Hi Alex: I think I've found how to pull the rug from under maths! Maybe you can finish the job? Could be fun!
Here's stuff collected from what I've written in various places:
-6. May I suggest, Dick, that you do to maths, what maths does to everything else; and what you did to physics, and what physics did to chemistry?
-5. Here's a suggestion how: Why is it that "the square root of minus one", that is so-called 'imaginary numbers'; work in practical engineering and all over physics?
-4. It is because it represents a vector which when multiplied by a similar vector gives a unit vector on the arbritrarily labelled negative axis.
-3. I said 'similar vector'; because when you look at it; it is misleading to assume one number can be the same as another, or be multiplied by (or added to) itself. 1 + 1 is actually 'this 1' + 'that 1'. Every number is actually composed of 'similarity' (or integral), 'difference' (or differential) and how do you know these two components apart? via a third component also 'difference' (or differential).
-2. In a way, maths is a myth. Numbers are all different. They must be; because if this 1 was the same in every respect as that 1; it would be that 1. To have the ability to even talk of 1 + 1; the two 1 s MUST BE DIFFERENT. This means that the square root of 1 is strictly two different 1s. This is very obvious with the square root of minus 1; where when you look at the multiplication of the vectors that give the answer '-1'; you find that their directions are different.
-1. One may say that the success of 'the square root of minus 1' in practical engineering provides prima facie evidence of the idea that maths is about pattern conservation but numbers are only partially differentiated in typical math operations.
Here is what I wrote (see paras 35 to 38!)
Something that physicist Dick wrote to Harv at Astronomy.net; seems very relevant to this forum. See "O.K. Let's be realistic!" July 29, 2001 and subsequent debate!
1. May I have a try at these issues: (my math isn't great so I'm going to clarify it as much as possible to myself here)
2. Suppose you are looking at the Earth from space. You see a weather system. It is a depression and it is moving east at an accelerating rate. Thus, a rate of change (acceleration) of a rate of change (distance per time). (Noticing the acceleration means differentiating that there are two rates of change; noticing how far the depression has gone means integrating them.)
3. Now; disregarding this big picture: within the air on one side of the system you are aware of a broad river of air; actually part of the rotation of the system but feels just like an airstream going straight ahead when you're in it. (you don't notice the space-view of the whole system moving sideways.). Suppose this airstream is accelerating. So we have a rate of change of a rate of change; superposed on the whole depression's rate of change of a rate of change.
4. Now; suppose you disregard the airstream movement. You are in an aircraft, a low-speed gyrocopter, and although the forward propellers are increasing in activity and your craft is accelerating (thus a rate of change of a rate of change); someone on the ground notices that relative to them, your craft is stationary!
5. So we have a rate of change of a rate of change (the accelerating gyrocopter); superposed on a rate of change of a rate of change (the accelerating airstream); superposed on a rate of change of a rate of change (the accelerating depression weather system).
6. Since I supposed that the gyrocopter is stationary relative to the ground; the acceleration and direction of the aircraft is just right to cancel out the acceleration and direction of the airstream plus the acceleration and direction of the whole weather system (or the sideways movement of the air-river, so to speak.)
7. Note the aircraft's movement relative to the ground is zero in the scenario I've chosen. Each of Dick's physics definitions in his website paper amount to stating an initial pattern conservation thus giving a fixed reference point hence a symmetry around zero.
8. Note that the aircraft, the air-river, and the depression, could all move back the other way (negative directions) to their current directions, and you would still get the aircraft stationary to the ground. You still get a zero sum move against the ground by the aircraft.
9. Note the relativity inherent in all this.
10. Suppose now: if you partially differentiate this scenario, you get specific patterns of pattern conservation. Say you differentiate or distinguish the depression movement only, against your zero-sum aircraft-ground reference point (equates one of Dick's definitions i.e. reference points). You will end out with the 'discovery' of the 'law' of the river-of-air acceleration in order to maintain the internal coherence of your initial definition or fixed reference/ pattern conservation.
11. But note that this 'necessary law' coincides with actual reality. But if you had not called it a river-of-air, but a special-force caused by an alien on board the gyrocopter; well; your physics holds but you are not describing reality other than mathmatically as required by your fixed reference point.
12. Is this what Dick is on about? That the laws of physics fall out of their own requirement for coherence and necessary symmetry required of the unknowns to maintain the zero-sum that the definitions themselves impose?
13. Has Dick differentiated physics itself? Then re-integrated it? And found the laws; of the laws of physics? Notice something about this? The reality of the existence of the aircraft's stationary ground position is non-local!
14. The 'one' of that position requires the 'three' of the three different accelerations! Could there be a lesson there, given that physicists have discovered that reality is non-local: www.aip.org/enews/physnews/1998/split/pnu399.1htm
15. If that reality must be conserved, then a change way over there (say in the acceleration of the air-river itself) must be accompanied by a change over here (in either the gyrocopter acceleration or the depression acceleration) so as to maintain the integrity of the pattern of aircraft-stationary-to-ground.
16. Physics particles may be 'pattern conservation' events, comprised of three complementary rates of change of rates of change. Thus you have complementarity and non-locality. And of course in this scenario you have mirror symmetry and you have relativity.
