Mirrors can be lots of fun. We've all fooled around with them as children, and as adults while shaving etc. Two aspects in particular are fascinating: the left-right reversal, and the angle of reflection. If you have two large mirrors mounted at an angle of say 120-degrees or thereabouts, like in a clothing store, there are multiple reflections. Worth the trouble to set up at home, for a more leisurely exploration. Perhaps your home has a mirror mounted on the back of the bathroom door, as well as one above the bathroom sink. Then you've got ideal experimental apparatus, and can change the angle of the mirrors, or adjust lighting as needed.

Things to do:

-- With a camera, take flash snaps. How many light balls can you get visibile in photo?

-- Investigate word reversal (sweatshirt lettering?), notice re-reversal on second reflection, trace light path which gives correct orientation - triangular? Angles which are involved?

-- Strings and tape, to trace light paths? Confirm angles, triangles. Use laser pointer as a smaller light source, vs camera? Illuminate along string to confirm string locations?

-- Polarization? I found a source of inexpensive polarizing filters, online, but haven't yet tried out their product.

-- Diffraction grating instead of mirror? Prisms? Fresnel lenses?

Yellow Trillium

You know, it's funny ... I thought for sure I had posted here last year about finding yellow trilliums in the woods. But I cannot see the post -- so will do so now. guess I put only the photos online (link below), and forgot the post at Livejournal. Doing it now!

Last May, we noticed yellow trilliums in our woods. We have lots of red trilliums (thousands) and hundreds of white. The yellow is a variant of the red -- same leaf shape -- different from the white's leaf shape. Sort of an albino red, I guess.

Photos at http://kensview.mirror1.org/post/2011/05/08/Trillium_Photos

Last year we found four yellows, and we marked their locations. The spring is faster advanced this year, maybe 3 weeks, and the reds have been out about 1.5 weeks. The yellows just bloomed. We have the same four locations, plus we found a fifth yellow. So the yellow runs true -- ie, it is something genetic, not just a soil pH thing or a one-year anomaly in flower growth. The yellows are found mingled with reds, another indication that it is not soil pH.

This is not a real yellow trillium. We saw an "official" yellow trillium at an open garden last year, and it has quite a distinctive shape, different from both reds and whites. Still I don't know a better name for these red-shaped yellows.

The yellows tend to run a bit smaller than reds, maybe 10 percent smaller, and droops a bit more.

While we're talking trilliums, I will tell you the wonderful story of how trilliums spread.

Trillium seeds have a waxy coating, that ants like to eat. The ants gather the seeds, take them down into their nests, and eat the coating later, leaving the seed. Come housekeeping time, the ants carry the seeds out, and spread them around. So the next time you see lots of trilliums, thank the ants for their work!

Wave Mechanics

It's customary to speak of wavelengths, and similar periodicities, in water waves. But when one examines the ocean, it turns out that waves are far from regular in shape and period. Today I went to the oceanside, and recorded a 3-minute video of waves coming ashore and crashing over a large rock. There was a moderate but steady breeze from offshore, perhaps 15 km/hr, and the time was about 1 hour after low tide.

Examining the video, each time the leading edge of a wave crashed over a particular part of the rock, I noted the time interval between that wave's arrival and the prior wave's arrival. A little perl program helped with recording the time information; I simply had to press the enter key everytime a wave was noted, and the program did the rest of the calculations.

The results: 22 waves arrived in the video, hence 21 intervals, total of 168 seconds or an average of 8.0 seconds between waves. Intervals ranged from 4.1 to 14.2 seconds, and the standard deviation of wave intervals was 2.8 seconds. Hardly a monofrequency wavefront!

I also noticed instances of waves running off at angles from the main wave front, water against water effects, not rock reflections, although it is possible there were reflections off the underwater bottom involved.

Serious study of wave mechanics, of actual waves, is not a trivial task!

Once again, we see that Hamlet has it right: There are more things in heaven and earth, than are dreamt of in our philosophies.


A stereogram is a pair of related photos which are slightly offset from one another. If each photo is viewed with one eye, you see a 3-D image. Think of the Viewmaster. There were some antique stereograms around my wife's parents home, some 40 years ago, along with a viewer.

The NY Public Library has some 40,000 stereograms in its collection, and has put them online, at http://stereo.nypl.org -- using an innovative presentation idea: Instead of viewing one photo with each eye, the two photos are overlapped in an animated gif image file, flipping back and forth about twice a second. A bit hyper, but one can get some impression of the 3-D scene.

The images in their gallery also link to the original stereograms, and you can look at them on your computer screen with your very own stereogram viewing device!

