Projects of Zack Booth Simpson

Probability Theory Lectures by Bill Press

2012-01-31T16:42:00.002-06:00

Last year at sat in on my friend Bill Press' computational statistics class. It was great. This year he has recorded it and posted it online. If you're into comp. stat., I *HIGHLY* recommend this series of lectures and this course page.

Enjoy.

Goldsworthy inspired algorithmic art

2012-01-26T19:22:00.001-06:00

I watched this documentary about Andy Goldsworthy today and was inspired to create the following in happyfuncoding.com

Edith Page video

2011-12-26T14:20:00.002-06:00

This is a video I made of Edith Page, a very special person to me. I shot this video about 10 years ago but just got around to making an edit in the last few days. It's filled with good Christmas spirit. :-) (I just talked to Edith today -- she is still doing well at 93!)

Infinite Uniqueness -- MAKER edition

2011-11-12T10:17:00.003-06:00

This is two of my students working on cutting out their clothing designs. The class is about creating parameterized clothing and the students have created some really fun designs. See an example of how it works here at happyfuncoding. Scroll down to the twiddler section, press the "Move this panel to side of canvas" link and try adjusting the various parameters by dragging up and down on them to change the clothing design. Works best in Chrome.

More cathedral

2011-10-10T02:19:00.004-05:00

More progress on my algorithmic cathedral. This is a fun little project. :-)

Algorithmic cathedral v 1

2011-10-06T20:06:00.003-05:00

Inside my algorithmic cathedral -- code generated in Sketchup Ruby. Standing in the main nave looking up and towards the side nave. Next I'm going to lessen the bulk of the cross vaults and build a roof (which is going to be hard!)

Acrophilia

2011-09-26T00:00:00.004-05:00

The other day I made up a game with Leah Davis. I've play-tested it three times now and it is certainly the funniest game I've ever played -- it induces almost nonstop laughing.

The game is simple. Each player takes seven letters from a scrabble set. One player is declared to be the judge on the first round. The judge uses his or her letters to make a acronym-sentence: one letter per word. Everyone else then makes up their own acronym-sentence with their letters and tries to make their sentence a logical follow-on of the previous sentence(s). The judge writes down all of the sentences and picks a winner based on whatever criteria he or she likes. The winning sentence is then moved into the middle of the table, the judge rotates one position, and another round ensues until there are no more letters.

Additional rules:

You must use all of your letters, no skipping "a", "of", "the", etc.
You can add any amount of punctuation you want. The more, the better.
Bonus points for punning or word-play
Bonus points for proper names
Bonus points for a sentence that is a direct response to the previous one.
Super bonus if you can make a palindromic sentence where you use all of the letters forwards and backwards to make a 14 word sentence!

A warning, this game gets ridiculous very fast. In all three play-tests it turned obscene, racist, sexist, etc. within a few turns. I've kept some of the play papers but decorum prevents copying any of it here. :-)

Happy Fun Coding v 2.0 now up!

2011-09-23T21:45:00.001-05:00

After a massive re-write, Happy Fun Coding version 2.0 is now up. New features include: better UI, source code highlighting, ability to change the canvas size, and better program navigation.

Cathedral in sketchup, v0.1

2011-09-13T17:16:00.003-05:00

I got it into my head today to create a cathedral in Google Sketchup. I really want to do this my writing a Ruby Sketchup plugin so that I'd have an all parameterized cathedral, but I started by just messing around by hand in the editor. It's tricky stuff getting Sketchup to make the weird geometry -- doing it algorithmically is going to be easier in some ways.

Web development testing: Cucumber & Capybara

2011-08-19T15:12:00.008-05:00

It's taken days to get my head around these web testing tools and more to get the tools working, but I finally got cucumber and capybara to work under both Mac and Windows.

I originally thought that cucumber seemed too high level but now that I've got it running, it's actually kind of fun and nice. Here's how it works.

Cucumber (and its backengine(s)) is an integration testing tool -- that is it tests the whole chain with a simulated web browser using the capybara gem as the back-engine interface to the simulated web browser. This is in contrast to rspec which is opening the models and controllers as actual ruby objects without the browser -- thus rspec is more limited in scope but way faster. You can apparently make cucumber/capybara do ajaxy things with special flag but I haven't tried that yet -- so far I've just filled in a form and pressed buttons without ajax.

Before running cucumber there's a bunch of little details you have to get right -- gems, dev kits, and then generate cucmber blah blah blah. Too much to document here. It was a multiday pain and required that I get a Gemfile from Sarah who had versions that worked. Also, I only got it working under rails 3 so I had to install ruby version managers and other stuff. It took tons of googling to get it all working.

It works like this. The cucumber generator creates a directory under the project root called "features" and under that folders called "step_definitions" and "support".

Into the features folder you put ".feature" files. Here is an actual one I just wrote (excuse the line spacing, this blog doesn't deal with "pre" tag very well):

Feature: Create account

As a new user

In order that I be able to store programs and data permanently

I want to be able to create an account



Scenario: Create a valid account

  Given I am on /users/new

  When I fill in the following:

    | Name          | zack     |

    | Password      | password |

    | Confirmation  | password |

  And I press "Create account"

  Then I should be on /users/account_created

  And there should exist a user named "zack"



Scenario: Create a invalid account due to mismatching passwords

  Given I am on /users/new

  When I fill in the following:

    | Name          | zack     |

    | Password      | password |

    | Confirmation  | passwo   |

  And I press "Create account"

  Then I should be on /users

  And I should see "Errors"

  And there should not exist a user named "zack"

The first four lines are pure documentation, cucumber ignores them. But the madlib style is standard and quite nice.

Each scenario is what's actually parsed. Think of each line under the scenario as a function call with various parameters.

The "function call" of the line is actually a regular expression that is put into the step_definitions folder. Cucumber installs a bunch of default "steps" (think functions) that are very handy and are in the step_definitions/web_step.rb file. I'm using a bunch of them here. Here's a sampling of one:


Given /^(?:|I )am on (.+)$/ do |page_name|

    visit path_to(page_name)

end

That is a "function" definition that says: when you see the pattern "Given I am on XXX" then run the command "visit" which is a capybara command that loads that page in the simulated web browser.

You can either use their existing steps or you create your own. If the step isn't found it emits a handy regular expression that you can copy and paste into your own step file.

So the long and short of it is that cucumber is a list of actions in very readable language that drives "steps" (i.e. test functions) in the "steps_definitions" folder that calls capybara (and maybe other gems?) to do the heavy lifting of running the simulated web browser.

The output of cucumber is a fairly well formatted color output that highlights each step in green if it passed, red if it failed, and yellow if it is pending (not yet implemented).

As Sarah said to me, it's actually kind of fun. You have a sense of pseudo-programming gathering your thoughts together as you edit the feature file and obviously the feature files are easy to read by non-technical types as they have no magical code incantations.

Thanks to @fablednet for help!

Vitalism: alive and well

2011-07-30T16:47:00.005-05:00

Yet another demonstration that the intuitive ideas of vitalism are alive and well. This NY Times article about Joyce's RNA self-replicator is dripping with vitalistic language starting with the title. For example: "They can make their own RNA and see if they can then breathe life into it."

Of course there is no bright line that separates the living from the inanimate -- at least they point out that "Biologists do not agree on what the definition of life should be or whether it is even useful to have one.". As Andy Ellington says: "'Life' is a word for poets, not scientists."

Geometric proof of the dot product

2011-07-30T13:30:00.002-05:00

This is a geometric proof of the dot product that I submitted to Mathematics Magazine for the "Proof without words" section. They rightly rejected it because it's only valid for the first quadrant. Cynthia and I tried to rework it for the other quadrants but it lost its elegance so we gave up.

(Oldish) images of my house

2011-07-27T10:18:00.001-05:00

These are nice pics that Bruce and Anne had taken of my house soon after it was completed.

Tutorials #10, #11, #12, #13

2011-06-19T19:59:00.001-05:00

Tutorials #10, #11, #12, #13 are now posted on happyfuncoding.com

Enjoy.

Tutorial #9 -- arrays

2011-06-18T16:45:00.001-05:00

Euler's equation

2011-06-18T16:05:00.003-05:00

Vector Projection Demo

2011-06-17T20:39:00.002-05:00

Use your mouse to move around vector A

Happyfuncoding Tutorial #8 -- for loops

2011-06-17T19:28:00.001-05:00

Trigonometry refersher.

2011-06-17T14:40:00.004-05:00

This is a simple little reminder of cos and sin written in happyfuncoding.com Roll your mouse over it.

Happy Fun Coding Tutorial #7 -- Operators

2011-06-16T16:13:00.001-05:00

Tutorial #7 -- Operators

Happyfuncoding tutorial #6 -- while loops

2011-06-14T16:09:00.001-05:00

Happy fun coding tutorial #6 -- while loops

Happyfuncoding Tutorial #5 -- if statements

2011-06-13T17:33:00.002-05:00

If statements

happyfuncoding.com now a github project

2011-06-13T16:21:00.002-05:00

Thanks to my visit with Sarah Gray and Corey Haines happyfuncoding is now a github project so anyone can contribute.

Embed of Happyfuncoding content!

2011-06-11T11:06:00.003-05:00

You can now embed programs from happyfuncoding.com onto your own website as demonstrated here!

Happy Fun Coding Tutorial #4

2011-06-07T20:16:00.002-05:00

Happyfuncoding Tutorial #4 -- Twiddlers!

Happy Fun Coding Tutorial #3

2011-06-07T16:17:00.001-05:00

Hypatia artwork by Hollyana Melear

2011-06-06T22:54:00.005-05:00

I commission a triptych about Hypatia from my friend Hollyana Melear for my garden. For those who don't know, Hypatia was a nerd martyr -- the only female curator of the great library of Alexandria, she was kill by an angry Christian mob for being an smart uppity female.

There are three panels shown from left to right. The center has Hypatia holding the scroll of knowledge while the angry Christian mob attacks her. Some versions of her demise have her splayed with an abalone shell so there's a real abalone shell in the center bottom. On the left panel is the light house of the Alexandria as the mob chases her down under the christian cross while on the right panel Cyril plots her demise while destroying a scroll symbolic of rationalism. Incidentally, Cyril, who many have blamed for orchestrating her murder was sainted for his troubles.

Happy Fun Coding Tutorial #2 -- Variables and animation

2011-06-06T17:21:00.002-05:00

Happy Fun Coding Tutorial #2 -- Variables and animation

Happy Fun Coding Tutorial #1

2011-06-05T20:59:00.003-05:00

This is the first of many tutorials I'm going to make about programming with happyfuncoding.com. If you've been curious about programming, it doesn't get any simpler than this!

More happyfuncoding!

2011-06-01T23:09:00.003-05:00

In the last few days I've put a lot of work into happyfuncoding.com -- my collaborative online programming environment that creates a place where you can fiddle with graphics code in an easy to use Javascript environment. It includes lots of samples, tutorials and challenges as well as a wiki so more experienced programmers can write tutorials and challenges for less experienced programmers.

Please, please pass it along! It needs people using it! :-)

happyfuncoding.com

2011-05-26T18:11:00.004-05:00

I'm please to announce the first version of my new learn-to-program environment called "happyfuncoding.com". It's a Javascript environment that allows novice programmers to create simple graphical programs with minimal fuss all from the web browser.

It also features an editable mini-browser with tutorial and challenge sections where more advanced programmers can create content to teach and challenge less experienced programmers.

I haven't added much in the way of tutorials yet, so if you're a programmer please come and help fill it out!

