Ooh, good! I have a question about doing math with infinities that’s been bugging me for a while:
In the Epic Level Handbook for Dungeons & Dragons 3rd Edition, there’s no upper limit on the enhancement bonus (the “plus”) of a magic suit of armor or a magic weapon. It’s theoretically possible to “roll” up a +infinity suit of plate armor or a +infinity longsword. Somebody wearing +infinity armor would have an “Armor Class” (AC) of infinity, and somebody wielding a +infinity sword would have an “Attack Bonus” of infinity.
When someone attacks somebody else, the attacker rolls 1d20 (a 20-sided die, which generates a random number from 1-20) and then adds his Attack Bonus to the number he rolled. If the sum of the die roll plus the attacker’s Attack Bonus is equal to or greater than the target’s AC, the attacker has scored a hit; otherwise, the attacker has missed. For example, if the attacker’s Attack Bonus was 5 and the target’s AC was 14, any die roll of 9 or higer would hit, and any die roll of 8 or lower would miss; thus, in this case, the attacker’s chances of scoring a hit are 60%.
My question is: If somebody with an infinite Attack Bonus attacked somebody else with an infinite AC, what are his chances of scoring a hit? I.e., what is the minimum number on the 1d20 tha the attacker would need to roll in order to score a hit?
without a formula to actually represent the AC or Attack Bonus it is impossible to say, tracer. In such a case, any result you pick would be equally valid/invalid.
Even given the forms I have above, not all can be evaluated. Many of them, in order to be evaluated, must be algebraically manipulated into other forms (&-& is an indeterminite form that can be evaluated if it can be adjusted to become a form of &/& for example). Even given an indeterminite form, there is no guarantee that there is, in fact, a limit. It might very will be infinity after all, which is to say, there is no limit.
A rational number is one that can be expressed as a ratio of two integers. Pi is by definition = C/D, however there are no pairs of C and D that are both integers. Thus pi is an irrational ratio. We teach pi because it exists and is essential for the understanding of calculus and physics.
I don’t see how >3, <4 has a bearing on pi not being infinite if infinity is considered process. 1/3 is finite, but the ‘floating decimal’ is what makes it infinite when the system of division is carried out. Maybe an interesting phenomenon that is blocking the squaring of circles is that there’s no way to determine whether a line is fundamentally being expressed as a square or an oval. Maybe all lines are ultimately oval and we’re not taking that shaving off of ‘geomorty’ into account when calculating a diameter/circumfrance ratio.
From following those links and thinking about the statement in general, it seems to me that this signifies that we actually cannot make a square or even ‘technichally’ observe a square - that squareness itself is fundamentally flawed perspective.
I also was wondering what would be considered the inverse of pi, and if people devote time to extracting some type of “pi and negative pi” combination with that regards - what might consistantly missing from the closest percieved structure which forms a cohesive link between the two.
I can’t deny that cultures have build wonderful things while doing things with pi - I’m just not convinced that this is actually what allows them to do it.
Ironically, I was just thinking… if lines are ultimately ovals, which I believe to be the case at least in a ‘material sense’ (observing the line either away from or closer then the necessary location needed to hold the ‘square’ perspective), then a circle would be the only physical representation we would have of an actual line which is necessarily not an oval, as the ends would be looped to bridge this gap. When a line is not oval, the shape holds it’s circlidity regardless of whether or not you move far away or zoom in on it.
Oh, I consider it a process. I tried to indicate I was only speaking of my own ideas, given that we can’t have a concept of infinity, but we can operate with it. I doubt most mathematicians would call it a process, though they do describe it that way. “It isn’t a number”, or “You approach it but never get there” and so on. In this sense I choose to call it a process, it isn’t a concept but a way-of-doing. Maybe I could say, even to a platonist, infinity is not an ideal form.
If I understand what this means:
That is interesting, and I would agree that a circle is then the smallest line of a given thickness, but this requires that the drawing object itself be circular already, which sort of causes some problems in describing circles.
Circlidity… you certainly have a way of making interesting words.
I have thought about the philosophical and religious implications of math, and I agree with a lot of what Justhink is saying (and I think I even understand a good portion of it). The fundamental idea of a world that is both perfect and irrelevent to this one, and exists only by its own arbitrary definition, is a defining feature of both religion and math. In fact, if you define perfection in a more mathematical context, such as a perfectly straight line with zero thickness, instead of a human context (a perfectly moral being), and define God as the embodiement of perfection, I think the two are not only equivelent but have merged into the same thing.
If I understand Justhink’s point correctly, maybe I can help explain one point. I think he is using pi not as the argument itself, but as an illustration of the point that all of math is ultimately arbitrary, based on definitions of lines, circles, infinity, etc. (like religion). The fact that math does in fact have practical applications…I’m not quite sure what the meaning of this is, but in any case, that is secondary. As my 12th grade math teacher said (paraphrased): “Everyone always asks what the practical applications of math are, and as teachers we’re supposed to have answers, but for mathemeticians, that isn’t even a concern. They do what they do because they find the equations themselves beautiful.”
And this is the danger of imprecise discussion of mathematical concepts. It leads to wacky conclusions which make no sense in the correct context. Justhink is spouting nonsense.
