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Infinite tetration and superroot of infinitesimal
Hi Andrew

To expand slightly:
Numbers are being built as part of informational world organizing itself. Not all numbers exist in smallest scales, and , as they are built, they acquire the properties they have by including the process of their creation- so Numbers as such are much more complex entities than we think. They have a history, and a scale where they naturally appear.

On more thing is non-linearity - may still early- but in my view, pixels which has complex internal infinitesimal structures, can have at least 2 additional properties:

1) depth- how many scales below are fixed to that point - it can be 1, it can be many- so pixel can be fixed in its place just in 1 scale, or many. If entity is described by differential equation, that would be the order of differential equation.

2) Non-linearity - entities can be stretched and compressed creating variations that make each place almost unique in space, increasing or decreasing their Reynolds number ( ratio between content of information inside and exchange with flow around them) and that changing their inertia and speed of information transfer- including speed of light and change of gravity field in scale just below quantum scale. Again, if entity represents a differential equation that works on infinitesimals, this means it is non-linear.

So every process or structure of infinitesimals described by differential ( and integral) equation involves as many scales simultaneously as is the order of differential equation. I see differential equation as a machine ( differential combination) that connects more scales in a given place in space then just 2. Linear differential equation processes only 2 scales of infinitesimals, so that is the complexity it can represent. And we do not know, usually, between which 2 scales we look at the problem , in mathamatics. In physics, we usually know.

27th order continuous differential equation is a structure of different complexity differentation machines at different infinitely distant infinitesimal scales below quantum scale which simultaneously connects 28 scales, it works on them , kind of lets them flow through it while itself not changing or perhaps, changing itself- adaptive differential equation.

So we can see that first: we do not understand numbers as we do not know how they form as complexity grows
Second- we do not understand that differential equation are relative , and first order differential equation will always connect only 2 scales of different complexity, but which 2?

Non-linear differential equation of 4 order might already fit something interesting because i has a cycle of 4 , and 168th order non-linear differential equation applied to 168 SCALES below quantum might have very interesting and exact properties.

If we include above quantum world, we have to be careful to keep the infinitesimal scales involved pertinent to addressable problem, plus mix discrete difference and continuous differential equations to describe the system we are looking at, checking against Reynolds numbers at each scale if we want to make approximations.

So now differential/integral equations has been added to the picture as wellSad

Messages In This Thread
RE: Infinite tetration and superroot of infinitesimal - by Ivars - 01/05/2008, 09:38 AM

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