Einstein, Newton, and the two Pascal brothers are playing hide and seek. Einstein has his eyes covered and is counting. The two Pascal bothers run and hide but Isaac Newton does not. He draws a square around him in the dust and stands waiting. When Einstein finishes counting he says, “I see you Sir Isaac standing there.” “No you don’t.” says Newton. “You see two Pascals: there’s one Newton in half a square meter area.
Pi in therapy, a division sign is the councilor.
The working title of the joke is wife of pi.
Robert Buxbaum is now on the board of a new charity
I’m now on the board of directors for two non-profits (lucky me), plus for my own hydrogen company, REB Research. My first charity seat is for The Jewish Heritage Foundation; it’s really one rabbi who takes donations to make tapes about topics he finds interesting. He then gives away or sells the tapes. We meet once a year to go over the finances and decide what his salary ought to be — basically we rubber stamp.
The second board seat, one I’ve been elected/appointed to just this week, is with a group call “The First Covenant Foundation” they’re semi-religious, trying to get people to behave decently. The first covenant is the one with Noah — God won’t destroy the earth but we have to behave sort-of OK. It’s certainly worthwhile to get people to keep to this minimal standard: no murder, no bestiality, don’t eat the limbs off of living creatures… Then again, if God has trouble keeping folks to this standard, I’m not sure how effective the 1st covenant will be. So far they’ve done nothing illegal or immoral that I’ve seen, so that’s good. Unlike with my first my board position, my contract with first covenant includes a sanity clause. They’re more inclusive that way; as expected, the Jewish heritage group didn’t believe in any sanity clause.
As for REB Research, our aims are simpler: to make and sell good hydrogen-related products, to make money, to pay our workers and creditors, and to develop our workers through training associated with the making and selling of good hydrogen products. Simple enough. My board meets 3 or 4 times a year over pizza; the salary of board members is the pizza. So far we haven’t done anything illegal either, that I know of — and we’re even making money.
Dwarf joke
I tripped over a dwarf the other day; I know — bad news. The fellow gets all huffy with me, and seems to think I was looking down on him (So weird, if I’d been looking down on him, I’d never have tripped!).
At any rate he says, “I’m not happy.” “That’s OK.” I say, “So which one are you?” And he gets all upset. These dwarves are all the same, they’re so small.
For parents of a young scientist: math
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It is not uncommon for parents to ask my advice or help with their child; someone they consider to be a young scientist, or at least a potential young scientist. My main advice is math.
Most often the tyke is 5 to 8 years old and has an interest in weather, chemistry, or how things work. That’s a good age, about the age that the science bug struck me, and it’s a good age to begin to introduce the power of math. Math isn’t the total answer, by the way; if your child is interested in weather, for example, you’ll need to get books on weather, and you’ll want to buy a weather-science kit at your local smart-toy store (look for one with a small wet-bulb and dry bulb thermometer setup so that you’ll be able to discuss humidity in some modest way: wet bulb temperatures are lower than dry bulb with a difference that is higher the lower the humidity; it’s zero at 100%). But math makes the key difference between the interest blooming into science or having it wilt or worse. Math is the language of science, and without it there is no way that your child will understand the better books, no way that he or she will be able to talk to others who are interested, and the interest can bloom into a phobia (that’s what happens when your child has something to express, but can’t speak about it in any real way).
Math takes science out of the range of religion and mythology, too. If you’re stuck to the use of words, you think that the explanations in science books resemble the stories of the Greek gods. You either accept them or you don’t. With math you see that they are testable, and that the versions in the book are generally simplified approximations to some more complex description. You also get to see that there the descriptions are testable, and that are many, different looking descriptions that will fit the same phenomena. Some will be mathematically identical, and others will be quite different, but all are testable as the Greek myths are not.
What math to teach depends on your child’s level and interests. If the child is young, have him or her count in twos or fives, or tens, etc. Have him or her learn to spot patterns, like that the every other number that is divisible by 5 ends in zero, or that the sum of digits for every number that’s divisible by three is itself divisible by three. If the child is a little older, show him or her geometry, or prime numbers, or squares and cubes. Ask your child to figure out the sum of all the numbers from 1 to 100, or to estimate the square-root of some numbers. Ask why the area of a circle is πr2 while the circumference is 2πr: why do both contain the same, odd factor, π = 3.1415926535… All these games and ideas will give your child a language to use discussing science.
