Why are things in nature more ‘different’ than ‘same’? Why is ‘difference’ the norm and similarity the exception, as against otherwise?
An intuitive Mathematical explanation – Arithmetic and Geometry.
Arithmetic – Consider 2 bags, each full of numbers – the same numbers (say, 1 to 1000). Pick up a number from the first and one from the second bag. There is more probability of they being UNEQUAL, than they being THE SAME. The chance of picking up a ‘47’ from the second bag too, after picking up a ‘47’ from the first bag is very very less. Inequality can happen in many ways; equality in only one special case. Thus there is more chance for inequality to happen.
Consider a vertical line as shown above. Draw curves on both the sides such that the line is a tangent to the curves. Keep drawing one curve on the left and one on the right, as shown. The chance of them coinciding / being the same is very less. They will be distinct like as seen in the above figure. Only when the radius of curvature of both the curves is infinite (when the curve coincides with the vertical lines) will the curves coincide and be the same. That’s the special case. Difference is the norm, sameness the exception.