Here's how: Take a piece of cardboard, eg the back of a pad of writing paper, and hold it up beside your head. Trace, or have a friend trace, the outline of your front profile on the cardboard, and cut that shape out of the cardboard -- keep the rest of the cardboard. When you hold the cardboard up to your face, it fits well enough that you are looking with each eye on different sides of the cardboard, with no opportunity for line of sight crossover.

Hold the cardboard up to your computer screen, on which a stereogram is displayed, with the far edge of the cardboard touching the screen. Your eyes will be about 20 cm away from the other edge of the cardboard, ie the stereogram image. If you defocus your view slightly, try not to focus on the screen but on the picture beyond the screen, you will see the 3-D image.

I recently ran across stereograms in a physics book, "Methods of Theoretical Physics", by Morse and Feshbach, 1953. They want to show some 3-D surfaces, and printed them as stereograms. Interesting technique. Think of the careful work needed by the illustration draftsman!

Nowadays, I think colour-tint encoding might also help with presenting good stereograms.


If two materials are joined, and the junction is heated, electric current is generated. For instance, an steel wire and a copper wire, with the junction heated. Current flows while there is a temperature gradient within the wires. The phenomenon is called the thermoelectric effect or the Seebeck effect. It is also sometimes termed the Peltier effect, but strictly speaking the Peltier effect is the reverse phenomenon: a flow of current can produce heating or cooling at the junction of the two materials.

Metal-to-metal does not make a great thermoelectric generator, as the thermal conductivity of metals is high, and the temperature gradients in the wires can rapidly disappear -- unless there are heat sources and sinks available. Such as the hot surface of a woodstove, and the cool room air. Better thermoelectric effects are obtained using semiconductor materials, and there are modules available, suitable for experimenting or commercial use. For instance, this youtube video was made a home experimenter, showing production of 1+ volts at 1+ amps, sufficient to light a 12-LED flashlight head. He used only hot and cold water from his kitchen sink tap.

http://www.youtube.com/watch?v=tbdtulL44ms -- Seebeck effect video

A commercial product is the Ecofan, which is a small fan for the top of a woodstove. A woodstove ordinarily heats the room by radiation. By using an electric fan, one can push air around, and also heat the room by convection. However, that requires electricity. Instead, one can use an Ecofan, which is powered by the heat of the woodstove. The ecofan is not nearly as powerful as an electric fan, and is really pretty inefficient, but it makes a nice conversation item, and it does do something to move a bit of air.

I ran some tests using an ecofan, to see what the temperatures and fan blade speeds were. My fan has a 20 cm diameter metal blade. It consists of two large metal heat sinks, one which sits on the stove top and has a thermoelectric module on its top, and one which is mounted on top of the module, and sticks up into the room air. The temperature differential of importance is that between the stove top, and the room air.

With a ceramic-top woodstove, operating with top at 75 C with moderate fire, and with room air temperature 20 cm above the stove at 25 C, the fan blade rotates at 360 rpm. A ceramic stove runs relatively cool on top. With a metal-top woodstove, operating with top at either 100 C or 145 C, ie low or moderate fire, the fan blade rotates at 560 rpm. I didn't try a repeat of the measurements of rotation speed, so this preliminary results of "no increase" of rpm with temperature increase from 100 C to 145 C, would deserve independent confirmation.

The metal stove's flue operating temperature is hotter than the temperature of top surface. In the two tests, the flue operating temperature was 180 C (creosote formation risk region) when stovetop was 100 C, and 280 C (satisfactory operating region) when stovetop was 145 C.

Here is a link to a supplier of Ecofans. I'm sure there is more info available online.

http://www.ecofan.co.uk -- Ecofan website

A really good technical book about thermoelectricity is by H. Julian Goldsmid, "Introduction to Thermoelectricity", Springer, 2009. Goldsmid has worked on thermoelectricity for over 50 years.

Max Born - Physics in My Generation

"Physics in My Generation" is a collection of essays, on scientific philosophy and social topics, by Max Born. It was published (2nd revised edition) in 1969, and collects essays from 1921 to 1966. Born is an interesting thinker and writer. This book of his essays has been my frequent reading companion for the past month. Now that I've finished, I plan to re-read some of the essays -- they are that thought-provoking.

Some of the highlights for me... scientific essays on Einstein's statistical theories, physical aspects of quantum mechanics, and whether classical mechanics is deterministic, and social essays on the atomic age, the atomic bomb, and scientists' responsibilities.

Menger Sponge Business Card Project

A conversation today reminded me about Jeannine Mosely's Menger sponge business card project. See the URL http://theiff.org/oexhibits/menger02.html for photographs and a link to the pdf file with full instructions. I made a level 1 sponge several years ago, and it sat around a long time until the dust level got unreasonable! So today, just for fun, out came the supply of business card stock, and my granddaughter and I made some constructions. With 12 cards, you can make a very nice little 5-cm "gift cube" for someone.

