7 Gpeople

While at a conference in Istanbul, I went to the İSTANBUL ARKEOLOJİ MÜZELERİ, which was an absolutely fascinating archeology museum. Istanbul has featured prominently in the growth of civilization, and I struggled to keep track of the many different civilizations and cultures that occupied the region at one time or another. I had to find a youtube video to help me sort it out.

There was a very nice exhibit on Troia (Troy), which apparently really existed; it's ruins were unearthed in a farm field not too far from here. It was settled, destroyed, and resettled in 9 different epochs before being ultimately abandoned. Even back then, it seems that anything you dug up had a 1000-year history. Buildings were built on top of buildings. The reconstruction of the different settlements was interesting.

It was really hard for me to get my head around how small cities were in comparison to now. Istanbul currently has 13 Mpeople living in its greater metropolitan area. In 3000 BC, that was the human population of the world. The largest cities in antiquity were ~250 kpeople. It made me wonder if all of our advancements in technology and culture in the last couple hundred years could be attributed strictly to 1) more people to do the work and 2) longer tails on the normal distribution of people with various abilities.

So just how many people were there as a function of time? The log-log plot above from wikipedia shows current best estimates. Apparently, some 70 kyears ago, possibly as a result of a major volcano eruption, the human population was reduced to something on the order of 1000 to 10,000 "breeding pairs." Since then, the population rapidly recovered to several million, where it remained stable until agriculture was developed. This is all in a nice video tracing genetic migration via mDNA.


Since then, there has been exponential growth (a line on log-log plots) with a transition to a slower growth coefficient at ~400 BC. Occasional Black Plagues aside, the human population has increased dramatically. I remember hearing once that half the people who ever lived are alive right now. That's actually definitely false--it's closer to 6%. Also, everyone seems to think that population growth is accelerating (remember this video from the 80's ?). The graph above definitely shows that's not true, either.

But what is true is that this growth cannot continue unchecked without hitting its head on something, be it food supply, global warming, danger of pandemics, warfare, declining birth rates, or whathaveyou. It's estimated that in October of this year, 2011, there will be 7 Gpeople on the planet. This map shows where the population currently is, but it's estimated that much of the growth in the next century will happen in poverty-stricken Africa. Things pretty much have to plateau around 10 Gpeople, though.

So what to do? The most effective ways to reduce birth rates, which is key to controlling population growth, global warming, saving the environment, and many of the rest of our problems are:

1. contraception
2. improving the standard of living (ending poverty)
   
3. education (and education about contraception)
   
4. and reducing infant/child mortality

That last item is counter-intuitive. The reason it is important is that when survival rates are low, couples have more children to compensate, including a buffer for uncertainty. Having a predictable path from birth to adulthood allows for more precision in family planning.

The "New" Zodiac and the Earth's Spin

The latest rage in popular astronomy seems to be the realization that the Sun may now move through 13 constellations instead of 12. I haven't personally checked this, so I'm going to take their word for it. What's bothering me is something else that's being repeated in connection--that this is "due to shifts in the earth's rotation and orbit", or more flagrantly, that "since the zodiac periods were established millennia ago, the moon's gravitational pull has made the Earth 'wobble' around its axis in a process called precession".
Someone (I guess, me) needs to make it clear that any shift in the apparent path of the Sun through the background constellations can only be caused by a change in the inclination of the Earth's orbit (possibly as a result of the precession of the Earth's slightly inclined orbit around the Sun), not the precession of the Earth's axis of spin.

The reason the Sun appears to move through background constellations is because we're moving around the Sun (see figure to left). From the perspective of Earth (blue dots), the Sun (orange) appears in front of a different set of stars at different times of year, when the Earth is at different positions in its orbit. The project of the Sun from the perspective of the Earth is shown with dashed lines.

Now the thing is, that dashed line from the Earth through the Sun doesn't depend at all on the Earth's spin. To see this, imagine you remove the Earth from one of those locations and instead place yourself floating in space. You could turn any which way you want--upside-down, rightside-up, twisted alley-oop--the Sun is going to be in the same place relative to the stars behind. Similarly, the Earth's spin (and any precession in that spin axis) can change the orientation of the Earth, but makes no difference in what stars the Sun appears in front of.

What actually can change where the Sun appears relative to background stars is the physical location of the Earth.
This is a change in the Earth's orbit, not spin. One way to change where the Sun appears relative to background constellations is to move the Earth to different places in its elliptical orbit. This will move the Sun through the standard set of zodiacal constellations. In order to move the Sun out of the normal zodiacal progression, you need to move the Earth up or down. The way this can happen is if the plane of the Earth's orbit precesses around another axis, so that the "high" point in the orbit moves slowly around the Sun.

So to clarify, if the Sun appears to move through a new constellation, it is because the Earth's orbit around the Sun has changed, not because the Earth's spin has changed.

Distribution of Actual Births Around Estimated Due Date

Given that we're now in overtime here for our second child, I have become very interested in the question of what our "due date" meant in the first place.

The plotted on the left are data from a study of Canadian births, 1972-1986 (Arbuckle & Sherman 1989). I then started trying to aggregate some data for my own plots.

The first thing I noticed required a little attention was the "fence post" problem relating to recording gestational age. If a study A records births in the 39th week, where exactly is that on the x axis? Well, if we assume that they started counting with 1, then the 39th week is actually 38.5 +/- 0.5 weeks (they are counting fence). But if study B records births from week 39-40, the implication is that they started at 0 (they are counting fence posts), so 39-40 is 39.5 +/- 0.5. That was a little tricky.

Then we have studies that bin over different time intervals. If another study C records births at 37-41 weeks, how do we relate that to A and B? The intelligent way to plot this would be to use the probability density of going into labor, which divides out by the length of time over which the observation was made. So we should be careful to do that.

