In calculus we talk about finding tangent lines to curves and using these lines to describe phenomenon of the real world....
We talk about finding how many lines make up a circle... If you take 2 points on a circle (which each take up no space), and you move them together until there is no space between them, you get one of these sides, a tangent line to the circle. So, one answer that seems to make some kind of sic twisted backward since is that the number of lines in a circle are the same as the number of points that make up the circle. And that the length of one of these lines is greater or equal to the square root of (2 times the radius of a point), when you have the least possible precision, or are saying that there are 3 points and 3 lines in a circle, or that a triangle is a circle. The length of the lines that make up a circle can not be greater than the diameter of a point, because then the angle between the two lines would be a straight line and would never curve back upon itself...If you wanted to you could calculate the derivative of the change in error when lines are added. This should be some kind of exponential equation, I believe...BUT…
This doesn't make any since to me for many reasons. First of all, a plain is something with infinite length and width, but absolutely no thickness... There is no such thing as a plain in reality. A point is a dot which takes up absolutely no area on a plane that does not exist. Everything we know of that exists takes up or is located in a space, so points also do not exist. A line is something that goes through two points that don't exist on a plane that doesn't exist, continuing on infinitely in both directions. They too do not exist. Neither do circles exist!
To answer the question of how many straight lines make up a circle, I propose that this number is the same as the number of apples that make up an orange... The answer is not infinity, but rather never!!!!!!!!!
I believe that the problem is that the question is in itself backward and messed up! Why would we create things that do not exist to try to explain things that actually exist?
So I propose that we should rather start with what we think we know exists to try to explain properties of other things that exist.
We think that spheres exist, such as drops of water in space not being acted on by outside sources of energy; atoms can also be partially explained by spheres, as well as their parts.
So what we should ask instead of how many straight lines make up a circle is how many spheres does it take to make a group of the spheres seem like a cube for the specific situation being discussed!!!!!!!!!!!!!!!!!!!
Obviously, no amount of spheres make a cube, but no amount of lines make a circle either, and the question of how many spheres make up a cube is at least explaining things in a way parallel to how they work in nature.
ty :)-- fity, Mar 27 2005 non-point ~bz [bristolz, Mar 29 2005, last modified Jun 28 2005] How to square a circle http://patricktimon...ven.com/photo4.htmlbicone-cylander sphericon has a square cross section and a circular cross section [JesusHChrist, Mar 30 2005] Plains do indeed exist ;)-- Laimak, Mar 27 2005 Numbers don't exist either though, I mean you can't find any exact numbers in nature, so how would you describe the spheres?-- JesusHChrist, Mar 27 2005 A single plain can not truly exist. If 2 plains are put together we can form a 3D coordinate system which exists, but no single plain exists... Integer numbers are a product of linear thinking... In nature God doesn't use numbers. There are patterns, though, which humans have stumbled upon and tried to explain linearly. Energy fields, waves, and smaller spheres, and other things are used to describe the spheres. None of these things are 2D.-- fity, Mar 27 2005 2 plains together = 1 savannah, or 0.147 of a migration route.