Cappella Emiliana

A while ago, I mentioned my hope to visit the Cappella Emiliana in Venice, particularly to see the pentagonal antechamber. I was there, and saw it -- a very interesting solution to a novel architectural problem, Namely, how to join a hexagonal structure (the Cappella Emiliana) to the corner of a rectangular church building (San Michele in Isola), in a way which is visually appealing and feels natural as one makes the transition between the spaces.

My original post is "Peas in a Pod", July 4th 2011, and you can find the Weyl "Symmetry" book reference there. The other book reference, obtained on my visit, is "Venezia - San Michele in Isola: Guida Pratica Illustrata", by Paolo Franceschi (no date), which is a excellent 118-page guidebook, in Italian. It can be obtained at the entry to the church -- donation 5 Euro. It might be easier, if one is not going to be in Venice, to track down the 2-volume work from which the guidebook is drawn: "San Michele in Isola - Venezia" (1962), by Vittorino Meneghin.

Pages 42-47 of Franceschi's guidebook discuss the Cappella, with several photos, and in particular a photo of the pentagonal vestibule on page 47. There are also photos on pages 2,4,6,8,9 which show the relationship of the Cappella and the main church building.

Imagine, if you will, a huge rectangular church, and you are standing at the back left corner, facing towards the front which is, say, at 12-oclock.. A hexagonal building is to be built outside, at roughly 8-oclock orientation. How shall a doorway and short passageway be constructed from where you are, into the new annex? You do not wish the transition from rectangular space to hexagonal space to feel awkward.

The solution: A pentagonal vestibule forms the passageway. You depart the church thru one side of the pentagon, and enter the cappella thru another side. Two sides of the pentagon are to your right as you pass thru, and one side is to your left. That makes the transition from church building, which is at right angles, feel quite natural as you enter the cappella at 8-oclock.

The passageway is hardly visible in exterior photos, which are dominated by the very striking and beautiful cappella. But the interior design is perfect.

It truly is a sight worth seeing.

Not many tourists bother to visit the cemetery island. No photos are taken and the atmosphere is subdued and respectful. The many cypress trees are a refreshment. You can get there on the #41 or #42 vaporetto (water bus). If you take the bus from the Fondamente Nove stop, on the walk there you will pass some stone cutting shops, artists who make gravestones, along with some flower sellers.

The Cappella Emiliana was built 1527-1543. I've read that a non-rectangular building is quite unusual for Renaissance architecture.

Fluidized Beds, and ICFAR

Yesterday evening was an open house at ICFAR (pronounced "I see far"), an institute working on chemicals and fuels from alternative resources. Website http://www.icfar.ca for info.

Very interesting. They are doing good work. The process discussed during the tour, was fluidized bed decomposition of farm waste (chaff from field harvesting) to obtain a diesel fuel. Much more at the website.

What I want to talk about in this post, is fluidized bed clumping problem. A fluidized bed is a container of sand, with air bubbling thru it; visually, the surface looks like a pan of water in a rolling boil. The reactants are introduced, and the sand provides plenty of reaction surface, and the air provides plenty of mixing, for some desired reaction to occur -- even at an industrial scale -- for instance, part of the process of going from tar sands to syncrude.. Typically at high temperature (500C), perhaps pressure. But there can be a clumping problem -- the sand can clump, resulting in less reaction surface. So how to break up the clumps? Or discourage their formation?

A few ideas, some actually used, some oddball: Mechanical mixing. High-speed jets of reactant or of other substance (water). Ultrasonics. "Worms", tiny corkscrews which tend to destructively interact with clumps. Resonating the ultrasonics to the worms, or to clump parameters at formation stage. Perhaps an electrostatic charge (two types of sand?), with fluctuating electric or magnetic field.

Other suggestions?

Faraday - The Forces of Matter

Michael Faraday's book "The Forces of Matter" is my latest read. It is a transcript, with illustrations, of the series of six lectures for young people which Faraday gave at the Royal Institution during the 1859-60 Christmas holidays. Quite some time ago I read Faraday's "The Chemical History of a Candle", another series of juvenile Christmas break lectures, and it earned a place on my list of ten books that I wish (at age 51) I had known to read much earlier (at age 21). The "Candle" book is the best illustration of how to do practical experimental science that I've ever seen.

Faraday's "The Forces of Matter" is equally engaging and informative. Only 84 pages. Reprinted by Dover, quite inexpensive. The forces he considers are gravitation, cohesion, heat, chemical affinity, electricity, magnetism. He illustrates them with simple experiments which were performed in the lecture hall, and relates the various forces together. For example, when solid matter particles dissociate into liquid state, they take up heat -- thereby cooling their surroundings. He shows an example. Today we would think of how ice cream is made, by adding salt to crushed ice within a bowl, and the bowl then cools the nearby cream mixture.