Several people have written asking for educational projects to occupy their kids during the pandemic. I've answered with a number of ideas, but it hit me chindōgu could be the perfect ticket for many. It's the absurd Japanese art of useless inventions aimed at solving everyday problems with roots in Rube Goldberg machines and the art of the kludge - a clever but inelegant solution to a problem. A number of good examples are shown here. I've recommended this approach to a number of middle and high school teachers. At least one has had a lot of fun with it making a "how to program things" module more fun. It's also become a recreational art form at an animation studio you've heard about.
Thinking that way can be unexpected powerful. It cuts through barriers combining critical thinking and play with the goal of humor. Failure is fine and can be a powerful learning experience. Simone Giertz has been credited with getting more teenage girls interested in engineering than other person or program. She's famous for useless robots - "shitty robots" as she calls them. Here's her TED talk (one of the few useful TED talks I've seen).
Here's her YouTube channel. Earlier pieces may be more accessible to beginners as she's become more sophisticated in her craziness. And she has done much of this with brain cancer. A remarkable inspiration.
So start off small with supplies around the house and just have fun. There aren't any downsides and you can spend as much or as little as you want. You're only limited by your imagination and sense of humor. And if you are building them, you can draw or write about them.
There was a bowl of M&Ms for after the oral exams Our grades were based on homework assignments and three oral exams. Four of us would take our turn at the blackboard. The professor had this natural ability to ask question you hadn't thought about, but should be able to solve.
Mr Crandall: Does a clock at the center of the Earth run faster or slower than one on the surface? If so how big is the difference since the Earth was formed?
(It wasn't as bad as that might sound - he was nothing like John Houseman.)
First a little diversion is in order. You've probably heard the Global Positioning System needs to account for relativity. Two effects are going on. In one the satellites are moving with respect to GPS receiver on the ground. Each satellite has a very stable atomic clock that is synchronized with the other GPS satellites. Your receiver look at position and time information from at least four satellites to determine your position. To get the necessary level of accuracy the system needs to account for the effects of both special and general relativity.
Special relativity tells us moving clock appears to run a bit slower than one at rest. Almost everything around us moves too slowly for this to be important , but a clock on a GPS satellite would lose about seven microseconds a day. That may not seem like much, but that's enough to cause a position error that increases by about two kilometers a day.
The curvature of spacetime is the bigger problem. A result of general relativity is the direction where time runs more slowly.1 The further a clock is from a mass, the faster it runs. Clocks on orbiting GPS satellites gain about forty six microseconds a day. Add the special and general relativistic effects and the satellite clocks gain a bit under thirty nine microseconds a day. Left uncorrected the system would be useless in a few minutes and the error would increase by over seven miles in a day. The satellites correct for both of these effects before the signal is transmitted.
All of this is key to the original question. Time at the center of the Earth will pass more slowly. The question is how much?
The purpose of these oral exams was not so much to test if you had learned the course material, but to encourage you to quickly frame a problem and come up with a ballpark estimate. In the spirt of the type of education pioneered by Comenius it was supposed to be playful and even fun. This type of thinking with a piece of chalk is core to thinking through new ideas and working with others on certain stages of problems. A few marks of chalk might represent dozens of pages of calculations if done in detail. Unfortunately its protrayal on television and in movies can make the field seem artificially difficult to outsiders.
A quick calculation showed the center of the Earth is about 1.4 years "younger" than the surface.2 Long lived radioactive elements at the core decay slightly less than their counterparts at the surface. I can still remember the "wow" in my mind as took a handful of M&Ms. A not very great fountain of youth is under your feet. Since then I've learned exercise and eating right are better approaches to aging.
Since then I've done a more accurate calculation. The inner Earth isn't homogeneous. I found an estimate of how density changes and came up with about 2.5 years. The initial estimate was ten or fifteen minutes with a piece of chalk vs at least a day's worth of work. In the process I found time dilation due to special relativity was a thousand times smaller and reasonable to ignore. Moving to the Sun I got about 30,000 years with the simple estimate for the Sun's density.
The more important point is many fields develop mechanisms for dealing with either too much or too little data by coming up with simple ways to reframe and think about the task. I've seen it in math, art and sports and assume it's a common approach to playful problem solving - probably so common you don't think about it. The playful and fun part is key. That's a space where you can be creative.
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1 You can learn special relativity with high school math and a bit of logic. It's not at all difficult. General relativity, on the other hand, requires much deeper math. And a tip. "Down is the direction where time runs more slowly" on a t-shirt is a good way to find other physicists in a crowd.
The effect is known as gravitational redshift as you usually measure this by looking at frequency shifts. Atomic clocks are so good these days that you can measure the effect in a lab by raising one a few meters.
2 If you want the details send me a note. First derive an equation for the gravitational potential inside a homogeneous sphere. Next think about the frequency of a photon in a gravitation well to get change as a function of change in gravitational potential. Then it's just remembering some constants to get the number.
"No - we took all of that out years ago. It's just not relevant anymore."
Fifteen or so years ago I visited the local high school to see if they had an adult education program that would let me use the student shop. We don't have enough space or cash for a proper shop at home and frankly I'm not that good at wood or metal working, but every now and again the urge strikes.
