1905: Annus Mirabilis – Photoelectric effect

This is the first in a series of posts that will cover the outcome of the 4 fundamental papers published by Albert Einstein in 1905, the so-called “Annus Mirabilis”, or miracle year. This article was originally published at the sent2null blog and is reposted here courtesy of David Saintloth. The remaining 3 posts in the series are to follow.


1905 was a great year for physics – in this year a 24 year old patent examiner in Bern, Switzerland published 4 fundamental physics papers in 4 disparate areas of the field. The topics included special relativity, the relationship between energy and matter, Brownian motion, and the subject of this post, the photoelectric effect.

Next to his paper on Brownian motion, Einstein’s paper on the photoelectric effect was probably the most practical: it provided an answer to a long-standing problem in electromagnetic theory at the time that had stood as an embarrassment to particle physics. This embarrassment was a legacy of the work of James Clerk Maxwell and his fundamental equations of electromagnetism: by using a continuous wave analog to describe the energy of propagating fields, Maxwell was able to astonishingly explain the riddle that was the relationship between electricity and magnetism in clear mathematical terms. He was also able to show how light itself must be an electromagnetic wave, by showing that all such waves are limited by the speed of light (c), roughly 186,000 miles per second.

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Amy Chow, Polymath

Project Polymath’s vision is to create a whole army of da Vincis, spreading across the world with their diverse skills and talents in art, music, medicine, mathematics, science, and many other fields of study.  Since Leonardo da Vinci was from another time and culture, though, I have wondered what form modern polymaths might take.  I thought back to my days as a gymnast and realized that I already knew of at least one: Amy Chow, Olympic champion gymnast, concert pianist, elite-level diver, and doctor.

Amy Chow

During the summer of 1996, I watched the USA Olympic Team Trials.  I was twelve years old, I made straight A’s in school, and I very much enjoyed my piano lessons and gymnastics classes.  So, of course I took note when the commentators talked about Amy Chow and her elite-level piano skills, her 4.0 GPA, and her daring tricks on the vault, bars, beam, and floor.  (Her skill level was much more impressive than mine.)  On the second day of the Olympic Trials, she fell off the beam and hit her head, but she finished the routine (by the end of the competition, one could see a purple bruise right by her eye).  Because of her perseverance, she made the Olympic team, and I was even more amazed on the night I saw her and her teammates make history by winning America’s first team gold medal in gymnastics.

Amy became a two-time Olympian in 2000, after which she went to medical school at Stanford University and specialized in pediatrics.  In more recent years, Amy has done both diving and pole-vaulting.  Her skills in gymnastics lent very well to other sports and helped her go from recreational-level diving to national-level diving in approximately a year’s time.  She may have even advanced to the 2012 Olympic Trials for diving, had she not suffered an injury prior to the meet.

Amy summed up the heart of the polymathic pursuit when she said, “I like learning new things”.¹  She has described integrating and synthesizing her areas of expertise; she has a particular interest in sports medicine and helping children enjoy a healthy, meaningful athletic experience.²   She sets goals that are high but realistic for her, and she then takes the steps necessary to pursue them.  From her experiences, she has learned important life skills, including responsibility, dedication, problem solving, perseverance, and teamwork.²  Any budding polymath would do well to emulate these qualities.

Watch Amy’s beam routine here

Watch Amy’s uneven bars routine here

Hear an interview with Amy


¹ Palo Alto Medical Foundation. (2012).  “Amy Y. Chow, MD, FAAP.”  Retrieved 4 January 2012 from http://www.pamf.org/dr-amy-chow.html .

² Peters, Keith. (2011). Olympian Amy Chow dives into a new challenge.  Palo Alto Online Sports.  Retrieved 4 January 2012 from http://www.paloaltoonline.com/news/show_story.php?id=21806 .


Photography: exposure and metering

Want to take pictures like this?

Waves of Nacre

Waves of Nacre

Mediterranean Sunset

Golden Leaves

See The Light

Then you’ll need to master the art of exposure – controlling the amount of light which enters your camera.


What is exposure?

Like the eye, cameras operate by recording light when it strikes a sensor in the camera. The camera’s sensor is made of a grid of semiconducting material (the number of light-sensing “buckets” in this grid determine the resolution of the photograph). When light strikes a “bucket”, the incoming energy frees paired electrons in the material, causing an electric current to flow. This electricity is picked up by a processor in the camera (its “brain”) and the responses from the “buckets” are compiled to form an image.

The amount of light striking the sensor while the camera’s shutter is open determines how much light is recorded in the image. In other words, the more light that enters the camera (or the longer the camera is exposed to a constant source of light), the brighter the resulting image will be. This is called the exposure.
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Michael Barnathan

January 3, 2013

Welcome to the official blog of Project Polymath! We’re excited to get the discussion going on the future of education, and to share many of our insights and interesting finds within and across many areas of study.