The Miser Project

Miser Project astraendo Notes
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2014-04-18 -14:06 -0700





The Content Material here was successfully repaved as part of the
2007-11-11 stage of the Site Repaving Project.  Check those pages for additional details of the approach to correction and upgrade.

  2014-04-18 Review these notes for ones that can be successfully moved down into relevant folios, if any.
  2014-01-29 The structure model, <Ob, Of, Ot> has counterparts in other structures that are modeled via Miser.  The general case might be discussed here in Astraendo.
  2014-01-13 I suppose if Wolfram's smallest UTM and his principle of computational equivalence is raised, so should Chaitin's work.  I think there is more, for Astraendo, with regard to higher-level algorithmic systems though.  Just a little marker here.
  2014-01-13 I need to recover my notes on the representation of the tiny UTM that the Mathematica folk claimed.  There is something about that on Numbering Peano, I think.  Also, here's the Wolfram riff on the accepted proof. 
  2014-01-13 I was thinking about initial tapes and how one could produce a non-terminating initial state.  Obviously, it can be the tape that another machine is producing.  In this case, one needs to be able to know when the machine has made some amount of tape (let's assume this is the left side) that will never be backtracked into.  So the ability to know there are increasing no-backtrack positions is important to generate the input to the second machine.  That there is a progression of no-backtrack positions is essential to being such a producers.  I wonder if one can show that there is no possible finite machine that will rewrite over the left while continually extending it "left-ward" in a way where the same could not be done without backtracking (so far).  That is, apparent growth on the far left is actually accomplishable by growth on the right.  (This seems to have to do with the inevitability of cycles.)   Then the question is whether or not one can systematically transform a machine in some manner, or whether it is not necessary.   One could forbid machines that sense the left end of the tape, I suppose.  That seems to lead to too-trivial machines, though.  If the machine can ever move left, there has to be something about the initial state that has it always able to cease leftward movement without reaching the left end of the tape.  I think that is now enough musings for now.
  2014-01-13 The "Mathematical Structures in Computer Science" Call for Contributions first reminded me of the notion that there is a certain very simple Universal Turing Machine, according to the Mathematica folk.  I don't know what the status of that machine is, but I recall looking at how to implement it using oMiser.  The basic idea is that the tapes to the left and the right are basically stacks (implemented by list structures) and the current position is, by arbitrary convention the top of one or the other.  I was thinking that it is handy to avoid so much creation of destructed pairs if one kep a list of all previously-longer versions.  There's something perverse in this notion, but one peculiarity of it is that one should be able to detect if a previous state ever recurs.  That is, the machine is in a loop involving a finite set of tape conditions.  oMiser does not permit cyclic constructions so it is only this literal recurrence that would be detectable.  On the other hand, one might be able to use this technique to also detect (some) cyclic recurrences where the machine is not stopping but is making more and more tape forever.  I suppose this opens the possibility about how long one needs to let the machine run, based on the original tape, before concluding that it will not halt.  Then there is the question of whether it will not repeat (given a finite initial state) although it would seem that a repetition in terms of some cyclic structure must happen if it will not terminate.  So a non-computable real would be one where the machine never enters a cyclic repetition and presumably that can never happen given a finite initial state.  So, is it the case that the detection of this inevitable cycle happens in some interesting bound, and what is the memory impact in that case?  Can one tell anything about/from memory consumption?  [This is a big note to self.]
  2014-01-13 The "Mathematical Structures in Computer Science" Call for Contributions had me thinking about some things from Introduction to Mathematical Thinking and the manifestation of the reals to the extent that is possible in Computable Analysis.  I had been thinking about continuity (and, I suppose, completeness) as it would be modified for representation of "computable reals."  I also wonder how this fits with Turing's approach.  This is clearly an Astraendo topic.  There is a nice treatment in Petzold that I must dig into.
  2014-01-09 The introduction of dim and the requirement to have computational completeness makes a parallel argument with the computational completeness of Peano-arithmetic representations in oMiser.  This will give at least three ways of looking at this: under the Java UTM, under the oMiser UTM, and as combinators themselves.  That and under- case is needed to discern the results of the combinator case is also interesting.  There are some type-theory issues too, especially in discriminating combinators as part of an arithmetic.
  2014-01-09 We are repaving: Construction Structure plus gathering of more abstraction notes. 
  2006-02-20 Explain the value of the choice to use dim with regard to computational completeness.
  2006-02-20 Prepare for the legitimization of dim as a function on Peano Numbers.
  2006-02-20 Figure out how to much can be removed entirely from the /astraendo level and how much has to be shared as include pages (the non-.htm pages cannot be shared that way). [dh:2014-01-09 I am not too concerned about broken links in this case.  We should do the include page trick and clear or redirect the rest.
2006-02-20 Share and split a040601 pages to the lower folder.
2006-02-20 Create 2004/06 substructure
2006-02-20 Look at upgrading the construction structure here but don't do anything about it.  [dh:2014-01-09 That's changing.  We are going to do the construction structure and repaving.]
2006-06-06 The construction templates need to be moved and the creative commons license needs to be brought here. [dh:2014-01-09 I think this happened some time ago.  I am closing this.  The Creative Commons part will be cleaned up along with the definitions for attributions.]
2006-02-20 Create 2006/02 (or /03) to begin capturing new notes on the list for Numbering Peano.  [dh:2006-06-06 this starts with 2006/06]
2006-02-08 Switch Astraendo to the standard accession structure using astraendo/yyyy/mm subfolders for content.
2006-02-20 Create a folio for Peano's Axioms.
done 2004-06-05 Get all of the font sizes in these table entries to be the same and keep them the same.  This is a recuring problem and I don't quite know how to fix it except using the Format Painter a lot.
done 2004-06-05 Get rid of the stray centering on these description entries, making them all left-justified
done 2004-06-05

Make the links to the collateral materials from astraendo/index.htm more emphatic.

not done

Build a note that collects links to material on abstractions and especially the business about interfaces and formal syntax, semantics, and higher-level "meaning."  I don't need to call this out at this point.  The existing material and resources are drenched in it.

done 2004-06-03

Build a note that anchors the initial discussion context that led to Numbering Peano

done 2004-06-03

Customize a note section solely for astraendo that is used to make Ayymmnnx notes accessions.




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$$Date: 14-04-18 14:07 $
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