We know that the speed of light in a given medium is a constant and that the speed of light in a vacuum appears to be an absolute limit and that E=mc^2. However, can anyone prove to me mathematically (ie without resorting to experiments that measure the speed of light or deduce it from interference patterns etc) why c is the value that it is and not some other value? Is there a way of deriving c from first principles which shows it to be the only rate that electromagnetic radiation can propagate at in this universe and why? i.e. We can prove without resorting to measurement why PI is the value that it is, can the same not be true for c?

The bridge building contest I’m entering in consists of putting more and more weight on the model bridge made of pine wood until it goes smashy smashy. You're bridge efficiency is determined by the load it carried before bridge failure divided by its own mass. There is a bucket that hangs down from the bridge where you then put the weights.
The bucket that hangs from your bridge is 2kg and you have a whole mess of weights at your disposal, either 1kg or 0.5kg. Finally, my question: is it good to put the weights in as fast as you possibly can or should you stall just a little bit before putting the next weights in and if so, approximately how long (half a second, a whole second, etc.)?

I have been taught that 2 distinct "instances" (i.e. an increadibly small momment in time) when added toghether will produce a single instance, by sheer definition if instance itself,
      However I do not understand how one measure can be added to another identical measure, and produce the initial ammount.