If you've never programed before, here's your chance to write your first "Hello world!"

Create an account to save your programs or edit the pages. Please report bugs by editing the "bugs and features" page off the home page in the mini-browser.

Traitwise, PGP, data standards and the OSI model

2011-05-24T20:39:00.004-05:00

I spent the day with Jason Bobe of the Personal Genomes Project. PGP is a public effort sequence a large number of genomes. Traitwise has formed a partnership with them to serve as part of the phenotyping solution.

Jason's role at PGP puts him in the center of a growing number of people who have competing desires to control / provide services around personal health (or "quantified self" as some are calling it). Jason therefore is in the unique position to promote and evangelize.

An interesting part of the conversation focused around the need for open standards of public health and trait related data. I used the OSI networking protocol framework as a model of how conceptual standards can be incredibly useful to increase innovation. One of the best things about the OSI model is that it didn't attempt to actually define any standards but rather it serves as a conceptual framework that defines how standards interface with each other. From that model has emerged a number of interoperable standards at all levels and without it we certainly wouldn't live in the networked world we live in.

One of the aspects of the human data problem is privacy which has "levels of data privacy" and this, it occurred to us, was somewhat analogous to the OSI layer framework.

Layer 1 - Raw identifiable data (post-privacy)

Layer 2 - Anonymized raw data (HIPPA compliant)

Layer 3 - Algorithmically open data (sand-boxed, machine readable)

Layer 4 - Aggregated data

Layer 1 data is non-private. It requires a consent certificate of some sort to go along with the data.

Layer 2 data is considered by many scientists to be adequate for protection in many research circumstances and indeed HIPPA seems satisfied with this. However, for open projects such as Traitwise I personally don't think that it suffices as de-anonymization has been shown in many circumstances such as the infamous AOL search records scandal.

Layer 3 is perhaps the most interesting and least discussed. A Layer 3 system would allow an algorithm written by a researcher to run against raw data but within a sandbox that only allows the aggregated results to emerge. I haven't put a huge amount of thought into this, but it seems plausible to write an API that could enforce such constraints. But, even without such an API, a human code reviewer could accomplish the same thing.

Layer 4 is what Traitwise and others are currently focusing on -- aggregated data that is not deanonymizable.

This is just one aspect of the data and communications problem, but it is an important one and it was fun talking to Jason about it today.

Freshman Research Initiative -- First Semester Results

2011-05-16T12:31:00.003-05:00

We just finished our first semester of the Freshman Research Initiative on Genetic Algorithms for Pattern Design. We paired up students from Computer Science with students from the Fashion/Textiles department and had them create algorithmic patterns that could be bred genetically. The results are on this page. Next semester we're going to print these patterns on fabric and make clothing from them.

Fire pit - Day 2

2011-02-27T09:54:00.003-06:00

Filled in the seat corner.

Fire pit day 1

2011-02-20T17:23:00.002-06:00

I started on the brick fire pit in the back yard. There'll be one more layer on top of this one.

Final gate installed

2010-11-08T14:28:00.002-06:00

This is the fourth and final gate to my garden -- a project that has taken me about 3 years to complete finally done. Thanks to my mom for the help.

Tree Generator

2010-11-07T14:37:00.004-06:00

Dan and I have been working on a new Shadow Garden piece called "tree" that generates random trees as you hold up your hands. Here's a recent screen shot.

Staircase lighting

2010-11-02T18:54:00.005-05:00

I had grand plans for staircase lighting that illuminated whenever you stepped on the first steps. I carefully engineered a board and had it all working on the bench using IR reflecting detectors to sense the footsteps. But upon installation I discovered that the sensors sucked -- their practical range was only a few inches and they generated a lot of false positives. So, until I can find a new sensor system the lights are just boringly connected to an old-fashioned light switch. But, at least I can tread safely on the stairs at night now!

Side gate complete

2010-10-26T17:28:00.001-05:00

Finished up the side gate. Thanks to Angel for the help!

Pics from Hawaii

2010-10-10T20:45:00.005-05:00

Right after Spain, I flew across 12 time zones to Hawaii. Here's a few random pics.

Looking towards the caldera at Kilauea.

A lovely little fiddle head in Volcanoes National Park.

We rented a plane and flew out to see where the lava reaches the ocean.

Yes, I still remember how to fly!

Pics from Spain

2010-10-10T20:25:00.008-05:00

A few pics from Spain...

Inside of Casa Batllo. The inside had been closed off when I lived there so that was a pleasant surprise. Bruce, just look at that staircase!

This is a scale model of the attic of La Pedrera. Each of the slats is in reality a ~14ft brick catenary arch. It's stunning inside.

Roman aqueduct still standing in Segovia.

This is a model of the roof of the school house built next to Segrada Familia. It was from this roof line that I was inspired to make my porch roof.

Oh my god, the face on mars has moved into the light fixtures at the Reina Sophia! :-)

Gate

2010-10-10T20:14:00.003-05:00

Today I built another gate for the backyard. I don't think I could have designed a much more labor-intensive gate design; it took me about 5 hours to mill all the 2x2s. Next, trim the edges and hang it.

Sagrada Familia sketch

2010-09-22T11:14:00.001-05:00

A little tiny piece of Sagrada Familia. There's no place to sit down outside so I had to hold the pad in one hand while drawing which made things all wobbly!

La Pedrera attic sketch

2010-09-21T05:06:00.003-05:00

Apologies again for the bad contrast.

This is the attic of Gaudi's La Pedrera in Barcelona. It is a twisting series of hundreds of catenary aches (the shape of a hanging chain but upside down). It is a magical space, like being on the inside of snake with windows. I think it is one of the most, if not the most, beautiful space I've ever been in.

Casa Batllo sketch

2010-09-20T10:02:00.002-05:00

Forgive the lack of cropping and contrast correction, I don't have access to my usual editor suite. This is a small section of the casa Batllo fascade. When I lived in Barcelona this house was not open to the public so today I got to see inside for the first time which didn't disappoint. Unfortunately it was so crowded that there was no place I could make a sketch.

Barcelona gothic cathedral sketches

2010-09-20T05:55:00.006-05:00

For me one of the pleasures of vacation is having little or no plan -- I see less but feel more relaxed about it. This morning I strolled over to the gothic cathedral in Barcelona (I've been there many times before) and just sat and drew images.

I love the intersecting lines of the arches in the gothic style. The arches in this particular church have a interesting asymmetric large-small-small-small rhythm. The intersections where the main supports hold up the central bay as well as three other smaller bays are very complicated tangles of these converging patterns. I can sit and stare at them for hours, absorbing their intricate masonry.

Traitwise Beta 2

2010-09-13T13:21:00.002-05:00

We're pleased to announce the beta 2 version of our health-engine "Traitwise". We've simplified question making, added discussions, and generally improved a lot of things. Please come and check it out -- and tell your friends and family!

www.traitwise.com

Vent Hood 1

2010-09-06T14:14:00.002-05:00

Today I started on a mosaic for my vent hood. I'm more or less shamelessly copying one of me favorite local artists Aly Winningham who did the candy island mosaic in the Whole Foods mother ship. Her stuff looks a hundred times better but she has, after all, been at it for years!

Final tree mural

2010-09-05T09:44:00.002-05:00

I finished up the tree mural this weekend by painting the air duct grills and going back over it with a lighter pink to blend in the branches a bit. Thanks for Michael and Holly for the help.

Video games and person

2010-08-30T08:54:00.006-05:00

This morning I read Alexander Nehamas' opinion piece about Plato and popular media. The piece was comparing the critical analysis of video games to the same sorts of analysis in ancient times. He lumped in video games with other popular media in a way I found to be typical of someone who doesn't play video games. As analysis by non-game players tends to, it failed to note important differences between video games and other forms of media. The most important of which is, IMHO, person.

All traditional media no matter how they are painted, written, acted, or performed are actually in the third-person. Only a psychotic person confuses actions written in a novel as "I ran" or "I said" as actions they, the reader, actually took. No matter how you try to frame a book or movie, you are not confused by who actually took the action. They took the action -- you observed it.

In all video games the opposite is true. No matter how the fiction is presented, it is actually in the first person. Only a psychotic person would say: "And then Pac Man decided to turn left". A rational person says, "I made Pac Man turn left" or more usually, "I turned left" because Pac Man is not your agent but rather your avatar.

Of course literature, movies, etc. can induce sympathy and strong emotions as if the scene were happening to you. Indeed, they are surprisingly capable of making you feel those emotions more intensely then if the situation had actually happened to you. And conversely, just because some video game is in the first person doesn't mean that you must have a deep emotional connection to it -- many video games try and fail to create such a connection.

But that said, there's a dramatic difference between games and narrative. Analysis that doesn't bother to note that games are real actions taken in a simulated world while narrative is simulated action in a simulated world is missing an enormous piece of the critical puzzle. Play is a complicated emotional state where you are taking real (but possibly attenuated) actions while staying aware of the fact that your motivations are pretend.

Regardless of where one stands in terms of video games as art, if one is going to analyze their role in society one one should at least be familiar enough with them to understand that they are a profoundly different form of art. As in the article in question, I find direct comparisons to literature and literary criticism tend to be overly simplistic.

Upstairs tree mural

2010-08-29T17:46:00.002-05:00

With some help from Michael and Rechelle, I started on the tree mural for the upstaris landing. I've had this planned for some time and finally got around to it this weekend. There's still work remaining but pretty good for a few hours work.

Several old videos

2010-08-21T07:15:00.002-05:00

I just discovered that someone taped my 2005 talk at the Austin Museum of Art for their 22 to Watch show. It's a 5 minute explanation of the piece I made for that show "Moderation".

Here's another art talk from a show in Sao Paulo, Brazil around 2004. This one also features my friend Adam Chapman talking about his art at the same show.

Gate support v 1.2

2010-08-16T10:29:00.003-05:00

I had still more left over material and I felt like it needed a little more so I'm up to v 1.2 on this thing. I threw out the rest of the wood to stop the temptation of adding more!

Radio Interview on Studio 360

2010-08-13T21:38:00.004-05:00

My friend Lindsay Patterson produced this really nice piece about my work for Studio 360 this week. Thanks Lindsay, sounds great!

Gate support v 1.1

2010-08-04T10:20:00.002-05:00

I thought it needed a little more and I had some leftover material so I added this spiral-y bit.

Gate arch

2010-08-01T12:42:00.004-05:00

The gate I made for the side is so heavy that it was causing the post to lean inwards making it hard to open. I couldn't put a tension wire on the opposite side because of an adjacent driveway so my only solution was to add a compression element pushing the post away from the house. To keep with the tree and vine theme I built this from a glued up laminate of 2x2s.

Traitwise coding survey

2010-07-26T14:42:00.013-05:00

We're almost ready to release the beta version of our survey engine: Traitwise.com. As a test of the embedded private surveys, I've created this short 10 question survey for my nerd friends to resolve a couple of hypotheses I have about coding styles and coding experience. So, to all my coding friends -- please take a few seconds to honestly answer this survey and to report any bugs or problems you find in the engine.

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Chemotaxis CheZ position experiments

2010-07-18T20:23:00.006-05:00

From freeversity.org

Bacteria swim by their noses. That is, they smell food and swim towards it; they smell waste and swim away. The molecular basis of this amazing feat is the most well studied molecular signal transduction system and as such serves as a model for other lessor-studied bio-molecular signaling.

