Radio Interview on Studio 360

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

ScienceNews

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

My conversation with Alpha

I tried out Wolfram's Alpha this morning. First, something technical and mathematical as it suggests:

Where are the tidal phase singularities?
> Wolfram|Alpha isn't sure what to do with your input. ...

The same search on Google not only brings up links to maps but also brings up the scanned and OCR pages from Winfree's book -- via Google books -- where I got the phrase! Google is amazing.


Why should I use wolfram alpha?
> Wolfram|Alpha isn't sure what to do with your input.

The same search on Google came up with the pages on Wolfram's own site and many more reviews.


Why is Stephen Wolfram so cocky?
> Wolfram|Alpha isn't sure what to do with your input. ... person: Stephen Wolfram ... chemical element: element Wolfram

Tungsten (according to Wiki) is also called "Wolfram" which is why it has the the chemical symbol "W", but nowhere on Wolfram's summary page about Tungsten does it mention this. If you do this same search on Google the first hit is a Slashdot article about the outrageous TOS on alpha that's only *16 hours* old! Google continues to amaze.


How big of an ego does Stephen Wolfram have?
> Wolfram|Alpha isn't sure what to do with your input. ...

The same search on Google returns all kinds of hits from book reviews and whatnot complaining about his inflated ego.


All joking aside, I did like its stock summary page (one of its suggested searches). When you do ask it about something it knows does present a very well formatted result with lots of good technical information. But the TOS is absurd.

Understanding Principal Component Analysis via cool Gapminder graphs

Gapminder.org is a wonderful site full of "statistical porn". This chart in particular is a fascinating graph that demonstrates the correlation between income and child mortality rates. It is also a great example to teach about a cool statistical tool: "Principal Component Analysis".

In this graph of regions there is an obvious negative correlation between infant mortality and income illustrated by the fact that the data points scatter along a line from upper left to lower right. In other words, if you knew only the infant mortality rate or the income of a region you could make a reasonable guess at the other.

Principal Component Analysis (PCA) is a statistical tool that’s very useful in situations like this. PCA delivers a new set of axes that are well aligned to correlated data like this -- I've illustrated them here with black and red lines. For each axis, it also returns a “variance strength” which I’ve represented as the length of the black and red axes. (Actually I just hand approximated these axes by eye for the purposes of illustration).

The strongest new axis returned by PCA (the black one) aligns well with the primary axis of the data. In other words, if one were forced to summarize a region with a single number it would be best to do so with the position along this black axis. The zero point on the axis is arbitrary but is usually positioned in the center of the data (the mean). Positive valued points along this black axis would be those regions further toward the lower right and negative valued regions would be those further toward the upper left. Let’s call this new axis “wealth” to separate it in our minds from “income” which is the horizontal axis of the original data set. Increases in “wealth” represent an increase in income and drop in infant mortality simultaneously.

The second axis returned by PCA is shown as the red axis. Countries that lie far off the main diagonal trend-line (black axis) have particularly unique infant mortality rates given their wealth which we’ll assume is because of something unique about their health care systems. Points well below the black axis are regions that have very good health care given their wealth and those above it have particularly poor health care given their wealth.

Because PCA gives us convenient axes that are well aligned to the data, it makes senses to just rotate the graph to align to these new axes as illustrated here. Nothing has changed here, we've simply made the graph easier to read.



Before you even look at specific regions on these new axes, one could guess that socialist countries would score more negatively along this red axis and those whose economy is heavily biased towards mineral extraction -- where income tends to be very unevenly distributed -- would score more positively. Indeed, this is confirmed. The most obvious outliers below the black axis are Cuba and Vietnam where communist governments have directed the economy to spend disproportionately on health care and the outliers on the other side are: Saudi Arabia, South Africa, and Botswana -- all regions heavily dependent on resource extraction where the mean income statistics hide the reality that few are doing very well while the vast majority are in extreme relative poverty.

