Mathematics is one of the many human languages. It is written in very impressive hieroglyphics that can include multitudes of “terms”, many of which are given Greek letters. This language has been very much in fashion since the Enlightenment and in the popular imagination anything written it has an automatic aura of truth.
To decipher this language it is necessary to define the “terms”. Recently I had a go with watts.
A watt is defined as one joule per second. Very nice. We know what “1” is and our clocks tell us what a second is, but what is a joule?
A joule is the energy required to move one kilogram one meter using one newton of force.
Um, if the newton is doing the work, why do we need the joule? A supervisor, perhaps.
Will we ever know what a watt is? They just keep adding new terms.
Ok, a newton is the energy to move one kilogram one meter at the RATE of one meter per second squared.
Hooboy, we ALREADY moved that kilo a meter back when it was a joule. The crowbar we used was a newton. Now they say our crowbar was just the energy to produce a certain (and seemingly arbitrary) rate of movement across a meter. Is a definition circular if the energy to move a kilo a meter is defined by the energy to move a (presumably different) kilo a meter in the square root of a second? Why are we squaring the seconds, anyway?
We delved into this squared thing a while back. Sir Isaac just loved squares and his finding that gravity diminished (crudely) with the square if distance may be the hazy rationale for our definition of a newton. Yet our watt, if we can remember back that far, is already a rate. We are defining a rate with a rate.
So here is our evolved hieroglyphic for a watt:
1w=(1k/m/s2 moving 1k a distance of 1m)/s
w=((k/m/s2)km)/s or some such.
At least it is a precise definition, but somehow I still don’t feel I really know what a watt is, and if that is the precise definition, why didn’t they just say so to begin with?