Shallow Thoughts

Upheaval Dome: New research confirms impact theory

Kurt Fisher wrote to draw my attention to the latest Lunar Photo Of the Day (LPOD), a lovely shot he made of one of my favorite places anywhere, Upheaval Dome in Utah's Canyonlands National Park.

Upheaval Dome has long been strongly suspected to be a massive, eroded impact crater, but the LPOD highlights a study that finally puts this (non-)controversy to rest, Elmar Buchner and Thomas Kenkmann's Upheaval Dome, Utah, USA: Impact origin confirmed, documenting shocked quartz grains in the Kayenta sandstone of Upheaval's outer ring.

It's about time -- it's been pretty clear for many years that this structure was an impact formation, not a collapsed salt dome (the relative lack of salt in the core might have been a clue) but the park service doesn't seem to have gotten the message, giving equal weight to the salt-dome theory in all its Canyonlands literature and signs. Perhaps the Buchner and Kenkmann paper will finally convince them.

Reading about this gave me the push I needed to update my own Upheaval Dome page, adding links to the latest research and to the excellent Upheaval Dome Bibliography Kurt has put together. My page also badly needed a bigger view of the crater itself, so I stitched together a quick panorama of the view from the rim that I'd shot on a trip several years ago but never assembled.

Tags: geology, astronomy, trails, impact crater
[ 12:15 Nov 29, 2008    More science/geology | permalink to this entry ]

Bright naked-eye comet: 17/P Holmes

I finally got a chance to take a look at Comet 17/P Holmes. I'd been hearing about this bright comet for a couple of days, since it unexpectedly broke up and flared from about 17th magnitude (fainter than most amateur telescopes can pick up even in dark skies) to 2nd magnitude (easily visible to the naked eye from light-polluted cities). It's in Perseus, so only visible from the northern hemisphere, pretty much any time after dark (but it's higher a little later in the evening).

And it's just as bright as advertised. I grabbed my binoculars, used a finder chart posted by one of our local SJAA members, and there it was, bright and obviously fuzzy. Without the binoculars it was still easy to see, and still noticably fuzzy.

So I dragged out the trusty 6" dobsonian, and although it has no visible tail, it has lots of structure. It looked like this:
It has a stellar nucleus, a bright inner area (the coma?) and a much larger, fainter outer halo. There's also a faint star just outside the coma, so it'll be fun (if we continue to get holes in the clouds) to see how fast it moves relative to that star. (Not much motion in the past hour.)

It's nice to have a bright comet in the sky again! Anyone interested in astronomy should check this one out in the next few days -- since it may be in the process of breaking up, there's no telling how long it'll last or what will happen next. Grab some binoculars, or a 'scope if you have one, and take a look.

Tags: science, astronomy
[ 21:51 Oct 28, 2007    More science/astro | permalink to this entry ]

Traffic Science

NPR this morning had a program on speeding. One of the "experts" they brought in was Richard Retting, senior transportation engineer with the IIHS (that's the Insurance Institute for Highway Safety, a group funded by auto insurance companies).

Early on they asked him why speeding was bad. He said there were three reasons. The first two were straightforward: when you're going faster, you (1) travel farther before you can react to something, and (2) take longer to stop. No problem there, and I waited for the third reason, presuming it was going to be kinetic energy.

Well, almost. The third reason, he said, was energy. "Remember that equation E = mc² from high school?"

Wow! If I drive faster than the speed limit, I'm converting my mass into energy? For those who haven't studied physics recently, he was probably confusing Einstein's equation relating energy, mass and the speed of light with Newton's formula for kinetic energy, KE = mv²/2. The host responded incredulously "The speed of light?" but Retting didn't seem to notice, and pressed on: "When you're going faster, your energy is disproportionate and exponential."

Okay, you're talking on the radio and you have a brain-o. I'm sure we've all said silly things when we knew better, like reciting the wrong equation then not noticing the gaffe. But he also seems confused about what "exponential" means, perhaps because of that "exponent" of 2 in the equation. An exponential curve is when you have something like 2^X, not X². Admittedly, the dictionary of "exponential" includes vague definitions like "Pertaining to exponents", and I suppose there is an exponent of 2 involved. But really, folks: kinetic energy increases as the square of speed.

A little later in the program, someone called in to mention studies showing that higher speeds don't necessarily correlate with accidents, and Redding chastised him for doing google searches for studies: "That's not how we do science in this country." Hey, Mr. Retting -- it might pay to be a little more careful with your own science if you're going to be dismiss callers with remarks like that.

