omenti

finding the dimensions of play

Minipost

You've probably heard about softball pitcher Jennie Finch striking out major league baseball players. 

 

She's standing about 43 feet from the batter rather than the 60.5 feet seen in major league baseball.  Her fastest pitch is about 70 miles per hour giving a 0.42 second flight time for the ball. What's interesting is human reflexes aren't fast enough to allow even the best batter a hit.  He's not thinking about it, but all of those year playing baseball taught him to read the pitcher and some clues.  Clues up until the time the ball is released and perhaps a very short time afterwards.

 

The fastest fastballs travel about 145 feet per second (apologies to those who use sane units.  Most of the readers here are American).  Human reaction times range run between 0.25 and 0.35 seconds with most of us a tad below 0.30 seconds.¹  Even with superhuman reflexes a the ball has traveled more than halfway to the plate before the batter notes it has left the pitcher's hand.  Real time adjustments are hopeless as Jennie Finch has demonstrated. 

 

That brings up an interesting question.  If you're designing a ball a stick game - a game where a ball is thrown and hit by a stick or an arm - is there a characteristic time of flight that tests the best athletes?  Another way of putting it is "is there an optimal distance for the ball to travel?"

 

For baseball, using 95 mph,  we get 60.5 feet/140 feet per second for men .. that's about 0.42 seconds.  For women the shorter path length and ball speed give the same number.

 

In tennis the maximum length used, neglecting the vertical component, is the diagonal of a 27 by 78 foot court - about 82.5 feet.  The fastest reliably measured serve in the men's game is about 140 mph or 205 feet per second - about 0.40 seconds.²

 

Venturing into cricket we have a pitch that is 66 feet long.  The fastest bowlers are a bit over 100mph - apparently a bit faster than baseball.  The batsman generally stands about three feet in front of the wicket so we have 63/150 or about 0.42 seconds.³

 

Beach volleyball works out much the same for men...  around 0.4 seconds flight time for the fastest serves.

 

four tenths of a second

 

 That's the interesting number for all of these sports and perhaps it tells us something about human capabilities. When you subtract reaction time it emphasizes the importance of reading the other player. 

 

Experiments have been made where baseballs are pitched from 50 feet.  Now flight times are under 0.35 seconds and the game is unplayable.  Once the pitches slow down playability returns.  The numbers here ignore quite a bit, but are probably good to five percent or so.  Some of these games are at the edge of playability and that makes them interesting. 

 

A comment on beach volleyball.  The women's court is the same size as the men's only the net is lower. A fast serve is useful, but like the other sports there is much more going on.  The slower ball speed allows for more strategic play.  About a month ago Kareem Abdul-Jabbar, writing in The Guardian, said:

One of the most significant contributors to the sport’s growing popularity is the dynamic play of the women. Although their games are generally not as explosive as the men’s, they play with greater technique, variety of shots, and chess-like thinking, often making their matches more compelling.

It makes one wonder about interesting physical limits and sweet spots in other sports.

 

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¹ Curiously enough MLB players have average reflexes and some of the greats are slower than average.  You can easily test your reaction time with a ruler and a friend. 

² note that I'm ignoring air resistance..  that will add a couple hundredths of a second in tennis and a bit less in baseball.  In tennis the bounce adds a few small amount.

³ the ball bounces off the ground once, but the collision is highly elastic.. many a couple hundreds of a second are lost.

 

mad science

It seems Apple released a new smartphone yesterday. This one has several reasons to make me want to upgrade, but the most drool-worthy is its power as a computational camera.  I'll leave it to other to write the reviews and compare it to Google's efforts - a new iPhone isn't in my budget this year.  But perhaps a few words on computational photography are relevant.

 

Computational photography has been around for over sixty years.¹  In particle physics you slam particles into each other and carefully study the wreckage that emerges from the collision. About sixty years ago bubble chambers came into use.  The idea was to record the wreckage in three dimensions.  A chamber was filled with a transparent liquid like liquid hydrogen, kept just below its boiling point. Just before a fast moving particle entered the chamber a piston at the bottom of the chamber was dropped suddenly causing  the liquid to superheat. The incoming particle collides with a particle in the liquid - usually a proton if the liquid is hydrogen - and charged particles from the collision leave a trail of tiny bubbles in the sensitized superheated liquid.   Three cameras at right angles to each other simultaneously captured three views of the bubble tracks and the piston is moved back into position waiting for the next collision.  

 

A large magnet surrounds the chamber causing the particles to bend one way or another depending on their charge.  The slower a charged particle moves, the more it curls.  The photographic sheets are developed and "girls" - it was considered women's work - would trace the tracks by hand with digitizers creating lists of coordinates for each track that a computer program could use to compute the fundamentals of each collision.²  This type of computing was the most demanding of the day.   In the late sixties and beyond recording the collisions directly in digital form using a variety of "counters" took over and the scale of experiments and necessary computation exploded.

