Uber Mensch

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Aspiring to be a rational thinking machine

Aspiring to be a rational thinking machine

23 followers

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At last -a textbook on category theory for scientists! And it's free!

• David Spivak,

"This course is an attempt to extol the virtues of a new branch of mathematics, called

"I believe that the language and toolset of category theory can be useful throughout science. We build scientific understanding by developing models, and category theory is the study of basic conceptual building blocks and how they cleanly fit together to make such models. Certain structures and conceptual frameworks show up again and again in our understanding of reality. No one would dispute that vector spaces are ubiquitous. But so are hierarchies, symmetries, actions of agents on objects, data models, global behavior emerging as the aggregate of local behavior, self-similarity, and the effect of methodological context."

"Some ideas are so common that our use of them goes virtually undetected, such as set-theoretic intersections. For example, when we speak of a material that is both lightweight and ductile, we are intersecting two sets. But what is the use of even mentioning this set-theoretic fact? The answer is that when we formalize our ideas, our understanding is almost always clarified. Our ability to communicate with others is enhanced, and the possibility for developing new insights expands. And if we are ever to get to the point that we can input our ideas into computers, we will need to be able to formalize these ideas first."

"It is my hope that this course will offer scientists a new vocabulary in which to think and communicate, and a new pipeline to the vast array of theorems that exist and are considered immensely powerful within mathematics. These theorems have not made their way out into the world of science, but they are directly applicable there. Hierarchies are partial orders, symmetries are group elements, data models are categories, agent actions are monoid actions, local-to-global principles are sheaves, self-similarity is modeled by operads, context can be modeled by monads."

David Spivak asks readers from different subjects for help in finding new ways to apply category theory to those subjects. And that's the right attitude to take when reading this book. I've found category immensely valuable in my work. But it took

Thanks to +Charlie Clingen for pointing this out!

• David Spivak,

*Category Theory for Scientists*, http://arxiv.org/abs/1302.6946."This course is an attempt to extol the virtues of a new branch of mathematics, called

**category theory**, which was invented for powerful communication of ideas between different fields and subfields within mathematics. By powerful communication of ideas I actually mean something precise. Different branches of mathematics can be formalized into categories. These categories can then be connected together by functors. And the sense in which these functors provide powerful communication of ideas is that facts and theorems proven in one category can be transferred through a connecting functor to yield proofs of an analogous theorem in another category. A functor is like a conductor of mathematical truth.""I believe that the language and toolset of category theory can be useful throughout science. We build scientific understanding by developing models, and category theory is the study of basic conceptual building blocks and how they cleanly fit together to make such models. Certain structures and conceptual frameworks show up again and again in our understanding of reality. No one would dispute that vector spaces are ubiquitous. But so are hierarchies, symmetries, actions of agents on objects, data models, global behavior emerging as the aggregate of local behavior, self-similarity, and the effect of methodological context."

"Some ideas are so common that our use of them goes virtually undetected, such as set-theoretic intersections. For example, when we speak of a material that is both lightweight and ductile, we are intersecting two sets. But what is the use of even mentioning this set-theoretic fact? The answer is that when we formalize our ideas, our understanding is almost always clarified. Our ability to communicate with others is enhanced, and the possibility for developing new insights expands. And if we are ever to get to the point that we can input our ideas into computers, we will need to be able to formalize these ideas first."

"It is my hope that this course will offer scientists a new vocabulary in which to think and communicate, and a new pipeline to the vast array of theorems that exist and are considered immensely powerful within mathematics. These theorems have not made their way out into the world of science, but they are directly applicable there. Hierarchies are partial orders, symmetries are group elements, data models are categories, agent actions are monoid actions, local-to-global principles are sheaves, self-similarity is modeled by operads, context can be modeled by monads."

David Spivak asks readers from different subjects for help in finding new ways to apply category theory to those subjects. And that's the right attitude to take when reading this book. I've found category immensely valuable in my work. But it took

*effort*to learn category theory and see how it can apply to different subjects. People are just starting to figure out these things, so don't expect instant solutions to the problems in your own favorite field. But Spivak does the best job I've seen so far at explaining category theory as a*general-purpose tool for thinking clearly*.Thanks to +Charlie Clingen for pointing this out!

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A PhD burnout "testimonial".

Its follow-up discussion on HN:

http://news.ycombinator.com/item?id=5098873

(HT +Marcin Kotowski for showing it to me.)

Its follow-up discussion on HN:

http://news.ycombinator.com/item?id=5098873

(HT +Marcin Kotowski for showing it to me.)

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How is poverty measured? What is the "poverty line"? Watch this short video to find out.

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An important new dataset collection just opened up. And looking at the "recent updates" section it seems like it won't just be another "dead" collection but will be actively maintained.

This is great news!

This is great news!

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This Thursday Dec 13th, 8.30-11.30am we'll have my Stanford Machine Learning class' poster session. With over 250 posters, we're 2/3 the size of the NIPS conference, but compressed into 3 hours. With ~575 students presenting, this will be the biggest machine learning event of the year in the Bay Area. Feel free to reshare. Come see the cool projects the students have done!

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Internet Archive - donate to preserve Internet against tides of time http://archive.org/donate/ (I gave $100, and I'm only a PhD student)

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Try this really good graphing calculator inside your browser

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Created a Google+ page for MOOC

People are welcome to contribute

People are welcome to contribute

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