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Michael Kleber
Works at Google
Attended Harvard
Lives in Newton, MA
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Michael Kleber

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I enjoyed reading +Yonatan Zunger's post[1] about the jellyfish[2] (they look like squid to me) and yet I was left with a desire to know how long it would actually take for the squid to all return back to the place they started.

If we number the squid 0-255 then we can describe the state of the image with a 256 dimensional vector.  The squid start out with number 0 at the top and number 255 at the bottom.  Then the moves can be described by 256x256 permutation matrices.

The identity matrix is the permutation matrix  that leaves everything right where it was.  In the images below that is represented by a solid black line from upper left to lower right (element 0 goes to 0, element 1 goes to 1, etc). 

The animation is made up of three moves repeated over and over.  In these permutations squid either move left and right within a row (near the identity diagonal, but just off it) or up and down a row (which appear as the diagonal lines away from the center line).

As the moves continue the squid move farther from home. In the animation below the intermediate frames have squid scattered all over the field, much as it feels when you try to watch them.

Repeating the moves is the same as multiplying these permutation matrices. Asking "how long will it take for the squid to return home" is the same as asking "how many times do I need to multiply the matrix by itself before I get the identity matrix back".

If the squid were only moving in one fixed pattern, it's clear that it would take 256 steps: each squid visits the location of each other squid exactly once before they all end up back at their starting locations in unison, like a big, convoluted, squid conga line. This is exactly what we find, if we raise the matrix corresponding to one of the patterns to the 256th power, we get the identity matrix back. That matrix is the 256th root if the Identity matrix.

The really tedious part is extracting the permutation matrices to begin with. For that, I manually extracted the frames from the GIF from the points in time where the squid are just arriving at their next location, while their tentacles are still visible.  Then a very simple vision algorithm picks out those tentacles and writes down the permutation matrix inferred by the direction of motion.

Once we have the three matrices for the three patterns, we multiply them together to get the overall permutation matrix for one loop of the animation.

Then we just multiply that by itself until we find the identity matrix again, and we finally get there after 2064 steps.

Te animation has 75 frames played with a 40ms delay, so if you want to see the quid return home, you'll need to watch for a little over 100 minutes.

Go code for the curious: https://github.com/cwren/squid

I have an animation of the whole 2064 step cycle but g+ won't accept it for some reason, so it's here instead: http://imgur.com/4CzDl2j

[1] https://plus.google.com/+YonatanZunger/posts/4urrnW3sZsi
[2] http://wavegrower.tumblr.com/post/126854522925/currents-if-i-had-the-time-i-would-check-if-one-of
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Michael Kleber

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Great gallery of pictures from this year's Bridges conference.  Bridges celebrates the connections between math and art.  The art has changed a lot over the last 15+ years, with as much laser cutting and 3D printing as you might expect.  But there is lots of lovely technology-free math art as well.
The Bridges Conference is an annual event that explores the connections between art and mathematics. Here is a selection of the work being exhibited this year, from a Pi pie which vibrates the number pi onto your hand to delicate paper structures demonstrating number sequences.
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+Heidi Burgiel No, I've always just watched from afar.
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The Intercept is doing an okay-if-not-great job writing about the Snowden-leak-based "revelation" that the NSA uses large-scale speech-to-text on the large-scale collection of phone calls it records.  These days everyone's Android and iPhone do this all the time; it hardly seems like it should count as a revelation.  When I worked at BBN 8 years ago, the NIST-run competitions had worse error rates than we do now, but they were already running on a single machine at 10x faster than real-time.  None of this was secret; read http://www.itl.nist.gov/iad/mig/tests/ace/2007/doc/ace07_eval_official_results_20070402.html if you're a glutton for punishment.

But The Intercept's focus on the question "Are they creating a transcript of everything?" is misplaced.  If you wanted to find all phone calls that contained the word bomb, you would be stupid to make your one-best-guess transcript of the recording and then grep for "bomb", missing all the cases where the text-to-speech produced "balm" or "calm" or "slalom" errors.  Instead you would have your computer scan the audio, using a model that's specifically trained to look for bomb (and the other thousand words you most care about), and flag the bits that sound like they might match, even if your models say "balm" is a slightly more likely transcription.