If your child is old enough to read, I’d definitely suggest you buy a few books with nice pictures and practical examples. I’d grown up with the Giant Golden book of Mathematics by Irving Adler, but I’ve seen and been impressed with several other nice books, and with the entire Golden Book series. Make regular trips to the library, and point your child to an appropriate section, but don’t force the child to take science books. Forcing your child will kill any natural interest he or she has. Besides, having other interests is a sign of normality; even the biggest scientist will sometimes want to read something else (sports, music, art, etc.) Many scientists drew (da Vinci, Feynman) or played the violin (Einstein). Let your child grow at his or her own pace and direction. (I liked the theater, including opera, and liked philosophy).
Now, back to the science kits and toys. Get a few basic ones, and let your child play: these are toys, not work. I liked chemistry, and a chemistry set was perhaps the best toy I ever got. Another set I liked was an Erector set (Gilbert). Get good sets that they pick out, but don’t be disappointed if they don’t do all the experiments, or any of them. They may not be interested in this group; just move on. I was not interested in microscopy, fish, or animals, for example. And don’t be bothered if interests change. It’s common to start out interested in dinosaurs and then to change to an interest in other things. Don’t push an old interest, or even an active new interest: enough parental pushing will kill any interest, and that’s sad. As Solomon the wise said, the fire is more often extinguished by too much fuel than by too little. But you do need to help with math, though; without that, no real progress will be possible.
Oh, one more thing, don’t be disappointed if your child isn’t interested in science; most kids aren’t interested in science as such, but rather in something science-like, like the internet, or economics, or games, or how things work. These areas are all great too, and there is a lot more room for your child to find a good job or a scholarship based on their expertise in theses areas. Any math he or she learns is certain to help with all of these pursuits, and with whatever other science-like direction he or she takes. — Good luck. Robert Buxbaum (Economics isn’t science, not because of the lack of math, but because it’s not reproducible: you can’t re-run the great depression without FDR’s stimulus, or without WWII)
Heisenberg joke and why water is wet
I love hydrogen in large part because it is a quantum fluid. To explain what that means and how that leads to water being wet, let me begin with an old quantum physics joke.
Werner Heisenberg is speeding down a highway in his car when he’s stopped by a police officer. “Do you know how fast you were going?” asks the officer. “No idea” answers Heisenberg, “but I know exactly where I am.”
The joke relates to a phenomenon of quantum physics that states that the more precisely you can know the location of something, the less precisely you can infer the speed. Thus, the fact that Heisenberg knew precisely where he was implied that he could have no idea of the car’s speed. Of course, this uncertainty is mostly seen with small things like light and electrons –and a bit with hydrogen, but hardly at all with a car or with Dr. Heisenberg himself (and that’s why it’s funny).
This funky property is related to something you may have wondered about: why is water wet? That is, why does water cling to your hands or clothes while liquid teflon repels. Even further, you may have wondered why water is a liquid at normal conditions when H2S is a gas; H2S is a heavier analog, so if one of the two were a liquid, you’d think it was H2S.
Both phenomena are understood through hydrogen behaving as the quantum car above. Oxygen atoms are pretty small, and hydrogen atoms are light enough to start behaving in a quantum way. When a hydrogen atom attaches to an oxygen atom to form part of a water molecule, its location becomes fixed rather precisely. As a result, the hydrogen atom gains velocity (the hydrogen isn’t going anywhere with this velocity, and it’s sometimes called zero-point energy), but because of this velocity or energy, its bond to the oxygen becomes looser than it would be if you had heavier hydrogen. When the oxygen of another water molecule or of a cotton cellulose molecule comes close, the hydrogen starts to hop back and forth between the two oxygen atoms. This reduces the velocity of the hydrogen atom, and stabilizes the assemblage. There is now less kinetic energy (or zero-point energy) in the system, and this stability is seen as a bond that is caused not by electron sharing but by hydrogen sharing. We call the reasonably stable bond between molecules that share a hydrogen atom this way a “hydrogen bond.” (now you know).
The hydrogen bond is why water is a liquid and is the reason water is wet. The hydrogen atom jumping between water molecules stabilizes the liquid water more than it would stabilize liquid H2S. Since sulfur atoms are bigger than oxygen atoms, the advantage of hydrogen jumping is smaller. As a result, the heat of vaporization of water is higher than that of H2S, and water is a liquid at normal conditions while H2S is a gas.
