DrakeCennedig

(Just a disclaimer: I'm no mathematician. I have nought but the wisdom of fools.) I've been thinking a lot about dividing by zero. It's lack of definition is one of the least sensible details of mathematics. It seems to me that the only way to give 1 / (1 / 0) any kind of rational meaning would be to call it zero. The very term undefined is, to my line of thinking, just an excuse for not explaining the mathematics. Consider this. If you were to take a perfect geometric cone, how would you calculate the number of points around one of its circumferences? You would have to divide the finite circumference by an interval of zero for each point. This would be "undefined" : yet we know that there are an infinite number of points around the cone. Therefore, shouldn't 1 / 0 be infinity? Likewise, what would you get if you multiplied that infinite number of points with a circumference of zero? You would get one point, the tip of the perfect geometric cone. To my mind, this would imply that infinity * 0 = 1. In fact, a whole multiplicative family could be concluded from these "invalid" arguments (which I will note are based on valid geometry) : 1 / 0 = infinity, 1 / infinity = 0, infinity * 0 = 1 Another, related topic is 0 / 0, the undefined unit. If we are to simply accept the statement that any number divided by itself is equal to one, then 0 / 0 would have to equal 1. Evidence for this is the self-divided identity function, f(x) = x / x. For all values x ("except" 0), x / x = 1. Basic calculus will tell you that as x approaches 0, the limit of f(x) is 1. For some reason, the common consensus of mathematicians is that lim f(x) x --> 0 = undefined, but it certainly seems more sensible to say that x / x = 1, period. I can't imagine why an awkward codicil to a sensible law should break an otherwise continuous function. Returning to the cone, we know that any two circumferences of a cone will have different sizes. One circumference might be one-pi long, and another might be 2-pi. To my uneducated mind, one circumference twice as big as another should have twice as many points, even if that means a larger version of infinity. A circumference of two divided by an interval of zero is what I would call 2-infinity, or two-times-infinity. It makes no logical sense to say that the number of points is the same across two unequal distances. Yes, both are infinite, but could not one remain larger if multiplied by zero? Finally, this logic could also extend to zero itself : One empty box contains zero items, and a hundred empty boxes also contain zero items. We know that in each case, we have the same nothing: but just try storing a hundred empty boxes versus one, and you will find that a hundred boxes actually contain a lot more nothing. In all mathematical seriousness, I would say that in one box, you would have 1(0), or one-times-zero, and in a hundred boxes, you would have 100(0), or one-hundred-times-zero. Both values are nothing, but one can become larger. For what would you have if the postman comes to multiply the amount within each box by a single infinite amount, 1-infinity? If you only had one box, you would have one item, but if you had a hundred boxes, you would have a hundred items, for a hundred empty boxes, though they contain nothing, can contain much more than a single empty box. If we were to accept the above arguments as true, the function 1 / (1 / 0) would follow order of operations and rationalize as 1 / 1-infinity, which would come out as zero (one-zero to be specific). Incidentally, calculus tells us that this is the limit of the function, as described in previous posts. This mathematics would work the same way as the limit of any polynomial equation. For example, if you find the limit of f(x) = 2x as x approaches 4, you get 8. This is exactly the same as if you had solved for f(4). Some words about the idea that infinity is not a number: We are taught from grade school that 1 + 1 = 2, 2 + 3 = 5, and 4 - 4 = 0. Zero is a very basic concept in mathematics, so basic that even gradeschoolers will eventually try dividing by zero whenever they start fiddling with their calculator. At its core, the concept of zero is of something that is infinitely small; infinity, by extension, is the concept of something infinitely large. It seems to me like petty semantics to say that infinity is "merely a concept", while zero is a "useful placeholder". After all, multiplying by zero gives us follies like 1 * 0 = 0; 2 * 0 = 0; 0 = 0, therefore 1 * 0 = 2* 0 and 1 = 2. Furthermore, when students are taught that any number divided by itself equals one, and they think to treat zero the same way, it seems fruitless to add a useless codicil about how zero is an exception to the rules. It doesn't seem particularly useful to say that some numbers defy the laws of mathematics; many curious people would consider such an answer to be of the caliber as "because I said so." I would define infinity to be as much a placeholder as zero, I would extend both their jobs to include multiplication terms. 1 does not equal 2, thus, 1 * 0 does not equal 2 * 0, even though both are forms of zero. 1 * 0 = 1(0), just like 1 * x = 1x. 2 * 0 likewise equals 2(0), just like 2 * x = 2x. 1 * 0 = 1(0), which does not equal 2(0), and thus, 1 * 0 does not equal 2 * 0, and neither does 1 = 2. The practical usefulness of answers like these is in all honesty, trivial or nonexistent; but such answers do give us solutions to problems like, (1 * 0 + 2 *0) / 0. We could say that (1(0) + 2(0)) / 0 = (3(0)) / 0 = 3 (0/0) = 3(1) = 3. Just use a few infinite values and you come out with 3, just like limit theorems have suggested time and time again. One final thought experiment, this time using the old standard, pies. One pie can be broken into two servings, creating servings of one half a pie (for one divided by two equals one half). If one whole pie is only half a serving of pie, then we obviously have very small pies, and two whole pies must equal one serving of pie (for one divided by one half equals two). If we were to break our pie into an infinite number of servings, each serving would be so small, it would quite literally be nothing (for one divided by infinity must equal zero). And finally, if our pie is infinitely small, it must quite literally have no size at all, and it would take an infinite number of them to make any serving (for I would say that one divided by zero must equal infinity). Again, I am not a mathematician. I am not one who has devoted my life to the study of numbers and their relationships. I am merely a high-schooler learning calculus for the first time, and hence truly do have nothing but the wisdom of fools. But without some theorem proving the exceptionable quality of zero, I hardly think it reasonable to accept it as true. Science and math, after all, should require proof before acceptance as truth, and I, a humble student, have found none.

