Pure Math, Pure Joy 315
e271828 writes "The New York Times is carrying a nice little piece entitled Pure Math, Pure Joy about the beauty and applicability of pure math as carried out at the Mathematical Sciences Research Institute. There is an accompanying slideshow of pictures of mathematicians in action; I particularly loved the picture titled Waging Mental Battle with a Proof."
That's the nice thing about math (Score:2, Insightful)
Re:Is this really true? (Score:5, Insightful)
However, seeing as how every science consists largely of mathematical models, the ends justify the means, so to speak.
In other words, while a mathematician isnt looking for a way to make a longer lasting lightbulb, his or her ideas eventually work their way into science and engineering applications, even if it takes decades to happen.
Re:Is this really true? (Score:5, Insightful)
terrible journalism (Score:3, Insightful)
Re:Is this really true? (Score:3, Insightful)
If mathematicans aren't really interested in helping understand the world, why should society fund them?
Because they're able to create beauty, like artists and writers and musicians do. Not all human activity should be measured with money, even if money is needed to make it happen
Re:Is this really true? (Score:5, Insightful)
These are two separate things. Many people are attracted to the natural sciences, and even engineering disciplines, not because of a desire to improve the world, but because they find pleasure and abstract beauty in those fields. Yet undeniably work in those areas can lead to benefits for "society", and therefore people doing research in those areas are funded, even if their personal reasons for doing the work have nothing to do with those benefits. Likewise with mathematics, many ideas thought of as purely abstract and disconnected from practical application have turned out, later on, to be useful tools in understanding various real-world phenomena.
It is totally unscientific and ultimately counter-productive to close off areas of inquiry because at the time they are undertaken no one can know exactly what the consequences will be. And ultimately the motivations of the people involved are irrelevant; we know based on history that there could turn out to be uses for it in the future, even if neither "we" (the society making the decision to support the research), nor those doing the research, can see any at this time, and this potentiality alone should justify providing support.
Re:Is this really true? (Score:5, Insightful)
Guess what? It gets worse.. it's not only the mathematicians, but just about anyone and everyone involved in fundamental research.
I know I am.. I do theoretical chemistry.. and although I'd love to see something useful come out of what I do, I cannot see any immediate uses for my work.
The point is: It's the foundation research, the fundamentals, that lead to the big, *big* innovations. Although it might not seem useful at the time, it may (or may not) turn out to be very very important in the future. However, by it's nature, we can't know which research is going to pay off in practical terms.
Einsteins work on stimulated emission probably didn't look very useful back in 1910 either, but it lead to the devlopment of the laser, which noone could've predicted at that time.
That's why we need to fund this stuff.
Re:Is this really true? (Score:3, Insightful)
Asking why you should fund mathematics is asking why you should fund art. Who ever got cured by art?
I certainly know that a major motivation for my career in science is the beauty of it.
It's like the sunset outside my window, it's like Dido's new single emerging from my speakers. Today I spent studying for my thermodynamics exam and even the simple mathematics used therein is beautiful. Wednesday is my Quantum Mechanics exam and if it weren't for the beauty of the mathematics of the Schrödinger equation it would be a whole lot less intruiging. I make that exam for the joy and beauty I find in the mathematics and physics, not because it makes your cd player work.
Beauty. That is why you should fund mathematics. The fact that it helps society is a secondary concern. But hey, that's just my opinion. And that of the Pythagoreans, to name a few.
Beauty can be found in more things than a painting or Natalie Portman. It's in logic, in mathematics, hell, it's even in code. It's in patterns, it's in reason, it's in deduction as much as it's in nature, an individual or a thought.
Slahsdot reproduces NYT in it's entirety. (Score:4, Insightful)
Pure Math, Pure Joy [slashdot.org]
Does Google = God? [slashdot.org]
Harry Potter and the Entertainment Industry [slashdot.org]
a recent experience with matrices (Score:4, Insightful)
If it's in the NYT.. (Score:0, Insightful)
Re:Is this really true? (Score:5, Insightful)
Re:Is this really true? (Score:2, Insightful)
Thus mathematicians aren't scientists.