One particularly interesting outlier is Washington DC which is located as far along the red axis as is Botswana! In other words, based on this realigned graph, you might guess that the wealth in DC is as unevenly distributed as it is in Botswana. Fascinating! (The observation is probably at least partially explained by the fact that it is the only all urban "state" and urban areas will tend to have wider income distributions than rural/suburban areas.) Also note that all of the points in the United States (orange) are well into positive territory on the red axis -- our health care system is as messed up relative to our wealth as is Chad, Bhutan, and Kazakhstan -- countries with completely screwed-up governmental agendas. Think of it this way: the degree to which our infant mortality rates are "good" owes everything to our wealth and is despite the variables independent of wealth! In other words, countries that provide average health-care relative to their wealth like El Salvador, Ukraine, Australia and the UK fall right on the black axis but we fall significantly above that line -- roughly the same place as countries that are, independent of their wealth, really messed up like Chad and Kazakhstan. (A caveat: the chart is on a log scale so the comparative analysis is more subtle than I'm making it out here.)

PCA returns not only the direction of the new axes but also the variance of the data along those axes. To understand this, imagine for a moment that all the regions of the world had exactly the same health care given their income; in this case all the points would align perfectly along the main trend line (the black axis) and the variance of the red axis would be zero. In this imaginary case, the data would be “one dimensional”, that is income and infant mortality would be one in the same statement; if you knew one, you'd know the other exactly. Now imagine the opposite scenario. Imagine that there was no relationship at all between income and infant mortality; in that case we would see a scattering of points all over the place and there wouldn’t any obvious trend lines. Neither of these imaginary scenarios are what we see in the actual data. It isn’t quite a line along the black axis but neither is it a buckshot scattering of points, so we can say the data is somewhere between 1 dimensional and 2 dimensional. If both variances are large and equal to each other, then the system is 2 dimensional while if one of the variances is large while the other is near zero, then we know the system is nearly 1 dimensional. In other words, PCA permits you to summarize complicated data by finding axes of low variance and simply eliminate them. This technique is called “dimensional reduction” and is a very powerful tool for summarizing complicated data sets such as would arise if we looked at more than two variables. For example, we might include: car ownership, water accessibility, education, average adult height, etc to the analysis at which point performing a dimensional reduction would help to get our heads around any simplifications we might wish to make.

External link: My Manhattan Project

This is an excellent article in New York Magazine about a software engineer on Wall Street.

Some quotes and thoughts.

> "Over time, the users of any software are inured to the intricate nature of what they are doing."

Well put. This is the heart of all software successes and failures. Software is the perfect tool to lie to others and lie to ourselves with. It is the ultimate obfuscatory tool if you let it be.

Thomas Jefferson fought against a Hamilton-supported economy based on industry and banking. Hamilton was right, of course, but Jefferson had a good point. A detail of that eighteenth century debate that has intrigued me is: If financial instruments were already obfuscated to Jefferson in the 18th century, imagine what it must be like now? This article confirmed my intuition for what must have been going on: software sold and maintained by an external company helped to obfuscate the transactions to everyone involved. Of course the technology should have allowed it to be understood too but sounds like some monopolies of thought took hold because it was short-term profitable for them to. It was Jefferson's worries manifest in twenty-first century technology. Maybe there is some law lurking like "The Law of Constant Obfuscation" -- at any given time technology will permit obfuscation to a constant level.

> “Mike,” he told me when denying my request, “can you really look for people dumber than you and then take advantage of them? That’s what trading is all about.”

Ha!

> "I was very good at programming a computer. And that computer, with my software, touched billions of dollars of the firm’s money. Every week. That justified [my salary]. When you’re close to the money, you get the first cut. Oyster farmers eat lots of oysters, don’t they?"

Rationalization is such a powerful force! As is momentum. Feynman has an excellent point in one of his books where he's talking about forgetting why he worked on the Manhattan Project. He joined because, like his collaborators, the idea of Hitler having unilateral nuclear power was unimaginably scary. But, after Hitler was defeated, he forgot why it was he was working on this project and the momentum of the technical challenge remained. He regretted that he didn't re-evaluate his thinking after the VE day.