I know it's wicked to mock the afflicted, but it sure is fun. As my penance I will bun this even though I have no idea what it's about. :0)-- moomintroll, Mar 27 2005 "Numbers don't exist either though, I mean you can't find any exact numbers in nature, so how would you describe the spheres?" Well, if I step outside, I can see one moon. Is that exact enough?-- Basepair, Mar 27 2005 points exist just fine - a center of mass of an object is a point - you may say "zero thickness" doesn't exist - but the boundary between being less than a certain distance from somewhere and greater than that distance. "how many spheres make a cube" seems like nonsense - spheres can't tile space, so they don't make sense as a baseline for calculating volume.-- Random832, Mar 28 2005 So where does the one moon end?-- JesusHChrist, Mar 28 2005 I am so damn confused. <blows on bubble pipe>-- 2 fries shy of a happy meal, Mar 28 2005 Tiles are made of atoms which are spherical and made out of spheres, energy fields, ect... Not lines. Tiles are used to tile space, but they are not made out of lines, it just looks like that to us, because we can't see the small spheres interacting with eachother. How can a point exist as a center of mass, when a point takes up no space? Where would you put it? Any dot you draw will take up space, and this is the fatal error in thinking, because you ARE giving the point space, even though you are defining it as not taking up any space. The center of mass varies within a given space inside of an object such as the moon. The moon is always changing just like the tinny spheres that make it up... :)-- fity, Mar 28 2005 "how many spheres does it take to make a group of the spheres seem like a cube", mwell, it depends on the size of the spheres, the size of the cube and the desired accuracy of the approximation. There is a similar question, "how many sine waves does it take to make a square wave?". Can you say "Fourier", boys and girls? I think you can.-- half, Mar 28 2005 This is, like, the most perfectly named idea.-- phundug, Mar 28 2005 If you impose your point of view on anything, that thing may be misrepresented ... its a risk all matter shares with all consciousness. Focus on this: (‡‡) while you click on your browser's back and forward buttons. Just for a minute there, (‡‡) was gone. What you may not have noticed was that for a brief second it was something else, maybe (#). As [half] states above, you need be satisfied with the accuracy of the approximation you are generating.-- reensure, Mar 28 2005 Spheres don't exist either. Everything physical is made of atoms, and therefore aren't continuous. A "bumpy sphere" may exist (the bumps being the atoms this sphere is made of), but everything physical is in motion, so even if you mathematically defined what you mean by a bumpy sphere, the bumpy sphere you are describing will have a different geometry every instant.
Math (and by extension geometry, calculus, etc.) is just a model of physical concepts in our universe. Without creating a model of our world we cannot learn anything from it. By creating these models we've been able to do anything from create the great pyramids to landing on the moon to creating the computer you are typing on.
Oh, and it seems to me that you're in your first semester of Calculus. It took me until my 5th semester until everything really clicked into place and it became enjoyable. Hang in there - it can be worth it in the end. I miss my optimization class.-- Worldgineer, Mar 28 2005 [mfd] philosophy, theory, bad science (I changed my mind - there are interesting anno's and now a [bz] drawing - I don't have the heart to mfd it.)-- Worldgineer, Mar 28 2005 Thanks Wordgineer for the incouragement. Humans have to make models to represent reality, because in its entirety it is much to complex to understand... The idea here is not that, but rather that the ideas of mathamatics should be changed inorder to fit what we now know about reality. Mathamatitions and Engineers and Physicists like to think that enough straight lines @ large enough angles can make something seem like a curve to within an insugnificant margine of error...But that is backwards to what Chemists and advanced Physicists know... Atoms that are extreamly small make up this table and make it look flat even though it is not... and not the other way around... That is all. :)-- fity, Mar 29 2005 True, but we've always known that our models are approximations. We use approximations because it makes the math (comparitively) easy. The trick is to not forget it's an approximation. If you are trying to calculate something so precise that you need to take the molecular structure into account, then it's generally a good idea to start with the approximation anyway. You can then refine the details.
Oh, and atoms aren't really physical things either. They are blobs of electron clouds, with the electrons and the components of the nucleus made of more exotic and strange things. Of course, there is a further problem once you approach the plank scale of even knowing where something is at any given time. A math invloving all of these factors would be far too complex at a regular size scale, and generally wouldn't give you any added precision.-- Worldgineer, Mar 29 2005 World is right. Atoms are fuzzy things, not spheres. They aren’t even real in the way you are thinking. The halfbakery is a fuzzy thing too, and it isn’t real. And, as hard as I try <I’m sweating here> I can’t force an analogy. So maybe the best thing to do is to take a powerful hallucinogen and ask yourself the question: “How do I square a circle?” The Greeks asked the same question, and their civilization collapsed.-- ldischler, Mar 29 2005 I read somewhere that the earth even with its mountains, valleys and equatorial swelling is still smoother than a billiard ball of the same size.