I'm not arguing that shop class was well thought-out or even useful - it wasn't when I was a teenager - but there's something to being able to design and build something. On my own I did build a few things: a couple of telescopes, some amateur radio gear, model airplanes and a seismometer. Although the attempts of a kid, they were enormously powerful learning exercises. I learned how to solder, how electronics works at the component level work and a bit of practical optics. I even got to the point where I designed a transmitter and a simple analog computer. Commercial equivalents were better - they were designed by people who actually knew what they were doing - but I was learning the basics for design and that is much more powerful.
In grad school the ability to design and build was essential - so important even the theory students had to learn a few basics.. I knew enough about electronic design, but had never done any metal work. Metal shop was wonderful. The shop was well equipped and managed with expert help around most of the time. We were given a couple of simple projects. Once you made those you had to show you could do it with greater precision. We were finally given shop keys when they thought we wouldn't destroy the machines or ourselves. They encouraged us to come in and play.
I remembered a project in an ancient issue of Popular Science that fascinated me when I came across it in the library as a kid - a Stirling engine. I decided to build one of my own based on a bit of insight into better materials. The first was very inefficient - about 30 watts at the flywheel using a hot plate for a heat source. A minor redesign moved it past 100 watts. The design and construction was a wonderful diversion to the classes I was taking.
Times have changed. While engineers generally know how to build things, Spending a bit of time teaching in Oberlin's Technology in Music and Related Arts I found art majors and music students more adroit at "making" than computer science students. Programming is clearly building, but it's useful to tie it to the physical world every now and again. Some schools stress that more than others.
It doesn't happen often, but when someone mentions their kid is interested in learning about computing I recommend simple inexpensive computing modules that interface with the real world. Arduino and Raspberry Pi for example. An enormous amount of "how to" videos and documents exist and beginners can start with very cheap kit. They can have quick success getting something working from cookbook like plans. At first no real skills other than patience and the ability to follow instructions are necessary. Then, with the application of curiosity, learning begins, You change this and that to change what it does. You can write simple or complex programs and you can buy interface modules, usually called shields, that interface with the outside world.
People with that spark - the desire or need to do something they can't go out and just buy - make this interesting.. A dance major at Oberlin learned about Raspberry Pis in her computing for arts class. She sewed an accelerometer to her leotard and connected it to a raspberry Pi on a belt. Information was liked to her laptop via by bluetooth. For fun she connected it to lights that changed color with changing acceleration. A friend on the women's softball team saw it and thought it would be useful in pitching practice. Another version with software tuned to the needs of softball was built and the coach is thinking. Of course you can do this with an Apple watch, but its much more difficult to make it do just what you want and this way you develop a deeper understanding.
And so these things go.. Which brings me to something exciting.
People who build and design get good at it with practice and are on the lookout for new challenges. A few of you may be familiar with Panic - a tiny company that makes a few very nice applications for developers. They're profitable by themselves but use some of that profit to fuel their need to explore. A few years ago, out of nowhere, they came out with a video game called Firestarter. It wasn't one of your multi million dollar developments, but many people loved it because it was beautiful, clever and absorbing. They more than broke even which wsa good enough. There has been anticipation about another game in development called the Untitled Goose Game. But again out of nowhere came something completely shocking and wonderful.
Hardware
These guys decided to build a minimal hardware game player called the Playdate. People who have seen it seem to be somewhere between excited and ecstatic. 'Impossible to resist' keeps coming up. I won't go into details because I'm not a game player and I don't know much other than care appears to have gone into every step of development. They even wrote their own operating system. (that actually makes more sense than Linux for a very small game). They made it for themselves because it was a challenge they couldn't resist. Maybe it will break even, maybe it won't, but it won't break the company if it flops. I'll probably get one and I'm not a gamer.
People sometimes ask me why I'm passionate about a few odd things that not many other people find interesting. Many of us have a spark - a playful spark. They're all different and that's wonderful. Some of us aren't very good, others are the opposite, but that's not why we do it. We may or may not get paid, but that probably doesn't matter much. Sometimes I think it's better to not be paid as there's more freedom (assuming what you do is cheap). Often you find yourself learning a variety of things you never thought about as part of pursing your spark. In my case that can mean designing and building. I'm not very adroit at that part, but it's a useful tool and I slowly improve with experience. I'm in awe of those who thrill to be beauty of creating design and objects.
About fifteen years ago I found a poem that sums it up ..
To be alive: not just the carcass But the spark. That's crudely put, but… If we're not supposed to dance, Why all this music?
The other day I saw something that a few of you might want to consider for a kid or even yourself - the Turing Tumble Mechanical Computer.
It turns out digital computers are mostly switches. A lot of switches these days - perhaps a trillion in your smartphone. As a teenager I built a very simple relay based digital computer based on a column in an old Scientific American. Later I built an updated version that substituted transistors for the relays using some (free) components from the high school physics teacher.
Playing with these beasts is an excellent introduction to understanding how logic circuits work. You'd be surprised how many computer programmers are hazy on the subject (of course they work at a level of abstraction far above the silicon - or what old timers called the iron). The early machines of the 30s were very important and set the stage for the dramatic developments that followed. Here's an outstanding non-technical short history of those early days. (recommended!)