And then there's just the general problem that a lot of studies list percentages for births in each time bin, but don't list total populations or error bars, so we don't know what the errors in their measurements were. Ugh. So I crossed my fingers and hoped they followed good practices with their significant figures: I assigned an error equal to the last significant digit they list.


I got most of my data from this semi-thorough compilation of census data and going to some of the original sources. The data aren't great, but they are adequate (see plot to left). I fit to the data an increasing exponential tail to the left, plus a normal distribution. The fit isn't great (despite some claims in the literature of it being normally distributed), but it captures enough of the overall distribution.


The width of the normal distribution was 1.5 weeks, centered at 39.5 weeks. This seems consistent with several sources that suggest ~10% of pregnancies would go into the 42nd week if they were allowed to. It also suggests that the "due date" means the mean of the normal portion of the distribution. Yet fully 1/2 of pregnancies will go beyond the expected due date, and 1/6th will go past 41 weeks, according to this coarse fit.

Of course, none of this accounts for biases that we know exist. The growing prevalence of inductions and C-sections move births earlier artificially. Although the statistical significance may questionable owing to systematic biases (self-selection for uncomplicated pregnancies, etc.), it appears that the recorded midwife births go later than the aggregate (presumably hospital-dominated) births at the 2-sigma level. This may potentially indicate that without intervention biases, the distribution of birth dates around the expected due date could be broader and weighted toward later dates.

Listening to the Astro2010 Decadal Survey

Here are some streaming comments as I'm listening to results of the 2010 Decadal Survey. A shortlink to the report is here.

11:10 am EDT: Excellent placement of "what were the first luminous objects, and when did they form" second from the top of "Major questions to address this decade".

11:20 am EDT: Ooh, even better. "Cosmic Dawn" is the first of the 3 over-arching fields. Good fielding for EoR as a top science priority in the next decade!

11:23 am EDT: Now we're starting into descriptions of the panels. I was involved in several of the RMS (Radio, Millimeter, and Submillimeter) submissions, and am looking for HERA (the Hydrogen Epoch of Reionization Array). I'm also rooting for the Allen Telescope Array's Radio Sky Surveys Project. Finally, I'm hoping for some mention in the TEC (Technology development) program of prioritizing the development of shared solutions to digital signal processing hardware and libraries, which was the recommendation of a white paper I drafted with the help of the CASPER community.

11:45 am EDT: Mention of SKA as a priority for Radio Astronomy, unsurprisingly.

11:47 am EDT: Looks like Roger's wrapping up here. Turning to Q&A.

Meanwhile, I'm reading through the report. I see radio instrumentation is listed as a funding priority on ES-4, linking to 7-39. A good sign.

A painful line on 1-18: "U.S. participation in projects such as the Square Kilometer Array is possible only if there is either a significant increase in NSF-AST funding or continuing closure of additional unique and highly productive facilities." Ouch.

But on 2-12, my own sky map (well, with "permissions pending" for now). Now that's something!

12:01 pm EDT: An interesting question. "Why such a priority on habitable planets in the decadal review?" Sounds like the answer is that it's particularly primed to make big breakthroughs. I think I agree with that. I wasn't surprised that it was on there. There's some rumors going around that Kepler has found earth-like planets in earth-like orbits.

12:02 pm EDT: What about the surplus of post-docs relative to faculty positions? Answer: there are a wide range of careers and positions available to astronomers, so it's not unreasonable to have a larger number of post-doc positions where budding astronomers get training. I'm not sure that answer fully appreciates the scale of the problem.

Continuing with reading, on page 3-13, "The HERA program, a project that was highly ranked by the RMS-PPP and included by the committee in its list of compelling cases for a competed mid-scale program at NSF, provides a development pathway for the SKA-low facility. Progress on development of the SKA-mid pathfinder instruments, the Allen Telescope Array in the U.S., the MeerKAT in South Africa and the ASKAP in Australia, and in new instruments and new observing modes on the existing facilities ... will provide crucial insight into the optimal path towards a full SKA-mid." That's good to see mentioned. Sounds like it lays the groundwork for a strong future proposal to get funded. It's not a promise of funding, though. Not that such a promise was expected.

12:11 pm EDT: Second use of "tripwires" for projects. A very colorful phrase.

Interesting plot on 4-15: papers in all astronomy fields are increasing. Instrumentation papers seem to be low in number, but holding their own against other fields (same percentage contribution to total paper number).

On 5-14 for Data Reduction and Analysis Software: "Flexibility, openness, and platform independence, modularity, and public dissemination are essential to this effort. Focused investment in a series of small-scale initiatives for common tool development ... may be the most cost-effective approach, although there are undoubtedly synergies with the pipeline development needed for the large-scale projects." Sounds helpful for some of my projects like AIPY, SPEAD, and CASPER.

12:18 pm EDT: Comments on the SKA? Answer: SKA is the future, but the US can't pay for the construction on the proposed time scale (but slower might be ok). Technology development should be prioritized though. Low-frequency SKA, though, targets EoR, and we're interested in projects targeting that. Yes!

On 5-21 for Technology Development: "The committee received community input in the form of white papers on the funding needs for technology development in areas such as ... high speed, large N correlators. In these areas and others, researchers ... had come together to plan a coherent strategy for the decade. The OIR and RMS panels made a convincing case that the current level of ATI funding needs to be augmented in order to successfully pursue these highly-ranked technology development programs and roadmaps." Looks like my white paper fell on receptive ears.

12:28 pm EDT: Neil Tyson is closing down Q&A. He is one cool dude. I'm glad he was on the panel.

On 7-7 for Science Objectives for the Decade: "Find and explore the epoch of reionization using hydrogen line observations starting with the HERA telescopes that are already under construction." Wham. And in Table 7.1 on 7-32, Priority 2, Projects thought compelling: HERA.