Somewhere in the middle? Middle-of-the-road is a good general strategy, but in this case, I think the answer is clear in favor of Morris. While it is true that minute events can radically alter a particular given series of events, minute events are happening constantly, and there is a general pattern to how each one of these minute events play out. No particular butterfly that flaps its wings in the Amazon will probably ever have a chance to start a tornado in Texas, because there are so many other butterflies flapping their wings and causing opposing cascades that might... you see where I'm going with this? Random potential stimuli happen constantly, so large scale events are very VERY rarely changed by any particular small scale event. Even if one particular ball doesn't fall into one particular place in the bell curve, the overall shape of the curve is not threatened. And with evolution, we're talking about A LOT of balls in the bell curve. More concretely, however, Morris is right because for any given set of conditions, there can only be one most fit answer. On planet Earth, for our global average temperature, and our gravitational force, and our abundance of water and carbon and et cetera, there can only be one set of most fit life forms. Large lumbering plant eaters wouldn't have had to evolve from archosaurs in particular; but as soon as there were plants which grew taller than the animals of the day, some creature would logically start to grow taller to feed on that new source. If life on Earth were replayed, the Mesozoic might have included giant pillbugs instead of Ankylosaurs; large land-dwelling squid instead of Diplodocus; or mammalian fliers instead of Archaeopteryx. But one thing I think is fairly certain: all of those forms would have existed at the same time as that particular environment. Intelligence, it would seem to me, must follow the same principle; that whenever intelligence becomes a major advantage, it will arise. The branch it comes from is irrelevant. (Just think; If it had evolved in troodontids, Dragon-Men! In ants, Hive-Minded Bug People! etc.) But if conditions are such that a trait is an advantage, it will arise, no matter how many butterflies say otherwise. And the macroconditions of the planet are not easily changed.

<br><br>Now I'll be clear here. ID cannot be disproven. Anywhere randomness enters the picture, such as with random genetic variations, the possibility for a master controller enters with it. You cannot tell me the Creator isn't creating by deciding those random mutations anymore than I can tell you He is. <br><br>I'm no seven-day creationist, and I don't think randomness is entirely incapable of producing diversity. I am, however, claiming that the existence of ID (or lack thereof) is a question beyond the realms of science.<br><br> <br><br>I'm no biologist either, but it seems to me like there has to be some sort of fundamental determinism. Consider this: all sciences from math to sociology can be boiled down to increasingly complex series of equations, and it would seem to me that like any equation there will be a few fundamental answers that simply work out. Obviously there's more to it than that, but I figure that some structures should evolve multiple times, simply because they're better suited, and whatever advantages they provide will provide that advantage no matter who evolves them. That is, after all, the whole point of evolution in the first place.<br>