There's one little detail of the chemotaxis system that caught my attention a few years ago. The signal is transmitted from sensor to motors via a diffusing molecule called "CheY". When CheY has a phosphoryl group attached to it, it activates the motors in a certain way; when it loses that group it reverses the motors.

There's a very interesting subtlety to this system. The part of the system which "charges" the transmitter (to borrow electrical engineering terminology) is a kinase called CheA. The "discharging circuit" is the enzyme CheZ. It turns out that these two enzymes are, counter-intuitively, co-located. That is, it seems odd that the enzymes responsible for pulling-up a signal are co-located with the enzymes that pull it down. It would appear that the system is spinning it's wheels -- undoing what it just did. Why shouldn't it have the pull-down phosphatase evenly distributed or co-located with the motors?

When I first read this detail a few years ago in Eisenbach's book "Chemotaxis" it mentioned this counter-intuitive fact and I thought to myself, "I bet I know why -- it reduces saturation and evens out the signal." I wrote a little simulation years ago and convinced myself that this was indeed the case (at least for my toy simulation). Then I got distracted for years didn't get around to improving the simulations.

My hypothesis is that by co-locating CheZ and CheA the signal will saturate less near the transmitter and become more spatially uniform. My intuition is that when the external signal is rising and transmitter wishes to control the motors it needs a supply of free un-phosphorylated CheY in order to communicate this. Because CheY is produced at one end and diffuses to the other regions, there's a 1/r^2 distribution of it as it produces it. If it turns on the transmitter at some moment then a few moments later there will be an excess of CheY~P near the transmitter but a lot less further away. But, if CheZ is located nearby the transmitter then it is right where it is needed most -- where there's an excess of CheY~P.

Honestly, it's easier to see the effect than to describe it.

In the following figures, the top row has the CheZ co-located with CheA on the left side. The bottom row has the same amount of CheZ evenly distributed. These are space-time plots. Space is on the X axis with the transmitter on the left. Time progresses from the bottom of the graph towards the top. The right plot is the power spectrum of the right most spatial position which simulates the most distant motor's response. In the top row we see two things. First, the distribution is much smoother from left to right than it is in the bottom row. This is good for the bacteria as the motors are scattered throughout the cell and the controller depends on them to synchronously changing state as it switches from laminar movement to chaotic tumbling. Second, the non-linear clipping harmonic (the little spike on the right) is taller in the bottom row and the primary response (the big peak) is a little smaller. This indicates that there's a (mild) fidelity improvement in the co-location of CheA and CheZ. Given the simplicity of this argument I submit that such co-location is probably a common motif in other kinase/phosphatase (and similar pull-up/pull-down type) systems.

Caveats -- this is a scale-free simulation. I made no attempt to model actual parameters but rather went on the assumption that the bacteria probably operates near peak efficiency so I just twiddled the parameters until I saw what appeared to be peak efficiency. Of course, this is hardly rigorous so the next step will be to try to get accurate rate and diffusion constants. If anyone knows where they are conveniently located in one paper, that would be nice. :-)

2D stadium wave

2010-07-18T09:49:00.007-05:00

I finally got around to making my previous stadium wave simulation run in 2D. It makes pretty patterns as I expected it would. The fascinating thing about it is that there's these interior waves that back propagates as the outer wave spreads out. There's some sort of instability that causes little imperfections (probably due to the imposed spatial lattice) that gets these little eddies started and once their started they tend to collide and make interesting things happen. The simulation is torodial so once the wave hits the edges it interacts with itself and then all kinds of beautiful things happen. (Note, the image looks wider than it really is -- what looks like an oval is actually a circle.)

The similarity between New Testament textual analysis and bacterial plasmid phylogeny

2010-07-11T16:26:00.010-05:00

In Prof. Bart Ehrman's excellent lecture series from the Teaching Company called "From Jesus to Constantine" he spends some time explaining the history of the documents of the New Testament. He describes various motifs of textual mutation caused by scribes' errors and theological corrections.

I was struck by the similarity between these motifs and the same motifs in biological DNA mutation.

The most obvious are the point mutations. There are many tens of thousands of spelling differences among the Greek and Latin manuscripts. The vast majority of these are irrelevant as they do not change the interpretation of the text. In biological terms, we might call these "point mutations of synonymous coding regions" which is a really fancy way of saying "spelling mistakes" that do not change the interpretation -- the functionality -- of the DNA. Prof. Ehrman points out that, including these textual point mutations, there are more differences in the Greek manuscripts of the New Testament than there are words!

The second motif is selection. As theological beliefs wandered throughout the centuries, the scribes forced "corrections" on the text to make it more in line with contemporary thought. One example he mentions is the story in Luke of Jesus and his family visiting Jerusalem. In the story the family accidentally leaves Jesus behind. 3 days later (!) they realize they forgot him and go back to find him in the Temple. In the Greek manuscripts Mary says: "You're father and I have been looking all over for you." But at the time the manuscript was being copied many centuries later, the theological orthodoxy had incorporated the story of the virgin birth so how could this passage be right: "your father and I have been looking..." so it was changed to "we've been looking...". This adaption was more "theological fit" than its cousins and was thus selected for in manuscripts over the ages.

The third -- and most incredible -- is the similarity between bacterial plasmids and marginal insertion mutations. The copied manuscripts were used by teachers and would sometimes end up with marginal notes -- writings in a different hand scribbled in the margins of the book. One example of this is the line in first Corinthians chapter 14:34 that "women should remain silent in the churches". Sometimes a scribe would read these marginal notes and think: "that's a good bit, I will maintain it into the next copy." What begins in separate hand becomes a marginal note now written with the same hand as the main-line text. Another generation or more later another scribe comes along and sees this marginal note and thinks: "What's this doing in the margins?" and inserts it into the main line text.

Similarly, in bacteria and other organisms, there's sometimes extra loops of DNA that are independent of the main-line chromosome called "plasmids". These stand-alone pieces of DNA are copied independently of the main-line but are occasionally inserted into the main-line. Once inserted, like the inserted marginal text, they cannot be distinguished from the original thus they become a permanent part of the main-line code. Because we have the sequences of thousands of bacteria, we can see evidence of this throughout history.

Math Series 10 -- Euler's equation

2010-06-20T14:00:00.014-05:00

And today we reach the first major milestone in my series: Euler's equation.

Math Series 9

2010-06-19T18:29:00.010-05:00

Antenna analogy

2010-06-19T17:49:00.002-05:00

An old fashioned radio without an amplifier.
Image from http://homepage.mac.com/msb/163x/faqs/radio-spark-crystal.html

How can a radio pull power out of the thin air sufficient to hear a radio broadcast many miles away? And what does this have to do with how bacteria swim? They both require an understanding of antennas.

I've been developing an analogy to with my friend John to help demystify antennas; the analogy is also intended to help my chemist friends see how the concepts of antenna design apply equally to all communication systems -- even biochemical ones.

Imagine a boat out at sea on a moonless night. Suppose there are waves rolling by on the ocean. How could we build a device on the boat to detect the invisible waves? A simple solution is to trap a marble into a slot and attach a switch a either end.

As the boat buoys up and down with the waves the ball will roll back and forth hitting the switches on either end. Consider why this works -- when the wave passes it lifts one side of the boat before the other. This lifting creates gravitational potential energy between one side of the boat and the other. Whenever there's a potential difference, anything free to change state under that potential will do so. In this case the marble will convert that potential energy into kinetic energy (and friction) which is detectable as the marble hits the switch.

There's a few non-obvious aspects of this that are easy to see when using this boat analogy and harder to see when talking about other kinds of antenna. Understanding these subtleties permits one to have much greater intuition for antenna design in other domains be that electrical or biochemical.

Aspect #1) It only works if the boat is rigid. If it was not rigid, say like a inflatable raft, the boat would simply deform to the shape of the wave and the marble could just sit in one place as the wave passes by.

Non-rigid ship.

#2) The length of the boat relative to the wavelength is important. Imagine how our marble-based water-wave receiver system would behave under two extremes: the boat being very short compared to the wave (top picture below) and the boat being very long compared to the wave (bottom).

When the boat is very short compared to the wave length, it hardly feels any potential energy difference between the bow and stern and thus the marble will not respond well to the wave. Similarly in the other extreme. If the boat is so long that many waves can pass under the it at the same time then again there will be little potential difference between bow and stern and the marble will not roll. We can therefore see that there is an optimal length range for our boat-antenna that is approximately equal to the receiving wave-length.

#3) The friction of the marble is important. A marble traveling through a denser medium will be slower to accelerate than will a marble going through a low viscosity medium. Imagine the marble moving through honey so that as the wave passes by it hardly has a chance to move at all before the wave has passed. Obviously this would be a bad detector because the ball wouldn't hit the switches.

Conversely if the ball were able to move too quickly, it would get all the way to the end of the rail very quickly and it would just sit on the switch. Although that might not matter for a simple-minded wave detector that only wished to detect the absence or presence of the wave (a binary sensor), it would matter if you were using the marble's velocity to drive some other system; for example, if we were making a recording of the marble's position to make a picture of the invisible waves. When the marble is able to travel so quickly to the end of the detector that it just sits uselessly at one end or the other it is called "saturation" or "clipping" and introduces a very particular kind of distortion called "clipping harmonics" and can be easily seen in the power spectrum with and without the clipping as seen below.

#4) You don't need a "ground" to detect a wave. The reason that a pilot can use a radio in the air is that that detecting a wave has only to do with detecting the difference in potential between the "top" of the wave and the "bottom". Indeed you need to be careful not to ground yourself in many cases because by "grounding" yourself you're creating an antenna that is the size of the earth!! For example, consider a boat mooring.

If you were to connect your boat to the ground then you'd be detecting the potential difference between ground and any wave even waves the size of the whole earth -- the tides. This can be very dangerous as the potential might be so great that it could destroy a ship. That's why in the picture below you see that boats that are moored to docs have to have rollers on them to isolate them from ground.

If there rollers weren't there the moored boats would be dangling from the ropes when the tide went out or deluged when the tide came in!

All of this stuff about length and friction boils down to a time constant. You need the marble "sensor" to have roughly the same time constant as the wave you're trying to detect. If the detector responds too slow (because it is too long or too burdened by friction for example) then you won't detect the waves very well. If your detector responds too fast (because it is too short or too frictionless for example) then the sensor will saturate.

This analogy demonstrates that an antenna is a "rigid" device that has a tuned response to a changing potential energy. This is true no matter the technology. And this lesson teaches us that antennas of any variety be they electrical, chemical, or anything else must be tuned to respond at a time scale in the ballpark of the speed that the signal of interest changes.

For example, an electrical antenna is a metal rod inside of which there are mobile electrons that are analogous to the marbles. As an electromagnetic field passes by the antenna the front and back of the antenna have different electrical potential so that electrons rush from end to end to try to cancel that potential just like the marbles did. And just as was the case with the boat-and-marble antenna, the length and tuning of detector circuit matters to optimize the response of the system to the wave.

All sensors of any technology are driven by changing potential energy. Consider a beautiful example of a biochemical "antenna" -- the bacterial chemotaxis sensor.

The receptor/sensor is a trans-membrane enzyme complex that undergoes a conformational change when it binds to a ligand of interest. The concentration of the ligand is variable in space and time and thus the bacteria needs to have a tuned antenna that responds at the same time scale. Imagine two extremes. Suppose the kinetics of the receptor enzyme were extremely slow to release the ligand. In that case, the bacteria would believe that the ligand was a high concentration even after it swam somewhere it wasn't. Conversely, imagine that the kinetics of the system were such that the motor was quickly saturated with signal. In that case, you'd get clipping distortion as described earlier. Both situations would reduce the performance of the chemotaxis system thus we'd expect that the bug would have evolved a circuit that is tuned to the time constants in the same rough proportion to the speed at which ligands change in the environment it is searching.