External Link: Energy Flux Graph from Lawrence Livermore Nat. Labs

I love this graph from Lawrence Livermore National Laboratory illustrating the flux of energy through the US economy. Some things that surprised me:

1) The amount of energy wasted in the transport of electricity is staggering, slightly more than the total amount of oil imported (in energy equivilent units); technological improvement in that sector would make an enormous contribution.

2) Transportation, as I expected, is woefully inefficient. What I didn't appreciate was the magnitude, the energy wasted by transport is approximately equal to all the coal burned!

3) The residential / commercial waste is surprisingly low. One assumes that some fraction of that waste is insulation and so-forth, but even if you took a big bite out of that with building improvements, you wouldn't make a dent in the big picture. It boils down to this: if one's goal is to reduce waste (which is a very different goal than reducing consumption) then electrical and transport are the obvious primary targets.

Flagella assembly video (external link)

This is a really nice video about flagella assembly (thanks to Ken for the forward). One detail I didn't know before was that the flagella proteins are denatured for export through a ludicriously small 1 nm channel. All the stuff about the hook length measurements were particularly interesting. Very cool!

http://video.google.com/videoplay?docid=14997924975209807&hl=en

Molecular and Cellular Videos (External Link)

http://www.molecularmovies.com/showcase/index.html

OK, I thought I'd keep my blog mostly about only my projects but sometimes one runs across something really cool and blogging about it increases its Google score. My friend Eric Siegel at NY Hall of Science sent me this link to large collection of nice molecular and cellular animation videos.

I love videos like this. That said, I do have a very big complaint about the non-simulations (most of them) -- they make molecules appear to be intelligent agents. Molecules do not make deliberate choices; they do not see a complex forming and then think to themselves: "Hey, I think I'll whiz over there and insert myself into that growing structure!" For example, see the microtubule growth in Inner Life.

It is completely understandable that the animators of these videos have a hard time capturing the reality of molecules because the velocities at which things happen at the nano-scale are extremely difficult to comprehend and thus it is hard to create these animation without resorting to the "cheat" of "deliberateness". Unfortunately this cheat creates a major confusion -- I know because I remember being confused! In Segan's wonderful Cosmos series, there was an animation of DNA polymerase with its reagents all flying across the screen to assemble themselves into a growing polymer. I distinctly remember as a nine-year-old thinking: "How do the parts know where to go?" No one told me that 1) that's a great question and 2) they don't.

Here's the way animators to create these effects. They place the pieces of the model together in their final configuration and then they tell the animation program to fling all these pieces away in random directions with random tumbles. Then they simply play the animation backwards to create the effect of the individual molecules assembling themselves into the formation (that's the easy way to do it anyway). It creates the lovely assembling effect but it is a lie -- a very, very interesting lie.

Think about it -- in order for the animators to make it look like the molecules know what they're doing they have to run time backwards. That isn't merely a statement about animation -- it affords a deep insight into thermodynamics. Things which "know what they're doing" are, in effect, "running time backwards". Getting your head around this idea is the key to understanding what life is, why perpetual motion is impossible, and failing to understand it is central to many misconceptions especially among creationists.

Molecules don't know where they are going. They just thrash around randomly due to collisions. The sum of all that motion is what we call "heat" -- more heat, more violent thrashing around. If you were to put some molecules in a little pile they would bounce off each other spreading out into a more diffuse pile. Why should they spread out and not stay put or even compact themselves tighter? Because, as long as they aren't interacting with each other (we'll come back to this case) there are a lot more ways to be spread-out than there are to be compact. Scientist call this by weird name "entropy" -- it's the second law of thermodynamics: entropy (spread-out-ness) is always increasing. It's an idea that's so simple and yet so profound. Why is it true? Nobody knows; that said, try to imagine what the world would be like if it were false.

Suppose that molecules spontaneously created little ordered piles without interacting (again, we'll come back to interaction case). Those little piles are information. In other words, you could look at them and say: "Hey, there's a little pile there that shouldn't be -- since they aren't interacting they should have spread out, thus, something must have put them there." And then what? What are these little piles of spontaneous information forming? Are they spelling out Shakespeare? Or drawing a picture of a cat? Or writing out a cryptic secret that we can't read? See, it's nonsense; you can't turn it around. When you try to imagine a world that doesn't spread-out spontaneously then you end up with a world where information spontaneously appears out of nowhere and such a world would be indistinguishable from one where time was running backwards. In other words, the concepts of time and increasing entropy are the same concept.

