*Age*was asking something about the 9.8 m/s^2 acceleration due to gravity 'fact'. I

*may*be able to bridge the apparent conflict he/she has to uwot's expanations given somethings I had problems with before trying to make sense of the distinction of what many think is or is not 'empirical'.

Galileo's original 'proofs' were discussed in philosophical dialect similar to Plato's dialogues using Socrates as his voice. The original arguments made by Galileo were NOT empirical but strictly logical with a trivial non-measurement 'fact'. The follow-up experiments that Galileo used was intended to demonstrate his prior logic by USING measurement to express it. The incidental nature to find the measure of acceleration due to gravity is the 'fact' part that is trivially distinct from the logic. That 'fact' (the measure) is changeable and also only applies to a specific 'instantaneous' point in height from the center of the Earth as well as to other large objects, such as mountains that may distort literal local measurements.

The actual logic Galileo argued was dismissed for odd reasons by some people who took insult by his indirect reference to them with such names as "Simplicio" as a reference of insult of those who can't think logical. The brick with the imaginary link suffices to argue THAT objects accelerate. The actual experiments only provide direct experiment to those unable or unwilling to accept. The logic of the independence of the force of gravity was due to the following kind of thinking:

Imagine you are pulling your one or more of your children on a sled. The energy and/or force needed to pull two children of the same mass requires twice the force and expended energy. What Galileo was saying about gravity in contrast to Aristotle was that the Earth pulls on ANY mass with the same rate as though pulling two children is equivalent to pulling one ....or even a thousand, etc. Obviously if you were told this, it would make you ask how the Earth could 'know' what the mass is to adjust the manpower at will, greater for larger objects versus smaller ones.

Galileo used thought experiments with the trivial common knowledge that anybody without extensive experience could follow. If you hold up a brick and drop it from a specific height, we assume this to be the same if we repeat it precisely or even move slightly to the left or right to repeat this. Now imagine doing this simultaneously by holding two bricks at the same height. You can logically realize that intuitively that dropping the two bricks side by side would hit the ground at the same time. Now just imagine the two bricks, two distinct masses, be conjoined by an imaginary chain. Dropping one or two independently makes no difference. Thus dropping one mass versus twice the mass at the same height will hit the ground together.

There is more to these thought experiments that suffice to 'prove' using logic and a minimal of non-numerical measurements in order to determine that objects of different masses fall independent of their mass. What DOES differ would be what occurs when they hit the ground. The heavier objects would then have an additive effect and can determine more or less damage to something it falls on.

The point is this kind of 'fact' is the logical one and has closure. The experiment to demonstrate this with different inclines and measurements were to show that whatever the measure of the ratio of distance per unit time is for any mass, when you fix the distance, all masses falling from the same height will complete the fall (or drop from an incline) at the exact same time. He used the incline with the reasoning that although that would slow down the fall, the same would occur in sync with any objects from the same set up.

So the actual literal measure of acceleration due to gravity is irrelevant. THAT 'fact' is what

*Age*was confusing to the 'fact' that objects fall at the same rate. He also used Zeno's paradox of non-movement to show that objects should accelerate because if you begun with any relative time 0, that 'velocity' is 0. Any final velocity greater requires a CHANGE of variable continuous degrees of speed beginning at zero to that final rate. Otherwise the speed would instantly jump from zero to the final velocity.

So uwot, for future reference, maybe this might help to be clarified in distinction for others like, Age here, to differentiate between precise actual constants versus the proportional relationships. (most are not as familiar with the math part representing proportionality and the distinction of the relevant constants used, which may be arbitrary and changing.

[con't next thread]