To put it another way (Score:4, Insightful)
Re:It's not that obvious (Score:5, Insightful)
Anyway, I'm almost thinking you're trolling because the rest of your post demonstrates some sort of keen-ness for over-simplification. Maybe you're just not out of secondary school yet, but for your information, trig, calculus and the rest are useful for a lot more stuff than what you mention. All the different areas of maths often intermingle in any physical subject.
For the interesting tidbit of information, there has yet to be a mathematical discovery which has not found practical applications. Even group theory, which at first was thought to have nothing to do with physics or any engineering sciences, was found to be very applicable to some extremely interesting problems of fundamental physics (describing the symmetries of fundamental particles).
Daniel
Dumb question to "test" someone. (Score:5, Insightful)
How is e) (prime) less valid than the solution?
How about g) (The only number greater than 29)?
How about a) because its the "bad luck" number in Chinese culture (Too bad you missed out on that one, "white devil")?
How about j) (Because today is Sunday and I feel like its the correct answer)?
Re:Visualizing the solution... (Score:5, Insightful)
What is the next in the sequence of:
1,2,4,...
My answer was . The sequence is the largest number of separate enclosed areas it is possible to make by adding a single straight line to a circle. (i.e. 1 for no lines, 2 for one line, 4 for two lines)
I hate this kind of question, because it is possible to design a sequence such that any number comes next, so any test which includes the possibility of incorrect answers is just plain wrong. Of course you should have to justify your answer, but since the IQ tests are multiple choice...
Mensa is right based on Ockhams razor (Score:3, Insightful)
Well, anyone who knows a prime from a hole in the ground would choose (e), but the correct answer was (f), 8. And why? Because it is the only "symmetrical" number, as printed on the page!
Well, according to Ockhams razor I would argue that Mensa is right. The concept of symmetry is much simpler than the concept of prime numbers.
Tor
Re:Waging mental battle with a proof (Score:3, Insightful)
I thought this photo essay did an admirable job of conveying what thinking for a living is like, yet how does one make this approachable to the general population? I had a conversation with a film director once sitting in an airport (forget his name), but he was asking me what it was like to be a scientist and how one would impart that feeling in film. I responded that he would probably be best by following a scientist for a couple of weeks and shooting lots of time with rather tired looking individuals who had much passion for what they do but who spend lots of time thinking, applying for grants, staring through microscopes, writing code, writing papers, giving talks and talking with colleagues and above all, no matter what they are doing (eating, running, showering etc...), they are thinking. How do you impart that on film? I had some ideas, but he was probably thinking of an action movie.
All told however, this article with the accompanying photo essay was well worth the time spent, it would have been nicer to have a more in depth article however.
Re:Is this really true? (Score:3, Insightful)
i am a PhD student in maths... and obviously i will disagree with you. but i have a reason... we may not WANT to change/understand the world; but it happens!!!
surprise surprise, but the maths we create is used by physicists (about a 50->100 year time lag), which in turn is applied and picked up by engineers/chemists/biologists (another 10->50 year lag) which ends up being some new device or revolution for society to play with. you kill off maths, you kill off science as a whole.
perfect examples involve ANY piece of electrical equipment, communications, medical care and transport.
parent is a troll and is very VERY short sighted (see his home page ;-)).
Re:Mensa is right based on Ockhams razor (Score:4, Insightful)
No. I think the best way is to imagine that you have to explain both alternatives to somebody who is completely clueless, and see which is quicker and easier to explain.
Of course this method does not always work, but I think that in this case most would agree that the symmetry alternative is simpler.
"See if, you turn the paper, the 8 still looks the same. It is the same if you look at it from either direction. If you put a mirror in the middle it does not change. If you look at the other numbers, this does not happen; look!"
"See, the 5 is a prime number. That means that it can only be divided evenly by itself, and one. Division means that...[lengthy explanation]. Even division means that [lengthier explanation]. The reason that one is not included in the definition is that [....]. Now we can look at all the other numbers in turn and see that they are not prime numbers [lengthy calculations, or even lengthier explanations on how they can be indentifed quickly]. Etc. Etc."