But back to the Turing Tumble.. It's limited, but that's central to its beauty. The instruction book has about sixty examples to play with and an aha! just might strike leading to out-of-the-book insights.
It's also great to play around with extremely simple silicon digital computers - particularly those that you can hook up to sensors, lights and other interfaces to the real world. But getting down to the basics is usually a paper or YouTube exercise or, if you want to do it yourself, a frustrating experience involving a lot of soldering and a non-trivial amount of money. The Turning Tumble might be just the ticket. It is play and that is the best way I know of to learn. I didn't have much of a chance to play with it and can't do a thorough review, but I'll probably end up buying one to give to a kid. The caveat is that you have to spend some time with it to learn. If the user doesn't find it fascinating enough to devote time to there won't be any learning. But the same can be said about so many things.
The education link on their site has the following in addition to a set of resources:
Appropriate Age Range
Turing Tumble is for ages 8 to adult - and that is not a stretch! We find that kids 8-12 are able to get through the first 20-30 puzzles. Adults get addicted by puzzle 27, and their minds are blown by puzzle 35. Younger kids enjoy the first 10 and building their own computers.
It was really stupid - not quite Darwin Award stupid - but close. Now that my parents are gone I can write about it.
As a teen I became fascinated with the sensitivity of the human eye. It turns there are a lot of tricks you can use - I've written about playing with a few subtleties of your color vision to see colors in the night sky as well as my practice of night walking on dark nights without a light. Moonbows (like a rainbow, only from moonlight), very dim luminescent beetles, the phosphorescent decay of organic matter in still ponds and the reflection of light from the eyes of animals in starlight. There is a certain thrill in tapping your inner owl and walking around in near darkness. If you're a bit on the teenager side of the risk curve you can try running or cross country skiing without lights. And then the stupid thing I tried.
The night was exceptionally clear with only starlight. The hills were just black regions without stars. Night walking had opened up part of the outdoors I didn't know, but it made me wonder. Armed with a brand new driver's license and my Dad's old Ford Falcon, I had driven North of town past Benton Lake on Bootlegger Trail - far enough to be away from the light glow of town. I pulled over to the side of the road, taped over the instrument panel so none of the light came though and let my eyes adjust to the dark. I started the car without the lights and used averted vision to drive. It was easy to see where the road and even the center stripe was, but everything went away if you accidentally slipped and used the center of your eye. That's the hard part - you see a something and tend to focus on it. Suddenly your sensitivity drops off to less than a tenth of a percent of what it was and everything vanishes.
I probably drove that way for three or four minutes at up to thirty miles an hour. I did it again about a month later with a friend. He didn't have experience with averted vision so he didn't try, but I had a witness.
Don't ever try anything that stupid! But learning how to use your averted vision is a nice way to extend your view into the natural world. The world becomes a richer place when you learn how to see it a bit different. It is one of my forms of travel and particularly interesting when I'm visiting dark places for the first time.
You have three flavors of cones that are each sensitive to different "color" ranges. A total of about seven million and they're mostly in an area called the fovea near the center of your retina. There are also rods. One hundred and fifty million - approximately a boatload. They're generally more than a thousand times as sensitive than your cones and in some cases can be sensitive to individual photons. Learning how to use just the cones is the trick.
The fovea is small and densely packed giving you your detailed and color vision. It's what you usually think about when you consider vision. At it's center is a very small region about the size of a small dot of ink - about 0.3 millimeters or 300 microns. The thinnest blonde human hair is about 40 microns in diameter and the coarsest black hair about 120 microns, so its really small! It's all cones. If you plot the density of rods and cones on the retina going radially out from the center (the fovea centralis) you see the density of cones drop dramatically around twenty degrees out. The density of rods, on the other hand, is very low inside this area, and rapidly increases to a maximum around 20 to 25° out and then slowly drops off.1 Averted vision involves looking away from the center part of your vision. Ideally you want to be looking at least twenty five or so degrees out. Further out the density drops, but not that fast.. I aim for about 40° to prevent accidentally falling back into central vision. I can't do it without biting my lip - find your own technique:)
You can also use a camera to extend your range. Serious photography forces you to take careful note of what's in an image and you have any number of adjustments to play with. You can play with different wavelength ranges and see what is normally hidden to us. I like to play with different slices of time from tiny fractions of a second to minutes long.
We have fireflies around here in the Summer. Here's a simple 30 second time exposure. (f3.5, ASA 400 for what it's worth). Flashing signatures vary with species and I've found four in our area. It is relatively straight forward to analyze the signals and do serious observation. For something so beautiful it isn't deeply studied as one might think so you might discover new behavior!
Before stopping it seems reasonable to mention you can hack how your mind synthesizes and uses the vision it generations. Our brains turn out to be quite "plastic". Usage patterns can create new connections and destroy old ones. Playing a musical instrument develops certain regions in the brain as does speaking multiple languages fluently. Certain types of online interactions are currently under heavy study - it appears that multitasking leads to different neural optimizations along with easily finding answers without reflection. Jheri is mostly deaf - I've never met anyone as visually aware. She does an enormous amount of visual tracking and lip reads to the point where you don't realize she's hearing impaired.
