## Diversity Workshop at UCR

14 October, 2019

We’re having a workshop to promote diversity in math here at UCR:

Riverside Mathematics Workshop for Excellence and Diversity, Friday 8 November 2019, U. C. Riverside. Organized by John Baez, Weitao Chen, Edray Goins, Ami Radunskaya, and Fred Wilhelm.

It’s happening right before the applied category theory meeting, so I hope some of you can make both… especially since the category theorist Eugenia Cheng will be giving a talk!

Three talks will take place in Skye Hall—home of the math department—starting at 1 pm. After this we’ll have refreshments and an hour for students to talk to the speakers. Starting at 6 pm there will be a reception across the road at the UCR Alumni Center, with food and a panel discussion on the challenges we face in promoting diversity at U.C. Riverside.

All the talks will be in Skye 282:

• 1:00–1:50 p.m. Abba Gumel, Arizona State University.

Some models for enhancing diversity and capacity-building in STEM education in under-represented minority communities.

STEM (science, technology, engineering and mathematics) education is undoubtedly the necessary bedrock for the development and sustenance of the vitally-needed knowledge-based economy that fuels and sustains the development of modern nations. Central to STEM education are, of course, the mathematical science … which are the rock-solid foundation of all the natural and engineering sciences. Hence, it is vital that all diverse populations are not left behind in the quest to build and sustain capacity in the mathematical sciences. This talk focuses on discussion around a number of pedagogic and mentorship models that have been (and are being) used to help increase diversity and capacity-building in STEM education in general, and in the mathematical sciences in particular, in under-represented minority populations. Some examples from Africa, Canada and the U.S. will be presented.

• 2:00–2:50. Marissa Loving, Georgia Tech.

Where do I belong? Creating space in the math community.

I will tell the story of my mathematical journey with a focus on my time in grad school. I will be blunt about the ups and downs I have experienced and touch on some of the barriers (both structural and internalized) I have encountered. I will also discuss some of the programs and spaces I have helped create in my quest to make the mathematics community into a place where folks from historically under-represented groups (particularly women of color) can feel safe, seen, and free to devote their energy to their work. If you have ever felt like you don’t belong or worried that you have made others feel that way, this talk is for you.

• 3:00–3:50 p.m. Eugenia Cheng, School of the Art Institute of Chicago.

Inclusion–exclusion in mathematics and beyond: who stays in, who falls out, why it happens, and what we could do about it.

The question of why women and minorities are under-represented in mathematics is complex and there are no simple answers, only many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives “ingressive” and “congressive” as a new dimension to shift our focus away from masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women. Moreover I will show that abstract mathematics is applicable to working towards a more inclusive, congressive society in this politically divisive era. This goes against the assumption that abstract math can only be taught to high level undergraduates and graduate students, and the accusation that it is removed from real life.

• 4:00–4:30 p.m. Refreshments in Skye 284.

• 4:30–5:30 p.m. Conversations Between Speakers & Students, Not Faculty, in Skye 284.

• 6:00–6:45 p.m. Reception with Food at the Alumni Center.

• 6:45 – 7:45 p.m. Panel Discussion at Alumni Center with Alissa Crans, Jose Gonzalez and Paige Helms, moderated by Edray Goins.

## Climate Technology Primer (Part 2)

13 October, 2019

Here’s the second of a series of blog articles:

• Adam Marblestone, Climate technology primer (2/3): CO2 removal.

The first covered the basics of climate science as related to global warming. This one moves on to consider technologies for removing carbon dioxide from the air.

I hope you keep the following warning in mind as you read on:

I’m focused here on trying to understand the narrowly technical aspects, not on the political aspects, despite those being crucial. This is meant to be a review of the technical literature, not a political statement. I worried that writing a blog purely on the topic of technological intervention in the climate, without attempting or claiming to do justice to the social issues raised, would implicitly suggest that I advocate a narrowly technocratic or unilateral approach, which is not my intention. By focusing on technology, I don’t mean to detract from the importance of the social and policy aspects.

