Jeff Jones
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#Resist
#Resist
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Jeff Jones's posts
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Driving to infinity
A long time ago, before most of you showed up on Google+, I wrote a story about infinity. It featured a character who was recruited by the US government to fight in the War on Chaos. His mission was to explore larger and larger infinities.
You can see that story in my "bigness" collection - lots of posts, each one its own little chapter.
But I keep wanting to talk about infinity - it's endlessly interesting! I keep learning more about it. Some posts here by +Refurio Anachro re-ignited my desire to write about it, and now I have. Here's the first of three articles:
https://johncarlosbaez.wordpress.com/2016/06/29/large-countable-ordinals-part-1/
If you read this, you'll learn about the two basic kinds of infinities discovered by Cantor: cardinals and ordinals. Then we'll go on a road trip through larger and larger ordinals.
The picture here shows some of the first ones we'll meet on our trip. Omega, written ω, is the first infinite ordinal:
ω = {0,1,2,3,4,5,6,7,8,9,...}
Each turn of the spiral here takes you to a higher power of omega, and if you go around infinitely many times, you reach omega to the omegath power. There are many ways to visualize this ordinal, and I explain a few.
But my road trip will take you much further than that!
In this first episode, we reach an ordinal called epsilon nought, first discovered by Cantor. In the second episode we'll go up the Feferman–Schütte ordinal. In the third we'll reach the small Veblen ordinal and even catch a glimpse of the large Veblen ordinal.
All these are countable ordinals, and you can write computer programs to calculate with them, so I consider them just as concrete as the square root of 2. And yet, they're quite mind-blowing.
#bigness
A long time ago, before most of you showed up on Google+, I wrote a story about infinity. It featured a character who was recruited by the US government to fight in the War on Chaos. His mission was to explore larger and larger infinities.
You can see that story in my "bigness" collection - lots of posts, each one its own little chapter.
But I keep wanting to talk about infinity - it's endlessly interesting! I keep learning more about it. Some posts here by +Refurio Anachro re-ignited my desire to write about it, and now I have. Here's the first of three articles:
https://johncarlosbaez.wordpress.com/2016/06/29/large-countable-ordinals-part-1/
If you read this, you'll learn about the two basic kinds of infinities discovered by Cantor: cardinals and ordinals. Then we'll go on a road trip through larger and larger ordinals.
The picture here shows some of the first ones we'll meet on our trip. Omega, written ω, is the first infinite ordinal:
ω = {0,1,2,3,4,5,6,7,8,9,...}
Each turn of the spiral here takes you to a higher power of omega, and if you go around infinitely many times, you reach omega to the omegath power. There are many ways to visualize this ordinal, and I explain a few.
But my road trip will take you much further than that!
In this first episode, we reach an ordinal called epsilon nought, first discovered by Cantor. In the second episode we'll go up the Feferman–Schütte ordinal. In the third we'll reach the small Veblen ordinal and even catch a glimpse of the large Veblen ordinal.
All these are countable ordinals, and you can write computer programs to calculate with them, so I consider them just as concrete as the square root of 2. And yet, they're quite mind-blowing.
#bigness
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Our inaugural techblog post tells the story of how, earlier this year, I managed to reduce OkCupid's match system memory footprint by about 40%, saving us about 1.2TB of RAM ;-)
http://tech.okcupid.com/swiping-right-on-bloom-filters/
http://tech.okcupid.com/swiping-right-on-bloom-filters/
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My best attempt at addressing the question "So... what is the universe made of?" in 15 minutes or less. Share if you like!
https://vimeo.com/126743375
https://vimeo.com/126743375
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A progress report on the book I'm writing on theoretical physics. If you like this, please follow me on Medium!
https://medium.com/physics-as-a-foreign-language/physics-mistranslated-fa83efdfa314#.zhjy2yqt0
https://medium.com/physics-as-a-foreign-language/physics-mistranslated-fa83efdfa314#.zhjy2yqt0
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My new blog:
https://medium.com/physics-as-a-foreign-language
https://medium.com/physics-as-a-foreign-language
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Christian's new book, Dataclysm, is out today!
http://fivethirtyeight.com/features/christian-rudder-dataclysm-okcupid/
http://fivethirtyeight.com/features/christian-rudder-dataclysm-okcupid/
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