Tags: science
[ 17:37 Jun 07, 2007    More science | permalink to this entry ]

The Fibonacci Spiral and the Nautilus

or, don't believe everything you read

I've been working on a short talk on Fibonacci numbers for a friend's math class.

Back when I was in high school, I did a research project on Fibonacci numbers (their use in planning the growth of a city's power stations), and for a while I had to explain the project endlessly, so I thought I remembered pretty well what sorts of visuals I'd need -- some pine cones, maybe some flower petals or branching plants, graphics of the golden ratio and the Fibonacci/ Golden Spiral, and some nice visuals of natural wonders like the chambered nautilus and how that all fits in with the Fibonacci sequence.

I collected my pine cones, took some pictures and made some slides, then it was time to get to work on the golden spirals. I wrote a little GIMP script-fu to generate a Fibonacci spiral and set of boxes, then I went looking for a Chambered Nautilus image on which I could superimpose the spiral, and found a pretty good one by Chris 73 at Wikipedia. I pasted it into GIMP, then pasted my golden spiral on top of it, activated the Scale tool (Keep Aspect Ratio) and started scaling.

And I just couldn't get them to match!

No matter how I scaled or translated the spiral, it just didn't expand at the same rate as the nautilus shell.

So I called up Google Images and tried a few different nautilus images -- with exactly the same result. I just couldn't get my Fibonacci spiral to come close.

Well, this Science News article entitled Sea Shell Spirals says I'm not the only one. In 1999, retired mathematician Clement Falbo measured a series of nautilus shells at San Francisco's California Academy of Sciences, and he found that while they were indeed logarithmic spirals (like the golden spiral), their ratios ranged from about 1.24 to 1.43, with an average ratio of about 1.33 to 1, not even close to the 1.618... ratio of the Golden Spiral. In 2002,John Sharp noticed the same problem (that link doesn't work for me, but maybe you'll have better luck).

As the Science News article points out,

Nonetheless, many accounts still insist that a cross section of nautilus shell shows a growth pattern of chambers governed by the golden ratio.

No kidding! Google on fibonacci nautilus and you'll get a boatload of pages using the chambered nautilus as an illustration of the Fibonacci (or Golden) spiral in nature. It's not just the web, though -- I've been reading about nautili as Fibonacci examples for decades in books and magazines. All these writers just pass on what they've read elsewhere ... just like I did for all those years, never actually measuring a nautilus shell or trying to inscribe a golden spiral on one.

Now do a Google image search for the same terms, and you'll get lots of beautiful pictures of sectioned nautilus shells. You'll also get quite a few pictures of fibonacci spirals. But none of those beautiful pictures will actually have both the nautilus and the spiral in the same image.

And now I know why -- because they don't match!

(Happily, this actually may be a better subject for my talk than the nautilus illustration I'd originally planned. "Don't believe everything you read" is always a good lesson for high schoolers ... and it's just as relevant for us adults as well.)

Tags: science
[ 21:15 Feb 08, 2007    More science | permalink to this entry ]

On the Twelfth Day of Christmas, My True Love Gave to Me ...

At dinner last night, amid the ubiquitous miasma of egregious Christmas music which is inescapable in public places starting in mid November, during "The Twelve Days of Christmas" Dave got a faraway expression in his eyes. My mother asked why, and he explained that he was thinking about the mathematics of the song: how many items of each type have been given by the end, and which items are more numerous?

There are two ways to interpret the song.

On the second day of Christmas, my true love gave to me
Two turtle doves
And a partridge in a pear tree.

So by the second day, you have two turtle doves, and you have the original partridge -- but do you also have a second partridge, as a literal interpretation of the song implies? Or is the song simply repeating all the previous gifts, not implying that they're given again?

Most people seem to assume the latter, but let's take the song literally and assume that on the third day, you get three french hens, plus two more turtle doves (that makes four) and one new partridge (for a total of three).

My first thought was that at time step T, you double what you had in step T-1 (you're getting all the same stuff yet again) and add T for the new gifts. But that's not right: you get a new load of each item (one partridge, two doves, three hens, and so forth) but you don't double all the accumulated extras who are now crowding your back yard. Time to start writing down the sums.

At each time T, the quantity you have of the Jth item is:

	T
NJ,T =	Σ J
	i=J

That's easy: it's just N_J,T = J*T- J*(J-1) (pretend you've given J of the Jth object at each time step; but since you didn't give it before timestep J, subtract all the ones up to timestep J-1).

