I Blame Carl Sagan

As a young boy growing up in West Virginia, in the early 1970s, my family would take these road trips across the state. We went everywhere, usually with a Scotty camper in tow. Dolly Sods, Blackwater Falls, Bluestone River โ€“ everywhere. One day we were on another adventure when we passed a sign telling us to โ€œTURN OFF ALL RADIOSโ€ and as we topped the hill, we saw a valley filled with HUGE radio dishes. As an autistic child, I lost my damn mind, โ€œCAN WE GO? CAN WE GO? WE GOTTA GO? CAN WE? CAN WE? PLEASE!!!!!โ€

Frank Drake in front of the Green Bank Observatory’s 8G5-1 (Tatel) Telescope. the first telescope built on site and used in the first SETI research โ€“ Project Ozma

My grandparents, to their credit, wilted to my demands and we took a tour of the Green Bank Radio Observatory. On the bus, we heard the tour guide, โ€œthis dish has a surface area of more than an acre,โ€ โ€œthis is the dorm where the visiting scientists stay,โ€ โ€œthis is the ball field where we wind down on weekends.โ€ The ball field was filled with deer that day. The last thing she mentioned was that a visiting scientist was waiting for us in the auditorium and he had an educational film to show the group. The scientist, speaking with a distinct accent, gave a short lecture – setting up the premise for a film on SETI โ€“ the Search For Extraterrestrial Intelligence. He explained how our powerful radio waves have escaped Earth and continue out into the universe. Then he flipped it, โ€œwhat if we listen for the signals that alien species might be broadcasting?โ€

In those days I was already neck deep in Ham Radio and I damn near lost my fucking mind when I heard his thesis. After the lecture, after the film โ€“ when the tour was over, I was a bundle of questions. The scientist patiently answered all of my questions. The last question (I was a dumb young kid from West Virginia), was why he stopped working in the hospital and decided to search for aliens? He smiled and explained โ€œI am not a medical doctor, you can be a doctor in any subject.โ€ I enthusiastically replied, โ€œIโ€™m promise I am going to get one of those!โ€ I had no idea what I was talking about.

Years passed. My family soon moved to North Carolina. I was no longer serving time in the West Virginia Public School System. North Carolina education was light years ahead of West Virginia.

During high school, I had heard of this show on PBS titled โ€œCosmosโ€. I knew it was about space and that was about it. I geared up to watch the first episode. I had my cassette recorder, microphone, notepad and several pencils all set to record the knowledge of the universe there in our living room. And here came that man with that distinctive accent talking about the wonders of the universe! It was the guy! It was the guy that I met years previous at Green Bank. Wow, he was on TV! “I guess he finally made something of himself” said the dumb young kid from West Virginia.

I finished high school and charged my way through college. I took calculus-based physics back in 1984 and have been pissed off ever since. There were two brutal lessons I disliked in severe kinds of ways.

The first was entropy and the heat death of the universe. It wonโ€™t affect me directly or indirectly, Iโ€™ll never see it – it is something I could have understood and went about my life. But nope โ€“ a major depletion of serotonin and dopamine creeped into my autism-riddled brain. Greatly depressing.

The second one REALLY pissed me off and it is what pushed me down this path. In a greatly oversimplified description, in physics, we can know the velocity and vector of a particle, but we canโ€™t know the temperature. Or, we can know the temperature and velocity, but not the vector. I get the realities of observational thermodynamics, but that doesnโ€™t mean I am happy about it.

There has to be a way to know all three โ€“ there has to be a path to figure all of this out. We are taught that we are NOT able to know all three, but nature knows. The fabric of the universe canโ€™t exist if nature doesnโ€™t know. Physics would cease to work if nature was clueless about the properties of all objects. NOT knowing is an issue.

NOT.

Hmmm, โ€œNOT.โ€ That reminds me of something.

There is an idea there maybe -> NOT, NOR, AND, NAND plus many others added to calculus might create some interesting results.

At the time I took the physics classes, I had been studying Boolean Logic and circuit design for three years. We canโ€™t come up with a way to know all three, but maybe, just maybe, there may be a way to narrow the answer down to where these values are NOT. And thus my exploration of locative calculus (Loculus) began.

Since those sad and angry days of 1984, I have continued working on Loculus โ€“ on and off, mostly off, ever since.

The first step was to define Boolean Look-Up Tables (BLUTs) and they were a nightmare. All my ideas seemed like they were fighting me. If I change this, the model changes to that and melts down in a white-hot mess resembling Satanโ€™s taint.

โ€œIโ€™ll just set this aside for a bit,โ€ I would say after the panic attacks subsided.

This level of pearl-clutching, neurodivergent behavior would continue for decades. In 2022, I started on my fifth college degree, BS in Electrical Engineering. I just needed a few classes to complete that chore โ€“ I hated it. Online education is the worst. Donโ€™t even get me started on online testing proctors that will only speak to you in Arabic.

Yet, I survived and graduated while swearing that I am done with academics. I warned my friends and coworkers, โ€œif you ever see me on another college website, I have one word for you โ€“ chloroform.โ€

Bastards let me down.

I keep pen and paper by my bedside in case I dream something noteworthy โ€“ long story. Suffice it to say, a couple of months after I finished my last EE class, I must have had some sort of crazed dream because I woke up with this written on my nightstandโ€ฆ


โ€ฆ and on that gayly pink post-in note was the key I kept missing, the Loculus Object.
After furiously writing day and night for who knows how long, I now have seven autism-powered papers pre-pub ready, I have begun looking for PhD By Publication opportunities.

