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.

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.

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...

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.

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.

Interferometry File Formats

When astronomers talk about software done right, they often hold up FITS as the gold standard. I'll admit, FITS has done more to live up to its namesake (Flexible Image Transport System) than many believed possible. But unfortunately, there can be too much of a good thing. Sometimes too much emphasis is put on defining an end-all-be-all file format, when all we really need are good tools for converting between file formats.

Data formats are a problem in radio astronomy software. Currently, there are at least three major formats (MIRIAD, UVFITS, and MeasurementSets), each linked to a major software package (MIRIAD, AIPS, and CASA), with rudimentary/non-existant tools for converting between them. Many have taken this current state of affairs as a sign that multiple file formats are bad and that the community should decide on a single format. Since each format is intimately tied to major software package, this battle over file formats has escalated to a war between software packages.

The mistake made here was blaming the file formats. File formats are not the problem. The problem is that the software for reading them has not been circulated in easily accessible modules. I am encountering this problem as I'm trying to get AIPY to be agnostic about file formats by wrapping them all into Python. Here's where I am:

The MIRIAD file format was actually easily wrapped up, owing to MIRIAD having a developed programmer's API.

MeasurementSets (with CASA) are giving me a lot more trouble. It seems that CASA, with all of it's C++ objects that are passed between functions, is something of an "all or nothing" deal. If I want to read a MeasurementSet, I apparently need to wrap up the entirety of CASA. The failing here is code modularity.

UVFITS is giving me the opposite problem.
UVFITS was cooked up as a FITS-conforming file format to handle raw interferometric data. Unfortunately, interferometric data isn't in picture form yet, so an extension of the FITS format (the binary table) was cooked up to accommodate that (Cotton et al. 1995). The result was a file format that is so general that it does not tell the programmer what the data actually means.

File formats exist to support the needs of different applications. They've been created out of need, and should not be dismissed as unnecessary. I recommend to the radio astronomy software community that we embrace these file formats and work on modular code so that they are accessible from any software package.

Attiyah and His Theories

I guess when you're an astronomer, you have to expect to be the target of the occasional crackpot with their personal theory of the universe. My antagonist is Attiyah Zahdeh. I don't know where he's from (although devious research indicates he's on central time, so my current theory is Chicago), or how he got my email, but for a couple of years now I have been getting emails of which the following is the most recent example:

Attiyah's Planetary Motion I introduce this hypothesis in order to be discussed by scientists. I do not claim that I now have any mathematical proof or practical model to support Attiyah's Planetary Motion. I consider that the Kepler's second and third laws themselves support my hypothesis. It seems to me that Kepler failed to conclude that, relative to the Sun, the motion of the planets is the same as of the pendulum.Thus, he coined his second and third laws as alternative statements to express the laws of the simple harmonic motion of the planets. I'm inclined to say that Kepler (1571-1630 A.D.) was not aware of the work of Galileo (1564.1642 A.D.) on the pendulum and the laws of its motion he discovered. The hypothesis of Attiyah's Planetary Motion is four propositions: 1. The planets move not around the Sun but in front of it. 2. The planetary motion in front of the Sun is of the simple harmonic type. 3. The planet (the bob), gravitational force (the length, the line between the Earth's gravity center and the solar gravity center) and the Sun (the solar gravity center as the pivot point), altogether form a pendulum. 4. The planet oscillates in front of the Sun in a hemiellipse. Notes: 1. This hypothesis is an alternative of Kepler's first law only. 2. This hypothesis does not apply to the motion of the satellites.

I have also been spammed with Attiyah's Sun Theory, which I think says that daylight is caused by charged particles (or X-rays, or whatever) hitting our atmosphere--much the same as the mechanism causing the northern and southern lights, and with Attiyah's Hologeomagnetosphere, which asserts that the northern and southern lights are generated by electrical currents in the earth's molten core turning our ionosphere into a giant CRT monitor.

I once thought that these were created as jokes--that "Attiyah" was just the psuedonym of a humorist. Dozens of emails (and several years) later, I'm convinced that Attiyah is real and in earnest. In fact, I've discovered that he visits his theories upon astronomy message boards with some regularity, where he has revealed complete ignorance about how the scientific process works by demanding that others attempt to disprove his theories (the burden of evidence is on the newcoming theory) and by flatly ignoring the evidence that was provided against them. Two years ago, I myself was duped into providing a detailed refutation of Attiyah's Sun Theory, only to have my response disappear into the abyss of cyberspace.

But I'm not bitter. In some ways, Attiyah's doing a lot for science education by getting amateur scientists to review how we know what we know--reminding everyone that the reason we have such a widely adopted set of theories is that they are testably confirmed and mutually consistent. If only intelligent design, creationism, and young-earth hypotheses met with half the ridicule that Attiyah's theories meet on the message boards. Attiyah's only mistake, really, was failing to incorporate a little theology into the mix.