The above argument applies to any and all biochemical reactions. Ultimately every informatic aspect of a cell comes down to communicating information from place to place using diffusing metabolites. Therefore there's a lot to be said for thinking of the kinetics of these systems as "antenna" that are transmitting and receiving chemical messages at particular speeds with tuned circuits to optimize those communications.

[Revision 20 Jun -- thanks to my friend Sean Dunn for pointing out that I had incorrectly used a mass analogy where I should have used a viscosity analogy.]

Video-wiki documentaries

2010-06-17T10:09:00.003-05:00

Although I haven't played with it yet, now that Youtube has cloud editing, I predict that video based "wiki" documentaries will become a very cool new form of media.

I propose that a particularly good genre to start with is History. For example, start with a film of a lecture by an amateur but good historian (I as just talking to my history 7th grade history teacher Jerry Buttrey about this this morning). Others later contribute source material as it becomes availasble. For example, someone might live near a battle site and have footage of it. Someone else might live near a library where they can get images of documents and interviews with associated scholars. Someone else might have artifacts handed down from family members. It's easy to see how a strait-forward talking-head lecture could be edited over time with with more and more cuts to such external video shots with the lecture as voice-over and from there might have the narrative interrupted with other interviews -- mimicking the life-cycle of a typical wikipedia article.

A particularly good company to sponsor such activity would be the exceptionally high quality "The Teaching Company" whose lecture's I've enjoyed for a long time. They might be tempted to view such amateur media as competition to their products, but I think the opposite is true. If they would sponsored such endeavors (for example, by making a call for participation via their existing client base) I bet that they could increase their sales on related subjects as they'd tap into the social network of each project and with some clever marketing they could push their associated wares to a very receptive narrow market.

Finally, the very act of contributing to such a documentary, even if it's just going to a field and shooting a few seconds of video, would be a great way to engage pupils of all ages in history classes. I for one much more enjoyed our field trips than I did sitting in class, and had I had an active reason to collect documentation it would have been even more memorable.

Although I'm probably not going to make any of these forthcoming video-wikimentaries, I look forward to watching them.

Math Series 8 -- Velocity of rotating things

2010-06-16T23:03:00.009-05:00

Everyone has probably dealt with velocity before, but the velocity of rotating things is a bit trickier. But, it's very important to where we're headed...

Why I hate standardized tests

2010-06-16T15:57:00.002-05:00

Image by Peggy Monahan. Thanks Peggy!

One time my friend Bev asked me to help her with the GRE. I told her that I hate standardized tests and assured her that she didn't really want my help. She insisted that I was the only person she knew with math skills so I went over to help.

First question: If one car mechanic can fix a problem in 2 hours and another one can do it in 3 hours how long if the work together?

My head practically exploded at the absurdity of this question. First of all, if two car mechanics try to work together they'll end up drinking, smoking, and bull-shitting and nothing will get done. In the unlikely event that they actually tried to work on the same car at the same time it wouldn't get done faster because car repair is probably one of the least parallelizable tasks imaginable. I mean, what are they going to do -- both pull on a wrench at the same time and extract a nut twice as fast?

Of all the tasks in the world they could have chosen -- painting a wall, canvassing a neighborhood, etc -- they pick a nearly worst-case example. That said, understanding serializable vs. parallelizable tasks is extremely valuable knowledge so I spent 20 minutes explaining pipelining and caching strategies and then Bev understandably fired me exactly as predicted.

Here's another example from a Wonderlic sample test:

I simply abhore this questions and "puzzles" like this one -- it's completely subjective. I can make a case for all 5 of these being unique. 1 is the only one who's longest diagonal is equal to sqrt(2) of its sides. 2 is the only one that can be created by moving a single vertex from a rectangle. 3 is the only one with an anspect ratio greater than two. 4 is the only one that has regular angles greater than 90 and is also the only one with 6 sides. 5 is the only one with 2 acute angles. How is it that number of sides is somehow more important than the other features?

Questions like the two above make me feel that the author is a moron and that fact immediately makes me angry: Where does this moron get off judging me? And that gets me to why I hate standardized testing. It's a game about guessing what the author wants you to say using rules of thumb and pre-described algorithms versus demonstrating that you are capable of independent thought. And in a world full of computers that will slavishly follow endless and complicated pre-describred tasks, we don't need humans to do the same.

I don't merely reject standardized testing as a means of judging people's abilities, I reject the premise that standardized testing demonstrate anything positive -- society does not need more people who excel at slavishly following rules of thumb and formulas as those people's jobs are soon to be replaced by computers if they haven't been already. We need people who understand, who create, who invent now more than ever and this simply is not tested by standardized tests. While it is certainly the case that there are people who do well on standardized tests who are also creative, it is even more so the case that there are people who are very creative who nevertheless fail at standardized tests and unfortunately the tests tell those people "you suck" instead of "you're awesome".

Math series 7 -- complex numbers!

2010-06-14T22:06:00.019-05:00

And now we come to one of our first major conclusions: you already understand complex numbers! (Again, if you find these helpful please leave me a note, I'd like to hear some feedback.)

Math series 6 -- radians

2010-06-13T11:29:00.008-05:00

Finishing up with rotations before we move on to something (seemingly) completely unrelated.

Math series 5 -- Spinning wheels and waves

2010-06-12T15:53:00.014-05:00

Math Series 4 -- rotation = multiply

2010-06-11T09:28:00.006-05:00

And now we get to the end first of section. If you've followed along through these slides then congratulations! -- you've just learned about 12 years of math in 20 slides (Not really! -- but it does take traditional math classes 12 years to get to this point!)

Math Series 3 -- More rotations

2010-06-06T16:35:00.003-05:00

Today, more details about rotations. I promise, it gets to a good punch line before too much longer!!

Math series 2 -- Rotations

2010-06-04T16:55:00.005-05:00

Today we tackle rotations which are simple once you get the "trick". If you are enjoying these, please leave a note to encourage me to post more. :-)

Math series 1 - Vectors

2010-06-01T10:25:00.009-05:00

A long time ago I started writing a book to explain complex numbers and the Fourier transform. I never got around to finishing it and my friend Matt just asked for it so I think I'll try to finish it one bite-sized chunk at a time and post it here to the blog. This is panel 1-5 of about 80. It starts off at vectors and ends at the Fourier trasform via Euler's equation. If you like it, please leave feedback to encourage me to actually finish it! :-)

Preferential attachment in ecosystem mutalism

2010-05-28T17:37:00.015-05:00

Tree, vine, and bromeliad

In a previous post I made an analogy to illustrate the evolutionary pattern of "attenuated parasitism" -- a model for how antagonistic agents can evolve cooperation. I created that analogy while sitting on the edge of the Puerto Rican rain forest thinking about how it is that vines and trees can co-exist -- after all, being a vine is such a good strategy that it seems like they should have killed all the trees (and themselves) by now! That same day I had another idea that I didn't get around to writing down: such cooperative mechanisms should, given time, lead the forest to become one giant interconnected web of mutualist interactions.

The argument is simple. If a vine and a tree form an alliance while the same tree specie and some other specie, say, a bromeliad also form an alliance then it is logical that the vine and the bromeliad will have an increased probability of forming an alliance of their own owing to the simple fact that they co-occur in the same location (around the tree) more frequently than other random specie pairings. A small interaction network like this would likely grow by accumulating more and more interactions by the same mechanism.

There is a mathematical theory of such network growth called "preferential attachment" (also known by about half a dozen other names). The study of such networks dates back to at least Yule, 1925 who shows that such processes build what came to be called "scale free networks". Such networks end up with many more hyper-connected nodes than one might intuit. For example, the tree in the previous discussion is likely to become one such hyper-connected node with many, many mutualistic interactions both literally and metaphorically hanging off of it.

It is easy to imagine how the growth of such cooperative interdependence would tend to drive an ecosystem towards a single giant interconnected web of specialists. It is conversely hard to imagine how an outside generalist specie could successfully invade such a well-connected ecosystem. Therefore one would expect to see more internal differentiation from species whose interconnections into the web are already established as opposed to generalist invasive species whose ancestors came from the outside.

I haven't studied the field evidence well enough to know if this idea is supported or not. Following are a few random Google hits on the subject that I've only glanced at long enough to think that there's plenty of room for theory development in this field!

My friend Edward is on the front page of nytimes.com today!

2010-04-26T17:10:00.003-05:00

My friend Edward Marcotte is on the front page of Nytimes.com today! It's a good article about his lab's incredible "phenolog" work. Way to go Edward, John, Kris and everyone else involved!

Biological comparative advantage simulations 1

2010-04-25T12:50:00.022-05:00

I gave myself a few days break from Traitwise coding this week which was enough time to think about some science once again. As a result of a talk with Andy I got around to coding up a simple kinetic simulation of a hypothetical trading system between two cellular "agents". It is far from a completely justifiable molecular system but it does now capture the heart of the matter. It was a little trickier to write than I had imagined -- as usual there was some divide between the hand-wavy description and the accounting of each important detail.

Background
From economics arises a lovely little non-obvious theory called "comparative advantage" that demonstrates how trading pressure arises. I have a stock illustration of this which involves an old man and young man living on an island. (Yesterday I went and looked at the Wikipedia article and saw a very similar description and it took me a while before I remembered that I was the one who had written that part of the Wiki article!).

Imagine an old man and a young man are on an island. Suppose the following:

there's only two products needed by both: fish and water
neither man is close to satiated: i.e they want as much of both products as they can get
they both consume with a 1:1 ratio of fish and water
neither has or will ever meet the other

Each man makes a choice: he could only gather water and thus catch no fish or he could only fish thus gather no water or -- realistically -- he could find some combination of the two activities that maximizes his consumption. The area of "production possibility" can be visualized as in the following graph. The young man can allocate his efforts anywhere under the blue line and the old man anywhere under the red line. Under the assumption that neither man is satiated then the optimal production for each is at the intersection of the consumption line and the edge of their production possibility area. (Click to enlarge figures.)

One day the young man is hauling water back from a spring and stops for a break at a big rock. He accidentally forgets one of his buckets and continues on his way. The next day, the old man who knows nothing of the presence of the young man, stumbles upon the lost bucket of water while returning from a fishing hole. The old man values water more than fish because for him to gather one unit of water costs him two units of fish. Seeing the precious water just sitting there he decides to abandon two of his fish and picks up the water and heads on his way. A little while later the young man returns along the path and sees that fish sitting there on the big rock. The young man values fish more than water because if he wants a fish it costs him two units of water so he decides to leave two units of water behind and pick up that fish.

You can imagine this pattern of leaving-behind one thing and taking-the-other could repeat itself day after day. Both men are better off engaged in this trading game -- they both increase their consumption. Note that the men do not need to know about the others existence -- as far as they are concerned each are simply abandoning a less valuable product and picking up a more valuable one. The pressure to trade does not require understanding the mechanism nor personally engaging with the trading partner. Rather, the pressure to trade is a mathematical consequence of the comparative cost of production each agent. Given the simplicity, I imagine that such a "leave and take" trading system could easily exist between species (say micro-organisms trading metabolites) or between agents of the same species (such as members of the same microbial colony) given differences in micro-environments.