On B-2 for Program Priorization, in Table B.1, I see both ATA and HERA. I'd say ATA didn't necessarily win big in the review, but at least they're there.

And finally, in appendix D-1: "Hydrogen Epoch of Reionization Array ... is a multi- stage project in radio astronomy to understand how hydrogen is ionized after the first stars start to shine. The first phase (HERA I) is under way and will demonstrate the feasibility of the technical approach. The second phase (HERA II) would serve as a pathfinder for an eventual world-wide effort in the following decade to construct a facility with a total collecting area of a square kilometer and the power to make detailed maps of this critical epoch in the history of the universe. Proceeding with HERA II should be subject to HERA I meeting stringent performance requirements in its ability to achieve system calibration and the removal of cosmic foreground emission." We've got our work cut out for us!

Don Backer

Sadly, the world and I lost Don Backer on July 25, 2010. In addition to being an inspiring scientist, instrumentalist, and educator, Don was my graduate and post-doctoral advisor, and my close friend. He and I worked closely together from 2004 until last Sunday, when he died suddenly of an apparent heart attack.



Don was well known for discovering the first millisecond pulsar early in his career. More recently, he and I had been working on the Precision Array for Probing the Epoch of Reionization--and experiment for detecting the first stars and galaxies that formed in the universe. We recently had a made a lot of exciting progress with this experiment, and it is especially tragic to lose him at such a pivotal time.

Don was a very warm yet reserved man. He was always extremely busy, and I envied his ability to juggle a huge number of tasks at once. Yet every time I walked into his office, gave me a big welcoming smile, saying "Hi Aaron! Come on in." In that instant between when he looked up and when recognized me, I would sometimes see a hint of displeasure at being interrupted (a lot of people in the department walked into Don's office to hassle him about any of the many projects that he was involved in), but it was always gone the instant he recognized me, and I took pride in being someone from whom Don welcomed interruptions.

Don was always a model to me of how to be and instrumentalist and a scientist. I've long been interested in both building and using scientific instruments, and Don was a shining example of how to do both. I learned a lot from Don that helped guide me professionally, and I owe him a lot for his advice and generosity. It is sobering to consider that my next steps will have to be without Don's quiet support and encouragement. In many respects, though, Don's generosity has already helped pave the next steps for me. I'm sure I will continue to incur debt to him for years to come.

One of my favorite qualities of Don was his grand sense of adventure. Our foray into the Karoo desert to deploy PAPER in South Africa could not have happened without Don's enthusiasm for traveling, roughing it, and flying by the seat of the pants. I loved going on deployment expeditions with Don. He was always bright-eyed and smiling, summoning such energy at 66 years that I, at 29, struggled to keep up. It was not hard to see the Don of the black-and-white photographs, the same wiry energy and wry grin that stood in front of me.

Don was never very forthcoming with advice--he advised me more by example. I'm pretty sure this was a result of a very ingrained sense of humility. Don never said "you're wrong", or "you should". I think he didn't feel it was his place to pass judgment on people. Despite this humility, or probably because of it, Don was an effective leader. Without badgering people or using heavy-handed methods, Don brought people into consensus and helped move projects forward. Unfortunately, his effectiveness, coupled with his self-described "responsibility gene", meant that he was often called upon to bail out troubled projects, and he had a hard time refusing them. I often wished Don spent more time on PAPER. I think he did, too.

Don and I were a great team. I'm not a good multi-tasker. Don insulated me from a lot of project management, logistics, and distractions, carving out a space for me to work effectively toward our goal. Soon, some of the important products of our partnership will bear fruit, and I'm sad that Don won't be there to see it. But he knew it was in the works before he left, and for that I am thankful.

I'm sad to have lost a good friend and mentor. Things are hard now as we try to pick up the pieces of all the many things Don was managing. I'm sad that he's not here to help. He was always good at bailing us out.

Who Dominates Health Care Costs?

There's nothing like a little bout with MRSA to make one pay a little more attention to the state of health care legislation. Two nights in the ER are definitely making me thankful for health insurance. Knowing that it wasn't going to cost me an arm and a leg to get antibiotics through an IV (in fact, it probably saved me the leg) definitely helped me to seek care early, rather than waiting for the infection to get truly life-threatening. And that probably saved in health care costs in the long run.

I've heard it argued many times by the other side that universal health care will drive up the cost of health care for everyone, because so-called "healthy people" will be paying, through their premiums, for the bills of the "unhealthy". Ignoring that:

1. the above is a tautological statement about what insurance is
2. people routinely go from the "healthy" group to the "unhealthy" group and back again
3. we should maybe feel a moral obligation to care for the unhealthy

Yeah, ignoring that, I wanted to know if the underlying assumption was, in fact, true. Who dominates health care costs? Is it the small number of extremely sick people? Or is it the larger number of moderately sick people?

To answer that question, I went searching for the population distribution of health care costs. I found the following publication: Variations in Lifetime Healthcare Costs across a Population (Forget et al. 2008). To the left are reproduced Figs. 4 and 5.

Given all the hype, I was somewhat underwhelmed to see that these curves depict (with the exception of an excess at the lowest cost bin) a gamma distribution. This isn't surprising, because a gamma distribution is supposed to represent the sum of a bunch of exponentially-distributed random variables.

To find the contribution of people in each cost bin to the total health care cost of the population, we simply need to multiply the population of that bin (drawn from a gamma function) by the mean health care cost of that bin (a linearly increasing function). Setting the mode of the gamma distributon to $90k for females, and tweaking the k and theta parameters (I'll chi-by-eye it at k=4.5, theta=1.0) we get the following distributions of fractional population (black) and fractional total health care cost (red), as a function of lifetime healthcare cost:

So who dominates health care costs? Those just slightly above the mode, which is to say, the large number of people who are just a little sicker than most. And that really could be any of us, folks.

