Just a thought

I woke up from a dream about a complex linguistic operation that, for some -possibly anatomical- reason, turned out to be extremely simple. It reminds me that there may be a number of things that are actually topological in how we think: so that a homotopy is almost instantaneous.

What comes to mind as an example - now that I am awake - is the nature of dependence. For example: 

I depend on my grandmother sending me money to pay the rent

According to my theory, a dependency is a shortcut where the connection between getting money and paying the rent is so intuitive that it does not need to be said. How about:

I need warm clothing to enjoy a trip to Greenland

So let me wonder: is the shortcut is a homotopy? 

Similarly when someone describes what happened and someone else says: "Yes that is true".

I submitted "The Moving Topic"

I could not hold off any longer on submitting this article. It is my life's work - in so far as I started observing the behavior or "or" and "and" in college; spent time in graduate school inventing little notations; gave it all up to get a Ph.D. and a job. Over the years of working on applied math and algorithms I ended up doing a lot more user interface design than you would expect from a mathematician. So I have some skill in simplifying ideas. 

Then, in the 11th hour, these ideas were re-invigorated by a technical challenge of automatic text processing, at Dentsply. So I pulled out my love of inventing little languages, and put together "narrative notation", as a way to describe natural language expressions. User interface design skill has something to do with the narrative "elements" I settled on. I got focused on topic-specific language processing, and ended up building Narwhal which is a chatbot development platform. The ideas work pretty well but the approach is is labor intensive. 

When I started retirement, I focused on finishing Narwhal so I could be sure to have a working platform to demonstrate the ideas. When it was pretty much in place, I kept a couple pages of typed notes about the truisms. When I finished Narwhal, I was looking around for something else to work on. I mentioned to an older lady that I planned to write an archaeology book "later". She told me I better get going asap. So writing "A Shadow Under the Rock" became my main task. Which filled in the early years of the pandemic, then got self-published on Amazon. I have sold about 100 copies so far, with one or two new orders per month. This, again, left me with nothing to do. 

So I pulled out the two pages of notes on truisms and with a vague desire to give them a theoretical basis. I thought: Maybe if I start writing down what I know about truisms, some kind of result or mathematics will emerge. Miraculously that is what happened. 

I was focused on "narrative continuity"  - what makes language hold together and avoid non-sequiturs. The truisms play a key role in that definition. So what with one thing and another, I tightened the definitions and the ideas, as I wrote. And by the time I got to defining "continuity" clearly, I was starting to describe narrative equivalence and was able to make an almost casual observation: that continuous narrative "path" equivalence  - in any of a variety of ways -  gives the basic definition of truth. An amazingly simple idea, everyone understands intuitively, that never was clearly defined. This was the "content" I was hoping for. In the 11th hour I created a new branch of logic, a new approach to AI, and a wonderful collection of ideas.

I could not be happier with my intellectual activity during retirement . So, today I submitted the article to an "Oxford Journal" called (a bit pretentiously) Pbilosophia Mathematica. I have been polishing the article and the cover letter for months. It was time to submit it. 

And now, I have to figure out what to think about next.

I would not want to close out this discussion of history, without being clear that my insecurity has always been present. I was insecure to go to BU rather than MIT or Harvard. But I learned phenomenology in Boston - while the opponent theory was being promoted across the river in Cambridge, MA. When I submitted "The Moving Topic" to a journal, I made sure it was Oxford and not Cambridge. Because that other Cambridge, the one in Britain, was the original home of people like Russell and Wittgenstein who I both revere and hold in contempt. Brilliant guys who never figured it out - mainly cuz they were in too big a hurry to get to the math.

Update:  Of course it was rejected because the reviewer already knew all about Narrative.

Yellow shoes, umbrella, sweet potato, and oarlocks

 

Pegging Aristotle

I am pretty much done with my paper on the "Moving Topic". In it, I cover quite a lot of territory, from the basis of cooperative behavior, to irony, to the attractiveness of scientific theories of Newton, Lagrange, etc., to the definition of imponderables like: "truth", "causality", "free will", "space", etc.......Good Stuff!

I was and remain worried that the paper does not have any significant content but I have to recognize that figuring out a very reasonable definition of "truth" is, in fact, significant - especially since it is a topological concept of homotopy. Again, good stuff! But it is sad that I am not likely to be around when or if my theories are ever understood or praised. Also, I am afraid to stop writing because, I could forget all the details in the blink of an eye, and then what will my identity be?

The weird feeling I have is that I have sodomized Aristotle, and I am ducking, waiting to be spanked for the act. If I submit the paper to an academic journal, that is exactly what is likely to happen...that and the forgetting.

Black bean and cheddar empanadas

I had some left-over "blanks" from empanada making, rolled them out, and filled them with refried black beans from a can, bits of cheddar cheese, and baked at 420 for ~20 minutes. Something about them, perhaps the flakey dough, after it had rested 24 hours in the fridge, made them particularly good.

Dough - see empanada dough recipe for 2 cups of flour. Divided into 16 pieces.

Filling - Goya refried black beans (~4 tablespoons per empanada); a couple small pieces of cheese.

Bake at 420 for ~20 minutes.

A DeMorgan Law derived from Narrative

Wanting to relate narratives to the traditional Boolean “calculus”, here are some of the kinds of assumptions needed for a test case:

·        A kind of  temp_collection {A,B, C, … } that can be interchanged with the comma-separated narrative pattern ‘A,B,C,…’

·        Blocking this kind of temp_collection replaces it with a temp_collection having each of its elements blocked. In other words (A,B,C,…)* is equivalent to (A*,B*,C*,…).

With those assumptions we can limp towards a derivation of the De Morgan Law

not( A or B ) = not( A ) and not( B ).

First to represent “A or B” in our current framework, we put A and B in a temp_collection, along with a blockage of the alternatives. Thus ‘A or B’ is written:

{ []*, A, B }

To negate that, we write

{ []*, A, B }*

Distributing the outer blockage, gives us

{ []**, A*, B*}

Which “writes back out” as the narrative [], A*,B*. This is endpoint equivalent to ‘A*,B*’. The ‘,’ is transcribed as “and”.

This gives us a hint at doing traditional logic with narratives  - with a heavy reliance on temp_collection behavior and blockage properties. It would be worth isolating the narrative equivalences needed to support a discussion of the infinite. 

The definition of "truth"

Wow! I had no idea they were still so confused about the definition(s) of "TRUE". So here it is:

We distinguish three types of truth: 

• Tautological truth - which follows from the mechanics of symbol definition and persistence of meaning.
• A priori truth - which follows from definitions
• A posteriori truth - which is an observable equating of different paths towards the same outcome

Tautological includes "A=A" and possible others

A Priori includes at least two kinds of definition. The "x is a kind of y", leads to "peanuts are legumes". And the "x is part of y" leads to "you need ingredient to cook".

A Posteriori is the most interesting version of truth. It says: Two methods for producing the same outcome are equal  - if all you care about is the outcome. For example "2+2=4" is TRUE. Note that it is NOT true if you are listing partitions of 4. The truth depends on the assumptions you make.

I gotta crow a little cuz several thousand years of philosophers never spotted that ignoring intermediate step and the equality of outcome, is the definition of "truth". 

Update: OK, OK, maybe there is another kind of truth. There are behaviors whose repetition guarantees certain things: Adding material is transitive ("More is more"). Containment is transitive ("if a in b and b in c, then a in c"). Getting from A to B is transitive because if I can get to C from B, then I can get from A to C - it just takes longer. Another is: is A can be substituted for B and B can be substituted for C, then A can be substituted for C.