The philosophy of squaring > Why no f=ma^2

Please watch 05:00 to 08:00

http://www.youtube.com/watch?v=jbmFcGhTnS0

Force = Mass x Acceleration

So for example,

F=10 grams x 3 acceleration

What that really means is,

F=10 grams x 1 acceleration

F=10 grams x 1 acceleration

F=10 grams x 1 acceleration

So for every X amount of mass, you get X amount of acceleration. There's a relation here. The amount of mass you get for every acceleration is constant. It has to be. That's the logic behind multiplication. If you have 3 balloons, & multiply them by 3, you get 9. Because 3 x 1 + 3 x 1 + 3 x 1 = 9. If 3 x 1 didn't always equal 3, then the equation would collapse.

Let's go back to the example,

F= 10 grams x 3 acceleration = 30

If I double the mass, I get 20 grams. So, 60.

If I double the acceleration, I get 6. So, 60.

I'm not seeing this "building up of squares."

Leibniz was convinced that the energy of an object was made up of it's mass x it's velocity, squared

So why no f=ma^2

I guess I don't understand the difference between energy & force.