Temporary algebras

Systems with a fixed uncertainty constant  have indivisibility properties, thus have an algebra, a set of operations over integers. These system have the arc operator that converts from function space to index space, and we get algebraic bounds on indices.

The arc operation happens in run time and is approximate, a result of adaption.  The arc function appears as a generator, with an inverse, that takes us from an index sequence to a real number, and back.  But the arc operator is never completely accurate, and the algebra symmetries tend to be off, causing them to spiral a bit. As they spiral, bit error builds and we adjust the arc operator.

The TOE as applied to economics" It is the spiral effect, the approximate algebra, that forces us to pack sphere, it demands a third sequence to manage the spiral..

Do the Markov numbers correspond to the real economy?
The Markov numbers are a restriction, the only restriction, on sphere packing in three sequences. They tell us the transaction sizes, the index space, needed for the three sequences to pack a volume.

The economy cannot get close, but it rhymes. Consider the three sequences to be excess deposit transaction, excess loans to government transactions, and seigniorage transactions.  The respective demands on index space is clear, deposit change biquarterly, loans to congress every six quarters, and seigniorage every 200 quarters, or so. 

In the algebra of negiotatians we solve the multiplicity problem, fit their repeating sequences into an index stream, working in index space. We make algebraic statements like, "Oh, we get a tax boost late in the cycle", true or not, we are using our algebra, then late in the cycle we will be off, a bit, and reconstitute our algebra, in the process reserving index space for seigniorage to cover the currency losses. Now, sometime around next year, we do another requant, this time backing up the next rank, redoing the monetary regime.

But we can see why the Markov numbers have that extreme spread, a short widow take out a large chunk of the irrationality, it is the 2-3 prime combination makes for a lot of possible algebras, different way to arrange a dozen egg, for example.  Then you get a big jump to the next prime, causing that third number to explode.
Extend and pretend, for example, means we aim for the next node up n the Markov tree, and the seigniorage window jumps. Extend and pretend extends the monetary cycle another 80 years, some huge distance out.  We won't do that, we will requant.  How many of us, for example, would make an 80 year bet on the demographics of Maine, relative to California?