Here's another way to think about it. Suppose that you had a tiny ball in a tube trap. Say the ball can be on either side of the tube: left or right. If the ball and tube are not interacting in some biased way then there's just as much chance that you'll find the ball on the left as the right side. Say you tried to use this tube as a memory device with the position of the ball meaning different things. You reach in and move the ball to the left side and then shut the trap and hand it to over to a friend who examines it. You shouldn't be surprised that when they open it they are just as likely to see the ball on the right as the left. This is a terrible memory device! The reader of the information might as well have just flipped a coin instead of relying on this thing to remember what you entered. How would you fix this? You'd have to glue the ball in place somehow to prevent it from moving. So, how would you glue it? There's lot of ways, you could introduce a chemical bond that stuck the ball and tube together or you could jam in a plug or lots of other clever contraptions. But every way of "gluing" will have the same requirement: it will need an investment of energy. In other words, an investment of energy is the same thing as information. If you see a pile of energy laying around somewhere then you know that such a pile potentially holds information (what that information encodes or means, that's a totally different question). And vice-versa, if you know some information then it must be that case that energy was invested to make it known. The two concepts -- information and free-energy -- are the same concept! And this explains why you can't build a perpetual motion machine. If you could then it would be creating information out of nowhere which is the same thing as time running backwards. Or, to put it another way, if you do build a perpetual motion machine then (just try) to stay the hell away from it because that thing is running time backwards!

And this gets us back to life. If it is the case that things can't spontaneously assemble then how can there be living things which are made from spontaneously assembled molecules? The fact that life is so information rich, is this evidence that something made the investment of free-energy? Yes. Shall we call this investor of free energy some sort or god or spirit or vitalistic force? That's a reasonable question, and I've seen this argument in creationist literature, but the answer is: no.

This gets us back to the videos and what's wrong with them. The videos make it appear that molecules "know" what they are doing. The seem to "know" that they should fly through space and attach themselves to some cool growing nano-machine. But they don't. What they do instead is much more interesting. They bounce all over the place without knowing squat. Why don't the spread out? They do, but they are held inside of a bag -- the cell -- which keeps them contained. When they bounce around they accidentally find molecular partners with whom they interact. This is very different than what I described before with the ball in the trap where we assumed that there was no interaction. Now, there is interaction -- they stick like glue. As described, such gluing requires energy. Where does the energy come from? It is pumped into the cell from the outside. And when the interactions break, that energy is released at higher entropy (time moving forward) and that entropy is pumped outside of the cell to keep it from poisoning the inside. Living things are devices that invest free-energy from their environment to temporarily increase the information inside of the cell. This is only possible because they have access to the free-energy; no free-energy, no life. By the way, there’s lot's of things do this, not just life. For example, a whirlpool is a pretty clearly defined "thing" that it is possible because free-energy in the form of rushing water gets trapped into a shape that then dissipates the entropy out the bottom. Whirlpools, and living things, are not "things" in the sense that they are persistent collections of molecules -- they are things in the sense that they are persistent patterns of molecules -- the molecules themselves just pass right through.

What makes life really interesting and different from a whirlpool is that it is a self-contained computational device that stores the changeable instructions to copy itself. A whirlpool's pattern is created by the external circumstances around it -- the pattern of the rocks and the waterfall. In contrast, living things internalize the "circumstances" that build them (the DNA, the proteins, etc) thus living things can be viewed as a single package that makes decisions and evolves as a computational whole. The magic of living things is that no individual part (the molecules) "knows" what it's doing (my problem with these videos) yet the ensemble does "know" what it's doing! When we casually look at a living thing we can't easily track the energy flux in and the entropy flux out and thus living things appear unique, as if they were running time backwards -- exactly the trick the animators use to make the (wrong) animations. Ha!