AstroBaki on MediaWiki

I just started up a new wiki called AstroBaki. The main reason I did this was that my MoinMoin AIPY wiki was clunky to use and was getting spammed lots. I switched to the MediaWiki engine, which has better automated control over these kinds of things. As an added bonus, MediaWiki has support for latex math. This got me thinking...

When I started grad school, I had a hard time transitioning from feeling like I was producing and contributing (I was working as a development engineer for SETI) to just absorbing knowledge. To make myself feel better and more invested in learning, I started doing something for which I became moderately famous around the department: latexing lecture notes on-the-fly. For full disclosure, I should mention that I copycatted the idea of latexing on-the-fly from my friend Phil.

The key to success is to use lots of "defs", and to recognize when you need to def a sequence of commands. When the same sequence of symbols started popping up, I would pretend that I had already def'd the command and start using it, and when there was a pause in the derivation, I would remember to scribble down what that command should mean. In my later years, I also started drawing figures in paint for inclusion in latex.

Anyway, I now have about 4 or 5 latex'd class notes that I have put on my website. From what I hear, they are still regularly used in UCB classes, and I occasionally get happy emails from grad students thanking me for the effort. Meanwhile, I've been reading a book about Nicolas Bourbaki, a famous pseudonym for a group of (mostly French) mathematicians who collaboratively re-wrote mathematics from 1935 to the 70s. Nicolas Bourbaki was a wiki, ahead of its time.

"Now wouldn't it be cool," I thought to myself, "if students using these lecture notes could fix them when they are wrong (after all, they were written on-the-fly), and re-organize them to make more sense?" Could these notes become a sort of open-source textbook for astronomy? So AstroBaki was born.

The difficulty, I am finding, is in translating latex (especially latex heavy in defs) into mediawiki. The best tool I've found so far has been pandoc, which didn't do the defs, but did everything else pretty well. I'm loath to do things by hand, so I'll see what can be automated, and I'll keep you posted.

Where is GCC for FPGAs?

A lot of the digital signal processing that gets done in radio astronomy these days is done on Field Programmable Gate Arrays (FPGAs), and one of the projects I've been working on from the beginning in my research is developing open-source libraries for programming these chips. My part in this has generally been on the algorithmic/mathematical side: writing FFTs, filters, cross-correlation engines, etc. Another key aspect of this work, though, is a toolflow that allows people to design systems at a high level with parameterized algorithmic cores, and to turn that design into the wiring instructions that tell the FPGA how to implement the system.

We currently use a design entry system based on Simulink running on Matlab, and while it is an extremely powerful environment, we've also found it to be limiting, frustrating, and hard to maintain designs in. In October, I volunteered at an international workshop on astronomy signal processing to explore alternatives to this environment. My current favorite is MyHDL, which uses Python to generate lower-level code in Verilog or VHDL, and I may start looking more deeply into porting a design to use MyHDL.

Something that is bothering me, though, is that however much we work on porting our toolflow open-source equivalents, there is currently no open-source compiler for FPGAs. The state of affairs in FPGA-land is something like PCs in the '70s, when every personal computer had its own specialized compiler. For PCs, the problem was solved by GCC (the Gnu Compiler Collection), which became the default open-source solution for compiling most languages to target the many CPU architectures that exist in the world today.

I'm keeping my eye on gEDA, and notably Icarus, which seems to be a free synthesis tool (synthesis, mapping, and routing are the 3 main stages of compiling for an FPGA). Perhaps mapping and routing can never be open-source, since they tend to be very chip-specific. But here's hoping...

Hands-On Cosmology Education

Yesterday I spent the morning giving a gosh-wow talk about cosmology to a physics class at Athenian High School taught by my housemate Dave Otten. It was a lot of fun, and the students were all very enthusiastic. It was almost entirely driven by their questions, and they loved being pitched curveballs (time is reference-frame dependent, the universe is expanding, spiral arms are standing waves, etc). The hour-and-a-half lecture was over before we knew it.

Afterward, Dave mentioned that it would be really cool if there were a way to talk about galactic-scale astronomy and cosmology that was in keeping with the philosophy of their school, which emphasizes lab-based, hands-on learning. He mentioned that PhET is a free resource he uses for providing interactive simulations that make hands-on labs out of subjects that otherwise would be too slow, small, big, fast, or dangerous to perform live in a classroom. He also lamented that there aren't any galactic- or cosmological-scale simulators there that could help to understand how systems on this scale behave, and that could perhaps illustrate exactly where the problems of dark matter and dark energy are encountered. Has anyone seen something like this?

The Need for SPEAD

I've been absent for a good while now as a result of participating in a (successful) deployment of our PAPER experiment in South Africa. The Karoo desert in SA, where we were stationed, was very reminiscent of Rangely, CO where I grew up, except for the occasional baboon or kudu in the road. Though it came at a price of a lot of work piled up for me when I got back, and an awfully long time away from J, the isolation from all but our experiment helped ferment some ideas I'd been having about migrating the AIPY toolkit I've been developing to use a streaming data format that would avoid unnecessary disk accesses, would allow AIPY to be integrated directly with the correlators developed by our CASPER project, and would help our experiment develop a real-time analysis pipeline for compensating for ionospheric distortion in our data.

After chatting with a lot of guys working on the Karoo Array Telescope in Cape Town, we came up with a concrete protocol build on something already being used for CASPER correlator output. I just got done writing my first grant proposal to the NSF, funding a graduate student to work on this protocol--the Streaming Protocol for Exchanging Astronomical Data (SPEAD, pronounced "speed"). The process of writing a grant myself was a learning process, and helped me understand where a lot of the questions I got asked by my previous advisors were coming from.