Tor
Re:Visualizing the solution... (Score:2, Insightful)
Re:Mensa is right based on Ockhams razor (Score:3, Insightful)
Oh, I wouldn't argue that they were wrong; in fact I think that they set up the question this way deliberately to smack mathematically literate people who see numbers and assume that it's about number theory. They're measuring some function of intelligence minus education.
Pure Math (Score:3, Insightful)
Re:Mensa is right based on Ockhams razor (Score:4, Insightful)
It's sort of like the old biased college aptitude tests and the cup/saucer question where kids from well off white families would know that cup and saucer go together, but poor minority kids had probably never encountered a saucer in their life.
Re:Is this really true? (Score:2, Insightful)
That's why we need to fund this stuff."
Its a good point; even if you believe that mathematics needs to yield real world applications in order to be justified, it would be short cited to restrict research to topics with anticipated applications.
However, I think research in mathematics should be encouraged for more idealogical reasons. We enrich our culture whenever we add to our knowledge of anything. This is why we support the study of fine arts, literature, history, anthropology etc. We do not demand applications from these subjects; the payback is less tangible than that.
Pure mathematics gives us beautiful truths that are valuable in themselves even if they don't penetrate into the popular culture. The fact that pure mathematics provides a rich resevoir of knowledge that is heavily exploited by all fields of science and engineering should not be construed as its sole justification.
Anyway, when it comes to funding, you'll find it much easier to get support for research under the banner of applied mathematics or engineering than for research in pure math. The money available for the latter is probably more akin to that of the humanities than it is to that of the applied sciences. And that is fine, but there is no cause to whine about money being wasted on research in pure mathematics.
Euclid alone has looked on beauty bare (Score:4, Insightful)
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.
--Edna St. Vincent Millay
Re:Mensa is right based on Ockhams razor (Score:3, Insightful)
If you a) Write the number in binary it is not symmetric. Mind you, it is:) OK. Scratch that. b) If you use an OCR front it is not (the top part of the glyph is skew and smaller). c) If you do not write down the number but represent it in, for instance, a binary set of charges in capacitors ina dynamic RAM device I am not sure that the concept of symmetry applies at all. d) If you write it as a Maya numeral (Which would be 1 line and 3 dot on top of it) it would only be symmetrical in one axis, but so would some of the other numbers. e) Put your computer in a font which displays numbers with different glyphs and wham, no more symmetry. Try Adobe WoobBlock or something weird. So symmetry is NOT a property of the number itself. Primeness is though.
Yes, but the whole issue here was whether the symbol should be just a character or treated as an abstraction for a numerical quantity. All these points assume that we have decided that it is an abstraction for a numerical quantity (and that the symmetric property should hold for other ways of writing the same numerical quantity).
If the figure 8 is just a meaningless character, then you write it as 8, with the same font, in Maya as well.
You cannot asume the mathematical-abstraction interpretation to prove itself.
Tor
Re:Pure Math (Score:1, Insightful)
I'm a physicist; I'm only a notch lower than the mathematicians on the totem pole. Everything but math and physics is applied physics.
j
Re:You can trust the NYT (Score:3, Insightful)
Nowdays I teach, which I enjoy, but occasionally do some math where all I do is sit around and think. Now if I could just find someone to do the write-ups (which I hate). I don't do anything horribly insightful (although some of it has been published) but it is fun!
Re:a recent experience with matrices (Score:1, Insightful)
Generally, most classical mathematics was inspired by real-world problems. Geometry, for instance (literally "earth measure") came about as a way to mark off crop boundaries that got washed away after the river periodically flooded. But I'd say that since the golden age of mathematics (about 18th century), new mathematics has been created primarily for its own sake. Often the only "applications" are in proving theorems in other areas of mathematics as opposed to real-world problems.
Re:Mensa is right based on Ockhams razor (Score:3, Insightful)
So you are saying because numerical symbols are simpler to explain as shapes than as a field of philosophy, that any problem involving numbers should first consider their shape since any solution involving that would be simpler to explain?
