Satan n stuff, on 06 May 2016 - 01:54 PM, said:
All of the methods you conveniently forgot to mention give a different result. I'm not sure if you're aware, but coastlines aren't straight and they don't just roll out a giant tape measure to get the right number, they don"t even measure the same at different times of the day. Coastlines are measured point to point and that will produce completely different numbers depending on how many points you use to measure and exactly where you place them, making it the perfect comparison to my proposed measurement, so try again.
As far as your pseudo-mathematical drivel goes, do you really believe that the numbers would resolve the same as total surface area, when half of most mech's features don't even contribute to the profile unless they happen to be sticking out to a side when you're looking at them? Those little bits tacked on to mech torsos like arms, guns, legs, they all have very high surface areas compared to the whole thing especially when looking at the combined total, but they add very little to the profile, only about one and a half leg and and a fraction of everything else on average.
Please come up with a mathematical proof if you think there's a direct correlation between total surface area and profile, otherwise stop spouting nonsense. I'll give you one hint, it doesn't exist because there is no such thing.
About the Blackjack specifically, I don't particularly care if it gets bigger or smaller, I have hundreds of mechs so I'm not going to worry that one of them might be a little weaker. What I am worried about is PGI rescaling all the mechs in a way that might make entire weight classes useless and will completely screw over chassis whose size are the only thing they have going for them. But of course being a mathematical genius as you are, surely you already saw the big picture, right?
Well, you said it was LITERALLY IMPOSSIBLE. Now by your own admission, it's literally possible - now with the caveat of producing different results. Here's a question though... the different results... even though they produce different absolute values, would they still produce values that would have the same relative ratio if you compared two bits of coastline? Like, would the coastline of Australia and the coastline of New Zealand somehow change position if you used one method versus the other? I mean, no matter what system you used, Australia is still going to be listed with the longer coastline, right?
I mean, c'mon. Please reach more.
And as for profile versus surface area versus volume, I've really been over all this. I even brought pictures. There's nothing "pseudo" about the math. I've even addressed the practical result of using profile versus pure surface area on the elimination of erroneous surfaces, and how that would compare to volume. Hint - excluding erroneous surfaces from the surface area of an object actually makes the surface area and volume ratios closer. So if you COULD quantify an infinite series of profiles of a 3d object, it would more consistently produce ratios more in keeping with volume than a pure surface area ratio would. *GASP*
You, know, it's funny... I'd always believed that Math must have been an invention of Satan himself, but alas, that seems not to be true.
So, you want some proof between the relationship between profile and surface area and volume... some actual hard math. Ok, I'll bite.
Let's look at this relationship with a fairly simple object, a sphere. I don't want to go any more complicated than that since this is just a basic example, and I don't want to go over the slight differences produced by the impact of different shapes. Suffice it to say, we're going to use a basic shape, scale it up, and see what results we get from the ratios of profile, surface area, and volume between two examples.
Ok, so, I'm going to use two spheres. The first has a radius of 5, and the second a radius of 6.
You have the following equations to consider:
• Area. This would, in effect, be the profile of a sphere if you viewed it from one angle. Area = pi times radius squared.
• Volume. V= four-thirds times pi times radius cubed
• Ratio of surface area and volume of a sphere. SA/V = 3 divided by the radius.
So... for the profile, we'll take a picture of both spheres from 12 different views - the same exact views for both. 12 is a fairly arbitrary choice, it could be any number, but 12 is a good number. Like a 12-sided die. The result will be basically be 12 different depictions of the area of the sphere as taken from those angles. For the sphere, this results in the same area from every view, but the results would be the same for any shape.
So, for the two spheres we get the following set of numbers.
Radius of the sphere =5
Area of the circle (profile) = 78.5375
Surface area of the sphere= 314.15
Volume of the sphere= 523.5833
Surface area to Volume ratio = 0.6
12x profile surface area = 942.45
12x profile to standard surface area differential =3
12x profile surface area to Volume ratio = 1.8
12x profile and surface area to volume differential= 3
Radius of the sphere =6
Area of the circle (profile) = 113.094
Surface area of the sphere= 452.376
Volume of the sphere= 904.752
Surface area to Volume ratio = 0.5
12x profile surface area = 1357.128
12x profile to standard surface area differential =3
12x profile surface area to Volume ratio = 1.5
12x profile and surface area to volume differential= 3
Uh oh, looks like the hard math is against you here. It doesn't matter if you try to quantify 12 different profiles of the sphere, go just by surface area, or go by volume, the results are the exact same mathematical ratios.
The ratio of surface area to volume, as well as all these other basic geometry equations, were established in math thousands of years ago. I assume we can just accept those as pure truth.
As I've shown here, using a predefined set of profiles will produce a quantity that will have a fixed ratio to the actual surface area of the set of objects (in this case that differential was that the profile views produced a number that was exactly 3x the actual surface area). And, of course, the profile area to volume ratio was also exactly 3 times the normal value. There will be a certain amount of deviation between the profiles and the actual surface area, but that deviation will only result in the elimination of surfaces that do not contribute to volume. Thus, profile is probably more accurate to volume than pure surface area is to volume.
So if we scaled all mechs using a process like I've done here, basically taking a limited number of profiles and quantifying the basic area of the shapes it produces to coalate a sort of surface area measurement, it would produce a scale that would have the same relative results as if you just did it by surface area or by volume.
Except, here's the thing... you've just demonstrated that you're wasting your time doing profiles, since it's just going to spit out surface area anyway. You can just get get that right from your modeling software and it'd take a mere few seconds. You've also just demonstrated that profiles work better than surface area because it eliminates junk surfaces from your consideration. Of course, measuring by volume already does that. And, like surface area, we can just open our model file and get the volume of that model in seconds.
Sooooo, ergo and ipso facto...
VOLUME, is by far the smartest, easiest, most effing fool-proof and objective way to do this. So sayeth the maths. But even if it wasn't, any objective standard will yield the same relative result. It's just going to get you there a LOT slower.
And please, explain to me again how there's no correlation between surface area and profile. You were spouting off something about "nonsense" and "doesn't exist." Cuz, I dunno... that math up there? Pretty definitively says there is.
Edited by ScarecrowES, 06 May 2016 - 06:49 PM.