 

By the late 70s people were beginning to categorize medical x-rays and ultrasounds computationally and resonance imaging began to emerge.  The computational requirements were stiff in the day, but your phone could easily handle the computing required for your MRI.  It has been argued that this form of computational photography has had the largest impact on human health of any form of computation.

 

Playing with photographic images from telescopes and microscopes was  necessary in science, but the techniques quickly migrated to computer science labs.  Just as the Utah Teapot was the universal test for 3d imaging, a photo known as Lenna was the ubiquitous test for imaging algorithm research in male dominated CS departments during the 70s and 80s.  It wasn't unusual to see her image appear in several papers in a single journal issue.  Journal images today aren't as sexist.

 

Some of what went into academic image processing made its way into Photoshop in the late eighties.  Photoshop went on to be a preferred platform for creative artists to do computational post-processing of their images.  Take a photo on your camera and play with it on your computer.

 

But what if the camera and computer could be combined into something that could redefine imaging?  I'd argue that took place in science some time ago as the imaging part of telescopes, microscopes and particle detectors had began to require built-in computation.  It's been in the past few years we've seen the emergence of a new type of photography in handheld cameras.  Smartphones, with vast development resources, are leading the way and we're on the verge of an explosion of new techniques and ideas.

 

At this point it would make sense to talk a bit about the basics of 2d fourier transforms to get a sense of how that's done.  Here's a short non-technical introduction that gives a sense of a basic function.

 

 

The computational power of the latest smartphones is staggering and, at least in Apple's case, a good deal of it can be devoted to computational photography.  Currently much of it is used to improve snapshots that would otherwise be unusable.  Noise can be reduced while still keeping important detail - often using psychological models of human perception, the dynamic range of an image can be extended by taking a number of shots and bringing out detail in dark areas and suppressing burned out overexposed regions, realtime video can be overlayed with other information creating a computation synesthesia of sorts, machine learning is becoming useful in many ways,  .. the list goes on and on.  

 

I'll offer one that could appear in about a year with the next generation of smartphones.  Time of flight image sensing is now sort of practical for a smartphone and will probably be a feature in high volume phones like the iPhone next year. Basically a pulse of infrared laser light is sent out to an object and the time it takes to go out and return is used to calculate the distance.  This is done for a somewhat smaller image than your camera takes - a few hundred thousand to a million pixels. But these pixels now have distance information in addition to enough image information that it can be used to create a distance map for the full image from the main sensor.   This could be very useful in augmented reality, but here's one I'd like to see.  Take two or three phones on tripods and point them at a dancer, athlete or someone getting physical therapy.  A very accurate motion capture video could be quickly made and you wouldn't have to spend $50k and up on specialized equipment.  Coaches and physical therapists would be delighted. 

 

A thousand other uses will emerge we haven't thought about. Independent of their platforms there are strong reasons why Apple needs a great computational camera.  What will separate winners from losers will be usefulness, playfulness, and great user interfaces and experiences.  That's the hard part. 

 

For the best photos a good photographer is still required and the tiny lenses and sensors on smartphones are limited by basic physics.  But always having a camera with you and one that can correct basic mistakes is a serious plus.  That and there are emerging capabilities that will take photography in new directions.  

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¹ digital computational photography.  I won't go into details here, but optical computation has been around even longer.  If you're interested in the subject realize a lens is an optical computer capable of creating a Fourier transform.

² I like this example as a neutrino slams into a protron bangnig the vacuum hard enough that a D⁺ (d plus meson) appears.  It is composed of two quarks:  charm and anti-down.  I have a fondness for charm quarks:-)  Also this was made during the twilight of bubble chambers in the late 70s. 

 

 

 

fundamentally speaking

 In 1897 J.J. Thomson stood before the Royal Society and made the case for a charged particle a thousand times less massive than the hydrogen atom.  He had discovered the electron.   Initially many in the room didn't believe him.  Atoms were considered the smallest bits of matter and physics and chemistry were concerned with arranging their properties on periodic tables.  But Thomson's work proved solid.  Then a bit more than a decade later Ernest Rutherford discovered the atomic nucleus. There was something very small with a positive charge at the center of ever atom with electrons zipping around in a large amount of empty space "like a fly in a cathedral".   

 

Much of the revolution in atomic and quantum physics came out of the Cavendish Laboratory at Cambridge - a place that represents one of the greatest inventions of the 19^th century.  It had been set up with funding from the Chancellor of the University - William Cavendish - as something of a reaction to worries about falling behind other institutions that were engaged in understanding telegraphy.  Cavendish did something rather dramatic.  Rather than work on the immediate problem he set up an institution to focus on fundamentals and hired James Clerk Maxwell to run the place.  Maxwell started setting up a laboratory of shared resources and culture, but died not long after.

 

The next director, Lord Rayleigh, brought systematic instruction and further focused on studying the fundamentals rather than applied work.   Maxwell's earlier work sorting out electricity and magnetism was initially unwieldily, but it was clear light was made of electromagnetic waves and people realized wireless communication might be possible.  That would be a big thing - telegraphy without those expensive wires.  Rayleigh was asked to work on it, but suggested it would be far too expensive in terms of equipment they didn't have.  Instead the path would be less expensive explorations trying to stay at the frontier.   Not long afterwards Hertz, working in Germany, discovered how to do wireless communication.  The Cavendish Lab did more impressive work - they set the path for the next century.