Sadly, there's ample evidence that the FISA court's attempts at constraining the NSA are just as naive as The Intercept's way of reporting on it.  Surely there's nothing stopping the NSA from doing this, and so surely they do it.
Telephone calls involving Americans are recorded by the NSA through surveillance technically aimed at foreigners. Are they automatically transcribed, too?
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+Daniel Egnor Strangely, it seems like the "human listens to it" line is the one they have been arguing constitutes a "search", and so might need a warrant.  (If you believe that sort of regulation actually constrains their actions, of course.)
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Ow. Yes, it is true that you can convert from kilograms to pounds by multiplying by 2.2. That does not mean that doing so is the right way to modify every statement.
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The source is the book The Wacky & Wonderful World Through Numbershttp://www.amazon.com/Wacky-Wonderful-World-Through-Numbers/dp/1438005903.  It is a bizarre collection of things some of which I hesitate to call facts.  Let's just say it's a collection of sentences that each start with a number, all with zero context, and with varying degrees of correctness, confusion, and coherence.

You are welcome to peruse it next time you're over.
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Hi ho!  Kermit the Frog here, with another fast-breaking news story.
Is it a rainbow connection? Newly discovered frog looks like famous Muppet Kermit | famous, frog, dianae, newly, kermit, glassfrog, discovered, looks, species, muppet
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Life imitates art.
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Excellent article by Erica Klarreich on the recent mysterious discoveries of more Moonshine-like connections between sporadic simple groups, K3 surfaces, and mock theta functions of Ramanujan's that blew Hardy away.  (If I had remained a mathematician, this might have been in my zip code.)

https://www.quantamagazine.org/20150312-mathematicians-chase-moonshines-shadow/
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We should talk about that sometime. I spent a couple years as a student of Conway trying to understand some part of Moonshine, but in retrospect I was woefully underprepared.
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Michael Kleber

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Woo hoo!  So great to see this launched.
 
This is what I've been working on for the past year.  Very excited for it to have finally launched!
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If you've always wondered what neural nets dream about, we finally know the answer.  This is seriously amazing: a good read and great pictures.
 
All of these images were computer generated!

For the last few weeks, Googlers have been obsessed with a internal visualization tool that Alexander Mordvintsev in our Zurich office created to help us visually understand some of the things happening inside our deep neural networks for computer vision.  The tool essentially starts with an image, runs the model forwards and backwards, and then makes adjustments to the starting image in weird and magnificent ways.  

In the same way that when you are staring at clouds, and you can convince yourself that some part of the cloud looks like a head, maybe with some ears, and then your mind starts to reinforce that opinion, by seeing even more parts that fit that story ("wow, now I even see arms and a leg!"), the optimization process works in a similar manner, reinforcing what it thinks it is seeing.  Since the model is very deep, we can tap into it at various levels and get all kinds of remarkable effects.

Alexander, +Christopher Olah, and Mike Tyka wrote up a very nice blog post describing how this works:

http://googleresearch.blogspot.com/2015/06/inceptionism-going-deeper-into-neural.html

There's also a bigger album of more of these pictures linked from the blog post:

https://goo.gl/photos/fFcivHZ2CDhqCkZdA

I just picked a few of my favorites here.
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Oh, someone please make a movie of a continuous zoom.

Also, Pigsnail is the name of my next band.
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Hey +Henry Segerman, just received my order of Skew Dice, and they are indeed beautiful.  My 9-year-old's reaction "Those can not be fair!" was just as good as I had hoped; my 16-year-old is sitting here looking for axes of rotational symmetry.

I was surprised to note that you left in a square corner, with three right angles coming together, just like a regular cube!  (In fact there are two such, of course.)  Did you play with examples both with and without it, and make an aesthetic choice?  Packing eight of them around a corner is a pretty appealing thing to do, especially if you alternate the enantiomorphic forms...
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Sounds like you're getting some good reactions +Michael Kleber! +Robert Fathauer did the code for generating the large scale geometry. There's still a one-parameter family of shapes with the 90 degree angles - I think that assuming 90 degrees was a good way to cut down the number of choices we had to make.
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The @AmOrnithologist who helped start the #WorstBirdPic meme on Twitter is my cousin +Jesse Kovalcik!
Blurry, dark, or headless, your worst pics can be some of your best birding memories.
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Wow, I would have so many pictures to feed this meme (if I ever used Twitter).
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Woo hoo!  +TechCrunch article about my main project at work.  By June 30th, the ads that Google places on millions of web sites around the world will get to your browser securely, over HTTPS.

