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 232 – October 2024

Welcome to the 232nd Carnival and my fourth 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!


From Alice To The Mad Hatter: The Road To A PhD

By Storm Bear Williams

Everyone’s path to a PhD is different. Mine is more madcap than others.

LINK to the mayhem.

Editor’s Note: Please upload sanity. Thank you.


Double Maths First Thing

By Colin Beveridge.

Double Maths First Thing is Colinโ€™s weekly news bulletin. Although itโ€™s more like a nerfpelletin, honestly.

Hello! My name is Colin and I am a mathematician on a mission to help everyone find the joy and delight in figuring things out.

LINK

Editorโ€™s Note: Colin is already published four entries!


XKCD Game Theory Question

By Mark Dominus

This post is about the bottom center panel, โ€œGame Theory final examโ€.

I don’t know much about game theory and I haven’t seen any other discussion of this question. But I have a strategy I think is plausible and I’m somewhat pleased with.

(I assume that answers to the exam question must be real numbers โ€” not โˆžโˆž โ€” and that โ€œaverageโ€ here is short for ‘arithmetic mean’.)

First, I believe the other players and I must find a way to agree on what the average will be, or else we are all doomed. We can’t communicate, so we should choose a Schelling point and hope that everyone else chooses the same one. Fortunately, there is only one distinguished choice: zero. So I will try to make the average zero and I will hope that others are trying to do the same.

LINK

Editor’s Note: Inspired from the XKCD web cartoon.


Planar point sets with forbidden four-point patterns and few distinct distances

by Terence Tao

Iโ€™ve just uploaded to the arXiv my paper  โ€œPlanar point sets with forbidden 4- point patterns and few distinct distanceโ€œ. This (very) short paper was a byproduct of my recent explorations of the Erdรถs problem website in recent months, with a vague emerging plan to locate a suitable problem that might be suitable for some combination of a crowdsourced โ€œPolymathโ€ style project and/or a test case for emerging AI tools. The question below was one potential candidate; however, upon reviewing the literature on the problem, I noticed that the existing techniques only needed one additional tweak to fully resolve the problem. So I ended up writing this note instead to close off the problem.

LINK

Editor’s Note: Terance’s website if loaded with his work in mathematics.


Mathematics With Friends

by Ioanna Georgiou and illustrated by Asuka Young

“Mathematics with Friends” is a blog that takes a
maths-related dialogue from the Friends TV series every month and explores the
maths mentioned further. It comes with its own characters and amazing
illustrations.

LINK to the latest episode


Books That Are About Maths, But Not About Teaching It

By Tom Briggs

In the spirit of getting straight to the point without providing my entire life history, please click below for a list of books that are about maths, but not about teaching it. Read beyond the link if you’d like a bit of context.

The list has been put together at The StoryGraph[2]: it can be browsed without creating an account and it can be searched, sorted and filtered, which I thought would be helpful as there are over 160 books.

Link to the article.

LINK to the exhaustive list.


The end (or not?)

by Peter Cameron

This is an update from Peter on his retirement from St. Andrews and where he will go from there.

Yes, there is life after retirement. Don’t fret, it will all turn out ok.

LINK

OTHER LINK: Peter also has a nice article on the possibilities of a new mathematics open access journal. Could there be hope ahead?


Saying Goodbye to Tom Blyth

by Peter Cameron

A respectful story about the passing of a colleague. These things are never easy. Also an interesting correlation with Paul Halmos, the Hungarian-American mathematician. The full story is in the link below.

LINK


Whatโ€™s your mathematical style?

By Writing and Illustrations by Ben Orlin

Math teacher Ben Orlin writes and draws the (aptly named) blog Math With Drawings and is the author of a new book, Math for English Majors: A Human Take on the Universal Language. To mark its publication, he devised this entertaining accompanying quiz. You can read the Ars interview with Orlin here.

Math, we like to say, is math. It often seems that mathematics is something beyond our controlโ€”something unyielding, universal, inhuman.

But is it really?

Yes and no. Math may be the language of the cosmos, but itโ€™s also a human language, with its own quirky etymologies, classic literature, and hilarious regional accents. In fact, you could say that math has as many stylesโ€”as many idiolectsโ€”as it has speakers.

LINK

Editor’s Note: I loved this article!


Viterboโ€™s conjecture was refuted by Pazit Haim-Kislev and Yaron Ostrover

by Gil Kalai

Claude Viterboโ€™s 2000 volume-capacity conjecture asserts that the Euclidean (even dimensional) ball maximizes  (every) symplectic capacity  among convex bodies of the same volume. In the recent paper A Counterexample to Viterboโ€™s ConjecturePazit Haim-Kislev and Yaron Ostrover disproved the conjecture. 

There is some background on symplectic geometry in this post.  

LINK

Posted from Gil Kalai’s blog which is very bookmark-worthy

Editor’s Note: This deserves applause I think!


