41–50 of 65 posts
"What readability-per-line does mean, to the user encountering the language for the first time, is that source code will look unthreatening. So readability-per-line could be a good marketing decision, even if it is a bad design decision...The math paper is hard to read because the ideas are hard."
" Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis? " -Paul Halmos, inventor of "iff" and the ∎ symbol ( http://en.wikipedia.org/wiki/Paul_Halmos )
Interesting: > Halmos argued that mathematics is a creative art, and that mathematicians should be seen as artists, not number crunchers. He discussed the division of the field into mathology and mathophysics, further arguing that mathematicians and painters think and work in related ways.
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
as did Bertrand Russell (one of my favorite quotes):
Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
I suspect many mathematicians view themselves, at least to some extent, as creative types similar to poets.
Earlier quoted context omitted.
The problem is that the mathematical notation, while not perfect, works really well for those adept with its use. It's an efficient shorthand. For explaining things in depth we have pictures and and natural language. I fail to see how creating a new set of symbols would do anything but hinder communication within the math community. If you have any deeper argument to support your position, I'd be interested to hear i…
>I fail to see how creating a new set of symbols would do anything but hinder communication within the math community. I don't think this is just about the math community. The problem - at least as I see it, as a student myself - is that Math is a required part of many fields of studies. Fields which not necessarily have much to do with Math. And that's a problem for many of the students. I won't say that Math is ent…
Without this common language, we would have a specialized language for every field, allowing little "cross-pollination". As an example, in evolutionary biology, take the NK model of epistatic interactions which models gene interactions. It just so happens that this model is extremely similar to a thing in statistical physics called a spin-glass. Without mathematics the biologist would have to sit and work out all the details of these epistatic interactions before getting to actually do biology. So in short, mathematics saves you time by expressing common patterns or ideas.
That's a very elegant way of saying: "Communication in math is just as fucked up as you'd think." As an outsider who only ever needs to use maths as a "tool" for very specific things, maths books and general attitude by professors and teachers is just nightmarish. Somewhere behind that curtain of inaccessibility, it has to be their fault. Especially, since once you actually do understand certain mathematical concepts…
I'm working on something at the moment to try to explain exactly why what you've said here is, to a large extent, simply wrong. It's too long to include here, and it's not yet ready to "publish". You're about two weeks too early. But let me ask you this. It's easy to cut a square into identical pieces so that all the pieces touch the center point. In slightly more detail, the pieces are disjoint sets such that their…
An infinite number of ways this can be done.
Earlier quoted context omitted.
I'm working on something at the moment to try to explain exactly why what you've said here is, to a large extent, simply wrong. It's too long to include here, and it's not yet ready to "publish". You're about two weeks too early. But let me ask you this. It's easy to cut a square into identical pieces so that all the pieces touch the center point. In slightly more detail, the pieces are disjoint sets such that their…
So now, how many ways can this be done? No, it's not five. And no, it's not six either. An infinite number of ways this can be done.
Can you characterise the solutions? How many pieces do they contain? Some solutions have two pieces. Some have four. Are there other possibilities?
That's a very elegant way of saying: "Communication in math is just as fucked up as you'd think." As an outsider who only ever needs to use maths as a "tool" for very specific things, maths books and general attitude by professors and teachers is just nightmarish. Somewhere behind that curtain of inaccessibility, it has to be their fault. Especially, since once you actually do understand certain mathematical concepts…
Most math concepts -are- fairly easy to explain and, from the sounds of it, you don't actually want a math book. You want a book that gives you the executive summary or a run-down of specific tools for specific situations. The flaw is not in the books or the teaching, it is what you are expecting from mathematicians. Math is, in a very general sense, about understanding and reasoning about highly structured objects.…
Are you aware, for example, that there are functions that are continuous at all irrational points and discontinuous at all rational points?
Earlier quoted context omitted.