So why are we doing this?  Any number of news stories in the past year have made it clear that non-encrypted communication really is the target of both eavesdropping and tampering.  That would be reason enough.

But it's more than that.  Google is a big believer in "HTTPS Everywhere": the notion that all web sites should be encrypted; that if someone proposed unencrypted HTTP today, everyone would just laugh at the mistake and of course add encryption.  The privacy, integrity, and authentication benefits of encryption are hands-down winners.

But there's a catch.  If a web site owner wants the benefits HTTPS, then browsers demand that everything on the page must be delivered secure — so as not to leave an unencrypted "weakest link" lying around.  Entirely reasonable.  And in particular, that means that any ads appearing on that page have to be served up on an encrypted channel too.

Well, not all of the ads in the world come in encrypted form.  (Yet!)  So when a web page is encrypted, the auction that picks the best ad to show you can only choose from among the ones fully deliverable over HTTPS... and that means the winning ad is sometimes a little less good.  And the owner of the web page sometimes gets paid a little less money.

People have known this for years.  Articles like "Google AdSense Earnings Drop With HTTPS Migrations" (https://www.seroundtable.com/https-google-adsense-19035.html) talk about how bad the revenue hit can be.

My launch, coming up by June 30th, will make that a thing of the past.  We will be serving all ads over HTTPS.  And that means that web sites moving to HTTPS won't lose money by doing so.

The threat of decreased ad revenue has been a barrier to HTTPS adoption — but for sites that ask Google to place ads on them, that barrier is about to come down.
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Grats!
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Is this headline nonsensical word salad, or is it just me?

"Brrr! February introduced report cold to Northeast cities file snow to Boston"

http://www.thebeaconreview.com/us/brrr-february-introduced-report-cold-to-northeast-cities-file-snow-to-boston-h8654.html
February 2015 was one for the record books in the Northeast — the coldest month ever for four cities in New York and the snowiest ever for Boston.
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thebeaconreview.com appears to be another one of the short-lived domains used serially by a particular person or group that continues to hit Google News regularly.  I am posting about them on Google product forums as well as my blog here:

http://igibud.com/wordpress/?p=706

Please let me know if you additional info on this.  Thanks.
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Education
  • Harvard
    Math, 1989 - 1993
  • UC Berkeley
    Math, 1993 - 1998
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Mathematician, at Google, making the web faster.
Introduction
I'm a mathematician and algorithm designer.  I now work for Google making things go faster, and keep my finger in recreational mathematics on the side.
Work
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Software Engineer
Employment
  • Google
    Software Engineer, 2007 - present
  • MIT Math Department
    1998 - 2001
  • Brandeis Math Department
    2001 - 2004
  • Broad Institute at MIT
    2004 - 2006
  • BBN Technologies
    2006 - 2007
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Rockville, MD - Berkeley, CA - Cambridge, MA
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Triple Town
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Triple Town, by Spry Fox, is an original puzzle game in which you try to create a great city!

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5000+ puzzles & games for all ages. Toys to make you think and have fun. Unique gift ideas for the holidays. Convenient Coolidge Corner

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The dot & the line
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Once upon a time there was a sensible straight line who was hopelessly in love with a beautiful dot. But the dot, though perfect in every wa

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Cookie Monster spoofs Carly Rae Jepsen's song "Call Me Maybe." For more fun games and videos for your preschooler in a safe, child-friendly

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Bought a new C-Max hybrid here, just a week after they arrived at the first dealerships. Surprisingly pleasant and relaxed car-buying experience -- much nicer than the other hybrids we test-drove the same weekend. What's more, they had the car we wanted on the lot, and after checking around, no one could beat their price, nor offer us another dollar on our trade-in. Thumbs up.
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