Philip Hensloweโ€™s Card Trick

by Colin Beveridge

In a dimly-lit tavern on the South Bank of the Thames, Philip Henslowe โ€” builder and owner of the Rose Theatre โ€” is celebrating the success of Shakespeareโ€™s latest blockbuster, Henry VI Part I, among the cutthroats, actors and other lowlife of London. He spreads thirteen playing cards on a table in a circle. โ€œPick a card,โ€ he grins. โ€œAny card.โ€

And this article is complete with cryptic, vintage explanations!

LINK

Wiki Entry for Philip Henslowe

Editor’s Note: Now I want to visit the Dulwich College Archive!


Book Review: The Best Writing on Mathematics 2021

by Ioanna Georgiou

Mircea Pitici (Editor)
PRINCETON UNIVERSITY PRESS 2022, 320 PAGES
PRICE (PAPERBACK) ยฃ20.00 ISBN 978-0-691-22570-8

This book contains articles written in 2020. The editor speaks of the difficulties accessing libraries and resources, something we are all a bit too familiar with. Here I will comment on each of the twenty-six articles selected as the โ€˜bestโ€™ and draw an overall conclusion at the end.

LINK

Editor’s Note: We have to start doing a better job in archiving and making available the collective of human knowledge to everyone. The defunding of libraries has to stop. The abusive research publication industry has to stop.

What is SETI (Search For Extraterrestrial Intelligence)? | SciWorx Astronomy

The search for extraterrestrial intelligence (SETI) is a collective term for scientific searches for intelligent extraterrestrial life, for example, monitoring electromagnetic radiation for signs of transmissions from civilizations on other planets.

Scientific investigation began shortly after the advent of radio in the early 1900s, and focused international efforts have been going on since the 1980s. In 2015, Stephen Hawking and Russian billionaire Yuri Milner announced a well-funded effort called Breakthrough Listen.

Witness To Extinction: The Threat To Monarch Butterflies Of Pismo Beach California | SciWorx Biology

As a child of the 1960s, I vividly recall fields of Monarch butterflies (Danaus plexippus) feasting on the milkweed growing on my great-grandparents farm in West Virginia. Every year, they would come back, mate, lay their eggs on the underside of the milkweed leaves, hatch into caterpillars, cocoon themselves and then pop out as amazing butterflies. Once in their butterfly form, they would fly north until they reached their summer destination somewhere in Canada to repeat the process for their winter trip to Mexico – then start the whole process over again.

Never once, as a child, did I ever think that these creatures would become extinct in my lifetime.

Well, that is happening now.


A case in point; Pismo Beach, California.

The butterflies I grew up with in West Virginia, on the East Coast of North America, had a migration route from Canada to Mexico. The United States was just a rest stop. This is true for most of the Monarch butterflies EAST of the Rocky Mountains. For the most part, the Monarchs to the WEST of the Rockies migrate from Canada to coastal Southern California. There they winter over in eucalyptus and cypress trees in the moist sea air along the rocky California coast. 

Well, that is what they did do. At the Pismo State Beach Monarch Butterfly Grove, the Monarch population has been shattered. On December 14th of 2020, I visited this locally praised park, expecting to see an amazing colony of Monarchs, huddled together for warmth in the gently swaying leaves of the trees. 

As recently as 1990, park officials counted 230,000 Monarch butterflies nestled in the Pismo grove. On my trip I counted 15โ€ฆ not 15 THOUSAND, just just 15. Fifteen. 15.0 Monarch butterflies. That should sent off alarm bells the world over, but it didnโ€™t. Town officials loved using the butterfly grove as a tourist attraction to generate income for their tax base, but they are not taking the necessary steps to save the species.

The delicate grove has a very busy road and train track on one side, a RV campground on another side and a trailer park on the other. The city did plant some Monarch-friendly plants – they are sandwiched in-between the busy road and a pair of leaking Port-A-Johns. Seriously.

The grove has not been expanded, nor has any protections been added. There is no buffer area between the grove and the local overcrowded population. The only money the town seems to have spent for the grove has been for travel brochures and other marketing materials. โ€œCome See The Butterfliesโ€ the headlines read. โ€œBefore They Are Goneโ€ has been conveniently left out.

To help inform about what the Monarchs are up against, letโ€™s talk about the biological cycle of the Monarchs for a bit.

When the Monarch leaves its winter grove (either Coastal California or Mexico), they fly north to a source of milkweed that their ancestors visited. Once their, they will feed, mate, lay eggs on the milkweed and die. The eggs hatch, the caterpillars gorge on the milkweed, build a cocoon, metamorphose into a Monarch, eat more milkweed and then they navigate their way further north to another ancestral breeding area and repeat the process until they reach their final destination in Canada. The Monarchs that leave Pismo Beach never see the final destination, only their ancestors do. Not one single butterfly makes the complete round trip.

There is an odd caveat to that.

Once the Monarchs reach their final summer destination, they again mate, lay eggs as usual, but these butterflies go through a process of diapause. They are larger, more hearty and able to store more energy. These super Monarchs make the whole trip to their overwinter locations without the egg laying repetition we see on the migration northward.

This migration from south to north to back south has been repeated for probably around 175 MILLION years. And we are watching the species ground to an unfortunate halt.

