Medical researcher discovers integration, gets 75 citations • Hacker News Board

Re: Medical researcher discovers integration, gets 75 citations

#101

Post by roel_v » Fri, Dec 03, 2010, 4:23 PM UTC

d0mine wrote: post #98

roel_v wrote: post #73

Earlier quoted context omitted.

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?

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 ;)

Re: Medical researcher discovers integration, gets 75 citations

#102

Post by Someone » Fri, Dec 03, 2010, 4:36 PM UTC

whatwhat wrote: post #56

enneff wrote: post #49

Earlier quoted context omitted.

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…

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 un…

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.

Re: Medical researcher discovers integration, gets 75 citations

#103

Post by variety » Fri, Dec 03, 2010, 5:09 PM UTC

dmlorenzetti wrote: post #92

jfager wrote: post #46

Earlier quoted context omitted.

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.

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…

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.

Re: Medical researcher discovers integration, gets 75 citations

#104

Post by cscheid » Fri, Dec 03, 2010, 5:10 PM UTC

DougBTX wrote: post #82

roel_v wrote: post #73

Earlier quoted context omitted.

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?

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

Re: Medical researcher discovers integration, gets 75 citations

#105

Post by jacobolus » Fri, Dec 03, 2010, 5:15 PM UTC

tel wrote: post #50

whatwhat wrote: post #41

Earlier quoted context omitted.

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 def…

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 ye…

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

Re: Medical researcher discovers integration, gets 75 citations

#106

Post by gclaramunt » Fri, Dec 03, 2010, 6:08 PM UTC

carbocation wrote: post #13

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.

No, it should be the "Las Vegas method"

Re: Medical researcher discovers integration, gets 75 citations

#107

Post by mbreese » Fri, Dec 03, 2010, 6:18 PM UTC

roel_v wrote: post #72

mbreese wrote: post #35

Earlier quoted context omitted.

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…

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.

Re: Medical researcher discovers integration, gets 75 citations

#108

Post by hugh3 » Fri, Dec 03, 2010, 6:57 PM UTC

eru wrote: post #81

bluesnowmonkey wrote: post #60

Earlier quoted context omitted.

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 unfamil…

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.

Re: Medical researcher discovers integration, gets 75 citations

#109

Post by hugh3 » Fri, Dec 03, 2010, 7:07 PM UTC

pmorici wrote: post #55

carbocation wrote: post #32

Earlier quoted context omitted.

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.)

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?

Re: Medical researcher discovers integration, gets 75 citations

#110

Post by MaMa » Fri, Dec 03, 2010, 8:01 PM UTC

variety wrote: post #103

dmlorenzetti wrote: post #92

Earlier quoted context omitted.

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…

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?