Red shift could be caused by rotation rather than expansion

Anything that causes the shortest path between entities to lengthen will case a red shift. Expansion, where the entities are accelerating away from each other is only one way to lengthen such paths. Another way is for the entities to be on spinning a merry-go-round.

The definition of information, the definition of "life"

This is philosophy of universe week. So to start the ball rolling:

I think a theoretical physics that fails to subsume theoretical biology must be incomplete. The idea that somehow causality is suspended for that brief moment where "life is created" is just not scientific. Nor, for that matter, would a Deus Ex Machina make any more sense for the big bang "universe is created" moment. One thing at a time though.

Grant me the concept of a clock and here is a definition of information: a sequence of increases and decreases of frequency.

Grant me that definition and here is a definition of life: the preservation and perpetuation of information.

So here is that theological moment: the previous two posts on this blog outline a theoretical physics based on information such that the universe is populated entirely with objects interacting based on the information they maintain. According to this post here, that means life never starts, it is simply the stuff of the universe at different levels of complexity. For the benefit of a colleague at work who was using the word "consciousness", let's agree that everything is conscious of itself and its interactions and that collective conscious is possible.

Properties of a universal simulator

This is a long-term discussion with my eldest son about creating C++ objects that simulate or model the behavior of real world objects. The base class is required to have certain properties:

• It can "contain" other simulation objects
  
• It exposes one or more sequences of frequencies
• It maintains a clock with an update() method called once per tick, and sent to each of its contained simulations.
• the contained simulations must run their clocks in synch with the containing object's clock

A goal is to be able to populate a program with objects by declaring/initializing them, and then have the objects freely interact. But what is a "freely interact" supposed to be like when the classes do not know about each other and the programmer (me or you) does not have access to the header file definitions of the classes in use.

So what is a universal language of interaction? The only answer I can come up with is that when exposed frequencies "match" (in the clock of a containing parent class) energy can be exchanged and some kind of communication can occur between interactors. According to yesterday's post, such a "red-shift event"/interaction would need to generate a new class instance (a new "particle") with the frequency difference of the interactors - spun off as an offspring of the harmony.

I guess I don't want you to think I am another crazed mathematician. But I believe there is almost enough here to start creating prototype simulation class definitions, working programs, and some kind of approach to theoretical physics.

A physics of information and red shift

This is not a new topic and I know other people are trying to base a theoretical physics on the notion of information rather than the (tired) ideas of "mass" and "energy". My son and I have been going over it for years. Today I was talking with a colleague at work about how there is still something missing if all you have is information. There is something else needed for the theory. Which reminded me of a different conversation I have been having with my son about resonant frequencies between pairs of particles and how they can exchange information/energy if their frequencies are nearly matched. So a particle with frequency .99 and one of 1.0 could resonate but (according to my son) a 0.01 particle would have to be produced. As the first two particles resonate and experience harmony, they produce an offspring particle. The process is a red-shift event.

This red-shift event defines a spatial component between the two particles and I want to say it should be regarded as happening with a certain probability. One last crazy statement is that probably there still needs to be an observed/observer relation in their to cause probabilities to materialize into facts.

[Another discussion with my son that has been going on for years is about the class definition of a universal simulator.]

Ratio of chord length to arch length

Here is another "math-y" little thing from work, that reminds me of the "associated function" of Bill Pohl:
Given two points on a curve in space, we can compare the length of the straight line ("chord") between the points to the length of the curve ("arc") between the points. For a fixed chord length, the ratio of chordlength to arclength has a minimum value. Consider this minimum value as a function of the given chord length. So

F(d) = minimum { d/ archlength }

where the ratio is minimized over all pairs of points d apart. Equivalently

F( d ) = d/ max{ archlength }

calculated over all pairs of points on the curve, d-apart from each other.

For the circle,

F(d)=d/arcsin(d)

For the square of side length 1,

F(d) is sqrt(2)/2 for d <1and jumps to 1/3 at d=1, and descends from there back to sqrt(2)/2.

A lot like the associated function of the square.

Lots of obvious math questions around the relation of this F( ) to the associated function, around the relation of this F() to the isoperimetric inequalities, around geodesics. My interest, is related to measuring the possibility of taking a short-cut, all in a "lava lamp" sort of way - meaning when the curve gets too close to itself, change it to take a short cut.

To a math friend

I have been having the darnedest fun trying to understand geodesics on the surface z=x^2 + y^2. It turns out I got all the way through graduate school, including courses in differential geometry, without realizing that the book examples were cooked up to be do-able and that, for the most part, even simple expressions lead to unanswerable questions. For example you study curves using "arc-length" parametrization when, in simple cases like (t, t^2, t^3), the arc-length parametrization cannot be found easily.

Anyway, the geodesics on z=x^2 + y^2 that do not go through (0,0,0) can only spiral outward and will always have an infinite number of windings around the z axis. I don't know why it took a couple months to realize a geodesic cannot spiral inward without its curvature exceeding that of the surface and its velocity vector is always turning more in the horizontal direction than in the vertical direction - so it integrates faster in theta than in z - guaranteeing a winding. The lemma is that geodesic's velocity vector will always turn toward the direction of greatest bending of the surface.

Also, I find it interesting that winding number is a topological property of the geodesics but not of the surfaces. You can deform a surface just slightly and change the winding numbers dramatically. The lemma suggest other things to look at, like z=a*x^2+b*y^2 where the greatest amount of bending can be a horizontal direction in some places and vertical direction in others.

Anyway, lots of fun.

There was a hummingbird

I held up my hand and
it flew tight spirals around it
landed, and started pecking my finger
with its bill like a needle