Sports are another way to hack your sense of the world. People who are good at sports that require "field sense"- knowing the position and movement of others on the court and field- develop certain regions associated with orientation, but on a massive scale. They're doing it for multiple moving objects. I wonder if some people who are wonderfully athletic but aren't very good players in field and court sports have problems with this? (of course there are dozens of other areas that must work well too)
All of these changes seem quite normal to their owners - after all, we can't easily know what someone else experiences. A lot of questions arise. A few months ago a reader mentioned she was interested in how smell interacts with the body. It is certainly part of our interoception system and represents a nearly blue sky research area. There must be room for hacking. I've been talking to a neurologist and reading about dogs. But I'm out of time.
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1 the heights of the curves are different, but you get the idea - artistic license:-) This is from memory, but in the ballpark.
There is this dairy farmer with a problem. He's tried everything he can think of, but milk production from his herd just won't budge. The dairy new online push hormones, but no .. it was time for something unconventional. He hired three consultants - a mechanical engineer, a psychologist and a physicist.
A week went by and the engineer came back with a stack of papers. The problem, according to the engineer, is the farmer's milking machines don't develop enough vacuum and the tubes to the storage tank have too many bends. A special machine is proposed, but the farmer decides to talk to the next consultant.
The psychologist takes a lot of photographs and makes some sound recordings. He compares these with those of benchmark barns and after a week reports the barn is too disorderly and the sounds from the nearby highway make things worse. The recommendation is to hire an interior decorator and subscribe to Moozak.
Nope .. time to listen to the physicist.
The physicist listens to the farmer describe the problem. "hmmm..." she says as she pulls a half used Fieldnotes pad, pencil and slide rule from her backpack. Gazing up at the sky focused on nothing in particular she says...
consider a spherical cow
You've probably heard some variation of this. I like it as it describes how a lot of physics is done. Physics and the other sciences are usually poorly taught - it's anything but facts and equations to memorize and somehow apply. Rather it's mostly play at it core - at least how you think. You strip away anything that isn't necessary and see what you can learn. If the answer doesn't make sense you try a different approach. The trick is knowing how much to strip away and what to leave in and how to mix in other questions along the way. Ideally you're left with new insight.
A regular reader told me he was curious about my thinking process and asked if I could describe it. At first I ignored the request, but then decided to give it a try with a little real time play. Using the spherical cow joke as a seed I took a walk with a very smart friend as a sanity check. This isn't a transcript, but here's roughly how it unfolded.
First let's draw a picture of a cow. Consider a spherical cow of radius 1. I don't care what the units are and for now a sphere is the simplest shape to get started with.
Now draw another sphere of radius 2 - this will be our gigantic cow. What kind of milk production can we expect. Any linear dimension will be twice as big so we can see if barn door heights and widths will work. The udder will be part of the sphere. It will be 8 times as large as the regular cow .. the volume of any part of the cow scale as the radius cubed - it doesn't matter what part of the original spherical cow I choose, as long as the part on the larger sphere has the same shape, its volume will be r3 or 23 = 8 times as much.
Already a problem looms. What is the pressure in the udder? Pressure is just a force spread over an area (think pounds per square inch). The force in this case is the weight the udder has to support, which increases as the cube of radius. The area of a section of the sphere is 4πr2 times the fraction of the sphere the udder takes up. Now the udder fraction and the 4π are the same for a spherical cow of any radius. We'll be comparing the two by dividing so they'll cancel out. The pressure will be proportional (a physicist would say "goes like..") to r3 divided by r2 -- or just the radus r. Our giant cow has twice the pressure on it's udder as the standard cow. This may be a serious cow design problem and we would need to know more to make progress. But it gives a hint of another direction.
Now draw a more accurate picture of a cow and giant cow. A small sphere connected by a cylinder to the larger sphere. What about the force on the neck? The important innards of the neck are the spine and muscle. Strength goes as the cross sectional area. So if the double sized cow is a perfectly scaled version of a regular cow, it's neck will be r2 or 4 times stronger. It must support itself and the head, both of which will see their weight go up by the cube. The ratio of weight to strength is simply r or 2 in this case. Another design issue for giant cattle breeders.
But what of really big animals - like a dinosaur? If the head is much bigger than the neck it will be the limiting factor. Imagine something like a cow scaled up eight times in length. The head would quickly become too heavy. Something like a big dinosaur walking on four feet with a long neck would need a very small head.
Now it's clear why the dinosaurs went extinct.
Their brains were too small. This handicap meant they never developed a space program and were unable to deal with the asteroid.
Of course this is tongue in cheek, but this sort of playful approach is exactly how a lot of physics gets done. As you proceed detail and more critical questions are added. One gets to point where measurements of Nature are needed and then you see if you can predict -- if not it's just storytelling and not science.
Back to the example. It's an interesting approach to begin thinking about sports. What kind of body types are more suited to one sport or the other? People on the list range in height from something under five foot zero to six foot eight. One might consider gymnastics and the other basketball or volleyball. Neither would be a good distance runner... Soon you need to drill deeper, but the thought process stays the same. As detail enters, calculations need to be more robust. The observation and experimentation part can be very difficult to implement. LIGO - the twin observatories for measuring gravity waves are simple to describe conceptually, but making it work took over thirty years of hard work and invention of new instrumentation and techniques (some of which has had impact in engineering and medicine). This simple concept is a few minutes at a blackboard with no equations and a string of playful questions eventually led to an entirely new form of astronomy.
