The October Scientific American had a fascinating article on mathematics:
https://www.scientificamerican.com/article/infinity-category-theory-offers-a-birds-eye-view-of-mathematics1/.
I'm not a mathematician and most of the details are beyond my
understanding, but the premise is crystal clear:
"How is it that mathematicians can quickly teach every new generation of
> undergraduates discoveries that astonished the previous generation’s
> experts? Part of the answer has to do with recent developments in
> mathematics that provide a “birds-eye view” of the field through ever
> increasing levels of abstraction. ... As Eugenia Cheng puts it in *The
> Art of Logic in an Illogical World*, “a powerful aspect of abstraction is
> that many different situations become the same when you forget some
> details.”
The transformation of SPDX from v2 to v3 based on ideas from 3T is a
concrete example of abstraction. Everything in v3 is a *Graph *consisting
of Nodes with a uniform structure (classes derived from Element), connected
by Edges (various kinds of relationships). Starting with the logical model
(the highest level of abstraction), making design decisions at the logical
level and then validating them for feasibility at the information and data
(syntax) levels is the process we seem to be following, but that process
isn't explicitly described or universally understood. And syntax-based
design still seems to be with us.
We recently agreed that Elements are immutable. That is fundamental to
understanding SPDX as a graph - every Element in the continually expanding
Element graph is *created*, and once created it never changes. We then
don't need to understand any specific details about SPDX in order to know
that the set of all Elements ever created must be a DAG (directed acyclic
graph) which has a topological (partial) ordering based on creation time.
(A linear or total ordering would mean that no two Elements have the same
creation info, i.e., there is no such thing as an Element created within
another Element.)
So based on causality (the laws of physics) and immutability (our
agreement):
- A collection Element has a collection id and was created.
- Every Element that is a member of a collection logically either:
- a. has the same collection id and was created at the same instant
by the same entity as the collection (call them internal Elements)
- b. has different or no collection id and was created prior to the
collection (call them external Elements)
This is regardless of what if any creation properties are defined in the
logical model. An Element that exists was by definition created by some
entity at some point in time.
Do those bullets make sense?
Dave
-=-=-=-=-=-=-=-=-=-=-=-
Links: You receive all messages sent to this group.
View/Reply Online (#4237): https://lists.spdx.org/g/Spdx-tech/message/4237
Mute This Topic: https://lists.spdx.org/mt/86916688/21656
Group Owner: [email protected]
Unsubscribe: https://lists.spdx.org/g/Spdx-tech/unsub [[email protected]]
-=-=-=-=-=-=-=-=-=-=-=-