N_J,T = J * (T - J + 1)

If all you want to know is how many of each item you have at the end (on the 12th day), plug in T-12:

N_J,12 = J * (13 - J)

A quick sanity check: that means you'll have 12 of item 1 (partridges in pear trees), because you've gotten one new one each time, and 12 of item 12 (drummers drumming), which you got in one big noisy box on the last day. Likewise, you'll have 22 each of items 2 (turtle doves, of which you got two every day except the first day) and 11 (pipers piping), which you got on day 11 and again on day 12.

So the curve which interested Dave is an inverted parabola; you get the least number of the first and last gifts, and the largest quantity of the two middle gifts: six geese a'laying and seven swans a'swimming. How many geese and swans do you get in the end? Here's the surprising answer:

N_6,12 = N_7,12 = 6 * 7 = 42

Douglas Adams fans will immediate recognize this as the solution to the ultimate question of Life, the Universe, and Everything. Now you know what the question was!

One last question: how many items, total, of all types will you have by the end of the twelfth day?

Since you already know how many of each item you have, just add them all up:

	12		12		12		12
Ntot =	Σ j * (13-j)	=	Σ (j * 13 - j2)	= 13 *	Σ j	-	Σ j2
	j=1		j=1		j=1		j=1

Fortunately, we know that

A
Σ i	= A (A + 1) / 2
i=1

and

A
Σ i2	= A (A + 1) (2A + 1) / 6
i=1

so we can use those identities to figure out how many total items we'll have:

Ntot	= { 13 * (12 * 13) / 2 } - { 12 * 13 * 25 / 6 }
	= 364

So it turns out that true love packs a present for just about every day of the year into those twelve days!

(And I found an excuse to play with using HTML tables to display equations.)

Tags: science
[ 11:59 Dec 21, 2006    More science | permalink to this entry ]

Mercury Transits and Titan Occultations

Mercury transited the sun today. The weather forecast predicted rain, and indeed, I awoke this morning to a thick overcast which soon turned to drizzle. But miraculously, ten minutes before the start of the transit the sky cleared, and we were able to see the whole thing, all five hours of it (well, we weren't watching for the whole five hours -- the most interesting parts are the beginning and end).

I had plenty of practice with solar observing yesterday, showing the sun to a group of middle school girls as part of an astronomy workshop. This is organized by the AAUW, the same group that runs the annual Tech Trek summer science girls' camps. (The Stanford Tech Trek has a star party, which is how I got involved with this group.) It's the second year I've done the astronomy workshop for them; this year went pretty smoothly and everybody seemed to have a good time observing the sun, simulating moon phases, learning about the Doppler effect and plotting relative distances of the planets on a road map.

But what I really wanted to write about was the amazing video shown by last weekend's SJAA speaker, Dr. Ivan Linscott of Stanford. As one of the team members on the New Horizons mission to Pluto, he was telling us about Pluto's tenuous atmosphere. There isn't a lot of information on Pluto's atmosphere yet, but one of the goals of New Horizons is to take readings as Pluto occults the sun to see how sunlight is refracted through Pluto's atmosphere.

But that's no problem: it turns out we've already done more challenging occultation studies than that. Back in December 2001, Titan occulted a binary star, and researchers using Palomar's Adaptive Optics setup got a spectacular video of the stars being refracted through Titan's atmosphere as the occultation progresses.

This is old news, of course, but most of us hadn't seen it before and everyone was blown away. Remember, this is a video from Earth, of the atmosphere of a moon of Saturn, something most Earth-based telescopes would have trouble even resolving as a disk. Watch the Titan occultation video here.

Tags: science, astronomy
[ 22:38 Nov 08, 2006    More science/astro | permalink to this entry ]

Pluto is too a planet

The BBC had a good article today about the International Astronomical Union vote that demoted Pluto from planet status.

It was fairly obvious that the previous proposal, last week, that defined "planet" as anything big enough that its gravity made it round, was obviously a red herring that nobody was going to take very serious. Fercryinoutloud, it made the asteroid Ceres a planet, as well as Earth's moon (in a few billion years when it gets a bit farther away from us and ceases to be considered a moon).

But apparently there were several other dirty tricks played by the anti-Pluto faction, and IAU members who weren't able to be in the room at the time of the vote are not happy and are spoiling for a rematch. The new definition doesn't make much more sense than the previous one, anyway: it's based on gravitationally sweeping out objects from an orbit, but that also rules out Earth, Mars, Jupiter and Neptune, all of which have non-satellite objects along their orbits.

And of course the public is pretty upset about it for sentimental, non-scientific reasons. Try searching for Pluto or "Save Pluto" on Cafe Press to see the amazing selection of pro-Pluto merchandise you can buy barely a day after the IAU decision. (Personally, I want a Honk if Pluto is still a planet bumper sticker.)