The approach works in many areas where there is enough information to form some kind of a question - often one that sets limits. There are times when an hour of thinking gets you within a factor of two of a difficult problem that requires huge resources to answer to any precision. This is a good way for picking paths to follow. I've been called on to do this in scenario planning style exercises.
And for fun .. what about the folklore that the breath you just took at least one molecule from Julius Caesar's last breath. A minute or two of thinking gives the answer, but it raises some really interesting questions about the atmosphere.. The first time I thought about the problem as a teenager I was struck by the notion that the atmosphere for a plant is like a salty sea and the thirsty sailor. That leads you to think about fertilizer and the enormous scale of the process - probably the primary reason for the planet being able to sustain more than two billion people. Then you think about the energy costs and other natural limiters. This style of thinking is a great exercise for anyone who likes to discover dot connections.
Clearly one doesn't do this all the time, but it's great fun and I encourage folks to try it out. When you do it with others it's not brainstorming - brainstorming doesn't work. Rather it's a form of play. It can get addictive and can be physically dangerous for those of us who can't walk and chew gum at the same time. I naturally fall into this with one of you who has saved me from Manhattan traffic on several occasions.
A few years ago I was walking through the parking lot of JPL in Pasadena when a license plate caught my eye. It took me a few seconds to figure it out, but it had to be a vanity plate and one I wouldn't mind having. I pointed and exclaimed something like 'how brilliant' to a rather perplexed friend. Just a few days ago someone set a rather amazing Internet ad. It had an easter egg that grabbed my eye for the same reason, although this was much more explicit. There is a connection between the license plate and the ad. I'll get to that, but first I need to talk about some playful tools that physics and astrophysics types use.
Any sort of creative work needs a playful component. Its how you develop your intuition. I'm sure many fields have their own power tools for play and you may want to think about yours as mostly they are so natural that they become part of how we think. You need to try and discard a large number of ideas without fear of failure. Some of these can be rather silly. Often you build toy models in your head or at the blackboard. Typically they aren't practical .. if someone were to ask how many cattle are required to provide shoes for New York City you might say to yourself 'consider a spherical cow'.. Physics problems tend to exclude much of the real world so you can focus on just the bit of interest. Mental or blackboard math rules. You aren't worried about exact answer. I love the power of computer simulations but anything you have to type into would just slow you down and break the flow during the play stage. You want to create little visual models that seem like an extension of your mind so you can dance with them. People develop a certain affinity for numbers and you carry around a few rough rules of thumb. Things like π2 ≈ 10 to about 1.3% .. when you're only worried about 10% errors the arithmetic is easy. Some bits of Nature are stored in this fashion:
° there are π × 107 seconds in a year to better than a half percent
° the speed of light in a vacuum is close to 3 × 108 meters/second. An interesting coincidence is the original definition of a meter was 1/10,000,000 of the distance from the pole to a point on the equator. Distances can be measured in the time light takes to travel the distance. We're used to light days and light years, but light goes about a foot in a billionth of a second or a nanosecond. A very tall friend sometimes gives her height as six and two thirds nanoseconds .. about the time light takes to traverse her length.1
° a light foot is sort of practical when thinking about connecting parts of a computer. If modules are separated by 10 feet, a delay of at least 10 nanoseconds is introduced. This gets interesting when you're using a lot of fiber optics or physical wire as the speed of light is slower.2 The speed of light in the fiber is about 2/3s that of in a vacuum or air. A signal will traverse 1000 km in about 5 thousandths of a second, while a radio wave going through the air only requires 3.3 thousandths of a second. A very long time for a computer. The difference was large enough to justify the construction of a specialized microwave network between Chicago and New York City to give some traders an advantage based on the difference between the index of refraction of air and optical fiber.
° the acceleration caused by Earth's gravity is denoted by g and is roughly 10 meters per second2. It varies depending where you are on the surface, but unless you want to weigh a pound less or more, the rough figure works for quick calculations.
° the diameter of the Sun divided by the height of a person is roughly the same as the height of a person divided by the diameter of a hydrogen atom.
° it takes about 500 seconds for light to travel from the surface of the Sun to the Earth
° photosynthesis in crops and trees is usually under 0.5% efficient
° a cow requires about 10 times as much energy as the plants it eats to produce the same amount of energy
° ...
There are hundreds of little relations like this and a few curious numbers too. One of the most famous is the fine structure constant which describes the strength of electromagnetic interactions between charged particles. It is close to 1/137 and appears in enough calculations that every physicist knows it. If you want to flag one down in a stream of people (airports for example), just write 137 or 1/137 on a piece of paper and hold it in view. I've experimentally found this to be remarkably effective.
Some of the relationships aren't directly connected with Nature, but are just fun and sometimes are even useful. There are too many to list, but here are two..
