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Trifox
Account closed
Registered: Mar 2006
Posts: 108 |
calculating of square roots ?
hi all, for my newest project i am in urgent need to calculate the length of a 2d vector, reminding pythagorian math i remember that i have to calculate the roots of a fixed point (8bits.8bits) number, how can that be mastered in a convenient way ?!?!?!
thx
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Graham
Account closed
Registered: Dec 2002
Posts: 990 |
The Sierpinsky triangle has an area of 0 because it has a dimension of less than 2 (D = 1.585) and also the Sierpinsky pyramid (they call it "sponge") has a dimension less than 3 (D = 2) which means volume = 0. |
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Frantic
Registered: Mar 2003
Posts: 1648 |
Now.. Isn't this the philosophical question about the status of "World 3" (in poppers terms)? Yes, it is...
They even mention infinity in this discussion of it.
http://www.cs.joensuu.fi/~whamalai/skc/popper.html
Just for the sake of it, I'll mention the word "C64" in this post.
So long! |
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Trifox
Account closed
Registered: Mar 2006
Posts: 108 |
yes, it is funny, the menger sponge has infinity surface, but no volume, i made a nice screensaver about it:
http://download.verpicktewg.de/?filename=fractalmovies/screensa.. |
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chatGPZ
Registered: Dec 2001
Posts: 11386 |
i demand sierpinsky burgers. infinitly tasty but zero calories! |
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_V_
Account closed
Registered: Jan 2002
Posts: 124 |
Jackasser:
>1/+Inf = 0 is bogus since then 0*(+Inf) = 1 which it >clearly isn't... :D
Nopes, what actually is bogus is the statement 0*(+Inf) which isn't well-defined in the set of extended reals, whereas 1/+Inf is. Reason for this is that the inverse of both +Inf and -Inf is 0, hence the inverse of 0 is undetermined. Limits are one thing, doing arithmetics with extended reals another. Of course, you can also calculate limits within the extended real space.
Graham:
>Oh well... Infinity is just a concept and no number. It is
>not imaginable, only a few rules of how something infinite
>would behave is imaginable. But applying these rules is
>not equal to applying infinity.
Missing is the word "real" in front of the word "number" in the first sentence, but it's getting warm :). Now, it is important that "rules" and "elements" aren't mixed up. On the one hand, you have elements which may or may not constitute a set. It is then possible to define operators (rules) onto these elements which combine them in a certain way. When such an operator is applied to some elements, you are effectively using them. Thus, if one of the elements within the operation happens to be infinity, you are really, truly, honestly "applying infinity". And you will be able to recognise it as well.
This holds true with all numbers. Have you ever seen, heard, smelled, touched or tasted the elements 0, 1, 2/3, pi, etc.? Maybe you've tasted 1 apple, where you used a complex visual recognition process to denote a certain physical set as "apple, 1 in quantity". But 1 itself? Don't think so. 1 is - for the time being - a concept in our heads, an element we can apply operators on, an element we can recognise in our calculations. Just like infinity. Just like "0 volume". In a way, we're using a sort of "maths sense" to "imagine" and "work" with mathematical objects. At the very least, they exist in our heads. They may exist physically as well, but it remains to be seen what that form of existence is.
>Oh, and nopes, the Sierpinski Triangle does not exist.
>Only the rule of how you could build one IF infinity
>existed. But ofcourse: Infinity does not exist.
That's the answer I expected from the finitist. Now the infinitist's viewpoint: within complete metric spaces, the "contractive mapping fixed-point theorem" proves the Sierpinkski Triangle's existence and uniqueness. Feel free to provide a counterproof if you have one. If you have been talking about existing physically, see above.
Frantic:
>Now.. Isn't this the philosophical question about the
>status of "World 3" (in poppers terms)? Yes, it is...
Hmm, that depends, as Popper's expressing a viewpoint which may or may not correlate to the discussion at hand. |
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Copyfault
Registered: Dec 2001
Posts: 478 |
Thank you for all the details you give in your posts, _V_! I totally share your point of view! Are you working as a mathmatician at some university?
@Graham: No, computer science is definatly NOT an extension of math!!! It's rather the other way around: computers give us the possibility to apply _certain_ concepts that arise in math, but for sure not all of them. I'd tend to say that computer science is something like the "discretifying of math" ;)
CF |
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Graham
Account closed
Registered: Dec 2002
Posts: 990 |
Let me rephrase: Theoretical computer science is the extension of math.
http://en.wikipedia.org/wiki/Computer_science
(No, computer science is not "C++ programming" or "database adminship") |
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Copyfault
Registered: Dec 2001
Posts: 478 |
Quote: Let me rephrase: Theoretical computer science is the extension of math.
http://en.wikipedia.org/wiki/Computer_science
(No, computer science is not "C++ programming" or "database adminship")
Let _me_ rephrase: No, it's not! Even this wiki-entry just says that computer science is by some people considered to be among the scientific disciplines with a very close relationship to math, but it's nowwhere told that math is just a "part" of computer science (which would be a lie!).
I must admit I never studied "computer sciences" as a fulltime_job, but I did at least attend _some_ courses. Seen from a mathmaticians point of view all these courses seemed like some funny applications of mathmatical concepts - no more, no less!
But let me also rephrase: I think the notion "math" has different meanings to us (see one of my posts above).
CF |
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Graham
Account closed
Registered: Dec 2002
Posts: 990 |
Math deals around with lot's of logic and how to compute stuff, computer science extends that by asking about information, complexity and most important: computability.
If you look at computer science courses you will see lot's of math which build the base to lot's to follow. And ofcourse courses on how to apply all of this, after all you study all this to make a living and not levitate above earth on theory. |
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Copyfault
Registered: Dec 2001
Posts: 478 |
Math is the science of structure. It can ofcourse be applied to other fields in science, mostly to compute things, but it also exists on its own.
If you concentrate on the computational side of math, I can understand what you mean with "extansion of math", but in mathmatics you do slightly more than "computations and dealing around with logic". You try to investigate structures without any necessity of reality.
then again, I guess almost every "pure mathmatician" does not bother about "having to make a living" - until he badly has to ("Hmm, where's this dreamworld of beautiful structures gone? What idiot kicked me out of it??? Help, I guess this is reality" ;) ) |
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