see Bloom's taxonomy).

I'm saying that you still need memory to justify whatever domain your knowledge is in, and that memory seems to be the bedrock of further knowledge (understanding, creativity, problem solving etc.).

Am I missing something here? Do you not need some element of memory to explain things from first principles, and to have an understanding of something?

edit: I've just realized from reading wtallis' comment that I might be confusing two different forms of knowledge: memory and reasoning, insofar as reasoning can produce further truths. Is that what you are getting at?

You can easily manipulate symbols without understanding what's happening. The problem is it's hard to progress significantly past your understanding using this approach. Not that Math really has levels as such, but if you don't get Calculus at a fairly deep level DiffEQ ends up being fairly meaningless.

PS: It's a common thing for most calculus classes to redirive old formulas. Not because they stoped working, but rather because you really should understand why it's 4/3 pi * r^3.

It is similar to the difference between say svn and got: you should not remember the various revisions, but how to get there, because that will knowledge will be reusable in different branches.

As an example, I had a maths professor who derived the formula for solving a quadratic equation in class (in 30 seconds or so) because he did not remember it.

Depends, I had that opinion too until I took university maths. The proofs they give you to learn by rote are actually extremely useful, as they add techniques to your repertoire that you otherwise wouldn't have..and the difference between 'learning the proof by rote' and 'learning the technique' is usually extremely small.

Not the intended target, but I'll throw in my two c from doing a lot of applied math.

Math readily has two components. The first is a formulaic, formal component that can be readily overcome by rote. The second is the more freeform conceptual understanding that motivates and directs the first. I feel confident that if you ask anyone familiar with advanced math if they understand concept/theorem/tool X, they'll say yes if they know it in the second form and are confident that they can reconstruct the important parts of it in the first.

I think a lot of why people rebel against rote memorization then is that it, as a method, is very likely to prevent you from encountering the second side there. If you honestly use it to improve your fluency with the formal manipulations, it can be a great tool for learning more math. It's just easy to lose that honesty.

To really understand math, you need to recognize that it's a language you must both read and write. I suggest that if you do get strong benefits from rote memorization, then you should complimen t your reading by attempting to synthesize mathematical concepts you've not seen before. Read the claim of a theorem and then prove it yourself without knowing the answer. If you can honestly complete mathematical synthesis at that level as well, then rote memorization isn't hurting you in the least.

Thanks. That's a great response.

To elaborate on this, a working knowledge of some area of mathematics is not like a set of historical facts to be familiar with, or a list of fundamental particles and their properties, or a group of plays or novels to be quoted from, or a set of pigments and their interactions with brushes and paper, or even a code library’s API.

Mathematics is, fundamentally, about model building. The study of mathematics is about learning how to make maps even more than it is about the specific territory being mapped. In my opinion the largest part of mathematical fluency is the constant willingness to test mathematical structures and ideas against each other and against new data, to figure out how parts work at their deepest levels and then to go back and try to see how each one fits with all those known before. What matters in understanding a mathematical concept is not whether you can repeat a witnessed proof step by step or write down a formula, but whether you have an intuitive grasp of the abstraction(s) in question, whether you can explain them to yourself (an ability to explain them to others also recommended), and whether you can apply them to new problems which arise.

It is my belief that this kind of deep understanding and fluency can only be obtained by repeatedly interacting with these abstractions in a wide variety of problems and contexts, writing down the patterns and working through the proofs, questioning the axioms underlying them, asking how they generalize or how they apply to specific cases, and so on. Very little of this work can be done on flash cards, at least for me personally. Indeed, I believe it is precisely the teaching of mathematics as something which can be learned from flash cards which most impedes mathematical education and understanding.

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

Thanks.

To add to enneff's comment: procedural knowledge is at least as important as the end result of a derivation, and in the long run is more useful.

I had several mathematical classes that weren't actually math classes (eg. statistics and physics) where other students would cram to memorize a page full of formulas, and I wouldn't even know the names of most of them going in to the exams - any formula that I could derive in under three minutes wasn't worth memorizing.

When a major outstanding problem in mathematics is finally resolved, it's surprisingly rare for people to care much about the result. Generally, people have checked enough cases or used other methods to be fairly sure what the answer really is. What gets mathematicians excited is the fact that a new proof brings with it new techniques (because if a problem can be solved using existing techniques, it doesn't withstand attack long enough to become legendary).

Ok, I think I might understand what you are getting at. I seem to be confusing two different forms of knowledge: reasoning and memory (where reasoning can be used to produce other truths).

There are already some great answers to this question.

Math begins with intuition. We don't memorize facts in order to build intuition -- we explore, discover, and synthesize. Formalism is an impediment to the early stages of this process. The most blatant example is set theory. Nearly everyone has a basic grasp of naive set theory and hardly any layperson has a basic grasp of formal set theory.

Just as an aside, many of the most interesting things in mathematics are extremely counterintuitive. It also turns out that our intuition is broken and leads us to say crazy things. Again, set theory has clear examples.

Back to the point, the things you memorize help to organize your untamed mathematical data. I seriously doubt that you'd have any good results from memorizing something about which you do not have intuition.

Come on now, many of you proudly tout how you were taught integration in secondary education. Big deal. This person discovered it for themselves, and that is an achievement to be celebrated.

Rediscovering integration is wonderful. Managing to get it published in a peer-reviewed medical journal is not.

I think Michael Williams (third comment) has the right idea when he says "I’m sure you can find plenty of physicists saying spectacularly naive things about medicine...". Of course OP's discovery is amusing - even alarming - but approaching it with an air of condescension won't do much to advance either field.