Water sticks to cotton or your skin the same way, hydrogen atoms skip between the oxygen of water molecules and of these surfaces creating a bond. It is said to whet these surfaces, and the result is that water is found to be wet. Liquid teflon does not have hydrogen atoms that can jump so there is no band that could be made from that direction (there are some hydrogen atoms on the cotton that can jump to the teflon, but there is no advantage to bonding of this sort as there are only a few hydrogen atoms, and these already jump to other oxygens in the cotton. Thus, to jump to the teflon would mean breaking a bond with other oxygen atoms in the cotton — there would be no energy advantage. This then is just one of the reasons I love hydrogen: it’s a quantum-y material.
A visit to the Buxbaum laboratory from Metromedia
It’s a slow news day in Detroit, so the folks from Metromedia came to visit my laboratory at REB Research. You can visit too. We’re doing cool stuff most of the time, we’re working on a hydrogen-fueled plane that stays aloft for weeks (not that cool, actually, the Hindenberg did it in the 30s). On this particular day I’ve got a cool hat on, and a beige suit. I’m putting hydrogen in my car. Hydrogen increases the speed of combustion, and so it adds to milage — or it has when we’ve added it from electrolysis sources.
The fun thing about science is that there are always surprises.
Adding hydrogen to a Malibu at REB Research
Small hydrogen generators for cooling dynamo generators
A majority of the electricity used in the US comes from rotating dynamos. Power is provided to the dynamos by a turbine or IC engine and the dynamo turns this power into electricity by moving a rotating coil (a rotor) through a non-rotating magnetic field provided by magnets or a non-rotating coil (a stator). While it is easy to cool the magnets or stator, cooling the rotor is challenging as there is no possibility to connect it cooling water or heat transfer paste. One of the more common options is hydrogen gas.
It is common to fill the space between the rotor and the stator with hydrogen gas. Heat transfers from the rotor to the stator or to the walls of the dynamo through the circulating hydrogen. Hydrogen has the lowest density of any gas, and the highest thermal conductivity of any gas. The low density is important because it reduces the power drag (wind drag) on the rotor. The high heat transfer coefficient helps cool the rotor so that it does not burn out at high power draw.
Hydrogen is typically provided to the dynamo by a small hydrogen generator or hydrogen bottle. While we have never sold a hydrogen generator to this market, I strongly believe that our membrane reactor hydrogen generators would be competitive; the cost of hydrogen is lower than that of bottled gas; it is far more convenient and safe; and the hydrogen is purer than from electrolysis.
Why isn’t the sky green?
Yesterday I blogged with a simple version of why the sky was blue and not green. Now I’d like to add mathematics to the treatment. The simple version said that the sky was blue because the sun color was a spectrum centered on yellow. I said that molecules of air scattered mostly the short wavelength, high frequency light colors, indigo and blue. This made the sky blue. I said that, the rest of the sunlight was not scattered, so that the sun looked yellow. I then said that the only way for the sky to be green would be if the sun were cooler, orange say, then the sky would be green. The answer is sort-of true, but only in a hand-waving way; so here’s the better treatment.
Light scatters off of dispersed small particles in proportion to wavelength to the inverse 4th power of the wavelength. That is to say, we expect air molecules will scatter more short wavelength, cool colors (purple and indigo) than warm colors (red and orange) but a real analysis must use the actual spectrum of sunlight, the light power (mW/m2.nm) at each wavelength.
intensity of sunlight as a function of wavelength
The first thing you’ll notice is that the light from our sun isn’t quite yellow, but is mostly green. Clearly plants understand this, otherwise chlorophyl would be yellow. There are fairly large components of blue and red too, but my first correction to the previous treatment is that the yellow color we see as the sun is a trick of the eye called additive color. Our eyes combine the green and red of the sun’s light, and sees it as yellow. There are some nice classroom experiment you can do to show this, the simplest being to make a Maxwell top with green and red sections, spin the top, and notice that you see the color as yellow.