Consider the long-term consequence of our two-man island "economy". The old man finds that he can consume more of both fish and water by specializing in fish production and dropping the fish off at what he thinks of as the "magical" fish-to-water conversion rock. Likewise the young man finds he can consume more of both fish and water by specializing more in water and dropping off some water at what he thinks of as the water-to-fish conversion rock. Each would begin to push his production towards his personal comparative advantage as illustrated below.

The amazing thing about trade is that both parties end up consuming outside of the limits of their own production. Furthermore, the trade benefit is mutual despite the fact that the young man is better at both activities! This result may be counter-intuitive but perhaps is more obvious when stated as "a group is best off when everyone in the group is working in a way that maximizes the time spent on their best abilities." Note that this is not the same thing as saying: "everyone should work on nothing but what' they're best at" as that statement does not account for the fact that the consumption may not be maximal in that situation. There is *some optimal mixture* that is prejudiced towards each agent working on their best ability but is unlikely to be at the extreme for everyone.

Consider the limiting case of the two-man island economy: as specialization occurs, the old man will hit a vertex first; that is, he will end up doing nothing but fishing. In contrast, the young man will end up fishing *and* gathering water albeit more water and less fishing than would have been the case if there was no trade.

The long term consequences of this hyper-specialization can be profound.

If the old man completely abandons gathering water then he may lose his ability to do so. For example, his buckets may go un-mended, he might lose track of where the good springs are, etc. In the short-term the trading is mutually beneficial but in the long-term the old man's situation may become brittle. That is to say, if the trading were to suddenly stop for some reason (for example, the young man might be injured) then the old man might suffer a severe short-term inability to gather water. In the worst case, he might die before he could re-establish his water gathering skills.

Thus the short term benefits of trade may also lead to longer-term danger. It is this conundrum that should be at the heart of free-trade vs. protectionist debates. Both extremes are correct: free traders are correct that trade benefits everyone but protectionists can be correct to argue that free trade may create dangerous, brittle, dependencies. It is reasonable social policy to find a balance that reaps some fraction of trade benefits while also avoiding over-specialization as insurance against future catastrophe.

That said, one almost never hears the above reasonable trading arguments. Instead one hears a much more simplistic and selfish argument regarding "taking away jobs" vs "cheaper products". As the island economy story demonstrates, engaging in trade does not reduce total labor (both men are still working full-time in the island economy) yet it does increase total consumption. That said, in a macro-scale re-telling of the same story the specialization by the two sides would imply that one sector of the economy (say, the fishing industry) would either have to switch its investments and labor to water production or the labor and capital would need to be allowed (and be willing) to move from one area or country to the other. In reality, neither option is in the short-term best interests of the most effected minority -- the owners of the capital and and labor employed in the existing industry. Therefore one (quite reasonably) hears the loudest anti-trade voices coming from those few who are greatest effected. They're best rational argument against trade would be to demonstrate that the proposed trade was not in the long-term interest of their society by an over-specialization argument. Alas, the best rational argument is too rarely the best emotional argument and so instead one usually hears anti-trade rhetoric as status-quo preserving, supposedly job maintaining, often nationalistic, calls against some particular free-trade agreement.

Back to biology
The contrived island economy story is of course an over-simplification of any real human economy; however, it isn't that far at all from a plausible biological story.

Imagine two humble cells who find themselves in some micro-environment where metabolites might be exchanged in an unconscious "market" akin to the magical trading rock on the island economy. Instead of fish and water, imagine the cells exchange two kinds of molecules, let's say two kinds of amino acids.

Suppose that each of these cells can make make either amino acid on their own or their can import or export either of these. With no trade, each would homoeostaticlly regulate their production so as to match their consumption at the limit of their production as demonstrated in the following figure (a copy from above).

Using some hypothetical trading mechanism one imagines that they would be better off to export their lessor valuable products into the inter-cellular space when the are able to import their more valuable product. That said, they would have to defend themselves against parasites that took from the environment without returning any benefit (we'll return to this.) I suggest that a molecular implementation of such a trading mechanism is fairly easy to imagine and it is this that I've been simulating.

Suppose there's a molecular importer that, as a result of importation, has a side reaction. Suppose this side reaction regulates an exporter of a different product. The ratio of the import quantity to the export quantity is the "price function". Let's imagine that the price is established by some other mechanism, for example it might be hard-coded as a result of evolutionary pressure or perhaps it might be determined by dynamic measurement by cellular hardware . Further suppose that the exporter leaks a little bit to "advertise" the existence of the exported product. If two cellular agents implemented this same mechanism yet had complementary price functions, the system should spontaneously engage in unconscious and mutually beneficial trade as described above.

Simulation
I wrote a first approximation of this machinery in Matlab using the following differential equations.

kn = arbitrary rate constants

M0 = slope of the production possibility line of the "old" cell (the one with the worse production abilities)
B0 = y-intercept of "old" cell
My = slope of the production possibility line of the "young" cell (the one with the better production abilities)
By = y-intercept of "young" cell

So1 = storage of reagent 1 by the "old" cell
So2 = storage of reagent 2 by the "old" cell
Sy1 = storage of reagent 1 by the "young" cell
Sy2 = storage of reagent 2 by the "young" cell

Po1 = production of reagent 1 by the "old" cell
Po2 = production of reagent 2 by the "old" cell
Py1 = production of reagent 1 by the "young" cell
Py2 = production of reagent 2 by the "young" cell

E1 = environmental concentration of reagent 1
E1 = environmental concentration of reagent 2

Ro = "old" production ratio = Po2 / Po1
Ry = "young" production ratio = Py2 / Py1

With rules as follows...

"import in proportion to the concentration gradient between inside and outside of cell, never exporting more than you have"...
importO2 = max( 0, k1 * ( E2 - So2 ) )
importY1 = max( 0, k1 * ( E1 - Sy1 ) )

"leak a little bit to 'advertise' the availability of less valuable product"....
leakO1 = k2 * S01
leakY2 = k2 * Sy2

"export in price proportion to what's imported but never more than you have"...
exportO1 = max( 0, min( S01-leakO1, 2 * importO2 ) ) * (e ^ -k5 * E1)
exportY2 = max( 0, min( Sy2-leaky2, 2 * importY1 ) ) * (e ^ -k5 * E2)

"Slow exporting if the external concentration grows too high"....
exportO1 = exportO1 * (e ^ -k5 * E1)
exportY2 = exportY2 * (e ^ -k5 * E2)

"Consume in a 1:1 ratio. Consumption this limited by the least available product"...
consumeO = min( S01, S02 )
consumeY = min( Sy1, Sy2 )

"Regulate the production, moving along the production limit line so as to move the storage ratio towards a 1:1 ratio. (Bound production so that it doesn't go negative)"...
targetPo1 = max( 0, min( -Bo/Mo, Ro * Bo / ( 1 - Ro * Mo ) ) )
targetPo2 = Mo * targetPo1 + Bo
targetPy1 = max( 0, min( -By/My, Ry * By / ( 1 - Ry * My ) ) )
targetPy2 = Mo * targetPo1 + Bo

Integrate with the following 10 differential equations...

d/dt So1 = Po1 - exportO1 - leakO1 - consumeO1
d/dt So2 = Po2 + importO2 + consumeO2
d/dt Sy1 = Py1 + importY1 + consumeY1
d/dt Sy2 = Py2 - exportY2 - leakY2 - consumeY2

d/dt Po1 = k3 * ( targetP01 - Po1 )
d/dt Po2 = k3 * ( targetP02 - Po2 )
d/dt Py1 = k3 * ( targetPy1 - Py1 )
d/dt Py2 = k3 * ( targetPy2 - Py2 )

d/dt E1 = exportO1 - importY1 + leakO1
d/dt E2 = exportY2 - importO2 + leakY2

Results
The result is more or less as expected. If you remove exporting, importing, or leaking, the cells will move to their respective maximum production/consumption points. If you permit the trading, they will adapt to each others exports and regulate their production. Each ends up consuming outside of their personal production hulls as predicted. The "leak" rate can be very small -- it changes only the time it takes before they find each other. Once the symmetry is broken by the leak, the trading regime can emerge rapidly.

One part of this system that I initially omitted turned out to be very important (and obvious in retrospect!) -- the cells must monitor the external concentration of the exported product. If they export based solely as a function of their imports then as the system reaches saturation the "young" one will continue to export when there is no ability for the "old" one to consume any more. As a result, the external concentration of the "young" cell's export product will rise indefinitely thus preventing that cell from increasing it's consumption further due to wastefully dumping product into the environment. At saturation, the exporter must recognize that the exported product is not being used (for example, my measuring high external concentration) and respond by attenuating its export rates.

Returning to parasites. Imagine that one of these agents or some third party tries to "cheat" the system by consuming the export products found in the environment but not exporting anything of its own. In that case, the exporters would reduce their own exports because they're would not be receiving sufficient inputs. In other words, the system is robust against cheaters -- it simply returns to the state as if the trading paradigm didn't exist. Thanks to the small leak, if the cheaters disappear the trading will resume. In this regard, the simple proposed system is an analog computer version of "tit-for-tat".

Next I'm going to try to build a more "molecularly" realisitic simulation and then run many of these systems in parallel. In particular I want to simulate the group behavior in plausible experimental setups such as in a petri dish or chemostat. Especially on a surface, I suspect that spatial constructs will spontaneously emerge as waves of cooperation and defection propagate around the environment as has been shown in similar digital simulations by Axelrod.

Tree sculpture in bedroom

2010-04-15T00:27:00.003-05:00

I've barely had a chance to do any house projects because of work on Traitwise, but recently I did finish up the tree sculpture in my bedroom/bathroom. This is one of the first ideas I had for my house and one of the last to actually get implemented! This view is looking up from my bathroom toward the shared ceiling with my bedroom on the other side of the green wall.

Traitwise alpha general release

2010-03-18T17:31:00.004-05:00

We've made a lot of progress on Traitwise our engine for permitting people to ask and answer seemingly random health-related questions. From this public Q&A we find correlations among all the participants and permit you to understand yourself in a larger context. We also hope that in the long term this gigantic dirty database of answers will reveal interesting things about human health. And, even through we've only barely begun to populate the database, already the correlation engine is turning up intriguing things. For example, some I've looked at today...

Reporting that you "have trouble regulating your emotions" is strongly correlated to experiencing significant forgetfulness.
Experiencing dry mouth is correlated to napping
Being irritable is correlated to being clumsy

While some of these might be statistical flukes (we are, after all, already testing about half a million hypothesis!!) the engine will soon be able to crank up the sampling of those high-interest correlations so that we can asertain if these are statistical flukes or not. Of course, this all depends on participantion, so I beg all of my friends to go to traitwise.com and participate as well as forward the link to whomever they can.

http://www.traitwise.com

Traitwise alpha -- Call for participation

2010-03-07T15:51:00.004-06:00

As many of my friends know, I've been working on a project for sometime that aims to develop a user-friendly interface for answering and creating health-related questions. We are excited to release the alpha version of http://www.traitwise.com and hope you'll help us by participating.

Traitwise is about giving us all a voice in our own health care. Not only can you answer questions, but you may develop questions of your own about any health related subject. We would very much appreciate it if you would create an account and then create questions,
especially about specific diseases or conditions based on your own experience -- after all, no one knows better about a condition than those who suffer from it.

The question creation process is very easy, and don't worry about making mistakes -- all questions go through a review process.

