After he saw one of my first Klein Bottles, Martin Gardner encouraged me to make them for recreational mathematics enthusiasts. "Even if the Klein Bottles don't work out, you'll have fun meeting these folks"
And so began my zero-volume business.
In high school, I followed his instructions to make hexaflexagons and fooled with Knights tours on chess boards. Much later, I was honored to correspond and meet him.
In person, he was just as curious, creative, and encouraging as you would expect from his writing.
Along with others here, I will miss Martin Gardner - his Scientific American articles, his wide ranging books, and his warm support. He leaves a wide wake behind him.
I graduated high school in 1968. Used to mow the grass of a neighbor -- a crotchety old woman who was apparently the niece of Herman Hollerith.
And yes, she used to shoo the kids off her lawn...
To prevent injury from rotary table saws, a company called SawStop makes a finger-detecting rotary saw. If your finger gets into the blade, the saw instantly stops.
It detects finger or flesh by electrical conduction, it mechanically and electrically stops the rotation of the saw blade - so quickly that your finger is not injured.
The finger detection is impressive - if a hot dog is pushed into the fast rotating blade, the blade stops with less than a millimeter of cut into the hotdog.
This is not simple proximity detection or optical sensing. I think that the sawstop system detects contact of the sawblade with a human through capacitance. Much like a high-gain, high input impedimenta audio amplifier will create a loud hum if you touch the input.
I can imagine future robotics also using similar electrical detection of humans.
Details at http://www.sawstop.com/
Over at Evans Hall at UC/Berkeley, stroll down the 8th floor hallway. On the wall, you'll find an envelope filled with flyers titled, "Why is Floating-Point Computation so Hard to Debug whe it Goes Wrong?"
It's Prof. Kahan's challenge to the passerby - figure out what's wrong with a trivial program. His program is just 8 lines long, has no adds, subtracts, or divisions. There's no cancellation or giant intermediate results.
But Kahan's malignant code computes the absolute value of a number incorrectly on almost every computer with less than 39 significant digits.
Between seminars, I picked up a copy, and had a fascinating time working through his example. (Hint: Watch for radioactive roundoff errors near singularities!)
Moral: When things go wrong with floating point computation, it's surprisingly difficult to figure out what happened. And assigning error-bars and roundoff estimates is really challenging!
Try it yourself at:
Making many assumptions, the human eye has about 500 to 600 megapixels of resolution.
But determining visual acuity is nontrivial. Lots of physics, physiology, and neuroscience enter into it.
Visual acuity depends on a number of physical limitations set by the optics of the lens of the eye as well as the sampling on the retina.
For example, the point spread function of the lens roughly matches the sampling of the retinal mosaic (well, within a factor of 3 or so). A nicely evolved system!
Our eyes' acuity are influenced by
- Refractive error (out of focus lens, often correctable by glasses or contacts)
- Size of the pupil (physical optics tells us that a wide open iris will reduce diffraction)
- Illumination (brighter scenes give more photons, and our neuroprocessing can do more
- Time of exposure to the field
- Area of the retina exposed
- State of adaption of the eye (night [scotopic] vs day [photopic] vision.
- Eye motion & object motion in scene
For a good review of visual acuity, see:
I agree with many of the Slashdot posters who've commented on my article of 15 years ago. There's a great deal to munch on - plenty of hilarious mistakes as well as several ideas still worth thinking about.
That 1995 article grew from my questioning attitude. When I hear nearly unanimous commentary without any critical dialog, I become skeptical. Perhaps too skeptical, as that article shows.
At the time, I saw my role as encouraging questions about then-common predictions. As a way of introducing dialog through debate, if not deliberation.
Clearly, I'm no futurist, able to extrapolate across decades. If anyone, I suspect that school teachers are the most in touch with future generations.
Now? Oh, I try to stay away from predictions; two teenagers gleefully keep me informed of my daily mistakes. I teach physics, speak at meetings, and write the occasional article for Scientific American. I make Klein Bottles
Best wishes to all,
-Cliff (in Oakland California, on a Monday afternoon without sunspots)
Well spoken, PFI_Optix!
Perhaps more than 50% - I can imagine meetings amongst the labels to set some number.
Your method is reasonable, discreet, equitable, and practical. It saves face for the labels, sends the proper chill to the downloader, and leaves the door open for further action.
Most air freight shippers use dimensional weight to charge extra on high volume/low mass items. Charging by weight alone won't recover the costs of shipping lightweight items. For example, a pound of popped popcorn will cost more to ship than a pound of popcorn kernels.
Typically, a shipper assumes that typical freight has a nominal density of about 0.2 gm/cm^3
Of course, humans have a density of about 1gm/cm^3, so we wouldn't be charged extra, should we decide to be shipped airfreight.
For the past 12 years, I've been making & selling Klein Bottles. A quick analysis of online order email addresses (no, I don't spam!) shows the decline in AOL domain for people ordering onesided manifolds:
1997 13% (about)
1998 15% (about)
1999 16% (about)
Yep, same guy.
Before Cuckoo's Egg, I was better known as a planetary scientist. My PhD dissertation relied on polarization data taken by Pioneer 10 & 11 to understand the scattering characteristics of Jupiter's upper atmosphere.
Pioneer 10 and 11, of course (not 11 and 12)
The Pioneer 10 & 11 spacecraft both flew by Jupiter, and Pioneer 11 went on to Saturn encounter.
I remember it well - while a grad student at the Lunar & Plantetary Labs, I helped with the Imaging Photopolarimeter during Saturn Encounter.
The spacecraft, designed in the early 1970's, had essentially no onboard memory, so instructions had to be uploaded in real time. The several hour-long communications delay made for real excitement at encounter (Did the spacecraft survive the ring crossing? Did the instruction arrive? Did the sensor point in the correct direction? Is it returning images?)
We'd spent months in advance, preparing alternative sequences for the encounter. Each sequence was on punched papertape. Then, at encounter in September 1979, we'd pick the tape, mount it on a teletype, and send the data out over the NASA deep space network, then anxiously wait to see if the instructions worked on Pioneer 11.
A prime number can represent information which is forbidden to possess.
This goes back about a decade to the AACS encryption key controversy.
Want your kids to learn physics? Throw away the computer simulations. Build things with them. Run experiments. Observe and think about the results.
To teach physics, start with things like C-clamps, string, rubber bands, wire, springs, low-friction carts, compasses, magnets, thermometers, balloons, weights, scales, and pulleys.
More advanced stuff: a voltmeter/ammeter (analog stuff), an old oscilloscope, an air table (a kids' hockey table), vacuum pump & bell jar, countdown timer/photogate, etc. Many of these things show up on craigslist for cheap (I picked up two free oscilloscopes and have given them to my sharp high school students).
Computer simulations? Naw. Have your kids do real physics:
A pendulum made of a bowling ball and rope. Time the pendulum swings and then ask: which will change the period - changing the lenghth of the swings, changing the weight, or changing the length of the rope?
Fool around with a signal generator, an oscilloscope, and a microphone. What's a sound wave look like? How is frequency related to period?
Play with thermometers, ice, water, and fire. What's the temperature of ice and water? Can you get water colder than this? How hot is water from the kettle? Can you get water hotter than this?
Get a voltmeter, wire, and some magnets. Can you really induce a voltage by moving a magnet nearby?
Don't sidetrack your kids with simulations & computer graphics. Real physics starts by fooling around with reality.
Obs Feynman quote: "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."
Never keep up with the Joneses. Drag them down to your level. -- Quentin Crisp