It'll be interesting to see if the decision sticks.

So do I have a viable definition of "planet" which includes Pluto but not Ceres or the various other Kuiper belt objects which are continually being discovered?

Why, no, I don't. But the discussion is purely semantic anyway. Whether we call Pluto a planet doesn't make any difference to planetary science. But it does make a difference to an enormous collection of textbooks, museum exhibits, and other science-for-the-public displays.

Pluto is big enough to have been discovered in 1930, back in the days before computerized robotic telescopes and satellite imaging; it's been considered a planet for 76 years. There's no scientific benefit to changing that, and a lot of social and political reason not to -- especially now with New Horizons headed there to give us our first up-close look at what Pluto actually looks like.

There are two possible bright notes to the Pluto decision. First, Mark Taylor pointed out that it has become much easier to observe all the planets in one night, even with a very small telescope or binoculars.

And second, maybe Christine Lavin will make a new updated version of her song Planet X and go on tour with it.

Tags: science, astronomy
[ 21:56 Aug 25, 2006    More science/astro | permalink to this entry ]

The Hayward Fault -- Exposed!

Today was opening day for the Hayward fault!

Well, okay, the fault itself has been there a while, but it was opening day for the Hayward Fault: Exposed! exhibit in Fremont. They've dug a trench into the Hayward fault as part of the 1906 San Francisco Earthquake Centennial activities, so people can walk a stairway and stand right in a fault and see what it looks like.

I'm a volunteer docent for the exhibit: one of the people who help answer questions about the fault, the trench, and earthquakes in general, and who also help with details such as setup, safety, and getting people to sign the liability waiver as they enter the exhibit. (My photos and fault facts here.)

Opening day was a bit hectic even aside from the usual opening-day flutters because it was a big day in Fremont Central Park: there was a huge manga festival at the Teen Center right next to the fault trench, complete with live band all day, and over at Lake Elizabeth at the other end of the park was the annual "Splashdown" rubber ducky race.

We expected chaos. But we didn't get it: everything went surprisingly smoothly. We got lots of visitors who were there specifically to see the fault, not just spillover from the other events: apparently it had gotten press on the TV news and several newspapers. There may also have been word of mouth advertising: a surprising number of the visitors I talked to were CERT volunteers or otherwise actively involved in bay area disaster preparedness programs. They were already very well informed about seismic hazards and earthquakes, and eager to see the fault for themselves.

We ended up with about 600 visitors (perhaps a fourth to a third of them teens from the manga festival). Everyone was very well behaved, asked good questions and seemed to appreciate the exhibit. It's lovely to volunteer at exhibits where you spend all your time answering questions, chatting with people and explaining the exhibit, not worrying about policing people and enforcing rules.

(Well, maybe there was a little bit of chaos. The band at the manga festival included karaoke. It's not every day that one gets the opportunity to try to explain paleoseismology and radiocarbon dating while someone a few feet away is belting out "Bohemian Rhapsody" over a loudspeaker but forgetting the words.)

We were pleased to see that everyone spent a lot of time around the (excellent) poster displays from the USGS, which cover everything from earthquake preparedness to stratigraphy of this particular trench to geologic maps of the Hayward fault and the bay area. Most people missed the parking lot displays on the way in (a sign pointing to cracks in the pavement and an offset curb, highlighted with orange spray paint), but we told them what to look for so they could catch them on the way out.

The exhibit will get more press tonight: two or three different TV channels showed up today and interviewed Heidi Stenner, the USGS geologist organizing the exhibit, as well as some of the visitors. So with any luck we'll continue to get good turnouts. The trench will be open through the end of June.

Most of the other docents are either seismologists or seismology graduate students. It wasn't a problem: the questions most people were asking were straightforward questions I could answer easily. But it was fun listening to the other docents and learning from them, and when someone asks a tricky question, you sure can't beat being able to turn to the researcher who did the original study on this trench in 1987 (Jim Lienkaemper) and get the straight scoop! (He also developed the USGS Virtual Tour of the Hayward Fault web site).

The Hayward fault last let go in 1868, a magnitude-6.9 event called "The Great San Francisco Quake" until the 1906 earthquake on the San Andreas took over that title. Trench studies like Lienkaemper's have shown that historically this fault has a large earthquake every 130 to 150 years. Our visitors didn't need a calculator to do the math.

Tags: science, geology
[ 22:46 Apr 29, 2006    More science/geology | permalink to this entry ]