[bris] You lost a digit after the decimal point.-- FarmerJohn, Mar 29 2005 3 x smoother.-- bristolz, Mar 29 2005 The illustration is pointless.-- half, Mar 29 2005 God suffers from the same flaw as the crown of creation, that in order to make something grand and mysterious enough, it must be _huge_. Mistakes made at the unit level, at the nth degree of parsimony, appear ridiculous. Repeat cubit/pi/cubit until cyclical and stop to elaborate, and you get an enormous pyramid that boggles the mind and creates an unfathomable mythology. Start with the long count and extrapolate the underlying geometry, and you derive the most mystical Mayan calendar in exquisite accuracy ... start with the long count and neglect underlying geometry and you derive the absurd non-repeating Islamic calendar, with its "short" 24-hour long unit that require you to stare at the sun to comprehend. Realize that the concept of point integrates distance in physical reality, and you will serve to focus on the fundamental mathematical link to elements in our physical sphere.-- reensure, Mar 29 2005 [ldischler] >>“How do I square a circle?” see link for bicone-cylander sphericon, a 3D shape that has both square and circular cross sections that smooth into eachother as you turn it.-- JesusHChrist, Mar 30 2005 Good, the circle has been squared. Our civilization is safe.-- ldischler, Mar 30 2005 [worldengineer]//once you approach the plank scale// Things are harder to see on the mote scale, particularly with a Max Planck in your eye. [fifty] sp. "sense", "sick", "plane".-- AbsintheWithoutLeave, Mar 30 2005 Nice illustration bristolz! I love it! Ha Ha Ha...-- fity, Apr 01 2005 [JHC] "So where does the one moon end?" Why, at its rind, of course. My point was that integers exist whether or not you assign names to them. Now, whether other types of numbers or mathematical relations 'exist' and were therefore 'discovered' or are inventions is moot. (One of my favourite words, incidentally.)-- Basepair, Apr 01 2005 [Base] "integers exist whether or not you assign names to them."
I don't think we've ever really answered Zeno's questions. How can there be an infinity of things? That doesn't make any sense. It doesn't make any sense for there to be two things because there would have to be no thing inbetween them, and there can't be any such thing as no thing, that's an oxymoron. But there can't just be one thing either if there are not no things or many things because one is only one in opposition to many and none.
Language has subjects and verbs and objects because people have been reliably separate and consistant entities for a long time, but computers are making it so that the boudaries are changing a lot and often, so maybe things like boarders and lines and points and numbers and individuality will go the way of the edsel.-- JesusHChrist, Apr 02 2005 In between calculus, I suggest you go read Plato's theory of "Forms". Bottom line, how can we call so many things "chair" when they are all so different in reality? Because we have internal models / forms / representations that are not the real thing, but are useful as concepts in our heads.-- sophocles, Apr 21 2005 Huh, Plato - if he was so smart, how come he lived in a cave? ;-)-- moomintroll, Apr 21 2005 [JHC] "How can there be an infinity of things?" Well, it depends on your cosmology as to whether you can have an infinity of physical things. But there are many different, and perfectly respectable, infinities of 'potential things', like integers or reals or irrationals. " It doesn't make any sense for there to be two things because there would have to be no thing inbetween them, and there can't be any such thing as no thing" - why does there have to be no thing in between them? If I have apple- air-apple, I have two apples. By all means quibble about the exact boundary of each apple if you like. As far as I can tell, this discussion is drifting towards philosophy, for which I have always had the deepest disrespect when it goes beyond the purely recreational.-- Basepair, Apr 21 2005 [BP] >> quibble about the exact boundary of each apple...
I can't imagine an "exact boundary." The line that separates one thing from another either exists or it doesn't exist. If it exists then there are three things, one thing, a line, and the other thing, but then what separates the first thing from the line and the line from the second thing, etc? If it doesn't exist then what separates the two things? ,
The traditional answer to this is..., "Magic," but I can't get behind that.
>>"infinities of 'potential things', like integers..."
When you say "potential" I hear "magic".
>>drifting towards philosophy
I don't think there should be a line between philosophy and physics, there should just be what makes sense.-- JesusHChrist, Apr 23 2005 The largest number of points possible in a circle is a function of the circle's size and the planck length (therefore always precicely calculatable). The smallest possible circle is a triangle. How does pi fit in there?-- Voice, May 24 2007 Given that a circle is an abstraction (see many annos above), isn't that little Plancky triangle just the smallest approximation to a circle available to empirical science, rather than the smallest possible circle in mathematics?
And, if we're going to be bound by the laws of physics (oh, well...), wouldn't we say, when approaching this little shape, that 'circle' is no longer the most useful abstraction for it? In fact, we'd probably do that even earlier, at the point where Planck told us we'd have to make do with, as it might be, an octagon, or something.-- pertinax, May 24 2007 random, halfbakery