The technological issues are worth studying on their own, since they constrain what’s possible. For example: to draw down as much CO2 as human civilization is emitting now, with trees their peak growth phase and their carbon stored permanently, could be done by covering the whole USA with such trees.

## Foundations of Math and Physics One Century After Hilbert

10 October, 2019

I wrote a review of this book with chapters by Penrose, Witten, Connes, Atiyah, Smolin and others:

• John Baez, review of Foundations of Mathematics and Physics One Century After Hilbert: New Perspectives, edited by Joseph Kouneiher, Notices of the American Mathematical Society 66 no. 11 (November 2019), 1690–1692.

It gave me a chance to say a bit—just a tiny bit—about the current state of fundamental physics and the foundations of mathematics.

## Quantales from Petri Nets

6 October, 2019

A referee pointed out this paper to me:

• Uffe Engberg and Glynn Winskel, Petri nets as models of linear logic, in Colloquium on Trees in Algebra and Programming, Springer, Berlin, 1990, pp. 147–161.

It contains a nice observation: we can get a commutative quantale from any Petri net.

I’ll explain how in a minute. But first, what does have to do with linear logic?

In linear logic, propositions form a category where the morphisms are proofs and we have two kinds of ‘and’: $\&$, which is a cartesian product on this category, and $\otimes$, which is a symmetric monoidal structure. There’s much more to linear logic than this (since there are other connectives), and maybe also less (since we may want our category to be a mere poset), but never mind. I want to focus on the weird business of having two kinds of ‘and’.

Since $\&$ is cartesian we have $P \Rightarrow P \& P$ as usual in logic.

But since $\otimes$ is not cartesian we usually don’t have $P \Rightarrow P \otimes P.$ This other kind of ‘and’ is about resources: from one copy of a thing $P$ you can’t get two copies.

Here’s one way to think about it: if $P$ is “I have a sandwich”, $P \& P$ is like “I have a sandwich and I have a sandwich”, while $P \otimes P$ is like “I have two sandwiches”.

A commutative quantale captures these two forms of ‘and’, and more. A commutative quantale is a commutative monoid object in the category of cocomplete posets: that is, posets where every subset has a least upper bound. But it’s a fact that any cocomplete poset is also complete: every subset has a greatest lower bound!

If we think of the elements of our commutative quantale as propositions, we interpret $x \le y$ as “$x$ implies $y$”. The least upper bound of any subset of proposition is their ‘or’. Their greatest lower bound is their ‘and’. But we also have the commutative monoid operation, which we call $\otimes.$ This operation distributes over least upper bounds.

So, a commutative quantale has both the logical $\&$ (not just for pairs of propositions, but arbitrary sets of them) and the $\otimes$ operation that describes combining resources.

To get from a Petri net to a commutative quantale, we can compose three functors.

First, any Petri net gives a commutative monoidal category—that is, a commutative monoid object in $\mathsf{Cat}$. Indeed, my student Jade has analyzed this in detail and shown the resulting functor from the category of Petri nets to the category of commutative monoidal categories is a left adjoint:

• Jade Master, Generalized Petri nets, Section 4.

Second, any category gives a poset where we say $x \le y$ if there is a morphism from $x$ to $y.$ Moreover, the resulting functor $\mathsf{Cat} \to \mathsf{Poset}$ preserves products. As a result, every commutative monoidal category gives a commutative monoidal poset: that is, a commutative monoid object in the category of Posets.

Composing these two functors, every Petri net gives a commutative monoidal poset. Elements are of this poset are markings of the Petri net, the partial order is “reachability”, and the commutative monoid structure is addition markings.