If you are interested in creating questions, you may review the question creation guidelines here, which may make the process easier for us:
http://communities.traitwise.com/mediawiki/index.php/Question_Creation_Guidelines

For those super-technical friends of mine, be sure to check out the "Analytics" page and see a prototype of how it is that our system finds interesting patterns. (Try "sleep" as an example).

Please note that as this is an alpha release and thus there are plenty of bugs to find (please report them on the "Feedback" page) and many features missing. The most important of the missing features is "results" -- that is returning back to you the interesting findings about your health. As it is now, the system mostly takes from you (your answers and questions) but gives back very little (the results). By answering questions, you are helping us to gather a sufficient amount of data that we may fully develop the results pages.

Thank you for all your help!
http://www.traitwise.com

Closet, bathroom, and bedroom

2010-02-24T17:29:00.003-06:00

Bruce delivered the major pieces of my closet drawers and shelves today! Hooray, storage! We use the same CNC web-based box builder as before -- "Top Drawer Components" -- just love the results from them. Every box is dove-tailed, perfectly square, and already polyed at very reasonable prices. For the drawers I'll eventually put on drawer plates that will hide the slider hardware.

For some bathroom storage we ordered two different sizes of box and screwed them together for this nice effect. (There's several more bathroom fixtures yet to be installed.)

Meanwhile, last week we started on the "tree" element that spans out between then bathroom and the the bedroom. There's a lot more pieces to add to this, but all the heavy stuff is done.

Fountain pumps

2010-02-09T10:21:00.003-06:00

It's taken years to get around to, but the fountain by my back door finally pumps water. Still lots of details to clean up -- hiding the plumbing and finishing the brickwork, but progress nevertheless!

Meanwhile, I've commissioned a bas-relief sculpture of the nerd-martyrdom of Hypatia from my friend Holly Melear that will go on the top back along the wall.

Found art - child's game map

2010-01-27T10:14:00.005-06:00

I found this awesome playful game map laying carefully folded up in the park this morning. No doubt left by one of the neighborhood children, a game designer at heart. Game industry friends -- give this kid a job before school beats this wonderful playful world out of him/her! :-)

Camera ethernet

2010-01-10T19:00:00.001-06:00

One or the combination of drugs I'm on (buproprion and celexa) induce very vivid dreams. The other night I dreamed about allowing laptop computers, which now often have built-in cameras, to communicate with each other by flashing their screens at each other. If the 640x480 cameras ran at 30 fps at, say, 50% efficiency then you might be able to achieve 30*(640*480)/4*8/2 = 9 Mbits/sec which is about the bandwidth of first generation Ethernet. (Although realistically I'd be impressed if you got 1 Mbps.) Implementing this might be a fun student programming assignment.

(Yes, it's true, I have super nerdy dreams! What did you expect?)

Lego the idea vs. Lego the product

2010-01-10T17:56:00.006-06:00

Not Lego
(Absurdly custom modern Lego part from lego.com)

In engineering circles (such as the molecular programming conference where I am today), the word "Lego" is commonly used as a synonym for "an elegant and simple basis set whose parts can be arranged to assemble anything." The Lego company should be proud of the fact that their product has inspired at least three generations of engineers to the point where their name is evoked as the gold-standard of an elegant functional basis set.

However, the irony is that while engineers have adopted Lego as representing platonic perfection of elegant engineering, the Lego company itself has apparently abandoned the idea. Lego's current sets are monstrosities of custom non-interchangeable parts as shown in the picture above. The engineering-driven ethos that encouraged creativity to emerge from the arrangement of simple blocks has been replaced by a marketing-driven ethos of product tie-ins and creativity-free model building. At best, today's Lego users are encouraged to build their super-specific models where practically every piece is custom and then tear them down to reuse some of the pieces in non-intended ways. But, this is a far cry from starting from a bucket of rectangular bricks and then dreaming up one's own creations. As a result, Lego might make more profit, but new generations of engineers will not be inspired in the same way as before.

Other toys, such as the supremely well-designed K*Nex, have tried to fill Lego's lost role but the marketing people there have also apparently taken over the company and have infected K*Nex with the same kind of absurd non-generic parts as demonstrated by this Sesame St. tie I found on their site.

Not K*Nex
(Absurdly specific product tie in from knex.com)

The evolution of these toy companies from pure-nerd-vision to marketing-tie-in-sell-out is a perfect demonstration of how nerd-culture and marketing-culture will forever be in a violent struggle. As far as toys go, we're losing.

Full scale automaton

2010-01-02T15:31:00.006-06:00

British automaton
From Ray Bate's reconstruction

Torre dell’Orologio, Venice
From flickr user kukudrulu

Last night I had a beautiful dream where I was in a huge building that was full of an elaborate automaton -- gears, levers, etc. Part of the machine had real people acting like the characters of a traditional automaton in old costumes such as might have been worn by the little figurines decorating an medieval automaton church clock. I think it would be a beautiful piece of theater to make a set like this where the participants come in, explore the space, flip levers and knobs causing the the actors to animate -- perhaps interacting in a full-scale puzzle game where there's some sort of order-of-operations problem to be solved by the group.

Star Trek and Vitalism

2009-12-29T21:26:00.005-06:00

I've been watching all of the original series of Star Trek on CBS classics recently. Star Trek is full of conceptual contrivances for the sake of the plot. The list is almost unbounded. Faster than light travel, "humanoids" on every planet, universal English, teleportation, gravity control, etc. I'm willing to forgive most of these as stagecraft -- they either help advance the plot or are needed for obvious production reasons. There's also plenty of just plain silliness such as in Trouble with Tribbles when it is said "Odors can not travel through the vacuum of space" (of course they can) while we hear explosions from blasted space ships (which, of course, you can't).

However, one theme that annoys me constantly, and most certainly is not needed for plot advancement is the incessant evocation of Vitalism.

Vitalism is the idea that there's some sort of "elan vital" that animates the living. The idea seems obvious: living things are so different form non-living things that, surely, there must be some unseen force that defines the state of life. It is a wonderfully intuitive idea; it suffers only from the small problem that it's completely wrong as has been known now for more than a century.

The falsification of Vitalism and the unraveling of the molecular basis of life is certainly the most significant outcome of centuries of biological research. As counter-intuitive as it seems, everything we call living is "merely" chemistry -- made of the same material as dead stuff. We have explored all the way down to the bottom of the phenomenological stack and all that's there is molecules acting like molecules. There's no magic juju, there's no vital essence, there's no "spark" that separates the living from the dead. That said, just because life is made of "mere" molecules, that doesn't make it any less amazing or mysterious. Indeed, to me it makes it much more awesome and magical. I've talked to some people who seem to think that this deconstruction of biology into "mere" chemistry somehow lessens the magic. To me this is as nonsensical as saying that the transcription of poetry into "mere" letters lessens it's emotional impact.

Unfortunately, the news of the great accomplishments of the biological sciences have not infiltrated the consciousness of even the most well-educated. The ideas of Vitalism are just too intuitive to be undone by facts and thus it is still very much alive and well as demonstrated by its casual usage in "science" fiction such Star Trek.

A common example from the bridge of the Enterprise is that Spock will look into his scanner and announce authoritatively that there's only "one life form" on the planet. Inevitably they beam down and the planet is covered in alien plants. Apparently plants are not "life forms".

A more egregious example of Vitalism in Star Trek is the conflation of energy, life, and emotion. In Wolf in the Fold Spock says, "deriving sustenance from emotion is not unknown in the galaxy..." and later adds, "It's consciousness may survive consisting of billions of separate bits of energy floating forever in space, powerless." to which Kirk adds "But it will die, finally". This idea that emotion is some sort of expression of the vital animating spirit is at least as old as ancient Greece and Egypt. So too are the deistic explanations for the presence of this supposed force. And this too infects Star Trek. In Metamorphsis, Spock says to a nebulous "energy" creature called The Companion: "You do not have the ability to create life." and The Companion replies: "That is for the maker of all things." to which everyone seems to agree.

This lack of biological perspective is hardly unique to Star Trek. Pervasive in common knowledge is the idea that only things with "emotion" are "alive". If you ask people to name life forms on Earth, you'll typically get a list of big-eyed mammals. If you push hard you might get a bird. Only upon noting that things also live in the sea will most people remember fish. Forget invertebrates, nobody notices them except when whacking them with a fly swatter. And the most common life on the planet, micro-organisms, are only considered, if ever, under the heading of "nuisance" despite our total dependency on them for, well, basically everything.

Star Trek's lack of biological perspective is a real let down. Its unquestioning and casual acquiescence to Vitalism isn't a forward-looking intellectual challenge like anti-matter engines, teleportation, or sentient robots but rather is a backwards-looking reversion to pre-scientific superstitions.

Apparently I'm everything that's wrong with the world

2009-12-27T09:50:00.006-06:00

Good news: the source of everything that's wrong with the world has been located.
Bad news: it's me

For a Christmas eve activity, my neighborhood decided to have an outing in the park directly in front of my house. My contribution was a bonfire. As tends to happen at such gatherings, you meet some of your neighbors for the first time. One neighbor discovers that I'm the owner / builder of the interesting Gaudi-esque house we're standing in front of and proceeds to tell me how much he loves the house and how great it is that I tried something different, etc. After a little while the conversation changes to the historic housing tax exemptions that are common in my neighborhood (for which I, of course, am not eligible since my house is new). They were discussing how much money they would save on taxes by declaring their expensive beautiful houses to be historic. I casually pointed out that while I understoodd their desire for a tax break, and indeed would probably do the same thing if I was in their position, that surely they'd have to understand that I'd be against such tax breaks for obvious reasons. "Oh but what about the character of the neighborhood?" they replied. "Which character would that be?" I replied, "Faux American Colonial? Faux Craftsmen? Faux Gaudi? It's not that I don't like these houses, I do, that's one of the reasons I live here, but let's not pretend that they represent some great monument to human achievement. Again, that said, I totally understand why you guys would want to use the law in your interest and get a tax break. But if it came up for a vote, I'd vote against it."

This was not greeted well. An aggressive: "You don't think we should save historic things?" is quipped back. "I dunno," I mused, "Life includes a lot of change and renewal, sometimes we should embrace it."

And for this bit of shocking opinion on the meaning of life I am met with my neighbor angrily saying: "I can't talk to you anymore." and storming away. At first I thought he was joking because his reaction seems so out of proportion to the topic. Someone else quietly said that they agreed with me and this brought him back angrily shouting: "He said that he wants to destroy all historic things!" I replied calmly, "actually that's not what I said...." but before I could explain my position, he yelled at me while wagging his finger: "You're everything that's wrong with the world. Money! Money! FUCK YOU!!". As he stormed away I quietly replied: "Merry Christmas to you too."

For the record, my full position is that, of course we should save historic things -- I just think that we should do it collectively by purchasing landmarks with public funds and then leasing them out or preserving them. The current method that permits some people to receive a tax break for living in old, beautiful houses strikes me as an extremely inequitable tax reward exclusively benefiting a small cadre of rich people because "historic" homes are almost always in old, nice neighborhoods where the property values are high. Furthermore, the extremely lax standards of what makes something "historic" are capricious. For example, a house around the corner from me has been declared historic because a man who lived in it once was said to be a "prominent doctor" when they found a 1 inch newspaper column about him from the Statesman decades ago. (He's actually still alive so technically he's not quite "historic" yet). By these low standards, every house that has been occupied by a professional (i.e. practically every house in every well-off neighborhood) will become "historic" eventually.

