Lakes of Wada
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Lakes of Wada
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Re: Lakes of Wada
#2This entry needs a simple english page. I read the first paragraph and didn't understand anything.
Re: Lakes of Wada
#3This entry needs a simple english page. I read the first paragraph and didn't understand anything.
The article indeed conveys no meaning at all to those not acquainted with the mathematical jargon it relies on.
Many scientific Wikipedia articles have improved in this regard over the last few years, but this one (along with many others in the field of mathematics) remains of little interest to non-mathematicians unready to synthesize and internalize the vast quantity of information in the articles of relevant linked terms.
I don’t see this changing any time soon without a lot of concerted effort.
(For the record, I’m someone who did not grok the significance of the article’s subject in the slightest.)
Re: Lakes of Wada
#4This entry needs a simple english page. I read the first paragraph and didn't understand anything.
This article describes a way to split a square into three non-overlapping regions that all have the same border. It is very counterintuitive that this is possible. If you imagine a line on a square, you can define two parts of the square that share this line as a border – and how could there possible be three?
Hope that helps a little bit.
Re: Lakes of Wada
#5This entry needs a simple english page. I read the first paragraph and didn't understand anything.
I also had absolutely no idea what was going on, so I tried to emulate the physical generation of Wada basins. Post here: http://blog.jordan.matelsky.com/wada/
Re: Lakes of Wada
#6So imagine you have three fluids that don't mix which are colored red, green, blue. You can make drops of these fluids on a piece of paper, and manipulate their shapes e.g. with a pipette.
This article is saying that mathematically, it's possible to make three single, continuous but weirdly shaped drops of these fluids, that together fill a square, in a way such that if you consider the three drop outlines as seen from above (e.g. by a camera), they all have the same outline.
Re: Lakes of Wada
#7This entry needs a simple english page. I read the first paragraph and didn't understand anything.
It is a way to divide an area, let's say a square, into three "countries". Each country is connected: it constitutes a contiguous region without enclaves or exclaves. The countries, as usual, are also disjoint: no point is shared between two or more countries (points exactly on the border are not thought to belong to any country). Now, the border between the three countries has a very peculiar property: every point of the border separates all three countries!
That is, a bit more rigorously, no matter what border point you choose, you can always find points belonging to all three countries arbitrarily close to it. In non-pathological real-world borders this can only hold for a finite number of points (say, for instance, the point near Basel where the borders between France, Germany, and Switzerland meet).
Re: Lakes of Wada
#8This entry needs a simple english page. I read the first paragraph and didn't understand anything.
The article indeed conveys no meaning at all to those not acquainted with the mathematical jargon it relies on. Many scientific Wikipedia articles have improved in this regard over the last few years, but this one (along with many others in the field of mathematics) remains of little interest to non-mathematicians unready to synthesize and internalize the vast quantity of information in the articles of relevant linke…
OTOH the vast vast majority of people who will be reading this will be mathematicians who are familiar with the jargon. IMO it's perfectly fine for wikipedia to optimize for the primary audience, instead of optimizing for the rare curious person who has no relevant background.
Re: Lakes of Wada
#9Wada basins exist for any number of open sets. As you could probably guess from the article, the Newton method applied to x^n - 1 gives a Wada basin of n sets. These are fun counterexamples to the claim "given three nontrivial disjoint sets on a plane, their boundaries are not mutally equal."
Re: Lakes of Wada
#10Earlier quoted context omitted.
The article indeed conveys no meaning at all to those not acquainted with the mathematical jargon it relies on. Many scientific Wikipedia articles have improved in this regard over the last few years, but this one (along with many others in the field of mathematics) remains of little interest to non-mathematicians unready to synthesize and internalize the vast quantity of information in the articles of relevant linke…
OTOH the vast vast majority of people who will be reading this will be mathematicians who are familiar with the jargon. IMO it's perfectly fine for wikipedia to optimize for the primary audience, instead of optimizing for the rare curious person who has no relevant background.
There’s too much math to fit into one brain. It’s infeasible to expect every topic explained to a common denominator. Though, I definitely invite anyone interested to grok through all the math they can and cannot understand. Math, I hope, is more than just the academic practitioners.
I can attest to the enjoyment value in reading through math way beyond and outside my understanding. It’s amazingly beautiful, humbling, and can be surprisingly useful.