Third, any poset $P$ gives another poset $\widehat{P}$ whose elements are downsets of $P$: that is, subsets $S \subseteq P$ such that

$x \in S, y \le x \; \implies \; y \in S$

The partial order on downsets is inclusion. This new poset $\widehat{P}$ is ‘better’ than $P$ because it’s cocomplete. That is, any union of downsets is again a downset. Moreover, $\widehat{P}$ contains $P$ as a sub-poset. The reason is that each $x \in P$ gives a downset

$\downarrow x = \{y \in P : \; y \le x \}$

and clearly

$x \le y \; \iff \; \downarrow x \subseteq \downarrow y$

Composing this third functor with the previous two, every Petri net gives a commutative monoid object in the category of cocomplete posets. But this is just a commutative quantale!

What is this commutative quantale like? Its elements are downsets of markings of our Petri net: sets of markings such that if $x$ is in the set and $x$ is reachable from $y$ then $y$ is also in the set.

It’s good to contemplate this a bit more. A marking can be seen as a ‘resource’. For example, if our Petri net has a place in it called sandwich there is a marking 2sandwich, which means you have two sandwiches. Downsets of markings are sets of markings such that if $x$ is in the set and $x$ is reachable from $y$ then $y$ is also in the set! An example of a downset would be “a sandwich, or anything that can give you a sandwich”. Another is “two sandwiches, or anything that can give you two sandwiches”.

The tensor product $\otimes$ comes from addition of markings, extended in the obvious way to downsets of markings. For example, “a sandwich, or anything that can give you a sandwich” tensored with “a sandwich, or anything that can give you a sandwich” equals “two sandwiches, or anything that can give you two sandwiches”.

On the other hand, the cartesian product $\&$ is the logical ‘and’:
if you have “a sandwich, or anything that can give you a sandwich” and you have “a sandwich, or anything that can give you a sandwich”, then you just have “a sandwich, or anything that can give you a sandwich”.

So that’s the basic idea.

## Climate Technology Primer (Part 1)

5 October, 2019

Here’s the first of a series of blog articles on how technology can help address climate change:

• Adam Marblestone, Climate technology primer (1/3): basics.

Adam Marblestone is a research scientist at Google DeepMind studying connections between neuroscience and artificial intelligence. Previously, he was Chief Strategy Officer of the brain-computer interface company Kernel, and a research scientist in Ed Boyden’s Synthetic Neurobiology Group at MIT working to develop new technologies for brain circuit mapping. He also helped to start companies like BioBright, and advised foundations such as the Open Philanthropy Project.

Now, like many of us, he’s thinking about climate change, and what to do about it. He writes:

In this first of three posts, I attempt an outsider’s summary of the basic physics/chemistry/biology of the climate system, focused on back of the envelope calculations where possible. At the end, I comment a bit about technological approaches for emissions reductions. Future posts will include a review of the science behind negative emissions technologies, as well as the science (with plenty of caveats, don’t worry) behind more controversial potential solar radiation management approaches. This first post should be very basic for anyone “in the know” about energy, but I wanted to cover the basics before jumping into carbon sequestration technologies.

Check it out! I like the focus on “back of the envelope” calculations because they serve as useful sanity checks for more complicated models… and also provide a useful vaccination against the common denialist argument “all the predictions rely on complicated computer models that could be completely wrong, so why should I believe them?” It’s a sad fact that one of the things we need to do is make sure most technically literate people have a basic understanding of climate science, to help provide ‘herd immunity’ to everyone else.

The ultimate goal here, though, is to think about “what can technology do about climate change?”

## Applied Category Theory Meeting at UCR (Part 2)

30 September, 2019

Joe Moeller and I have finalized the schedule of our meeting on applied category theory:

Applied Category Theory, special session of the Fall Western Sectional Meeting of the AMS, U. C. Riverside, Riverside, California, 9–10 November 2019.

It’s going to be really cool, with talks on everything from brakes to bicategories, from quantum physics to social networks, and more—with the power of category theory as the unifying theme!

You can get information on registration, hotels and such here. If you’re coming, you might also want to attend Eugenia Cheng‘s talk on the afternoon of Friday November 8th.   I’ll announce the precise title and time of her talk, and also the location of all the following talks, as soon as I know!

