Window size and irrational sequences

The theory abut Lagrange  approximation requires that some irrational formuli be more irrational than others.  What do we mean?

Basket brigade theory has window sizes, an adaptable queueing window of transactions that are converted into compact generator, with an irrational 'quant' error term (I normally call this bit error).  This is like a rational approximation with an irratoonal continuing fraction.

If we incrementally increase the window and derive the best compact representation, then the bit error will either increase or decrease.  If the bit error increases, then that means a shorter window contained a partial rational algebra, rational relations. Like Pi, is the example used. It is irrational, be we get a good approximation at 22/7, then the next best approximation is some window of 200.  In between we get a lousy approximation from any window.

So Pi is less irrational than Phi, the most irrational.  With Phi I can always reduce bit error by increasing window size.  There is no 'gap' in my indices where information becomes redundant. Thus, all new remainders have innovations, not redundancy, it is maximum entropy.

This is something we keep in mind.  All of our generators carry the remainder from a rational compact graph.  The compact graph captures all redundancy, up to the current rank.  The window size is what is determined,the condition we have to meet. Generally that mans approaching one of the point on the Markov, but we are not as accurate as the roton in doing this.

Where is the queuing in all this?

  Convert the 'arc' isomorphism of the generator to normal form. Feed it with the incrementing indices and as it generates the typical sequence, the window size is queued up at the nodes in the generator.

There really are no number lines in math, they lied.  There are recursive algorithms, and all the math is protocol theory, the theory of queuing up when running recursive protocolss.

What if the bit error ends up with structure?
Hey, my agents are trying to estimate Pi, and went beyond 22/7. My bit error now has structure and will form a compact graph. In physics get quarks. In economics we get central banking.

In physics, when the compression is to great, essentially the virtual it bss cannot get on the bubbles and sort them. This is aliasing in algebra, the line of symmetry won;t support the transitions needed by the necessary motions. So, it way underamples, and gains structure and quantizes, we get a three color, side lobes.  This is the spectral version of relativity, and the better version.

Physics has a pit boss, called  the speed of light In spectral theory that is a fixed generator, in brigade theory it is still self measured and subject to uncertainty. The speed of light is like the least irrational of them all.