During that 175 million year period, the Monarchs had a more or less static environment to live, grow and thrive in North America. Even with the occasional glaciation on the continent, they survived. Now they are not. 

There are innumerable obstacles in the way for the survival of Monarchs. These threats are real and no one, no government is wiling to do what it takes to rescue the species.

First off there is the huge factor of climate change. As the planet warms, the delicate synchronous biological cycle the Monarch depends on has been disrupted. When the biological clock tells the Monarch to leave its southern home, it flies north and the milkweed in the north may not be at the same maturity level the plants had before climate change. The milkweedโ€™s cycle of sprout, grow, bloom and seed is now such that these fields the Monarchs depend on no longer matches the Monarchs arrival time. So many times the Monarch arrives in a field its ancestors visited no longer has milkweed at full maturity, the plants could be too juvenile or wilting, putting extinction pressures on the species.

Another factor is habitat loss. Some of the fields of milkweed have been plowed under for the sake of urban development, mining, logging, or industrial farming. As humans move in, the life cycles for all species are disrupted and sometimes they are disrupted to the point that it invites extinction.

Another type of habitat loss is related to climate change. As the weather becomes hotter, soil moisture goes down. This invites abnormal levels of wildfires. As the wildfires sweep the land, it consumes wildlife habitat. In 2020, the west coast of North America was hit very hard. 4.2 million acres of land was burned in California alone.

The last major factor that is fueling the extinction of the Monarch is pollution. Above and beyond the toxins in the air that are continually pumped into the atmosphere are the insane amount of pesticides and herbicides used in modern industrial farming.

One evolutionary trick the Monarch uses for survival against predators is the aforementioned milkweed. For most animals, milkweed is poisonous if not deadly. The milkweed contains a chemical called cardenolide glycoside. Cardenolide glycoside is a chemical that does not effect Monarchs. And since they need milkweed for egg laying and for food, they are full of cardenolide glycoside. Animals have learned to stay away from this colorful species of nymphalidae thus allowing the Monarch to fly great distances with little predator interaction.

Farmers hate milkweed and spend enormous amounts of resources to rid their farms of it. They donโ€™t want their livestock poisoned nor do they want their crops competing with milkweed for water or nutrients. The herbicides kill off the milkweed and the pesticides kill off all the insects, including the helpful species such as Monarchs.

So why do we have all this fuss over a simple butterfly? Is it just because they are pretty? No. The answer is a big, huge no.

Humans are tied at the hip and our existence hangs mercilessly between two tiny species. One is plankton. Half of the worldโ€™s oxygen comes from oceanic plankton. Without them humans suffocate. The other are species of pollinators. Without insects that pollenate plants like vegetables, grains and fruit, we die of starvation. Moths and butterflies are prolific pollinators. Behind species of bees, Monarch butterflies are among the SECOND largest insect group of pollinators.

We are all witnesses to extinction. As we watch the extinction of the Monarch butterflies, with shrugging slouched shoulders, we are also witnessing the extinction of ourselves.

It is on us to fix this. It is on all of us.

Storm Bear Williams

Copyright 2021 ยฉ By Storm Bear Williams. All rights reserved.

@sciworx on most social media services.

The Day I Met Carl Sagan

Carl Sagan

I was born in 1963 and grew up on large doses of Apollo. Anything and everything that revolved around NASA, I consumed it with a hunger only a geek could produce. During the 70s my family lived in West Virginia and we would take these trips to various places in the state; Blackwater Falls, Dolly Sods, Pipestem – just about anyplace where we could hike, do a bit of fishing and pitch a tent.

On one such trip we took a wrong turn and happened upon the Green Bank Radio Observatory. My head exploded. I had no clue such a facility was in my home state.

There was a tour offered so we stopped in and took a short bus tour of the facility – the guide pointing out the frolicking deer, the softball field and the radio dishes as we went.

The last stop on the tour was in a little meeting room where we watched a short film and heard a presentation. The presenter, with a very distinctive voice, introduced a brand new film titled โ€œThe Power Of 10.โ€ After the film, he gave us a short introduction to a program called SETI. If my young kid brain wasnโ€™t blown by then it was blown now. I had never even considered that other civilizations could be using radio. At that period in my life I was an avid ham radio nerd and knew it was possible to pick up on interstellar signals. Only in ham radio, we called such signals โ€œnoise.โ€ Whoever that guy was on the last stop of the tour gave me a lot to ponder.

A couple years later a new TV show about space titled โ€œCosmosโ€ was announced and I was thrilled! Like the geek that I was, I actually had a notebook so I could take notes as the show went along. As the narration started I instantly knew the voice. Loโ€™ and behold, here was that same guy from Green Bank now on television telling us how Earth was the shore of the cosmic ocean.

So, I met Carl Sagan before he was โ€œCarl Sagan.โ€ I remember at the presentation he was enthusiastic and actually engaged with the tourists. Even then, his passion for teaching was memorable.

I really lucked out. I know this was not his day job. I am sure he was just at the observatory and couldnโ€™t pass up a chance to give a new group of people a new insight to the stars.