The absurdity of this to me is that after I die my unique house will probably become "historic" and the owner after me will get a big fat tax break. But I, who actually did all the work to create this unique house, who literally hurt his back laying the bricks, who spent a great deal of money and effort to create something interesting that might be appreciated into the future, I get nothing. Meanwhile, my neighbor who hypocritically likes my new house yet has forgotten that something had to be torn down to build it will get a tax break for living in and maintaining a house that is supposedly in the "character of the neighborhood" despite the fact that his house is only one of maybe two or three adobe-style houses in this supposedly "historic" neighborhood.

Absurd NY Times headline...

2009-12-14T15:16:00.002-06:00

"Obama Tells Bankers That Lending Can Spur Economy"

In other news,

Cheney tells plumbers that pipes help keep people hydrated.
Clinton tells IT departments that working computers increase productivity.
Bush tells football players that scoring points increases odds of winning games.
Gore tells doctors that curing disease makes people healthier.
Pelosi tells real estate agents that houses may keep roof over people's heads.
McCain tells rodeo clowns that deflecting bulls' attention may improve rodeo riders' safety.

Talk for EAST tour tomorrow (Thurs)

2009-11-18T19:25:00.003-06:00

6pm at Clayworks, 1209 E. Sixth St. It's a bit of a repeat of the genetic art design talk I gave a few months back, so if you saw that you're not missing anything. Otherwise, please join us.

Mexican wave quiver plots

2009-10-27T12:26:00.009-05:00

A lesson about interactivity. Having realized that I should be using quiver plots to understand the dynamics of 2-variable differential systems, I went back to the Mexican wave and made a quiver plot. In Matlab it is a slow task to tweak a parameter and re-plot over and over again so I made a zlab (C++) version of it that allowed me to twiddle the parameters in real-time.

What a difference! What took me a week before trying to understand the parameter space of this system now took me only 3 minutes. It is proof again of the power of interactive twiddling. When twiddling the variables the fast response and ability to "scratch" back and forth allows you to quickly intuit both the action and derivative of each parameter. When twiddling I was saying things like: "Oh... this is causing all the arrows on the left to go up" and "this is moving the steady-state point." I understand this system a lot better now.

In the following plots, I show two time traces at different places in space as indicated on the northwest space-time plot.

Plot 1: the stable Mexican wave. The third quadrant of the phase plot means "sitting & excitable (not tired)". Note that there is a stable equilibrium in that quadrant so if the system ends up anywhere in the 3rd quadrant then it falls into that basin and stays there until disrupted by, for example, a neighbor who pulls it towards the standing side.

Plot 2: two stable points. In this configuration, the 3rd and 4th quadrants have stable points so it simply transitions from the starting point in q3 until it gets knocked into q4. I guess if I were to hit it with a pulse of "tired" then I could get it to transition back again so this system is akin to a 1 bit memory. Haven't decided how to take advantage of this yet, but I'm sure there's something cool to be done with it.

Plot 3: oscillator. Now the equilibirum point has been removed from Q3 and so the system just perpetually oscialltes. Note that the oscillating attractor is stable -- the green and blue traces converge into the same limit cycle. I'm not positive what gives it this property, I thought that diffusion might be helping to stabalize it, but that's not the case as shown...

... in the following with no diffusion.

Plot 4: a system that has the Q4 equilibrium right on the boundary with Q1 so that it momentarily seems to be commit but then gets sucked into a small oscillator around the origin. This oscillator, however, does not appear to have a stable limit cycle so it dampens out.

Plot 5: a pattern forming system. Here Q1 and Q2 have a huge shearing force compared to Q3 & Q4. Somehow this seems to make it into a chaotic attractor but I don't really understand how yet.

Stability analysis

2009-10-21T17:47:00.000-05:00

I haven't been posting for a few months because I've been suffering from another bout of depression (as I have many times before) which leaves me mostly bed-ridden and unable to concentrate. Thanks to Welbutrin and an SSRI I'm starting to get better although I still tire easily and spend many days partially in bed. That said, at least I can now concentrate long enough to get a little work done and use my brain for a few hours a day. This one blog entry has taken me about two weeks to write. Thanks to everyone who's been helpful and understanding while I've been sick.

To help with the amorphous computing projects, I've been trying to get my head around concepts of stability analysis in differential equations. In most of the textbooks I've read, stability is discussed with an analogy to balls rolling on curved surfaces such as the one below showing the ball (representing the state of some system) near an unstable equilibrium at the the top of a hill and thus tending to roll down into a stable equilibrium at the bottom (these analogies ignore the momentum -- its as if the ball, i.e. the system, is moving through viscous honey).

While these "ball rolling" analogies are helpful, they become detrimental to understanding when the functions have complex-valued curvature. This confused me for a long time until I realized that I should think about systems as fields using quiver plots like the following.

In a quiver plot, an arrow is drawn to indicate the solution to the function at each point and this permits viewing both the magnitude and direction of the field. In the above case, we see a 2D section of a counter-clockwise rotational field from the Lotka Volterra equation which is a simplistic model of a predator / prey relationship; the details of this system do not matter, suffice to say the model creates oscillating behavior as a rise in population of the prey creates a corresponding rise in the population of the predator which in turn reduces the prey which reduces the predator, etc.

If we were to start the system at some arbitrary point in this space, say 0.5 rabbits/acre and 0.4 foxes/acre and then we can integrate the system forward to get a trajectory representing the evolution of the system. In the following example, the system starts at the red star and then the blue arc is ticked off in equal intervals of time. As the rabbit population grows, so too does the fox population until there's a rapid turn around as the foxes over-hunt the rabbits causing the fox population to plummet. If we let it continue we see that it would get back to where we started and it would keep on cycling in this trajectory forever.

The idea of stability analysis is to examine such plots for patterns around the equilibria. The above case entails a fairly complex analysis, so let's start simpler and return to this case later.

Let's start instead with a simple linear system with a single stable equilibrium at the origin. No matter where we start the system, it will evolve into this equilibrium at the origin. This is a stable equilibrium as all the arrows point into the same place.

The above simple linear system is represented by:

where Z(t) is the 2-vector that is the state of the system and and M = [ -0.1 0; 0 -0.1 ]. Note that M in this case is a uniform negative scaling matrix.

Now consider the opposite: a uniform positive scaling matrix, we get the graph where all the arrows point outwards:

In this case, even if we start extremely close to the equilibrium, say at [0.01 0.01], the system diverges rapidly. This is an unstable equilibrium.

The following is the in-between case: stable in one direction, unstable in another. This is called a "saddle point" because of the shape of a saddle: curving up (from horse's nose to rear) and curving down (from side to side). This is M = [ +0.1 0; 0 -0.1 ] . In this case we have a change in convexity around the equilibrium so an approach from any direction towards the equilibrium causes a deflection. We can therefore see that only in the case that all directions point inwards will an equilibrium be stable.

So far, these systems are like the valley and the mountain analogies typically used. But now consider this linear system which isn't like those:

Here, M is a rotation matrix = [ 0 0.1; -0.1 0 ]. Here if we start anywhere we get a circular orbit. It's for this kind of linear system that the "ball-rolling" analogies fail. There is no "surface" shape that would make a ball roll around in an orbit maintaining whatever radii it started at. The "ball-rolling" analogies just don't make any sense but the quiver plot does.

Finally, for illustration, here's a case where there's rotation and a saddle point at the same time.

So, how can characterize these cases mathematically? Eigen decomposition.

First, we solve the system for the places where the d/dt is zero, i.e. the equilibria. For the above linear cases, this is extremely simple: the equilibrium is at the origin. Now, we look at the curvature of the system around that equilibrium. Again, for these linear cases, this is very simple: the curvature is the same everywhere. That is to say, no matter where you look, the percentage change of the arrows is the same.

Eigen decomposition tells us the components of curvature. Consider the following system which is unstable all directions away from the equilibrium but it is more curved (ie "more unstable") in one direction than another. In green are plotted the eigen vectors scaled by the eigen values. In this case, the eigen values are 0.1 and 0.3, both positive, telling is that this system is unstable in all directions. The eigen vector (ie. the direction of instability) doesn't really matter if we're just asking the simple question "is this stable or not?" but I've chosen to plot it anyways just for illustration -- as you can see, the eigen vectors point in the directions of maximum and minimum curvature.

The sign of the eigen values tells us about the local curvature. A system is only stable if all the eigen values are negative: i.e. all the arrows point inwards. If the system has rotation, then the eigen values will be complex valued. That's what complex value means: that there's rotation in the scale factor. For example, the following has eigenvalues 0.17 + 0.09i and 0.17 - 0.09i and you can see the rotation in the field. Note that the two eigen values are complex conjugates of each other. This is just saying that you can look at this as either clockwise or counter-clockwise rotation by just changing the sign. Complex eigen values will always come in conjugate pairs.

Another way to intuit the complex-valued eigen values is to consider the definition of eigen direction as those directions that don't change under the given transformation. Consider a rotation matrix. What direction is invariant under a rotation? Nothing in the plane of the rotation! Whatever vector is invariant must somehow be perpendicular to the plane -- and what do we call the direction perpendicular to any system? -- the (stupidly named) "imaginary" direction.

You can also see from this why the complex valued eigen values come in conjugate pairs -- both the out-of-paper and into-paper directions are valid rotational axes.

Now that we've seen positive, negative, and complex-valued eigenvalues for linear system, we're ready to look at a more complicated system. In a non-linear system there may be more than one equilibrium and the curvature may vary from place to place. However, the eigen-decomposition tool can only be used on linear systems so we look at the approximate linear system right next to the equilibrium. This is called "linearization".

For example, consider this plot for a dampening pendulum. There's two equilibria: one at the bottom (angle zero) and one at the top (angle pi). The one at the top is a shearing unstable point -- a tiny displacement either way will knock the pendulum away. By the way, the graph is periodic: read x axis 2*pi the same as zero. You can see that starting the pendulum higher near the top causes it to spin around a lot faster and more times as you'd expect.

It's taken me 2 weeks to write this part so I'll post it now and another entry later on linearization of complicated systems like this one and the stadium wave we're working on for the amorphous computing demo.

ScienceNews

2009-10-20T20:01:00.002-05:00

A few points from my talk yesterday made it into the web edition of ScienceNews today.

Talk at Council for the Advancement of Science Writing

2009-10-19T16:01:00.004-05:00

Just gave a talk for a conference of science writers. They shot some (not so high quality) video of it viewable here.

The slide deck is here.

New paintings by Heather Jarry

2009-09-08T20:00:00.008-05:00

I commissioned a set of watercolors from Heather Jarry, a friend I've known since 6th grade. I adore Heather and her work and wanted to fill my house with her playful, colorful images. A few months ago we went down to the UT life science's library and I showed her a bunch of images that inspired me ranging from the research plates of the 19th century expedition of HMS Challenger to the molecular renderings of David Goodsell. I'm thrilled with the results. Be sure to click through on these images and see the details. Now I just have to figure out where I'm hanging all this new artwork!

A river of fireflies, inspired by the stories of synchronized fireflies from Strogatz.

Closeup of the fireflies

Inspired by microscopic drawings from HMS Challenger

Inspired by a diagram in Visual Complex Analysis

"Actin and Myosin", inspired by a drawing in Machinery of Life by David Goodsell

Water.