No, you haven't realized a valid use of Ockham's razor. You are simply using the validity given to it, and twisting its meaning to make your argument seem more valid.
Ockham's razor, as it applies to philosophy, eliminates one of two theories trying to explain the same thing. For example, why do planets in the sky move in such a peculiar way? One theory says "the sun is at the center and we and the other 8 are going around it" the other theory spends a few pages of explanation about the earth being at the center and the planets going around it, and on another sub orbital on their major orbit... all kinds of craziness. Clearly one requires less multiplications than the other.
If you want to apply Ockham's razor here, you must have two theories explaining the same thing. But they don't. One theory says "8", the other says "5".
By your logic, 1 + 1 = X, because you can make an "X" by crossing the two shapes and it is much easier to explain two shapes overlapping than elementary arithmetic. Just because there is an easier explanation to get a different answer doesn't mean the easier explanation is right, or that Ockham's razor is in any way involved.
This is a circular argument. The whole point with the other solution is that "8" can be analyzed by just the properties of the symbol itself, and not by the properties of the mathematical abstraction. You assume it is a mathematical abstraction, and then use that assumption to prove itself.
Please quote me proving that it is a mathematical abstraction. I assume that they are numbers and not shapes and then using that assumption evaluate that one and only one is prime. But that doesn't prove that they are abstractions, merely that there is a valid answer if they are.
Re:Is this really true? (Score:2, Insightful)
This is an important question, and in my opinion has two particularly valid answers.
The first of these is the one that usually gets advanced - that (as with other pure scientific disciplines) we just don't know what `useless' knowledge might turn out to be useful or vital in fifty year's time. This is all well and good, and a perfectly decent reason to study something.
The other one, which I've come to believe more strongly over the past few years, is that which is often advanced in support of arts funding - that it benefits a society greatly (often in intangible and undefinable ways) to study and research things whether or not they have any practical use.
This is a point which, in the UK at least, a succession of education ministers have either missed or fundamentally disagreed with over the past few decades.
Last month, Charles Clarke, the current Secretary of State for Education made some very disturbing comments about how he didn't see the point in spending taxpayers' money on maintaining a group of ``mediaeval seekers after truth''.
He was initially misquoted as saying he didn't see the point in the study of mediaeval history, which rightly got a lot of historians angry, but a later statement clarified that he actually didn't see the point in studying any subject which didn't have a direct positive contribution to UK industrial or economic interests. Which I find even more disturbing - it's understandable (even ok) for the Chancellor of the Exchequer to have such a viewpoint, but I like to think that the Secretary for Education should at least see some worth in all of the education system.
A friend of mine [google.com] (an eminent evolutionary and reproductive biologist who's also helped design aliens for people like Anne McCaffrey, Larry Niven and Jerry Pournelle, and co-written a couple of books with Terry Pratchett) once said
which I rather agree with. Studying or researching any subject changes the way you look at the world - often for the better. It teaches you new or variant modes of thought which you can then apply (often unconsciously) to other areas of interest.
For example: A former office-mate of mine now works for the NHS Breast Cancer Screening Service. The topic of her thesis (permutation group theory) is irrelevant to what she does now. But I find it tremendously reassuring to know that there are people that well-educated, and who have been trained to such a high level in thinking clearly and carefully, involved in something that important and worthwhile.
nicholas
Re:Is this really true? (Score:2, Insightful)
In most cases society doesn't fund them to do mathematical research. Research grants among pure mathematicians are not so prevalent. They earn their keep teaching math to (mostly) scientists and engineers and then prove theorems in whatever time that leaves open.
Even aside from the argument that mathematics is intrinsically beautiful like music, art or literature, it doesn't make practical sense to expect everyone to have an eye on applications of their work. People have to specialize if they hope to learn enough to accomplish anything these days and a mathematician who also becomes enough of an expert in curing diseases to let that guide new mathematical research probably won't have time to prove new theorems.
Letting mathematicians do math so that everyone can pull out what theorems they might apply in their own field has been pretty effective historically.