IF I get these papers successfully published, and IF I find a school willing to listen to my madness, and IF they bestow a degree upon me, I will make a road trip to Ithaca, NY where Carl Saganโ€™s headstone lies. There I will recite my Loculus abstract.โ€จโ€จ

That will close the chapter on the promise I made to Carl, all those many years ago.

Seems like โ€œbillionsโ€ฆโ€

Photographer Unknown

The Big One

๐•ƒ=Vz

That turns out to be the key to the whole of my idea of locative calculus; Loculus for short.

I finally have the outline of the 5 part series of research papers.

Loculus I โ€” Foundations and Arithmetic of State-Bearing Variables
Loculus II โ€” Algebra, Functions, and Domains in State-Bearing Mathematics
Loculus III โ€” Geometry, Trigonometry, and Vector Analysis in State-Bearing Mathematics
Loculus IV โ€” Differential and Integral Calculus of State-Bearing Variables
Loculus V โ€” Ordinary Differential Equations and Dynamical Systems in State-Bearing Mathematics

Anyway, writing continues on my PhD – I need something to do after work and on weekends.

Carnival Of Mathematics 206 โ€“ July 2022

Welcome to the 206th Carnival and my third time hosting the event.

To see past entries in the Carnival Of Mathematics and future scheduled hosts, please visit The Aperiodical.

I am honored to again host the Carnival of Mathematics! I learn so much from hosting; things I usually wouldnโ€™t be exposed to are jam packed into every Carnival Of Mathematics post. Be sure to dig into the archive!.

Here are the entries. Enjoy!

Math Vs Culture

by Storm Bear Williams

A short little rant about all of those forgotten mathematicians from antiquity that hardly ever get the credit they deserve.


Mom Does Math

by Dr. Alyssa J Foss

Iโ€™m on the life long journey to recover from math-phobia. Which is why I have thrown myself into the math world head first! Next to momming and mathing, writing is my favorite thing. So, Iโ€™m trying to do the blog thing. This is my first post from September.

LINK

Editor’s Note: Her blog, Math Rehab, is really well written. Very worth the read!


What Is the Pascal Matrix?

By Nick Highham

In mathematics, particularly matrix theory and combinatorics, a Pascal matrix is a (possibly infinite) matrix containing the binomial coefficients as its elements. It is thus an encoding of Pascal’s triangle in matrix form. There are three natural ways to achieve this: as a lower-triangular matrix, an upper-triangular matrix, or a symmetric matrix.

Here Professor Higham steps his way through an example.

This article is part of the โ€œWhat Isโ€ series, available from https://nhigham.com/index-of-what-is-articles/ and in PDF form from the GitHub repository https://github.com/higham/what-is.

LINK

Editor’s Note: For more on Professor Highham; Twitter, Wiki, Google Scholar, Blog.


Ivan Guo: Financial models of the future

by Dr Ivan Guo

How can a 240-year-old logistics problem be used in quantitative finance? Dr Ivan Guo’s research lies predominantly in the areas of stochastic control and financial mathematics. In this interview with the Sydney Mathematical Research Institute, Ivan describes how stochastic transport theory applies in financial maths and how financial models are applied. He also debunks some misunderstandings about his field.


What does craiyon/DALLยทE mini โ€˜thinkโ€™ mathematics and mathematicians look like?

By Peter Rowlett

“You may have seen DALLยทE mini posts appearing on social media for a little while now โ€“ itโ€™s been viral for a couple of weeks, according to Know Your Meme. Itโ€™s an artificial intelligence model for producing images, operating as an open-source project mimicking the DALLยทE system from company OpenAI but trained on a smaller dataset.”

Peter Rowlett presents a good introduction to DALL-E and offers several awesome examples.

LINK


Two Saturday Morning Breakfast Cereal Cartoons

by Zach Weinersmith

The first fun cartoon is titled “Incomplete”. LINK

The second is titled “Mathematics” and we can all feel this one down in our bones! LINK

Editor’s Note: You can find out more about the author here: Twitter, Facebook, Tumblr, Patreon


G0lomb

by Sneak Thief

One of my (many) interest areas is in algorithmic music composition. But it was not until @CarnivalOfMath mentioned that content didn’t need to be blogs, that I thought to submit this.

This piece is one where I use the Golomb ruler to determine the bar position, and length, of notes in a composition. I wrote a short piece of JavaScript which creates the data, incorporate it with a MIDI library which exports a MIDI file, that in turn can be loaded into a sequencer. I then assign each note to specific sound, based on their duration and what my ear tells me is good. (Being a synth-based composer, some sounds change a lot over time and are therefore better for long notes.)

The notes are always determined by me, a human, to match a particular key signature (to they sound in tune) and varied according to previous trial runs of the algorithm. So, for example, if notes of length 10 and 11 do not appear simultaneously I can assign them the notes E and F which (normally) do not sound good together. Similarly, I try to ensure that the start and end of the composition include notes which give an element of “resolution” which is prevalent in most western music. (Just because it’s based on maths, doesn’t mean it has to _sound_ that way!)

Finally, I sprinkle additional sounds generated by a different algorithm.

Click the image within the link to see a representation of the music, and 
you’ll clearly see the ruler being used.

LINK