Calculus is taught in high school and expected to be basic knowledge for any physician, even if they don't use it often, and especially so for researchers. Calculus is fair game on their admissions exam, even! On the other hand, there's never an expectation that physicists know medicine.

Of course. I never claimed we don't have an egregious error on our hands.

Calculus is not taught to everyone in high school. Many students only make it as far as precalculus and many more, even if they take calculus in high school do not learn integration. At the college level, many biology students do not take calculus. As far as calculus being a requirement for entrance into med school, in many cases I am afraid you are incorrect.

http://www.cse.emory.edu/sciencenet/additional_math_reqs.pdf

Most pre-meds do not have the time in their undergraduate careers to take a two semester series in calculus, especially if they need to also take remedial courses such as precalculus first, and many do.

Calculus, per se, isn't a requirement, but physics is covered pretty heavily on the MCAT. And last I checked, you needed calculus for college level physics.

Calculus-based physics is not tested on the MCAT. Or, at least, no calculus is required for the physics portion of the exam.

To my utter shock - I thought it'd be one of the last bulwarks against premed memorization. When I learned otherwise, it was sad to think that those students who flocked to non-calc physics (and floundered; the classes are of course curved) really would have a good shot at medical school.

Most universities have a physics sequence that does not require physics. A major reason this sequence exists, at least at the university that employs me, is pre-med students. Also, physics is not "covered heavily" on the MCAT.

There's a big difference between "saying spectacularly naive things" and publishing in a supposedly respectable journal.

Plus, the guy deserves an academic weggie for naming a method after himself...

Yeah, you're right and I agree. Thanks for helping me rethink my position.

At least he followed Stigler's law.

"He" is a she

Did someone mention Kurzweil and his army of computer science yes men?

Or, as your Engineering professors used to say:

"A week in the lab will save you an hour in the library every time."

My outsider's opinion is that I think that a lot of cited articles are not always thoroughly examined, or of they are examined they are used to confirm the biases of a particular researcher.

I recently became interested in the idea of possible anesthetic neurotoxicity in infants and looked at a number of papers. The basic research seems solid, but the conclusions drawn are strangely inconsistent.

Neonatal rat, mouse and pregnant guinea pig models are used, and recent studies have been done on monkeys. It appears that there is a high incidence of cell death after exposure to anesthesia, but there is a relatively narrow window of vulnerability, which apparently peaks at 7 days postnatal in rats and rapidly diminishes. 5 day old monkeys were affected by prolonged exposure to ketamine, and 35 day old monkeys were not. Similar results were seen in guinea pigs.

What strikes me, is that this window of vulnerability is differently equated to human development by researchers, despite years of research into ethanol neurotoxicity (anesthetic studies seem to be more recent). Estimates for 7 to 14 day old rat-human equivalents range from pre-term infants to full-term newborns, to mid-gestation human fetuses and to children up to 3 years old. Two monkey papers, one using ketamine, and another using isoflurane also came up with different vulnerability periods based on similar data by using different sources of information on neurodevelopment, one published in the 1970's and one more recent.

I cannot understand how so many studies could have statements about possible windows of human neurotoxicity, without any certainty about what phase in neurodevelopment they were dealing with. And, oddly enough, the paper describing the model that is used to claim a mid-gestation vulnerability (based on a "bioinformatics approach") clearly states that it cannot be used to predict the "coordinated surge in synaptogenesis just prior to birth in primates", which is hypothesized to be the peak period of vulnerability to anesthetic-induced cell death. So why is it used as a source?

To extend my comment, there are dozens of citations for the 1970's era paper that assert that the "brain growth spurt" extends from the third trimester to the first few years of life. It is then equated with synaptogenesis or "peak synaptogenesis", even though this association may be unclear. The papers then further equate peak synaptogenesis with the period of vulnerability to anesthesia. Many then postulate mechanisms for anesthesia-related neurotoxicity in infants related to mechanisms of synaptogenesis. Not being an expert in the field, I can't refute this argument, but I do find the links between these phenomena to be rather shaky, especially when based on a throwaway reference to a decades old paper.

The lack of interdisciplinary collaboration is one of the major flaws of the US university system (I can't speak to other countries). The grad students I knew each had a specific toolkit that they had learned in their field but there was little or no sharing of those toolkits from domain to domain. That is unfortunate. Of particular importance in today's world are a toolkit of mathematical techniques (calculus, statistics, differential equations are probably the top three categories) and a category of basic programming skills (the ability to automate routine number crunching in particular, maybe "scripting" is a more appropriate word than "programming" - even recording and writing macros in Excel VB would go a long way).

To be fair, this letter followed soon afterwards :

http://www.ncbi.nlm.nih.gov/pubmed/7677819

Tai's formula is the trapezoidal rule.

Monaco JH, Anderson RL.

Comment on:

    * Diabetes Care. 1994 Feb;17(2):152-4.

Tai's model? Naming things after oneself is +20 points in The Crackpot Index.

Slightly off topic, but the other day someone asked how to do well in academia. Well, interdisciplinary work like this is a great way to get many well-cited papers - be well-versed in two or three fields (a lot of work, but not very hard) and apply things from one to the other(s). Don't call it '<your name>'s Method' but just present it as something groundbreaking (which it even may be, in that new field).

You can generate a paper mill out of this after 10 or 15 years of studying the various fields (including undergrad and grad school) - it doesn't require much hard thinking, just a lot of work.

Given that this is Obesity research, I'm just a little more inclined to believe all the claims of the NIH syndrome and biased analysis as described in Good Calories, Bad Calories.

Wow, I just dicovered gravity :) In all seriousness though this does highlight a problem with modern research - the sheer volume of information out there.

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