Dear Mr. Fisher:
Math shows only 2 things in reality. Math is really basically simple. We use it all the time. I wonder if the very fundamental idea that math works to help us define observations also describe our reality.
Math consists of 2 types of consideration - discrete (counting) and continuous (geometry).
The number system was created to count things. One thing plus one thing is 2 things, etc. When we talk of a thing in our scale (0.1 mm to 1000 km), we can say the thing is at that point or not. We could cahnge3 scale and still talk of integer things. For instance, 0.1 (mm) could be 100 (micrometers). Hence, a thing has a boundary.
Geometry talks of extended objects. A point can exist in the extended object. Descartes considered the continuous as infinitely divisible. Division presents a quandary in both maths. We can take 1 ft. and multiply by 3 and make a yard. But we cannot always take a thing and make 1/3 of the thing by a scale change. Where on a line is the point of 1/3? There is no such point. Is 1/3 real or is division an improper operation in physics?
Perhaps this discrete and continuous categorization of math is actually describing the reality of physics.
Consider Newton's idea for light. Light is a particle (discrete corpuscle) traveling and making waves in Descartes medium (called a continuous plenum). The particle causes waves in the plenum. The waves travel faster than the particle that then direct the particle. (Sounds like general relativity - matter distorts space which then influences mass motion.) Quantum entanglement is the result of the wave action on particles. If the frequency of the wave is related to the particle, resonance produces the entanglement.
If the reality were different, perhaps we'd be using a different math.
The idea of Reality Once seems to imply the NOW is a point in time. This seems analogous to the idea a line is a series of points. But the problem some of the ancient Greeks had (Democritus I think) was the question of where is the point of 1/3. They didn't seem to consider the weirdness of division. Instead the definition became an extension of a point (in space). Why not is time also?
"The gap between the specialized knowledge of the credentialed scientist and the common sense of the ordinary individual has become an unbridgeable chasm." is a good point. But interest is very high as science does amazing things. So FQXi and many other outreach programs are ongoing.
What I'd like to address is another point I think you make. The practice of physics research is highly mathematical to say the least. I was taught calculus in physics classes before the math class. All this number crunching leads to equations that may have little if any relation to the "reality" of our common sense observation. Consequently, the outreach programs attempt to form our scale analogies. This results in things like Schrodinger's cat, many universes, etc. This leads to discussions that are far from being reduced to a hypothesis. I think it is time to invert the practice of physics. Time to start from our scale observations and use the math only to relate umbers and geometries. Buddha suggested that if a person could understand what was seen while sitting under a tree, the universe could be understood. (some advertising) My essay suggested that the "fractal philosophy" should be a physics principle. The idea is that the universe is layered scales of self-similar physics. For example, a spiral galaxy has a disk. Our solar system appears as a disk. Saturn and other planets have rings. Perhaps the physics is the same in all these scales. Therefore, the common sense of our experience has instilled in us the patterns of how the universe works. Perhaps the abstractions are a diversion.
Well, I'm on a roll. One more comment.
For example, the field equation is basically gravity at a point is a function of the energy (kinetic and potential or momentum) in a volume. The right hand side (rhs) of the field equation is composed of measurements. The left had side (lhs) is composed of geometry equations. The problem GR is to solve is to calculate the motion (gravity) in 4 (space and time) dimensions. Riemann showed that such equations could be simplified by converting the rhs equations to a geometry - one parameter would be lost in the transformation. This makes the calculation easier. The rhs talks of clocks and ticks (measuring devices and measurements). The lhs talks of "t" (an abstract parameter labeled "time" whatever that is). Now the crux. Clocks and ticks are part of our world. The "t" is a number crunched abstraction called a transformation. Is "t" time real? The same thing exists in quantum mechanics. Are the waves of a particle real? This was a debate ended by the dictum "shut up and calculate". But in the meantime we're left with outreach programs creating some really odd analogies. To make matters worse for the outreach programs, there are many models that are being investigated. But the only one presented in the outreach is the more popular model.
I wonder if the outreach programs should talk conceptually of the many models in terms of assumptions rather than spending the effort in developing weird analogies.
You really got me going.
