Profile cover photo
Profile photo
Denise Case
22,634 followers -
The secret of life is two words: not always so :)
The secret of life is two words: not always so :)

22,634 followers
About
Posts

Post has attachment
Add a comment...

Post has attachment
Add a comment...

Post has shared content
Sunshine laws. Legislation that permits an industry to operate in secret is an acknowledgement that information would require change.

#factory #farming #dominion

#Animal from the Middle English: the noun from Latin animal, based on Latin animalis ‘having breath’ from anima ‘breath’; the adjective via Old French from Latin animalis

https://youtu.be/LpDJlEQsDoA
Add a comment...

Post has shared content
If this really continues, it is a very bad sign and will cause some major shifts in weather patterns. This could have major economic and societal impact.

And for those who keep saying that climate change is false - this here is one of the nasty changes that were predicted by the climate models with climate change. This may be one of the most drastic signs that those models were more correct and more terrifying than even some scientists hoped.

https://www.washingtonpost.com/news/energy-environment/wp/2018/04/11/the-oceans-circulation-hasnt-been-this-sluggish-in-1000-years-thats-bad-news/
Add a comment...

Post has shared content
Category Theory with +John Baez - looks interesting. :)
Applied Category Theory - An Online Course

Two weeks ago I started teaching an online course based on this free book:

• Brendan Fong and David Spivak, Seven Sketches in Compositionality: An Invitation to Applied Category Theory, http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf.

It's eating up the time I used to spend on G+. But I'm happy with that, because over 250 people have registered, and a bunch of them are very energetic. It's exciting!

Four days I week I write short "lectures" on the book. If you take the course you can read those lectures, read the book, try the exercises in the book and the puzzles I create, and discuss everything with me and the other students! The best part of the course, in my opinion, is the conversations. People are starting to dream up projects to work on together.

If this sounds interesting, go here and register in the box at upper left:

https://forum.azimuthproject.org/discussion/1717/welcome-to-the-applied-category-theory-course

Use your full real name as your username, with no spaces. I will get back to you, so use a working email address. You can move through the course at your own pace: all the discussions can go on indefinitely.

Brendan Fong was my grad student; now he's doing a postdoc at MIT with David Spivak. They're at the cutting edge of applied category theory, and I"m having a lot of fun working through their book by teaching it. Here is the preface to their book, just so you can get an idea of what it’s like.

Preface

Category theory is becoming a central hub for all of pure mathematics. It is unmatched in its ability to organize and layer abstractions, to find commonalities between structures of all sorts, and to facilitate communication between different mathematical communities. But it has also been branching out into science, informatics, and industry. We believe that it has the potential to be a major cohesive force in the world, building rigorous bridges between disparate worlds, both theoretical and practical. The motto at MIT is mens et manus, Latin for mind and hand. We believe that category theory—and pure math in general—has stayed in the realm of mind for too long; it is ripe to be brought to hand.

Purpose and audience

The purpose of this book is to offer a self-contained tour of applied category theory. It is an invitation to discover advanced topics in category theory through concrete real-world examples. Rather than try to give a comprehensive treatment of these topics—which include adjoint functors, enriched categories, proarrow equipments, toposes, and much more–we merely provide a taste. We want to give readers some insight into how it feels to work with these structures as well as some ideas about how they might show up in practice.

The audience for this book is quite diverse: anyone who finds the above description intriguing. This could include a motivated high school student who hasn’t seen calculus yet but has loved reading a weird book on mathematical logic they found at the library. Or a machine learning researcher who wants to understand what vector spaces, design theory, and dynamical systems could possibly have in common. Or a pure mathematician who wants to imagine what sorts of applications their work might have. Or a recently-retired programmer who’s always had an eerie feeling that category theory is what they’ve been looking for to tie it all together, but who’s found the usual books on the subject impenetrable.

For example, we find it something of a travesty that in 2018 there seems to be no introductory material available on monoidal categories. Even beautiful modern introductions to category theory, e.g. by Riehl or Leinster, do not include anything on this rather central topic. The basic idea is certainly not too abstract; modern human intuition seems to include a pre-theoretical understanding of monoidal categories that is just waiting to be formalized. Is there anyone who wouldn’t correctly understand the basic idea being communicated in the diagram below?

Many applied category theory topics seem to take monoidal categories as their jumping off point. So one aim of this book is to provide a reference—even if unconventional—for this important topic.

We hope this book inspires both new visions and new questions. We intend it to be self-contained in the sense that it is approachable with minimal prerequisites, but not in the sense that the complete story is told here. On the contrary, we hope that readers use this as an invitation to further reading, to orient themselves in what is becoming a large literature, and to discover new applications for themselves.

This book is, unashamedly, our take on the subject. While the abstract structures we explore are important to any category theorist, the specific topics have simply been chosen to our personal taste. Our examples are ones that we find simple but powerful, concrete but representative, entertaining but in a way that feels important and expansive at the same time. We hope our readers will enjoy themselves and learn a lot in the process.

How to read this book

The basic idea of category theory—which threads through every chapter—is that if one pays careful attention to structures and coherence, the resulting systems will be extremely reliable and interoperable. For example, a category involves several structures: a collection of objects, a collection of morphisms relating objects, and a formula for combining any chain of morphisms into a morphism. But these structures need to cohere or work together in a simple commonsense way: a chain of chains is a chain, so combining a chain of chains should be the same as combining the chain. That’s it!

We will see structures and coherence come up in pretty much every definition we give: “here are some things and here are how they fit together.” We ask the reader to be on the lookout for structures and coherence as they read the book, and to realize that as we layer abstraction on abstraction, it is the coherence that makes everything function like a well-oiled machine.

Each chapter in this book is motivated by a real-world topic, such as electrical circuits, control theory, cascade failures, information integration, and hybrid systems. These motivations lead us into and through various sorts of category-theoretic concepts.

We generally have one motivating idea and one category-theoretic purpose per chapter, and this forms the title of the chapter, e.g. Chapter 4 is “Collaborative design: profunctors, categorification, and monoidal categories.” In many math books, the difficulty is roughly a monotonically-increasing function of the page number. In this book, this occurs in each chapter, but not so much in the book as a whole. The chapters start out fairly easy and progress in difficulty.

The upshot is that if you find the end of a chapter very difficult, hope is certainly not lost: you can start on the next one and make good progress. This format lends itself to giving you a first taste now, but also leaving open the opportunity for you to come back at a later date and get more deeply into it. But by all means, if you have the gumption to work through each chapter to its end, we very much encourage that!

We include many exercises throughout the text. Usually these exercises are fairly straightforward; the only thing they demand is that the reader’s mind changes state from passive to active, rereads the previous paragraphs with intent, and puts the pieces together. A reader becomes a student when they work the exercises; until then they are more of a tourist, riding on a bus and listening off and on to the tour guide. Hey, there’s nothing wrong with that, but we do encourage you to get off the bus and make contact with the natives as often as you can.
Photo
Add a comment...

Post has shared content

Post has shared content
Discovery of a possible body-wide shock-absorbing organ may have gone undetected. Small, fluid-filled tubes collapse when not in use - but may provide a conduit for cancer cells and other material while in service.

#science #human #anatomy #biology
Wow.

A newly discovered network of fluid-filled channels in the human body may be a previously-unknown organ, and it seems to help transport cancer cells around the body.
Add a comment...

Post has attachment
The brain-changing benefits of exercise.
Add a comment...

Post has shared content
Add a comment...
Wait while more posts are being loaded