Study #1, elements of the Myosin, Actin can be seen here

Study #2

Study #3

A flag for the Nerd Republic

2009-08-12T10:56:00.003-05:00

When we are ultimately forced to leave the earth in the hands of the robot overlords, I propose this flag for our future Nerd Republic. ;-)

Thinking like a chemist

2009-08-07T19:43:00.010-05:00

Photo from flickr user zcreem

Suppose you were asked to mass produce a toy train car -- four little wheels connected to a small wooden chasis. Being an inhabitant of the 21st century you'd know exactly what to do: build an assembly line. After some tinkering you'd end up with some sort of jig that held the body into place and attached the wheels in a nice predictable fashion so that it could be repeated rapidly. Henry Ford would be proud of you.

But what if the wheels of the car were as small as atoms and the chassis a single molecule? Then how would you do it?

Such molecular assembly has been done for a long time, it's called chemistry. But chemists don't think about the assembly problem the way Henry Ford did. Their approach is fundamentally different.

A chemist would build the molecular toy car by putting four bazillion copies of the wheels into a bag full of water with a bazllion copies of the chassis and then they would shake the bag intensely assuring that some fraction, perhaps a minuscule portion of the original, would assemble themselves *by accident* into the toy car.

A chemist would then come up with a way to separate the fully assembled cars from all the left over parts that failed to assemble -- perhaps the vast majority of the pieces. For example, the chemist might dump the contents of the bag out over a pine tree. The un-assembled pieces, being smaller than the fully assembled pieces, might fall through the branches more easily while the the larger assembled pieces would be more likely to snag a branch and get stuck on the way down. As a result, the top branches of the tree would be more likely to hold the desired product. Then a chemist would snip off the top half of the tree and shake out the contents and repeat the process, knowing that for each repetition they have purified the sample a little bit. Having never even laid eyes on the target, they would declare that their end product was, say, 99% pure.

Seems absurd? It is. But it's also incredibly clever -- it permits the manipulation of atomic scale things by exploiting the fact that you are much, much larger than they are and can therefore easily move around quintillions of molecules inside of a "bag" no bigger than a drop of water. As a filter they'd use something like gelatin which at the molecular scale is a lot like the pine tree -- a big furry mess of interconnecting obstacles that would let some things pass though easily while inhibiting the movement of other things. As hard as it is to believe, this technique is accurate enough to allow separation by incredibly tiny differences in mass. Below is a picture of an actual gel, the light pink parts are the molecular batches (in this case DNA) that have been pulled through the gel which is the purple background. You can make out six tracks in this gel which is six different runs.

photo from wikicommons Gel_electrophoresis_2.jpg

Below is a picture of someone loading a gel. You can make out 10 "lanes" they are loading for their experiment. Into each lane they are placing a tiny drop of water using a pipette which is just a fancy eye-dropper. Each drop they are inserting into the gel might contain billions upon billions of the molecule of interest.

Photo from flikr user rocksee

Software prototypes

2009-08-07T10:30:00.007-05:00

(Images adapted from flickr users Duke TIP and Patrick Beeson)

One way in which software engineering differs from other engineering disciplines is that in software the prototype is often confused with the real thing.

Nobody looks upon a prototype 1/50th scale model of a bridge and says "Looks done, let's drive trucks across it now." Yet in software development such sentiment is commonplace -- "Looks like it's working, all we have to do is clean up the bugs and ship it!"

If this were merely a misunderstanding between the programmers and the business-types it would be understandable, but the unfortunate fact is that it's often the programmers themselves who believe this. This attitude of hack-and-patch contributes to the general lack of quality of software compared to other engineering disciplines and this is compounded by the perceived low-cost of failure. Structural engineers don't say to themselves: "If it doesn't work we'll just patch it in the field." Electrical engineers don't say: "Ahh, sort of works... we'll upgrade it after tape-out." It has never occurred to a mechanical engineer that they could hide their lack of quality control by creating an automatic update system that secretly updates their wares behind their customer's backs.

For software engineering to be done right -- like in every other creative discipline -- time and space have to be allocated for building *disposable* prototypes. There is no progress without failure, but you don't have to subject your customers to your failures either.

A month of web coding

2009-07-29T17:49:00.004-05:00

(Clever mug from stevenfrank)

I haven't posted anything in the last month as I've been on a web-coding sprint for our new bioinformatic enterprise: "Traitwise". This was the first time I've done any serious web-based development since about 1997. It hasn't changed much -- it's still a disaster.

The list of things that are wrong with web development would fill a book so here's my really short summary.

D/HTML is a disaster. It made a tiny bit of sense in 1994 when pages were, briefly, 99% text and 1% mark up. But now, even reasonably simple pages turn into 99% inefficient layout gibberish and 1% content. So the semantic premise of a web page has been inverted. Sarah told me that I should switch to the meta markup languages like HAML and she's probably right, but I didn't find out about that until too late.

CSS is a disaster. Obviously a committee with no programming experience and little vision of where the web was going came up CSS because only those ignorant of programming would be dumb enough to use "-" as a delimiter. But that's just a trivial gripe: the entire design of CSS is flawed. The base HTML semantic tags "p", "a", etc are not useful, only were for about 6 months in 1994, and now every page devolves into zillions of divs and spans each with a specific class moniker so you end up with a flat CSS "hierarchy" thus nullifying the CSS design and turning every page into a giant, un-readable mess.

JavaScript is a disaster. Actually, the core language is mostly OK but the portability -- the thing that really matters -- is a disaster. Thanks Microsoft! Oh, and also thanks to Google -- Chrome has broken JS even more. Chrome is the first product from Google that really pisses me off in a Microsoftian kind of way -- making the world a WORSE place instead of a better place. Attention Google, we don't need any more non-standard changes to the JS API. Please, just back away slowly from the browser market and let Firefox and the Internet standards committees lead the way. You're not going to profit from it anyway so please, just say no.

SQL is a (continuing) disaster. The inefficient mapping of the most rudimentary problems onto the relational database model is just plain wrong. The world needs a standard simpler transactional hash object that would do most of what you want as a web developer and be a lot simpler and faster. This is especially relevant given that environments like RoR are just building and mapping all these relationships internally thus nullifying the point of a relational database. RoR might as well just abandon the database and use its own transactional hash-oriented file system. The only reason they don't do so, one assumes, is the momentum of legacy databases.

Flash/Flex/AS3/MXML is a disaster. Let's sart with the marketing. What is the name of this product? Flash became Flex but is wrapped in MXML? Or is it AS3? Or is Flash the cleint-side run-time? Why do you compile .as3 files with an MXML compiler? WTF guys, how about version numbers, try them, they're great. I'm sitting next to Rob, a former Adobe developer, and even he doesn't understand the names -- we had a 15 minute argument sorting out which part of this product line is named what. There's so many confusing and broken things in Flash/Flex/As3/MXML/WhateverItsCalled I could go on for hours. I wasted untold days sorting out the simplest, stupidest things. I put "FLEXHACK" in my code next to every work-around or counter-intutive hack (like putting +5 on every textWidth) there must be 100 of those tags in my code and I got tired of putting them in after a while. Really basic concepts of object oriented programming are just flat out violated by their awful Flex design, for example the unclear dynamic typing, the UIComponent mess, and the lack of deep object duplication. But really, I could go on and on.... Like, how about the secret *deleting* of subversion controlled files off my hard-drive that the IDE didn't own -- that was just great! Or the secret deleting of comment lines at the top of the files in the IDE. Or the screwed up caching of a SWF in the wrong folder that frustrated me for several painful hours.)

The only thing that isn't a development disaster in my month-long experience was Ruby on Rails. There were a few odd things about it that threw me off (it was much stricter about type casting than I assumed it would be) but mostly it made perfect sense and Rails is obviously the work of a professional. Everything about Rails from the docs to the API's demonstrated that the author(s) knew what they were doing. I was impressed.

The nerd peacemaker

2009-07-09T12:28:00.003-05:00

Apparently these devices are also sometimes used to communicate with people and not just end arguments over the population of Mauritania or the mass of Mars, but I wouldn't know.

Updated birds and bees

2009-07-08T08:07:00.004-05:00

Daddy, where do babies come from?

Honey, when grown-ups love each other very much and decide to have a baby, which they do usually in their late thirties or early forties, they call an embryologist.

Em-bry-ol-ogist?

Yes dear. An embryologist gives the mother-to-be, assuming she's not just the egg-donor mother, in which case she'll be the biological mother but not the legal-mother, special shots which control her ovulation and then extract an egg from her ovaries under anesthesia. This is a tender act that only grown-ups do where the embryologist monitors the mother's follicles with ultrasound and may resort to a hormone antagonist to get the timing just right. Then the daddy-to-be, again assuming he's not just an anonymous donor in a cryobank, goes into a little room and uses provided magazines, or the gay magazines that are hidden under the sink, to auto-erotically put his germ-line in a dixie cup and gives it to a nurse. The two fluids are mixed in the precious beaker-of-love and that makes a zygote -- or, more typically, several zygotes.

Babies comes from goats?

No honey, not goats, ZY-gotes. Zygotes are single-celled fertilized eggs.

So then you have a baby?

Well, some people think so. Others think they're just tissue, like your skin or liver. Either way, the embryos get put in storage and whether or not you believe they are babies, everyone seems okay with freezing them solid.

Babies are frozen? Like popsicles?

Yup, that's how they come. Little babysicles. You defrost them like TV dinners and then you implant them in the mother's uterus, or the surrogate mother's uterus if the legal-mother-to-be can't or doesn't want to carry to term. But before you can do that, the embryos are graded for quality by how fast they grow.

Graded, like in school?

Yeah, like that, except those that don't win this race are destroyed.

You mean they're killed?

Well, some people think that. But then again, those slow ones were probably not going to implant much less make it to term so they would have died anyway.

Teacher said that my friend Tommy's not ever going to accomplish anything because he's slow since he goofs off. Are they going to destroy him?

Well, no, Tommy's not an embryo.

So, they should have been destroyed him when he WAS an embryo because he's slow?

Well, no, I mean, unless he was slow as an embryo, then yeah, I guess so. Anyway, pay attention, because this is where the act of love gets complicated since it's at this point where different insurance regimes have different policies. See, the procedure of baby-making is expensive, and the insurance companies in the US don't want to pay for more than one procedure so this puts pressure to implant more than one at a time. This increases the odds that at least one of the embryos grows to term but it's risky because you might get twins or triplets or even more sometimes. But in countries where there's single payer insurance then they just implant one because costs are better controlled. And that, honey, is why you have a fraternal twin brother.

But you said they plant three?

IM-plant three sweetie, not plant three. But yeah, they do, I mean, they did. You're sister or brother didn't attach so he or she didn't come to term.

I'm sad.

Yes honey, but not as sad as mommy and daddy were when the first two attempts at in vitro failed. The deductible almost killed daddy because back then daddy did contract work and could only afford catastrophic.

Cats a in trough?

No honey, "catastrophic" -- that's when the insurance company doesn't want to pay for baby making.

But what about baby sister? Why doesn't she have a twin?

Well, just to clarify, "baby sister" as you call her is actually older than you. See, she came from one of the frozen embryos from the first round of IVF because we switched back to the first embryologist on our third try because that doctor was then in-network to our HMO plan. So actually little sister was conceived two years before you, stayed frozen until you were three and was then unfrozen and implanted last year. She doesn't have a twin because her other two siblings didn't make it.

They died?

Well, yes, if you think they were alive in the first place. But that's something you'll have to decide on your own as you grow up.

I don't like baby making! I'm never-ever going to make babies! I don't want to talk about this anymore! WAHH! NO! NO! NO!

Listen, honey, you behave. Remember, we froze you once and we can freeze you again!

(Tip of the pen to Rob and Steve at lunch today)