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Can anyone provide some examples of practical applications of this?
by dvfjsdhgfv 8y ago
Can anyone provide some examples of practical applications of this?
- empath75 8y agoI can’t imagine there ever would be.
- gota 8y agoWell, the number of digits tell you the sign of the number, right? It could save a sign bit I think the ideal wikipedia page for this kind of thing has a 'Properties' section from which to start thinking about this
- vinceguidry 8y agoI don't think anyone ever imagined a use for imaginary numbers either, but those turned out to be quite useful for reducing dimensionality. Towards the bottom of the article it states that Donald Knuth proposed imaginary base numerical systems. So this may eventually find a use, likely with higher-dimensional math.
- ainar-g 8y agoIt will be really funny if there is some bit of new, undiscovered physics, that went undiscovered for so long just because it's best described using some esoteric maths like complex base numbers. Highly unlikely, but fun to think about.
- deleted 8y ago[deleted]
- throwaway37585 8y agoAre there any examples where the representation of a number matters in physics?
- jfoutz 8y agoI recall some effort in moving from imperial measurement to metric. Reality itself does not care, but the math sure gets easier if you carefully select units. Actually, another neat example is analog vs digital computation. your models can get very different answers. I recall some Mandelbrot guy talking about that.
- retzkek 8y agoSee Gaussian (cgs) units for an example, compare Coulomb's law in cgs and SI: https://en.wikipedia.org/wiki/Gaussian_units#Unit_of_charge https://en.wikipedia.org/wiki/Gaussian_units#Unit_of_charge
- roywiggins 8y agoImaginary numbers were useful as soon as they were invented. They are algebraically closed, unlike the real numbers, and are required for the fundamental theorem of algebra. https://en.m.wikipedia.org/wiki/Fundamental_theorem_of_algebra https://en.m.wikipedia.org/wiki/Fundamental_theorem_of_algeb... The first use of negative roots was to find the (real) roots of certain polynomials. They were considered a mathemathical hack: useful, but specious on their own. And then it turned out that if you take them on their own terms, they're fantastically useful.
- jerf 8y agoIn addition to the other points, imaginary numbers immediately added to the representation of things we could represent. Simply rewriting existing numbers in other ways isn't all that interesting; it doesn't add anything. We already knew there's an infinite number of ways to serialize numbers to symbols. Negative base numbers don't behave differently than positive base numbers, because "negative base numbers" and "positive base numbers" are artifacts of English and don't actually exist mathematically. There are numbers, which are written in different representations, but are not actually different entities. So there's no possible way this could be useful for "higher dimensional math" or anything, because there's no entity being added here. Higher dimensional math already uses numbers. At most there might be one or two concepts that might in some manner if you squint hard enough could be better represented by negative base numbers, but even then the positive base representation would probably still be how people actually understood it.
- vinceguidry 8y ago> At most there might be one or two concepts that might in some manner if you squint hard enough could be better represented by negative base numbers, That's what I was thinking.
- fwdpropaganda 8y agoSo in your mind people are just coming up with these things for no reason, is that it?
- empath75 8y agoIt’s fun and interesting to figure out. There are lots of ways to represent numbers but they don’t change the thing they represent.
- JadeNB 8y ago> There are lots of ways to represent numbers but they don’t change the thing they represent. Different representations of the same thing are not useless; one might make an argument (which I can only back up off the top of my head with mathematical examples, but I suspect that there are also many in the physical sciences) that they are at the root of much progress. The canonical example is to try to do positive-integer arithmetic with Arabic versus Roman numerals; they represent exactly the same thing, but I'll bet you can compute 16 ⨉ 17, but not XVI ⨉ XXIII (without converting), in your head.
- scentoni 8y agoXVI ⨉ XXIII = XVI ⨉ (XVI + I) = (XVI ⨉ XVI) + XVI = CCLVI + XVI = CCLXXII
- JadeNB 8y agoI didn't say that it wasn't computeable, only that I bet you couldn't do it in your head. Note that your calculation for some reason (EDIT: ah, maybe because my Arabic-numeral problem has 16 ⨉ 17?) replaces XXIII = 23 by XVII = 17, and then black-boxes the calculation XVI ⨉ XVI = CCLVI (which I at least wouldn't know without converting).
- jjaredsimpson 8y agoI agree. You can use the same algorithm for computing both. But Arabic has better constants. Because it's a discrete convolution instead of grouping and aggregating. 1 6 1 1 6 7 7 42 1, 6+7, 42 = 100 + 130 + 42 = 272 Same process in Roman X V I X C L X X C L X I X V I I X V I I X V I CC LL(=C) XXXXX(=L) VVV(=XV) III = CCCLXVIII = 16*23=368 This supports the arguments that Arabic numbers really are better suited for things like multiplying. They don't have the property that multiplication is convolution, so you can't even do things like truncate your computation to get an approximation. There's probably a way to formalize this with an entropy argument: that roman numerals are inefficient encoding. Because given some n-length string of numerals, firstly many are invalid encodings, and secondly among the valid numerals there isn't a uniform distribution from strings to integers. Something like that.
- wawhal 8y agoScience need not necessarily have any practical use. That’s why it is called Science. Science, the way I define it is: Study for the sake of it.
- Tepix 8y ago- Riddles. - Obfuscation. - Storing signed numbers in unsigned fields (nah, not really).
- pmarreck 8y ago“An intellectual is a person who has discovered something more interesting than sex.” ― Aldous Huxley