° e is the base of the natural logarithms and is of fundamental importance to economics and science. It happens to be irrational and transcendental, but the first few digits are easy to remember: 2.7 1828 1828 45 90 45 (1828 repeats twice, and the angles in a right angled isosceles triangle)
° of course there is Hardy–Ramanujan number. The story goes that G. H. Hardy was visiting his friend and colleague Srinivasa Ramanujan in the hospital. He had ridden in cab number 1729 and remarked that it was such a boring number. Ramanujan counted, pointing out that it was the smallest number you can express by cubes in two ways: 13 + 123 and 93 + 103. This has slipped into popular culture and has appeared in both the Simpsons and Futurama in the form of easter eggs. But then again some of the principals of those shows are mathematicians.
And number on a taxi brings us back to the number on a vanity plate. My eye was probably caught by the initial 23, which happens to be my favorite prime, but it looked suspicious - something close to 20 plus π ... I remembered eπ - π is just a bit less than 20. The number on the plate had to be an approximation of eπ. The connection with the ad is perhaps the most beautiful relation in mathematics : 3
eiπ + 1 = 0
While eπ isn't the real thing, it is suggestive enough to bring a smile. Of course there is the possibility the owner just considered eπ cool without thinking of eiπ, but this was the JPL parking lot.
If only vanity plates allowed superscripts...
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1 again an approximation. If you want to do this more exactly the speed is about 0.984 ft/ns ..
2 the speed of light in a material is c/n, where n is the index of refraction. n is close to 1.0 for air, but about 1.5 for optical fiber
In physics experiments signals are delayed with respect others to make logic gates work properly. You develop a sense that 8 inches or 20 centimeters is about a nanosecond in coax.
3 It links the two most important irrational numerical constants e and π, number i which is the base of the imaginary numbers which gives us complex numbers, the additive identity 0 and the multiplicative identity 1. It also answers the question "how many mathematicians does it take to change a light bulb?" Then answer, of course, is -eiπ...
If it seems strange that the exponential of a complex number could be equal to 1, consider what the number e is. It is closely related to compound interest ... ez is the limit of (1 + z/N)N as N goes to ∞. If you set z = iπ and do the math you get -1 + 0i or just -1. Here's an animated gif:
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Recipe Corner
Caramelized Carrots
Ingredients
° 3 pounds of carrots - go for the fancy colored ones if you want it to look good
° salt and freshly ground pepper
° 2 clementines or one large orange
° 1 tbl red wine vinegar
° 3 tbl butter or vegan margarine
° half a bunch of fresh thyme
Technique
° peel the carrots. you can quarter of halve them, but if they're pretty whole carrots with a bit of the tops on are beautiful
° put carrots in a large pan and just cover with water. Add a bit of salt and ground pepper and the clementine juice, the vinegar and butter
° bring to a boil and cook until nearly all the liquid has evaporated
° add the thyme sprigs, reduce heat to low and cook for about 5 minutes to caramelize
Although interesting and cool, it is unfortunate this has become his legacy. He was head of the instrumentation division at BNL for many years and was responsible for a large amount of innovation in high energy physics apparatus - innovation that had a profound impact on medicine and other aspects of human life. He was also a passionate force for nuclear non-proliferation. As a young scientist he was part of the Manhattan Project and, like many others, pushed for the elimination of the weapon. He went beyond the ordinary and cofounded the Federation of American Scientists.
The spinoff from experimental physics has been enormous. Physicists have to invent techniques to make their measurements. Although developments are often a historical chain, most of the instrumentation used in medicine has a direct link to physics. In the past few decades medical imagining comes directly from nuclear and high energy physics techniques. Perhaps the most direct example is positron emission tomography which was largely developed at BNL.
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recipe corner
This was really good, but I have a weakness for sweet potatoes
Sweet Potatoes with Mustard
Ingredients
° 2 large or 3 medium sweet potatoes
° 2 tbl vegetable oil
° 1 tsp brown mustard seeds
° 1/2 tsp cayenne
° 1/2 tsp tumeric
° some chopped fresh cilantro - one or two tbl
° salt
Technique
° bake the sweet potatoes in a 350°F oven for about 30 minutes. Let them cool a bit, peel and cut into half inchish chunks
° fry the mustard seeds in oil in a skillet on high heat until the seeds begin to pop. Cut the heat to medium
° mix in the potatoes, turmeric, cayenne and salt to taste
° cook about ten minutes until a crust starts to form.
The structure was small but, despite the amazing view, there was only one small window. A curtain was kept out sunlight. A cluster of electric cables connected the building to the cable car building a thousand feet distant. Twelve is an age when most of us are still at curiosity and society lets us get away with it. I knocked on the door.
My family spent a few weeks each Summer anywhere from the Bob Marshall Wilderness Area in Montana up to Jasper in Alberta. That year it was Banff. We had taken the Sulphur Mountain cable car to the viewing platform. On a clear day the view was nearly a hundred miles. The observation deck was crowded to capacity with tourists from all over the world. My parents and sister were talking to a couple from England when I left for the unusual building along the mountain's North ridge.
Physicists have a primal need to explain things as deeply as time and their audience's patience and curiosity permit. Almost immediately I was learning a bit about cosmic rays, muon showers, scintillators, photomultiplier tubes and so on until my father showed up. He had been looking for me for a few hours and happy wouldn't be the right word to describe his mood.