A lesson I got to take away from SA was this: the reason we were in SA (as opposed to Australia) for PAPER was because we had been working with the KAT team, sharing correlator development. The reason we were working with the KAT team was because CASPER and KAT started up a collaboration a few years before. And that collaboration was started up because Dan Werthimer went down to visit SA some years ago to help advise them in a review of the design of their telescope electronics. Dan was invited there because he struck up a fast friendship with Alan Langman (the KAT director) at an earlier conference. The moral of this chain of causes and effects being that sometimes large projects go in new directions because of personal friendships, and sometimes those friendships end up making the difference in the success of a project.

"Guess What I Was Thinking" Logic Puzzles (A Rant)

Probably more than most, I like logic puzzles. They're fun. But there's a variety of logic puzzles, especially prevalent in IQ/Mensa tests, that I really dislike. They are the "what's the next symbol in the pattern"-type of puzzles, and I HATE them. They are written like there is one (and only one) answer, and you must be dense not to see it. But can't I put anything in that blank space and call it a "pattern"? And what if the pattern that I see when looking at the provided sequence isn't the one you were thinking of? Is anyone with me in recognizing that these aren't logic puzzles at all? They're "guess what I was thinking of" puzzles! They aren't adequately constrained. They don't specify the parameter space from which the sequence is drawn. Anything can be a pattern! Anything!

What they actually want you to do is find the most likely symbol given several measurements and a set of priors about the likelihood of the author picking a particular sequence, but they neglect to provide you with any information about those priors. Maybe they assume that you can guess the priors based on estimates of your own sequence-picking priors, but that only works if your brain works the same way as the authors'. And quite frankly, if the authors can't appreciate that answers to these puzzles they are writing are indeterminate, I'm pretty sure their brain isn't working the same way as mine. Quit calling these logic puzzles! Put them on a Berkeley Psychic Institute entrance exam, not a college entrance exam.

Ok. Done ranting.

Graph-SLAM

After a trying, but ultimately successful month spent extracting the family from Puerto Rico and re-embedding us in Berkeley, I'm just starting to get back on top of things enough to think about posting...

I had lunch yesterday with a good friend of mine, Pierre, who co-founded a company that specializes in sensory and mapping systems such as those that are used to create Google's "Street View". I was impressed to learn about their system for combining data from GPS, LIDAR, car odometers, and IMUs to create a consistent picture of how a vehicle is located and oriented in space as a function of time. They've spent a lot of time calibrating their systems, and use some sophisticated MCMC post-processing methods for deriving the actual trajectory of a vehicle.

Although the antennas in the PAPER array (that's the low-frequency interferometer I'm working on), are much less mobile than a car, there was considerable overlap between the problem Pierre has been working to solve and the calibration problem I am facing the requires positioning antennas and celesital sources as a function of time in the face of ionospheric distortion, variable gains, etc. Pierre pointed me to Graph-SLAM as a formal description of the problem that we are trying to solve, and suggested that Kalman Filtering with RTS Smoothing was a powerful technique for converging to the optimal solution (with covariance information) in linear time.

The Voynich Manuscript: Bootstrapping Language

The internet is a powerful and dangerous thing. It all started when I read the latest xkcd, which warned me that visiting cracked.com was dangerous. Then I read about the "6 phenomena that science can't explain" (which was a very dramatic title for some underwhelming mysteries), and next thing I knew, I was reading about the Voynich Manuscript. I learned about cryptography, glossolalia, the Manchu language, among other things. Then I took a look at the manuscript and before I knew it, I had a transcribed version of the manuscript in electronic form using the European Voynich Alphabet. And it just went downhill from there.

To summarize, the Voynich Manuscript (hereafter VMS) is a handwritten text with some illustrations some 500 years old. It uses glyphs no one knows how to read, it is not clear if it corresponds to a known language, it may or may not be encrypted, and little progress has been made in deciphering any of it, despite the fact that some bright people have tried. So I decided to have a crack at it.

The reason I got interested is because of the similaries to SETI. Arecibo, back in 1974, transmitted a message off into space that had been designed to be decrypted. We might receive a message like that some day. Or we might intercept something much like the VMS--a bunch of data in a language that we have no prior knowledge of--and we may be finding ourself trying to figure out how to bootstrap a language. That is to say, to learn the grammar and semantics of a language from a static example, without outside help.

Is this possible? For grammar, I'm pretty sure of it. I can imagine an algorithm (maybe Maximum Entropy Modeling and Bayesian learning applied to grouping and parsing) that uses correlations in the appearances of language elements (starting with letters and building up) and correlations in the behaviors of these elements relative to one another to build a model for parsing a language. For the VMS, I used something similar to this (not the MEM and Bayesian part) to show that spaces, line breaks, and paragraph breaks show similar grouping correlations relative to other VMS letters, and so can probably be considered one grammatical element of whitespace. That's a pretty simple thing to deduce, but it was actually something I was worried about in getting started with the VMS.

Sematics is another issue. Once upon a time, I would have had an optomistic answer to bootstrapping sematics from text that was not written for that purpose. However, after watching my child mysteriously acquire language, illustrating how hard-wired the human brain is for learning language from another human, and how much it relies on shared experience and feedback, I'm less sure.

I would be interested to know if there is a field of mathematics that studies sematics and the properties that a self-contained system needs to have to be able to generate sematical relationships. The Arecibo message relied on a shared physical environment to try to bootstrap sematics. I wonder if it would be enough to describe the rules of the grammar of a language in the language itself. That one, once the reader had deduced the relationships between elements, you would have a shared knowledge of that subject that might enable a reader to correlate the structure of the descriptions with the grammatical structure and thereby establish the first sematical relationships.

Anyway, after preliminary analysis of the VMS, I'm pretty sure that it's not random gibberish (there are correlations between elements on levels ranging from letters to words), and if it's encrypted, it's a weak form of encryption that preserves these correlations. My pet theory, extended from the glossalalia idea, is that this is actually plaintext in a natural language with an invented set of symbols, but that the natural language might be the accidental or intentional creation of a savant or scholar.

