Here's the first half of the description:
The other half, I'm still working on.
Well, the scaling doesn't work linearly as you guys have suggested.
If you were to shrink an okay human down to the same "mass" as an ant, a human would be able to lift 100-150 times his own weight. This is just simple biophysics and deals directly with muscle cross-sectional area in regards to the mass of the creature being discussed.
Likewise, if you scale an ant up to the mass of a human, the ant will not be able to walk.
This is not "news" to Entomologists (arthropodologists) who also like physics.
Like I said, very simple physics: it's a cross-sectional area versus volume: volume increases faster than cross-sectional area beacuse it's adding an extra dimension. If you scale in reverse, volume decreases at a much faster rate because it is one dimension greater.
Think of it like this:
Pretend you have a creature cube that has a one side with a unit of measure equalling 2. To find it's surface area (we are translating this to a cross-sectional area of the muscle, as well...assuming scaling is the same (meaning, there is perfect congruency with each scaling)), you just raise it to the second power (meaning, just multiply it by itself.)
2 to the second power is 4. So it's surface area is 4.
Here is the cube I drew to represent this:
Image 1: Cube with 2 units on each side.
If you don't believe the math I did...just count the number of "units" on one surface: there's four.
Let's double the length of the side and pretend it is now 4 units. What is the surface area, now? 4 to the second power is 16. So it has a surface area of 16 units. Here's the new cube:
Image 2: Cube with 4 units on each side.
Count them: 16 surface units.
Let's double one of the sides yet again: the sides now have a measure of 8. 8 to he second power is 64. 64 square units of surface area! It scales fairly quickly, right?
Image 2: Cube with 8 units on each side.
Well, what happens if you add an extra dimension to our measure? Let's say we need to find volume. Keep in mind that our density times volume equals mass. Mass is important in determining how much weight can be lifted because the creature's own mass will greatly decrease the amount mass it can lift because it's based on the cross-sectional area of the muscles! Sounds confusing, right? Well, that's just how the biophysics work: cross-sectional area of the muscles scale with how much weight can be lifted...generally, in biophysics. It does fluctuate between species, but it is generally around the same.
So let's start out at the smallest cube creature size: One side is 2 so to find our cube creature's volume, 2 to the third power becomes 8.
Image 1: Cube with 2 units on each side.
See, 8 units of volume (some units are hidden from view, obviously. You must also count the hidden units to find your volume which is 8 cube units.
Let's double one side. 4 to the third power becomes 64.
Image 2: Cube with 4 units on each side.
See, 64 units. (Again, count the hidden cube units, as well, to get 64.)
And, one more time, double one side again. 8 to the 3rd power becomes 512. 512 volumetric units!
Image 2: Cube with 8 units on each side.
Even if you assume your original cube creature has a mass of one kg, that still means our biggest scaled cube creature has a mass of 64kg! If we assume the smallest scale creature which had a side length of 2 units, could lift 9 times it's own bodymass (meaning, it could lift 9 kg), we just have to find the ratio to the cross-sectional area AFTER we subtract it's mass from it. Sounds confusing, right?
Lemme explain:
Since you have to include the cube creature's own mass into the amount it can "lift", you must first subtract it's own mass from the total it can lift because it ALSO has to lift itself up while lifting that mass. It can lift 9 times it's own body mass. So it can lift 9 kg. So it's lifting 1 kg of it's own bodymass plus 9 kg of the "weights". The ratio to cross-sectional area would be lifting 10 kg to 4 units of area. That's a ratio of 10 to 4.
So let's apply that ratio to our largest scale creature which had a cross sectional area of 64. Scale up the your ratio of 10/4 to x/64. You can scale fractions, easily, but just dividing 64 by 4 to find the factor of scale. That's 16. So multiply 10 by 16 to find the weight the muscle cross-sectional area can lift: 16*10 = 160.
What is the creature's mass when it has a cube side of 8 units? 64 kg.
Now you must subtract 64 kg from 160 kg to find out how much the creature can lift. Why? Because, keep in mind, that it has to lift itself FIRST before it can lift additional mass.
160-64 = 96 kg. Now it can lift 96 kg. 96 kg is quite a bit more than lifting 9 kg, right? That's 9.6 times more weight. Seems like a lot, right? But wait (pun intended), we must figure out it's its lifting mass to its body mass ratio to see how THAT scaled: It has a mass of 64 kg and it can lift 96 kg. So it can lift 1.5 times it's own body mass.
BUT WAIT! When it was at it's smallest size, it could lift NINE times it's own body mass? WTF??!?!?!? See, it does not scale the same.
This is why "powers" can make a huge difference when you're scaling in math. This is also why architects have to take structural engineering classes: they have to know how much mass certain materials can support. The larger the structure, the more mass it has to support in a cubic relationship!
This was all explained to me in college physics.
I did some google searching and I found a similar example: this is a super good read and it does a better job of making it easier to understand than I did:
http://www.ftexploring.com/think/superbugs_p2.html#THIS