The ride down the mountain and then back to our camp was quiet - I knew better than to say anything. That didn't seem to matter at the time. I was completely engaged in what I had seem. Most of it was over my head, but seeing the existence of the remnants of a cosmic ray shower on a simple detector someone put together solely to explain what they were doing hit me deeply. I saw the beginnings of how people ask questions of nature and it had nothing to do with looking up things in a book. By the time Lyra was overhead I feel asleep knowing I would be either a physicist or an astronomer. It was a calling.
A month later I tagged along with my father on a trip to Los Angeles. He was taking a ten day workshop for a certification and I was seeing California for the first time. Friends and family recommended trips to Disneyland, Knott's Berry Farm, Hollywood, the beach and other things kids are supposed to see in Southern California. I wasn't interested and probably to my father's dismay managed to get my way. I visited JPL, and earthquake observatory, the planetarium at Griffith Park , and the La Brea Tar Pits.
Years later in grad school I came across a survey by the American Physical Society of recent graduates . A large majority of US born recent Ph.D.s, over 80%, had been raised in rural areas or near a natural history museum. This wasn't true of undergrad declared majors who mostly changed majors along the way but those who made it to the end were predisposed to have been in areas where some contact with Nature was likely.
Perhaps some areas are richer in sparks than others.
Some say kids are natural scientists. I disagree. Kids are wonderfully curious, but science isn't a grown-up version of child-like curiosity. Doing science requires learning and practicing abstract skills that are often not intuitive. Older students who have problems in something like a college chemistry class haven't unlearned an earlier ability, but rather
A few kids manage to get struck by a spark and dive in seeing the learning and work as play. This teenage dedication is far from unique to science. Music, sports, mechanics, art ... many kids spend their time picking up and honing basic skills that allow them to progress. These skills can be picked up at any time, but there are some kids who have a great head start - it isn't native intelligence as much as it is learning deeply.
There are two gaps that need to be jumped. First the initial spark, the calling for some, and then a longer gap that makes it possible to enjoy developing a somewhat different type of thinking than they're getting in school. This longer spark is a form of play.
The best day of the year at the old Bell Laboratories was the 24th of December. Employees brought their families and kids would wander around and see some real research often with some enthusiastic guides. Some departments went all out preparing demonstrations for the kids. After a few years kids became bored. They had home computer games were more interesting than anything at the labs. By the mid 90s kids weren't coming unless their parents dragged them along. Bell Labs had become a mostly spark-free environment. Where do you find events with spark potential these days?
Thinking about this earlier today I remembered the Lexus Hover Board ad...
The ad is real without digital special effects. It took me back to my first course in statistical mechanics. The professor was a low temperature theorist. We had been studying some of the oddities of liquid helium and he showed up with a dewar, a large beaker, a strip of metal and a magnet. The metal went into the beaker and was covered by the expensive liquid helium near absolute zero. He dropped in the magnet and we watched it levitate skittering around over the superconductor almost without friction. In the helium the metal had become a superconductor. The superconductor allows current to flow without resistance. When a material becomes a superconductor it excludes magnetic fields.
The field of the magnet induces current loops in the superconductor that exactly cancel the magnet's field. The magnet 'sees' a mirror image of itself and levitates. Its called the Meissner Effect.
Demonstrations like this fill your mind with questions and are entirely worth the cost of a bit of helium (there were only a eight students in the class). After Back to the Future II showed the Mattel Hover Board it was common to ask students to calculate what it would take to build such a device.
It gets even better...
Improvements in superconductors made it possible to levitate with (almost) dirt-cheap liquid nitrogen. In addition to the Meissner Effect there is something closely related called quantum flux trapping or flux pinning. I won't get into the details, but where the Meissner Effect shields the superconductor from the magnetic field, flux from the magnet enters tiny sites and is effectively pinned in place. With a bit of care you can fix the height and orientation of levitation and move objects along almost without friction.
Once you get a handle on flux pinning the Hover Board is just a matter of money.
These days there are any number of interesting YouTube videos. PhysicsGirl is doing terrific work that should inspire teenagers - particularly girls - much more than expensive produced television like Cosmos. That said I believe there is a need to see things for yourself and then begin to explore them on your own using real Nature rather than just watching videos or playing with simulations. This is partly broken, but perhaps we're seeing the start of it return. It is this hands-on component that encourages the hard work and experimentation necessary to move from the curiosity of a child to that of a scientist. Of course sparks for many things can come at any age - most of us are too busy to follow up, but every now and again something dramatic happens.
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Recipe Corner
An end of Summer salad. There are so many ways to go, but here's tonight's with sweet potatoes, apple and corn
Ingredients
° 1 medium sized sweet potato chopped into inchish pieces
° 1 large gala apple (or equivalent - a honey crisp would be good) chopped
° 3/4 cup cherry tomatoes sliced in half
° 1 ear fresh horn - husked
° some olive oil
° a couple of handfuls of arugula
° a quarter cup toasted nut pieces
° sea salt and freshly ground black pepper
° 1 tbl extra-virgin olive oil
° 2 tsp chipotle paste (I had some around - you could use powder)
° 2 tsp cider vinegar
° 1/4 tsp honey or maple syrup (I love maple syrup)
° salt and pepper
Technique
° heat oven to 375° F
° toss sweet potatoes, apple and tomato on a baking sheet with olive oil drizzle and pinch of salt and pepper. Roast for abut 30 minutes turning halfway through
° wrap the ear of corn in foil and put it in the oven for about 20 minutes
° whisk the olive oil, chipotle, vinegar, honey and salt and pepper to make a dressing.