>I fail to see how creating a new set of symbols would do anything but hinder communication within the math community. I don't think this is just about the math community. The problem - at least as I see it, as a student myself - is that Math is a required part of many fields of studies. Fields which not necessarily have much to do with Math. And that's a problem for many of the students. I won't say that Math is ent…
As a math major, my view is probably biased, but I feel like one of the reasons mathematics is so widely used and applied in other fields such as physics, CS, and even biology these days is that they express or model, to a high degree of accuracy, patterns that recur in all these fields. The mathematical notation is the most general and abstract form of expressing these patterns. My feeling is that to not learn the l…
It was Simpson's rule.
CORRECTION:
It was worse than that. It was the trapezoidal rule:
http://care.diabetesjournals.org/content/17/2/152.abstract
The author named it after themselves:
... The Tai model allows flexibility
in experimental conditions ...
http://fliptomato.wordpress.com/2007/03/19/medical-researche...
Unbelievable.
I like to say understanding God is like ink blots or cloud shapes.
I don't usually use random letters -- I prefer words -- but random letters show there is noise and it is obvious you use fuzzy logic.
Interpreting God must be done in context of whatever conversation you are having. You might only get one word, perhaps a syllible of a proper noun in the Bible that jumps-out as a response. The responses vary in how miraculous and how meaningful they are. Some are very miraculous, some very meaningful, some duds. There is a correlation between quality of offering and quality of response -- justice.
God says... t z e r a v n q z b p l p z u z p m m j c b r u e z z f d j q y w n p o t e z j v p q b c r o w o r h w e z q e h o u a o u k b p x n p k p k i v g g v s s t w r z t q n e e i v r k f c a j u f p g n a r l f n r r x b d l g v x d e f d p w d a k p z j o e d k r n h x v q m v x j p o w s a t y k e x e e u z v q v d j w n d
Jesus commonly uses the phrase, "for those who have ears to hear," though when He uses it, I don't find a correlation with a secret He just said.
This will further enlighten you.
http://www.usccb.org/nab/bible/1corinthians/1corinthians2.ht...
Earlier quoted context omitted.
So now, how many ways can this be done? No, it's not five. And no, it's not six either. An infinite number of ways this can be done.
Yes, but there's more that you can say. In particular, there is more than one infinite family. How many are there? And do all solutions belong to an infinite family? Or are there isolates/sporadics? Can you characterise the solutions? How many pieces do they contain? Some solutions have two pieces. Some have four. Are there other possibilities?
I think 8 pieces also works, but I think that may be it.
Earlier quoted context omitted.
>I fail to see how creating a new set of symbols would do anything but hinder communication within the math community. I don't think this is just about the math community. The problem - at least as I see it, as a student myself - is that Math is a required part of many fields of studies. Fields which not necessarily have much to do with Math. And that's a problem for many of the students. I won't say that Math is ent…
As a math major, my view is probably biased, but I feel like one of the reasons mathematics is so widely used and applied in other fields such as physics, CS, and even biology these days is that they express or model, to a high degree of accuracy, patterns that recur in all these fields. The mathematical notation is the most general and abstract form of expressing these patterns. My feeling is that to not learn the l…
I wasn't arguing that. In fact, I said that math is lending me and students of other fields tools to use and apply. The problem lies in the expression of said tools (which is exactly what I mean with "arcance notations") and the inability of many mathematicians - no offense - to separate those two concepts (tools/mechanics and expression) from another. They assume that they are completely inseparable, which is not only part, but a major source of the problem. Any attempts to somehow make math less obscure (or even just suggest it) is met, in great parts, with conservative hostility. I've seen mathematicans claim "that I was telling them that their profession is pointless and should be abolished" when all I was saying that a majority of the expression of math is incredibly obscure/arcance to most people which are not mathematicians and mostly not suited for practical appliance (as in, appliance in fields of science other than math).
Also, it's a valid point to say that we shouldn't have special syntax/language for every appliance of math imaginable. That would indeed not only be stupid, but actually /increase/ obscurity. We should, however, stop excusing the obscurity of math with "it's shorter to write". Readability and - most importantly - comprehensibility should /always/ come before convenience. Even in math.