Countability and Strong Positive Anymore

Seven or eight years ago, I discovered that I have a linguistic condition called "Positive Anymore." I was in college, chatting with my roommates, and said something like "Anymore, I just lift weights in the Leverett gym." One of my roommates just couldn't take it anymore. "I've heard you say 'anymore' like that for years now. What the hell does it mean?" A quick poll of those present revealed that I was the only one for whom that construction made grammatical sense. My aunt (a linguistics professor) gave me the prognosis: I had Positive Anymore.

I used to think that PA was a linguistic shortcoming of mine, but anymore I'm convinced it's more like a superpower. Whereas most English speakers can only use the word in negative constructions like "I don't drive anymore" I have the uncanny ability to use it positively as per the first sentence in this paragraph. Moreover, I don't just have PA, I have strong PA, which means I can, at will, detach "anymore" and put it anywhere in a sentence. "Anymore, I just take the bus." Astounded yet?
If you're still having trouble parsing that, replace "anymore" with "nowadays"--to me, they mean about the same thing.

I receive no end of flak from friends, relatives, and spouses about my PA, although it's not that uncommon a condition. In fact, I have caught several of my relatives (mostly on my dad's side) using PA even after making fun of me for my PA. They have it and don't even know it.

Anyway, S and I were trying to figure out if my use of PA was inconsistent with my use of "any", which I use according to the standard rules. But it turns out the standard rules are weirder than you might think. For example, "I don't want any spam" is a grammatical negative construction; "I want any spam" is ungrammatical and positive. "Do you want any spam?" is grammatical and seems positive, but it turns out that there is an implied negative in English owing to the uncertainty inherent in questions and subjunctives. Hmph. And then what about "I like any spam I can get?" That seems positive again, but the clause "I can get" is required to make it grammatical. And then the plot thickens. "I feed spam to any dog" is grammatical and did not require a clause to modify "any dog."

Our theory was that using "any" positively without a clause requires the noun modified by "any" to come in quantized units--to be countable. Dogs are countable; spam is a continuum, much like water or space-time. The best example we could think of that illustrated this was "fish". Fish can be countable noun (number of live fishes) or continuum noun (amount of dead fish to eat). If I say "I'll take any fish," the ambiguity in the countability of fish is broken--it's clear I'm talking about a live fish (or, perhaps, a type of fish, which is also countable). But if I say "I'll take any fish that you give me," the ambiguity is preserved.

The implication was that for my use of PA to be consistent with the standard use of "any" (which it may not need to be, since "anymore" is one word, not "any more"), I must be thinking of the time interval referred to by PA (i.e. now and continuing indefinitely into the future) as something countable rather than continuous. Maybe. I don't know. Anymore, I'm just really confused.

The Need for Speed

On the drive from San Juan to Arecibo this morning, I got to wondering about where my average driving speed fell in the distribution of drivers here in Puerto Rico. In the states, I felt like I was a pretty average driver, but here en la isla, the distribution of driving speeds is different. There are a lot of fast drivers, too be sure, but there is also a subpopulation of drivers whose speed is significantly (~10 mph) below the speed limit. This may be because relative to the US, PR is economically depressed and so more old cars are on the road, or as a reaction to the more erratic driving habits there seem to be here, but anyway, I definitely pass more people than pass me now.

So in an effort to discover where my driving speed fell relative to others (and in and effort to alleviate the boredom of driving 1.5 hrs alone), I started counting how many cars I passed and how many passed me as I was going 65 mph (the speed limit). Out of 55 pass events, only 9 involved me getting passed. To make this a tractable problem in my head, I decided to assume that driving speeds were normally (gaussian) distributed about a mean--even though this contradicts my anecdotal evidence above. Using this approximation, my first instinct was to say that 1/6 of the cars on the road were faster than me, and since ~2/3 of samples are within +/- 1 sigma of the mean in a gaussian distribution, 1/6 of the samples would be above +1 sigma. So I approximated that I was a 1 sigma driver.

But then it occurred to me that I needed to control for a significant sample bias. This is because the test I was doing wasn't randomly selecting cars and comparing my speed to them. Cars were far more likely to get selected if the difference between their speed and my speed was large. A car going the same speed as me would never pass me, and I would never pass it. But I would assuredly pass almost every car on the road that was going 10 mph as I went 65. The "road distance" that I sampled for different velocities is proportional to abs(v-v0), where v0 is my velocity. The effect this had on my samples was to underweight speeds close to my own and overweight the wings of the gaussian distribution I had assumed as my model. If I drove exactly the mean velocity, this effect would not be terribly important--if the model were correct, it would still be the case that as many cars passed me as I passed. But as my velocity moves away from the mean velocity, the "normal drivers" who are only going a little faster than me get undersampled, so I only see the drivers who are tearing around like a bat out of hell. At the lower end, I still see the real slow-pokes on the road, but I start seeing people who are going a bit faster than that, of which there are a lot more. The effect of this sample bias, it seems, would be to make it seem that I'm a farther outlier in my driving speed than I actually am.

So now, to figure out where I fall in the (normal) distribution of driving speeds, I need to know exactly what the mean driving speed and what sigma is, so that I can compensate for the abs(v-v0)
sampling factor. That means I need to figure out 2 numbers, but unfortunately, I only measured 1 number (that 1/6 of the passes while driving were me being passed) so I won't be able to properly constrain this problem. However, I should be able to figure out the mean on my drive home by finding the speed at which as many people pass me as I pass. For now, let's say this is 55 mph. Then all I need to do is find the sigma for which a gaussian distribution around 55 mph downweighted by abs(v-65 mph) has 1/6 of the area lying above 65 mph. I just solved that numerically on my computer, and it's saying that the best-fit sigma is ~22 mph. So that puts me at about +1/2 sigma. That seems reasonable.

