Tuesday, May 12, 2009

Single Valued Functions and Dolphins

Dolphins, Single Valued Functions and Intelligence
Mathematics is dominated by the single valued function. We have technology because physics on earth is essentially single valued. Since physics is single valued it is repeatable. We think of physics as deterministic.
When I tune my radio to 102.5 I always get KIOT. If I turn the wheel of my car a certain amount, the car always turns the same amount. Freeway driving would be impossible if cars drove like bumper cars. (At least bumper car steering always seemed almost random to me, no repeatability at all.)
All of our high tech engineering depends on being able to accurately predict how our airplanes, rockets and radar dishes react to given inputs. The engineers expect the same response to a given input.
Of course, neither the input nor the output is exactly the same each time since nothing is exact; since our measuring capability is limited we couldn't tell if either the input or the output was exactly the same each time. But they are, within our ability to measure, close enough to make the single valued function a useful tool in modeling physics.
This repeatability is so ingrained that it is hard for humans to imagine how it could be otherwise.
But dolphins live in a non-repeatable world. In the ocean nothing happens the same way twice. If you drop rocks in a swimming pool it takes neither the same path nor the same time for each of them to get to the bottom. The world of the dolphin is not deterministic, it is stochastic.
It isn't the lack an opposable thumb that keeps the dolphin from technology, it's the non-repeatable world they live in. The single valued function is of no use to dolphins so it is hardly surprising that they haven't developed them and the accompanying mathematics.
The dolphin, on the other hand, has some advantages that humans don't. They have an inexhaustible food supply. They have a free run of 2/3 of the planet and housing is not a problem for them. They have no natural predators; anything they can't outfight they can outrun.
Except humans of course. Humans are the predators of everything from ants to whales both of which humans eat. Humans are the universal predator and dolphins have not been given an exemption.
So while they don't have radios or fast cars, they don't have wars either. As far as I know dolphins don't have fights. What do they have to fight about?
Well, there's always women to fight over but dolphins seemed to have solved that problem, certainly better than humans have.
Humans think they are smarter than dolphins because dolphins don;t have guns and shopping malls. And humans kill dolphins but dolphins don't fight back, dolphins don't kill humans. In fact there are reported cases of dolphins saving the lives of humans. I mean, is that unintelligent or what? So often humans base intelligence on the sophistication of weapons used to kill.
On the other hand dolphins perform at Sea World and Disney Land so they can observe the human species up close and try to figure out what goes on with this weird species that is ruining their ocean. Is that intelligent or what?

No comments:

Post a Comment