17. From a three-way zero-sum pattern match scenario, you can solve every scenario in physics. Everything can contain everything, because all the sub-patterns could differentiate out of the one initial supersymmetry. The supersymmetry of the existence of just one fixed reference point.
18. Alex wonders what there is for God to do. God, Existence, is that fixed reference point. Through God everything contains everything. That reference point is clearly in everything. Creation is differentiation! God creates the changes, the new patterns, including us!
19. And you see how He is in us. You can see why we do well to have Him as our reference point; as if you start integrating with other patterns, your own pattern would become obscure! The gyrocopter pilot can enjoy the experience of the patterns of acceleration without becoming lost; as he is fixed relative to the ground. And if he should travel; he will need to maintain his relationship with the ground to avoid getting lost!
20. Integrate with God; and you are differentiated! Be still with God, and you can differentiate yourself and all the patterns and not get muddled!
21. Other thoughts: An aircraft in the air (say a gyrocopter as they can fly slowly) consuming fuel running it's engines yet stationary relative to the ground, is an example of a condition that requires symmetries. Certain symmetries must occur to explain this event. Even if it flies over the ground; the argument still applies.
22. When Dick says "If identical particles are exchanged, 'nothing has changed'; the logic is questionable because there is no such thing as 'identical' in the full sense (except God is 3 God is 1). To even use an 's' on the word 'particle'; to even talk of two; requires at least one difference; or you would have just one particle.
23. Are scientists in contact with reality? To even use the word 'contact'; requires that they are. To be in contact at all; requires at least some level of reality that you are in contact with. Or you couldn't even use the word "contact".
24. An illusion is reality in that it is a real illusion. A CD mistaken for a live band is not a live band; but it is a real sound! Regardless whether your senses mislead you on reality or misrepresent reality; you always have some reality or you could not talk of being in contact with anything.
25. There is a way you can know you are in contact with reality; logic: above I show it is a necessary fact that to be in contact with anything is to have some reality-contact at some level. The thing to do then is to differentiate with God (Existence). Honesty. Love (letting be).
26. By making God our fixed reference point we integrate with Him and are differentiated by Him; in Him we live and move and have our being; He is the Alpha and Omega.
27. "If you were to assume that there could exist a way to tell two electrons apart..." - electron's'? You can tell them apart or you would not be able to say 'two'. One must be before, the other after; or one to the left and one to the right; or one behind and one in front; or one above and one below; or one in one dimension, the other in another dimension.
28.If the electron's are otherwise identical; then their difference is a space-time difference and they may in essence be space-time distinction patterns.
29. Suppose there was no 'ground' to refer to in my three relative accelerations scenario. Suppose I arbritrarily chose one movement as a fixed-point. This may explain why some people think Dick is being anti-realist. Saying something is fixed and moving.
30. But it's not anti-realist. It's just saying "It's moving. It's movement is 'transforming' the perception of the other movements. None of the movements are known. So we have an undefined situation transformed by an undefined process. We choose to regard one movement as stationary for the purpose of differentiating the other movements.
31. When we do this; there are necessary symmetries, pattern conservations, and logic. If we find they match the laws of physics; we might regard physics as an elaborate mental construct to make sense (i.e. differentiate and integrate) a large number of facts. In my opinion, if we differentiate using 'Existence' as our constant; we get maximum differentiation possible, the differentiation of actual creation.
32. Suppose you fly over 'sphagetti junction' where overpasses in all directions carry many cars. Suppose you now regard one moving car as a rest-point. When you differentiate all the other cars' accelerations, you must note that they 'contain' your cars' acceleration. Choose another car as a rest-point, and your results for the others 'contain' your chosen car's acceleration.
33. Suppose someone in a court case tells a false story, then tries to maintain it as constant by everything else he says. More falsehoods occur. But tell the truth, and true patterns may be differentiated. Make Existence your constant; and you differentiate truth.
34. What I've been saying seems to have a lot to do with the Laplace partial differential equation: d sq. V / d x sq. + d sq. V / d y sq. + d sq. V / d z sq. = 0
35. Is this right?: Dick takes the 'totally unknown data' and notes it has been transformed by a 'totally unknown process' much as if you found yourself in a swarm of bees in a big sphere in outer space and you knew that your movement is coded into your perception of the other bees' movements. So your unknown movement has performed an unknown transformation on the other movements.
36. He makes some basic definitions; that is he chooses some arbritrary rest-positions to differentiate the other data from. Like stating that you'll regard a few bees as being at rest or in a fixed relation; and see how all the other data must behave or not behave because of the very fact of your chosen resting-places or fixed-relations (i.e. definitions or pattern conservations).
37. He looks at the logic and symmetry of the sums of partial differentiations. Because he is dealing with relationships of combinations and uncertainties I guess that's why quantum mechanics falls out.
38. Maybe the real constant in the Universe is differentiation itself. Thus the ultimate reference point is God = Existence who creates/ fully differentiates everything else. So gravity is the reaction to expanding space-time such as to make differentiation a constant. Universe expansion increases distance of particles so differentiates them more but not so as local gravity attracts them together to maintain a constant differential!