An interesting next step (which I'm not going to do right now since I need to get to work) would be to translate the sample error in my pass measurements into an error in the determination of sigma, and then the error in my driving speed percentile.

What are the chances?

I cringe every time that I hear this phrase. I heard it most recently when my friend had her car stolen from San Juan. It was recovered in a semi-drivable state in Bayamon. She invested a couple thousand dollars to get rid of the "semi", only to have the car re-stolen a couple of months later. This time, when the car was recovered in Dorado, there was no "semi" to be had, so she's currently trying to sell it for pieces. While the police were fairly understanding (though less than helpful) the first time her car got stolen, the second time was occasion for all sorts of raised eyebrows and skepticism. And in exasperation my friend uttered the phrase in question.

"What are the chances" is a Pandora's box of bad statistics. Statistics is about hedging your bets given incomplete information, but this phrase is always uttered after the fact, when we have (relatively) complete information: it happened. So unless you plan on repeating the experiment, the chances are one. It happened.

As an example, let's take the famous Goat/Car Puzzle. There are 3 doors; one has a car behind it and the other two have goats. After you pick a door, the game-show host opens one of the other doors and reveals a goat. You are then offered the option of switching your choice to the other door. If you play this game repeatedly, you'll win more often if you switch your choice. But the instance just played out, the car was behind one of the doors, and if that was the door you picked, your chances of getting the car were 1. If you didn't, your chances were 0.

You might object: "What were the chances beforehand, when I didn't know where the goat and car were?". But to do that, you need to make some assumptions. You need to assume that at each playing of the game, the cars and goats are randomly assigned and/or you randomly pick doors. Otherwise, it might be the case that the car is always behind door #1, and you always pick door #2. Your chances of success wouldn't be so good in this case. You might have decent prior knowledge of how cars, goats, and doors are picked in this example, but for everyday occurrences, we usually have much more limited prior knowledge. Are cars randomly stolen, or are certain brands targeted? Are certain areas targeted? People often assume that these processes are random, but they rarely are. With limited priors on these events, the question "what are the chances" can't be answered with any certainty and any answers given should be taken with a great big shaker of salt.

Furthermore, people have selective attention. We ignore whole heaps of ordinary outcomes and only pay attention to ones that strike us as interesting. As a friend of mine once said: "Low probability stuff happens pretty regularly because stuff is happening all the time." Even if the processes involved are random, unlikely outcomes are to be expected if the processes are repeated often enough. People tend to ignore the ordinary outcomes, exclaim at the extraordinary ones, and then assume that something deeper is afoot. In my friend's case, the police started wondering if she was being personally targeted or if she was really bad at locking her car. But even if we assume a random model of car thefts, some number unlikely outcomes doesn't automatically imply that our random model is wrong.

Finally, we also need to keep in mind that in complex systems like real life, there may be a huge number of possible outcomes. But something has to happen. When you roll a die, each number only has a 1/6 chance of coming up. Would you roll a die once and then exclaim: "Wow, it came up six! What are the chances?" In real life, there might be millions of outcomes, each with one-in-a-million chance of coming true, but the fact that one of them happens shouldn't be surprising.

Fighting against all of the pitfalls inherent in asking "What are the chances?", I've developed a reflexive response: "What are the chances?" One.

Ida y Vuelta: a Tail?

It was all over the news and the net yesterday: the missing link has been found! Darwin has finally been proven right!

Hold on a minute. There's no "missing link"--we have example after example of the evolutionary forebearers of Homo sapiens. Evolution was not in question--we already knew Darwin was right. Ida (the name of the fossil found) is not a direct ancestor of humans--the fossil represents a transitional form between lemurs and other apes.

I do not mean to denigrate what is obviously a very important and exceptionally well-preserved fossil that may provide important insights into primate evolution. My objection is to the media frenzy that gives the impression that this is the final resolution to a scientific debate about evolution that a) never existed and b) would not have been resolved by the fossil in question if it did exist.

We have Neanderthals, Homo erectus, Homo habilis, Australopithecus afarensis, and more. Why is Ida, who isn't even our evolutionary forebearer, the "missing link"? I have a theory: it's about the tail. I think that somehow, through all the monkey-human-common-ancestor debate, through the discovery of early hominids, through all of the discussion about increasing cranial capacity and tool usage, everyone has really been wondering "what about the tail? What happened to the tail?" The media was holding out for something it could tout as a human ancestor (or something close enough) with a tail to finally declare the "missing link" found and the evolution debate settled.

You might say that this is all for the best--that the false debate, however belatedly, is finally being put to rest with one last hurrah. But here's a scenario that makes be cringe just to think about it: suppose it turns out that this fossil, which was recovered from a private collection, turns out to be something other than the specimen that the scientist in question thinks it is. Scientists makes mistakes--that's what peer review is for. Then suddenly we've breathed new life into a misconception about evolution that has been hanging around for way too long already.

Golomb Rulers/Squares/Rectangles

Yesterday I came across an interesting example of the isolation of academic fields from one another.

A common design parameter for antenna arrays is to try to obtain uniform coverage of the aperture plane to get as many independent measurements as possible. Interferometers sample the aperture plane at locations that correspond to the difference vectors between antenna elements. For example, in one dimension, if I put four antennas at locations (0,1,4,6), then that array would sample the difference set of those positions: (1,2,3,4,5,6). However, if I put antennas at (0,1,2,3), the difference set would only include (1,2,3) with 1 occuring 3 times and 2 occuring twice. For the purpose of uniformly sampling an aperture, redundant spacings are lost measurements. We're looking for a minimum-redundancy array.
There have been a few papers in radio astronomy on minimum-redundancy arrays for the more useful 2-dimensional case, including Golay (1971), Klemperer (1974), and Cornwell (1988).