In what follows, the person actually giving the talk has an asterisk by their name. You can click on talk titles to see abstracts of the talks.

Saturday November 9, 2019, 8:00 a.m.-10:50 a.m.

• 8:00 a.m.David I. Spivak*, Massachusetts Institute of Technology
• 9:00 a.m.Brendan Fong*, Massachusetts Institute of Technology
David I. Spivak, Massachusetts Institute of Technology
• 9:30 a.m.Gabriel C. Drummond-Cole, IBS Center for Geometry and Physics
Philip Hackney*, Department of Mathematics, University of Louisiana at Lafayette
• 10:00 a.m.
Duality of relations.
Alexander Kurz*, Chapman University
• 10:30 a.m.Tobias Fritz*, Perimeter Institute for Theoretical Physics

Saturday November 9, 2019, 3:00 p.m.-5:50 p.m.

Sunday November 10, 2019, 8:00 a.m.-10:50 a.m.

Sunday November 10, 2019, 2:00 p.m.-4:50 p.m.

## Ordovician Meteor Event

25 September, 2019

About 1/3 of the meteorites hitting Earth today come from one source: the L chondrite parent body, an asteroid 100–150 kilometers across that was smashed in an impact 468 million years ago. This was biggest asteroid collision in the last 3 billion years!

Here is an L-chondrite:

A chondrite is a stony, non-metallic meteorite that was formed form small grains of dust present in the early Solar System. They are the most common kind of meteorite—and the three most common kinds, each with its own somewhat different chemical composition, seem to come from different asteroids.

L chondrites are named that because they are low in iron. Compared to other chondrites, a lot of L chondrites have been heavily shocked—evidence that their parent body was catastrophically disrupted by a large impact.

It seems that roughly 500,000 years after this event, lots of meteorites started hitting Earth: this is called the Ordovician meteor event. Big craters from that event still dot the Earth! Here are some in North America:

Number 3 is the Rock Elm Disturbance, created when a rock roughly 170 meters in diameter slammed into what’s now Wisconsin:

It doesn’t look like much now, but imagine what it must have been like! The crater is about 6 kilometers across. It features intensely fractured quartz grain and a faulted rim.

It seems these big L-chondrite meteors hit the Earth roughly in a line:

Of course the continents didn’t look like this when the meteor hit, about 467.5 million years ago.

One big question is: was the Ordovician meteor event somehow connected to the giant increase in biodiversity during the Ordovician? Here’s a graph of biodiversity over time:

The Cambrian explosion gets all the press, but in terms of the sheer number of new families the so-called Ordovician radiation was bigger. Most animal life was undersea at the time. This is when coral reefs and other complex ocean ecosystems came into being!

There are lots of theories that try to explain the Ordovician radiation. For example, the oxygen concentration in the atmosphere and ocean soared right before the start of the Ordovician period. More than one of these theories could be right. But it’s interesting to think about the possible influence of the Ordovician meteor event.

There were a lot of meteor impacts, but the dust may have been more important. Right now, extraterrestrial dust counts for just 1% of all dust in the Earth’s atmosphere. In the Ordovician, the amount of extraterrestial dust was 1,000 – 10,000 times greater, due to the big smash-up in the asteroid belt! This may have caused the global cooling we see in that period. The Ordovician started out hot, but by the end there were glaciers.

How could this increase biodiversity? The “intermediate disturbance hypothesis” says that biodiversity increases under conditions of mild stress. Some argue this explains the Ordovician radiation.

I’d say this is pretty iffy. But it’s sure interesting! Read more here:

• Birger Schmitz et al., An extraterrestrial trigger for the mid-Ordovician ice age: Dust from the breakup of the L-chondrite parent body, Science Advances, 18 September 2019.

Another fun question is: where are the remains of the L chondrite parent body? Could they be the asteroids in the Flora family?