Software and Math

Ari4 thoughts on software:

Software is best seen as a service, not as a product.

Open source is better, all else being equal.

Reasonable profits are good.

Complexity is an enemy.

A spreadsheet is often a database table lacking a primary key.

It is best to keep data processing close to the data.

Correlation does not imply causation.

Isomorphism does not imply computability.

If the goals above keep conflicting, take a break!

Category Theory.

Constructive category theory summary, noted 8/19.

arxiv.org/pdf/1908.04132.pdf

Reflection principles in the category of sets are equivalent to induction over well-ordered sets. (9/19)

arxiv.org/pdf/1909.00677.pdf

Broad category theoretic study of history and recent results in computability theory. Section 3 includes equivalence classes of proofs; 3.8 introduces topoi, exploring relationships between them and formal languages. Freyd gluing techniques are introduced in 4.4. Classical type theory and non-standard type theory may require consideration in separate categories. (1/20)

https://arxiv.org/pdf/2001.05778.pdf

Zorn's Lemma helps show connections between model theory, proof theory and programming. Intuitionistic and constructivist contributions are noted.

https://arxiv.org/pdf/2001.03540.pdf


Other items of current interest.

Benford's Law (2019)

arxiv.org/pdf/1909.07527.pdf

Probability Logic, a recent effort. (2019)

https://arxiv.org/ftp/arxiv/papers/1910/1910.06624.pdf

Algorithms for Beauty?

https://arxiv.org/pdf/1910.06088.pdf

Logic: interesting and useful recent completeness results. IMO K is a pretty strong assumption in a constructivist framework. The proofs themselves rely extensively on non-constructive elementary logic. Some things just never get old! (2019)

https://arxiv.org/pdf/1910.01697.pdf

https://arxiv.org/pdf/1910.00907.pdf

Amazing game-theoretic approach to welfare distribution. It helps illuminate several problems with socialism: the large economy is usually not decomposable into tractable sub-economies. Envy-free solutions in general contradict full decomposability. Adverse selection (IMO in Joseph Stiglitz’ sense) is still an issue. (2019)

https://arxiv.org/pdf/1909.11346.pdf


Envy: I would suggest that we cannot defeat it by using the closed preference sets assumption. In economics this would imply that every situation of resource consumption is zero-sum. Also, as at the end of this paper, the importance of individual leadership is minimized. (1/20)

https://arxiv.org/pdf/2001.03327.pdf


God as Ultrafilter? LOL! I can't help remembering Elizabeth Anscombe echoing Kant about the existence of God: ‘That is not the sort of thing you prove!’ I like to imagine her debating St. Anselm of Canterbury and St. Thomas Aquinas about this. With Karl Barth and Kurt Goedel in the audience taking copious notes? At any rate, this remarkable paper shows interesting and helpful results about reducibility of modal logic and reasoning to first order calculus. (12/19)

https://arxiv.org/pdf/1910.08955.pdf

Structure Theory: recent results in 2019.

https://arxiv.org/pdf/1910.10811.pdf


Recent results on orthostatic intolerance (med x stat). (2019)

https://arxiv.org/ftp/arxiv/papers/1910/1910.10332.pdf

Intuitionistic math: good summary and recent results. Also a constructivist re-presentation of work of Brouwer, Skolem and Lowenheim. (2019)

https://arxiv.org/pdf/1911.09477.pdf

Intuitionistic logic: more history. Although it may have a dubious metaphysical pedigree, it seems to help enforce very conservative procedures for managing computer memory.

https://plato.stanford.edu/entries/intuitionistic-logic-development

https://projecteuclid.org/download/pdf_1/euclid.ndjfl/1093958744

https://books.google.com/books?id=ah2bwOwc06MC&pg=PA271&lpg=PA271&dq=heyting+spread&source=bl&ots=dflNNUxi_c&sig=ACfU3U27rIGNCTv3uVuPWoMKFab1H_nGKw&hl=en&sa=X&ved=2ahUKEwir-oPVqYbmAhUPQK0KHYwFCPM4ChDoATAIegQICBAB#v=onepage&q=heyting%20spread&f=false



For engineering, interesting categories have morphisms and objects whose costs can be minimized.

Peter P. Chen

https://bit.csc.lsu.edu/~chen/chen.html

https://resources.sei.cmu.edu/library/author.cfm?authorID=4803

Cybersecurity Maturity Model Certification

www.acq.osd.mil/cmmc/index.html

Data Model as an Architectural View.

https://apps.dtic.mil/dtic/tr/fulltext/u2/a512388.pdf

References and free eBooks:


Teleology in Logic. You can almost see Prof. Serre's mind work!