 

Hertz was making use of the unification of the electricity and magnetism that Maxwell had figured out two decades before. In Maxwell's model there was an electromagnetic field that allowed waves to propogate through a hypothetical substance called the luminiferous ether.  It wasn't exactly right - ether was shown to not exist, but the notion of fields traveling through nothing persisted.  It gave physics a new way of thinking about influence at a distance.

 

So what is a field?  Usually they're described as a set of values at each point in space. Like temperature, air pressure, wind speed and so on.  Physicists have another way of thinking about a different kind of field that is a bit confusion to those on the outside.  That's the kind of field that's relevant here.  

 

Before Maxwell there was Michael Faraday - perhaps the last of the great non-mathematical physicists.  .  Pick up a couple of magnets and hold them so they're repelling each other - say north pole to north pole.  As you push them together you feel the force increasing.  You can't see it, but Faraday said there's something real there.  He called them lines of force - it later was called the magnetic field. He was first to understand if you move a coil of wire through a magnetic field, a current is induced in the coil.  He had discovered a link between electricity and magnetism.  It stunned audiences at his lectures   Fields were a deep thought ..  it took us about a century and a half to really appreciate the depth.

 

Over the next 150 years a revolution in physics taught us about quantum mechanics.  Rather than getting into the weeds  just note the bottom line is energy comes in discrete lumps rather than being continuous..   The exciting part comes when you combine the discrete nature of quantum mechanics with Faraday's continuous smoothly varying fields.  Quantum field theory tells us the discrete bits of the electromagnetic field come in little chunks we call photons. Skipping over an enormous among of work and a few dozen Nobel Prizes, the  remarkable thing is this general idea applies to every particle in the universe.   For each type of particle there's a field filling the universe ..  for example an electron field.  Little ripples in this fluid get tied into little bundles of energy and, in this case, the bundle of energy is what we call the electron.  All of the electrons in the Universe are just waves in the same electron field - think of it as sort of a fluid - that fills the entire Universe.

 

By 1970 it was known in addition to the electron field are two quark fields.  You may have learned protons and neutrons are each made of two types of quarks:  the proton is two up quarks and a down quark and the neutron is two down quarks and an up quark.¹  In this interpretation there are no particles in the Universe..  just ripples in fields.  Now we have come down from the periodic table with over one hundred elements to something much simpler:  an electron, an up quark, a down quark and something called a neutrino.  Or more fundamentally an electron field, an up quark field, a down quark field and a neutrino field.

 

It's a more fundamental way of thinking about things, but it's also an oversimplification. In the spirit of oversimplification here's the result. For some completely unexplained reason Nature like to repeat ins triplicate.  There are three families of electron like fields, three of up quarkish fields, three of down quarkish fields and three families of of neutrinoish fields.  Add to this four force fields and now there are sixteen fundamental fields .. plus another called the Higgs field which is partly responsible for giving these ripples mass.  (note - the image shows particles .. just think of them as fields)   Collectively this is know as the Standard Model. 

 

The idea of seventeen fundamental fields representing everything on Earth may seem unnatural, but where precision measurements can be made they compare with theory to astounding accuracy - much better than any other theory in any branch of science.  It has also been predictive of things we didn't know existed.   

 

The equation for the Standard Model is somewhat ugly.  It doesn't incorporate gravity.  Many suspect something more fundamental exists, but just because we might want it doesn't mean Nature works that way - maybe it is fundamentally messy.  On top of that the Standard Model describes only describes conventional matter which is only about five percent of the known mass energy of the Universe.  Another twenty seven percent is dark matter - something which we can detect indirectly, but have no real understanding of.²  Even more mysterious is the remaining sixty eight percent that we call dark energy.

 

Perhaps the Standard Model isn't the ultimate description of what we're made of.³    For now it's more fundamental than saying we're made of particles or atoms even though those are usually more convenient ways to deal with anything at the scale we're used to.   But I like to think there's something poetic about seeing each of us as constellations of tiny field disturbances bound together by force fields.  We're part of an enormous family of these constellations that spread through the Universe.    Our personal constellations are conscious and are capable of wondering if other constellations may have similar thoughts..  

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Last year I wrote another short piece about fields and what is known as the vacuum.  Both of these are very brief, but perhaps give an idea of the most successful bit of physics - arguably science - to date.

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¹ Up and down are just labels and nothing more... other than proof physicists are very poor when it comes to naming things.

² I once calculated about 250 grams of dark matter is streaming through the Earth at any given moment..  roughly a squirrel's worth of dark matter.  Also dark is a bad term..  it doesn't interact with conventional matter so in it's really perfectly transparent matter.

³ There have been a few theories designed, among other things, to add gravity.  Mathematically String Theory is appealing, but so far there are no signs that's how Nature works.  It may well be a cold trail.