° put arugula in a bowl along with the roasted pan contents. Slice the kernels from the corn and add. Toss the salad. Season to taste.
Someone asked if I liked to watch horror/scifi movies. It depends...
A few years ago I was trapped on a cross country flight and saw The Black Hole - one of those scripts that is so bad it is almost, but not quite, worth watching. Check out the trailer...
Most special effects and animated movies take liberties with physics. Starting with Disney many of the classic animation films created increasingly more interesting variations on physics to improve the storytelling physical worlds. There were any number of tricks to trick the viewer to better immerse them in the story.1
Special effects tend to suffer. I'm able to enjoy films like Guardians of the Galaxy, but poor scripts and acting break the story telling and I find myself spending most of my time thinking about the physics.
With that a mini-analysis of The Black Hole - (no plot is spoiled as I didn't notice one)
Somehow an there is an accident in a secret physics lab a hundred feet below St Louis. Physicists have managed to create a tiny black hole that escapes and trolls around under the city coming up for buildings like the great white shark in Jaws. At this point I'm completely out of story space and am thinking about small black holes.
Hmmm... about 30 meters underground and buildings on the surface are collapsing. I'll make the assumption it is a miniature classical black hole, more on that later, and suggest that the gravitational force from it at the surface is about ten times Earth's gravity - that should be enough to flatten a building. I could have picked other numbers, but we're just doing a little thought experiment and don't need to accurately understand how strong buildings are. With this you can work out its mass - roughly about twenty trillionths the mass of the Earth - a bit over 100 trillion kilograms. Now we're getting into interesting territory..
The event horizon of a black hole that mass is roughly a tenth of a trillionth of a meter - about ten thousand times smaller than a hydrogen atom.2 Put it on the ground and it won't feel any resistance to any material on or in the Earth. As soon as its created it will fall toward the center of the Earth picking up speed as it goes. It whizzes through the center at about eight kilometers a second and starts slowing down as it heads towards a point, judging from my globe, on the surface of the Indian Ocean well off the Australian coast. Maybe it dines on a fish before reversing direction and heading back about 42 minutes later.3 Back and forth, back and forth - we have an odd sort of clock.
Games like this turn out to be a central part of play in physics. You make a non-physical assumption - assume a miniature black hole is created just under St Louis - and follow what happens using established physics. In the process you can quickly deal with many questions and decide on those that are the best candidates for serious study. Now that we have our black hole tic-tocking between St Louis and the Indian Ocean, let's look at smaller black holes.
I mentioned this was a classical black hole. In 1974 Stephen Hawking proposed black holes can evaporate. The time required for one formed from a collapsed star is extremely long - it would take about 1067 years for one with our Sun's mass ... approximately forever when you consider the age of the universe is 13.8 billion years. But the rate of evaporation has a strong dependence on the black hole's mass and lighter black holes evaporate faster. The little St Louis black hole would last about a hundred times longer than the current age of the Universe.
Smaller black holes can have lifetimes small even on time scales we're used to. One with the same mass as a small car - about 1,000 kg - would evaporate in a billionth of a second and would be about 200 times as bright as the Sun. These super tiny black holes would make a very powerful and completely impractical doomsday devices - even more impractical than antimatter. In other words the perfect plot device for a movie.
I'll end with a problem for those who like to work things out. Send mail if you'd like hints.
The Master from Dr Who or a slightly annoyed Vogon captain approaches the Earth with a super slicer beam that instantly makes a cut through the Earth. What happens if the cut is through the equator and is one centimeter wide? What happens with a one meter cut? How about ten meters? Now work the problem with the same three cuts, but this time slicing from pole to pole. How does humanity make out in each scenario?
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1 If you have the slightest interest in animation The Illusion of Life: Disney Animation by Olie Johnson and Frank Thomas is just wonderful. Go for the hard cover and treasure it. Disney did amazing groundbreaking work, and other expanded wrote new rules. Chuck Jones created an animation for roadrunners and coyotes that is an art form. Even today the tricksters are still at it.
2 the Schwarzschild radius is proportional to mass rs = 2GM/c2. The point is it only goes linearly with mass while the mass of a star goes as the cube of the radius - the event horizon get small very quickly as mass drops. The Sun has an event horizon of about 3 kilometers ... far too small to contain it. rs for the Earth is 0.9 centimeters.
3 42 minutes through a frictionless tunnel is the result everyone calculates in physics 101, but that assumes the Earth's interior has a uniform density. Recent work giving a better understanding of the Earth's density distribution cuts a few minutes off the transit time.
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Recipe corner
I grilled some asparagus and used a homemade olive based dressing. Ideally the trick would be to layer pieces of tomato on a bed of the grilled asparagus before adding the dressing, but it isn't good tomato season (yet). Here's the dressing...
Olive dressing
Ingredients
° 3 tbl finely chopped kalamata olives
° 3 tbl extra virgin olive oil - a good one pays off
° 3 tbl red wine vinegar
° 3 tbl crumbled feta (leave off if you want it to be vegan)