Thinking that this might be a mathematical problem of interest, I ran it by a good friend of mine: Phil Matchett Wood--a mathematician at Princeton. He quickly uncovered the equivalent problem as formulated in math literature: Golomb rulers in 1-D and Golomb rectangles in 2-D. Some relevant papers on the subject are Shearer (1995), Meyer & Jaumard (2005), Robinson (1985), and Robinson (1997). These papers are on the exact problem and describe applications to "radar and sonar signal detection", obviously referring to the need for independent aperture samples in radar and sonar interferometers. Somehow, the differing nomenclature between these fields was never quite bridged, and so there has not been and cross-referencing between these two formulations of the same underlying problem. People like to talk about the possibility that relevant research in one field goes unnoticed by other fields. This is the first time I've across it myself, though.

Compressed Sensing and Wiener Filtering

Today I'm trying to expand my understanding of how we can best remove contaminant signals from the data we take with the Precision Array for Probing the Epoch of Reionization (PAPER). There is a specific problem I want to make sure we can solve for PAPER. Foregrounds to our signal, particularly synchrotron radiation, are expected to be very smooth with frequency. The idea put forth by the MWA and LOFAR groups is that by observing the same spatial harmonics at multiple frequencies, we should be able to remove such smooth components to suppress them relative to the cosmic reionization signal we are looking for. However, generating overlapping coverage of spatial harmonics as a function of frequency is expensive. My intuition is that since foregrounds do not have a spatial structure that changes dramatically with frequency, we shouldn't need to sample a given spatial harmonic very finely in frequency to get the suppression we want. This would allow us to spread our antennas out a little more and get measurements of the sky at a variety of spatial modes.

In many ways, our problem is analogous to what was done with the Cosmic Microwave Background (CMB). For foreground removal in CMB work, Tegmark and Efstathiou (1996) begin with an assumption that foregrounds can be described as the product of a spatial term and a spectral frequency term. This allows them to construct Wiener filters that use the internal degrees of freedom of their data, together with a model of their foreground and a weighting factor based on the noisiness of their data, to construct a filter for removing that foreground. For the most part, this is standard Wiener filtering, except they have to be careful about what they do to their power spectrum, so they apply a normalization factor to correct for a deficiency in Wiener filters. Tegmark (1998) goes on to generalize this technique for foregrounds that vary slowly with frequency. I'm in the process of wading through these papers, but they seem to be directly applicable to what we are doing, and seem to confirm my suspicions that synchrotron emission should be well-enough behaved to require only sparse frequency coverage of a wavemode in order to be suppressed.

Another tactic that I am investigating is that of compressed sensing which I was alerted to in talks by Scaife and Schwardt at the SKA Imaging Workshop in Socorro this last April. The landmark paper on this principle seems to be Donoho (2006), where it is shown that the compressibility of a signal (being sparse for some choice of coordinates) is a sufficient regularization criterion to faithfully reconstruct signals using a small number of samples. In a way, this technique has an element of Occam's Razor in it--it tries to find a solution, in some optimal basis, that needs the fewest non-zero numbers to agree with the measured data. At least, that's my take on it without having finished the paper.

The relevance of compressed sensing to image deconvolution is explored in Wiaux et al (2009), and it seems to be powerful. I'm excited by this deconvolution approach because it meshes well with the intuitive approach I've been taking to deconvolution, which was to use wavelets and a Markov Chain Monte Carlo optimizer to find the model with the fewest number of components that reproduces our data to within the noise. Compressed sensing seems to be exactly this idea, but is agnostic about the basis chosen, instead of mandating one like wavelets. Anyway, this technique may also be relevant to our foreground removal problem because we might be able to use it to construct the minimal foreground model implied by our data. For synchrotron emission, which should have smoothly varying spatial structure with frequency, I envision that this could construct a maximally smooth model that would allow us to use sparse frequency coverage to remove the foreground emission to the extent that it is possible to do so.

Is Tenure a Problem in Science Departments?

Somewhat belatedly, I wanted to comment on the New York Times Op-Ed by Mark Taylor that addresses some of the flaws of the current academic system and proposes some solutions. The central problems that Taylor highlights in his article are that academic departments are too isolated from one another and from the world, and that there aren't enough academic positions for all of the people who are getting doctoral degrees these days. Taylor makes some very good points, but his article is strongly influenced by his experiences in a humanities department, and I am not sure how relevant his suggestions are for a science department.

Astronomy suffers from many of the same problems Taylor describes. There are far more graduate students and post-doctoral researchers than there are tenured professorial positions, and yet students are trained as if they were all to be professors. However, science students are often not paying their own tuition (it is paid by the grant of a supporting professor) and there are more options for science students outside of tenure-track positions because of the many sources of external funding that support scientific research. Unlike the humanities, there are a variety of scientific programming and research positions for graduates who are not seeking professorial positions. These positions are aligned with the education students receive through their doctoral research.

This isn't to say that there is not a major problem in scientific disciplines concerning the ratio of student positions to professional positions. Rather, it is that the problem may not be as closely tied to tenure and the longevity of tenured professors as in the humanities. The problem may be that professional positions available to graduating students are being occupied by the students themselves. Scientific research in the United States relies on a large pool of skilled labor. Currently, this labor is being bought at well under market price in the form of cheap graduate student researchers. If more of these positions were filled by full-time research professionals, we might have a healthier employment system for scientific academia.

The problem is that this raises the price of research in the United States and may result in a reduction in the total number of projects (and therefore, researchers) that can be supported. From the perspective of researchers, this may be a healthier state of affairs--to not be misled into spending 5-7 years underpaid as a graduate student only to find that the only way to continue to do what you've been trained to do is to continue to be underpaid. But unlike in the humanities, science graduate students usually have not accumulated debt beyond their undergraduate education and they have been supported (however cheaply) through this process. The solution, then, may simply be to ensure that prospective graduate students in science are well-informed about what employment prospects they should expect after they file their dissertation.