[Eternal Student]

Hi.

Is it just a convention that c should be a very large number?

   Yes, more or less.  As far as physics is concerned, yes.  As far as human evolution is concerned, no.
Most units of measurement are going to be based on what seems sensible to a human being, the things we experience and the things we can do.   For example, we can't throw a stone or a spear all that far and people probably wanted to have vocabulary that is useful to tell others how far they should throw their stones.   If we had a notion of length where 1 unit = the diameter of our planet, then everything you can see is (approximately) 0 distance from everything else, it would be useless information.  The evolution of language was bound to be such that we would be able to describe smaller distances more easily.   Similarly, language would evolve with some notion or units of measuring time that would be useful instead of having 1 unit of time = 1 average lifetime of a galaxy.
   So recognising that our units of speed are based on what we can do, then c = 300 000 000  (in m/s) is telling you something - it's really fast.   If you were hunting an animal that moved that fast, it's gone, hunt something else.
   

I think that sometimes it is given the value 1.

  Yes.   (It's understood that this will put everything else we might be working with into different units as well).

Would it be equally possible  to give it a very small number so that  in the expression e=mc^2 we might have the impression that it would take a numerically  huge  amount of mass to  render a numerically tiny amount of energy?

   Yes but see above.   The amount of mass would now have to be measured in different units.  You can't change reality just by assigning c a small value,  all you will do is change the numerical description of the amount of mass that is equivalent to it.
 
Best Wishes.

[hamdani yusuf]

Light travels well fast that at it's top speed it does not perceive time.....weird eh ?   however, my kwescun is....




If you were to slow light down, would the photons then experience time ?

Even when the light is not slowed down, it still experience time, based on the fact that it has frequency. Phenomena like interference and Doppler effect support this idea.

[hamdani yusuf]

Light has no frequency, wavelength, energy, or even direction of its own. All these things are meaningful only relative to some inertial frame, and are different relative to any inertial frame.

Does it mean that every light is the same, irrespective of its frequency, energy, phase, polaritazion, direction, wavelength?
Human's frequency, energy, phase, polaritazion, direction, length, mass are also different relative to the inertial frame. Does it mean that they don't have experience on their own?