Well, several of the universal constants arguably define our units. For every base type of physical quantity (things like distance, time, temperature, and mass, but not, for example, speed, which can be constructed out of distance and time), you can set a physical constant to 1 if you're willing to change how you measure that property. For example, you can express distance in terms of time (measuring distance in light-seconds or light-years). By doing so, you can discard the speed of light: set it to 1. Speeds are now ratios of time to time: something moving at 30% the speed of light would move 0.3 (light) seconds per second: their speed would be the dimensionless quantity 0.3. You can drop many other physical constants in this fashion: Offhead, the speed of light, the gravitational constant, planks constant, the coulomb constant, and the Boltzmann constant can all be set to 1 without any trouble, and therefore don't count against your complexity budget.
First not: I'm not disagreeing with you so much as just giving more information.
This might buy you a few bits (and lots of high energy physics is done this way, with powers of electronvolts the only units here). But there will still be free variables that need to be set. Wikipedia claims (with a citation to this John Baez post) that there are 26 fundamental dimensionless physical constants. These, as far as we know right now, have to be hard coded in somewhere, maybe in units, maybe in equations, but somewhere.
In the post Complexity and Intelligence, Eliezer says that the Kolmogorov Complexity (length of shortest equivalent computer program) of the laws of physics is about 500 bits:
Where did this 500 come from?
I googled around for estimates on the Kolmogorov Complexity of the laws of physics, but didn't find anything. Certainly nothing as concrete as 500.
I asked about it on the physics stack exchange, but haven't received any answers as of yet.
I considered estimating it myself, but doing that well involves significant time investment. I'd need to learn the standard model well enough to write a computer program that simulated it (however inefficiently or intractably, it's the program length that matters not it's time or memory performance).
Based on my experience programming, I'm sure it wouldn't take a million bits. Probably less than ten thousand. The demo scene does some pretty amazing things with 4096 bits. But 500 sounds like a teeny tiny amount to mention off hand for fitting the constants, the forces, the particles, and the mathematical framework for doing things like differential equations. The fundamental constants alone are going to consume ~20-30 bits each.
Does anyone have a reference, or even a more worked-through example of an estimate?