In order to add some math to the analysis of sky color, I show a table below where I divided the solar spectrum into the 7 representative colors with their effective power. There is some subjectivity to this, but I took red as the wavelengths from 620 to 750nm so I claim on the table was 680 nm. The average power of the red was 500 mW/m2nm, so I calculate the power as .5 W/m2nm x 130 nm = 65W/m2. Similarly, I took orange to be the 30W/m2 centered on 640nm, etc. This division is presented in the first 3 columns of the following table. The first line of the table is an approximate of the Rayleigh-scatter factor for our atmosphere, with scatter presented as the percent of the incident light. That is % scattered = 9E11/wavelength^4.
To use the Rayleigh factor, I calculate the 1/wavelength of each color to the 4th power; this is shown in the 4th column. The scatter % is now calculated and I apply this percent to the light intensities to calculate the amount of each color that I’d expect in the scattered and un-scattered light (the last two columns). Based on this, I find that the predominant wavelength in the color of the sky should be blue-cyan with significant components of green, indigo, and violet. When viewed through a spectroscope, I find that these are the colors I see (I have a pocket spectroscope and used it an hour ago to check). Viewed through the same spectroscope (with eye protection), I expect the sun should look like a combination of green and red, something our eyes see as yellow (I have not done this personally). At any rate, it appears that the sky looks blue because our eyes see the green+ cyan+ indigo + purple in the scattered light as sky blue.
At sunrise and sunset when the sun is on the horizon the scatter percents will be higher, so that all of the sun’s colors will be scattered except red and orange. The sun looks orange then, as expected, but the sky should look blue-green, as that’s the combination of all the other colors of sunlight when orange and red are removed. I’ve not checked this last yet. I’ll have to take my spectroscope to a fine sunset and see what I see when I look at the sky.
Why isn’t the sky green and the sun orange?
Part of the reason the sky isn’t green has to do with the color of the sun. The sun’s color, and to a lesser extent, the sky color both are determined by the sun’s surface color, yellow. This surface color results from black body radiation: if you heat up a black object it will first glow red, then orange, yellow, green etc. Red is a relatively cool color because it’s a low frequency (long wavelength) and low frequencies are the lowest energy photons, and thus are the easiest for a black body to produce. As one increases the temperature of a black object, the total number of photons increases for all wavelengths, but the short wavelength (high frequency) colors increase faster than the of long wavelength colors. As a result, the object is seen to change color to orange, then yellow, or to any other color representative of objects at that particular temperature.
Our star is called a yellow sun because the center color of its radiation is yellow. The sun provides radiation in all colors and wavelengths, even colors invisible to the eye, infra red and ultra violet, but because of its temperature, most of the radiated energy appears as yellow. This being said, you may wonder why the sky isn’t yellow (the sky of Mars mostly is).
The reason the sky is blue, is that some small fraction of the light of the sun (about 10%) scatters off of the molecules of the air. This is called Rayleigh scatter — the scatter of large wavelegth waves off of small objects. The math for this will be discussed in another post, but the most relevant aspect here is that the fraction that is scattered is proportional to the 4th power of the frequency. This is to say, that the high frequencies (blue, indigo, and violet) scatter a lot, about 20%, while the red hardly scatters at all. As a result the sky has a higher frequency color than the sun does. In our case, the sky looks blue, while the sun looks slightly redder from earth than it does from space — at least that’s the case for most of the day.
The sun looks orange-red at sundown because the sunlight has to go through more air. Because of this, a lot more of the yellow, green, and blue scatter away before we see it. Much more of the scatter goes off into space, with the result that the sky to looks dark, and somewhat more greenish at sundown. If the molecules were somewhat bigger, we’d still see a blue sky, maybe somewhat greener, with a lot more intensity. That’s the effect that carbon dioxide has — it causes more sunlight to scatter, making the sky brighter. If the sun were cooler (orange say), the sky would appear green. That’s because there would be less violet and blue in the sunlight, and the sky color would be shifted to the longer wavelengths. On planets where the sun is cooler than ours, the sky is likely green, but could be yellow or red.
Rayleigh scatter requires objects that are much smaller than the light wavelength. A typical molecule of air is about 1 nm in size (1E-9 of a meter), while the wavelength of yellow light is 580 nm. That’s much larger than the size of air molecules. Snow appears white because the size of the crystals are the size of the sun wavelengths, tor bigger, 500-2000 nm. Thus, the snow looks like all the colors of the sun together, and that’s white. White = the sum of all the colors: red + orange + blue + green + yellow + violet + indigo.
Robert Buxbaum Jan. 27, 2013 (revised)