#PiDay Activity: Using chocolate chips to calculate the value of pi

Try this fun Pi Day activity this year. Mathematician Tim Chartier has a recipe that is equal parts delicious and educational. Using chocolate chips and the handy print-outs below, mathematicians of all ages can calculate the value of pi. Start with the Simple as Pi recipe, then graduate to the Death by Chocolate Pi recipe. Take it to the next level by making larger grids at home. If you try this experiment, take a picture and send it in and we’ll post it here.

For details on the math behind this experiment please read the article below which is cross-posted from Tim’s personal blog. And if you like stuff like this, please check out his new book Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing.

Chocolate Chip Pi

How can a kiss help us learn Calculus? If you sit and reflect on answers to this question, you are likely to journey down a mental road different than the one we will traverse. We will indeed use a kiss to motivate a central idea of Calculus, but it will be a Hershey kiss! In fact, we will have a small kiss, more like a peck on the cheek, as we will use white and milk chocolate chips. The math lies in how we choose which type of chip to use in our computation.

Let’s start with a simple chocolatey problem that will open a door to ideas of Calculus. A Hershey’s chocolate bar, as seen below, is 2.25 by 5.5 inches. We’ll ignore the depth of the bar and consider only a 2D projection. So, the area of the bar equals the product of 2.25 and 5.5 which is 12.375 square inches.

Note that twelve smaller rectangles comprise a Hershey bar. Suppose I eat 3 of them. How much area remains? We could find the area of each small rectangle. The total height of the bar is 2.25 inches. So, one smaller rectangle has a height of 2.25/3 = 0.75 inches. Similarly, a smaller rectangle has a width of 5.5/4 = 1.375. Thus, a rectangular piece of the bar has an area of 1.03125, which enables us to calculate the remaining uneaten bar to have an area of 9(1.03125) = 9.28125 square inches.

Let’s try another approach. Remember that the total area of the bar is 12.375. Nine of the twelve rectangular pieces remain. Therefore, 9/12ths of the bar remains. I can find the remaining area simply be computing 9/12*(12.375) = 9.28125. Notice how much easier this is than the first method. We’ll use this idea to estimate the value of π with chocolate, but this time we’ll use chocolate chips!

Let’s compute the area of a quarter circle of unit radius, which equals π/4 since the full circle has an area of π. Rather than find the exact area, let’s estimate. We’ll break our region into squares as seen below.

This is where the math enters. We will color the squares red or white. Let’s choose to color a square red if the upper right-hand corner of the square is in the shaded region and leave it white otherwise, which produces:

Notice, we could have made other choices. We could color a square red if the upper left-hand corner or even middle of the square is under the curve. Some choices will lead to more accurate estimates than others for a given curve. What choice would you make?

Again, the quarter circle had unit radius so our outer square is 1 by 1. Since eight of the 16 squares are filled, the total shaded area is 8/16.

How can such a grid of red and white squares yield an estimate of π? In the grid above, notice that 8/16 or 1/2 of the area is shaded red. This is also an approximation to the area of the quarter circle. So, 1/2 is our current approximation to π/4. So, π/4 ≈ 1/2. Solving for π we see that π ≈ 4*(1/2) = 2. Goodness, not a great estimate! Using more squares will lead to less error and a better estimate. For example, imagine using the grid below:

Where’s the chocolate? Rather than shading a square, we will place a milk chocolate chip on a square we would have colored red and a white chocolate chip on a region that would have been white. To begin, the six by six grid on the left becomes the chocolate chip mosaic we see on the right, which uses 14 white chocolate of the total 36 chips. So, our estimate of π is 2.4444. We are off by about 0.697.

Next, we move to an 11 by 11 grid of chocolate chips. If you count carefully, we use 83 milk chocolate chips of the 121 total. This gives us an estimate of 2.7438 for π, which correlates to an error of about 0.378.

Finally, with the help of public school teachers in my seminar Math through Popular Culture for the Charlotte Teachers Institute, we placed chocolate chips on a 54 by 54 grid. In the end, we used 2232 milk chocolate chips giving an estimate of 3.0617 having an error of 0.0799.

What do you notice is happening to the error as we reduce the size of the squares? Indeed, our estimates are converging to the exact area. Here lies a fundamental concept of Calculus. If we were able to construct such chocolate chip mosaics with grids of ever increasing size, then we would converge to the exact area. Said another way, as the area of the squares approaches zero, the limit of our estimates will converge to π. Keep in mind, we would need an infinite number of chocolate chips to estimate π exactly, which is a very irrational thing to do!

And finally, here is our group from the CTI seminar along with Austin Totty, a senior math major at Davidson College who helped present these ideas and lead the activity, with our chocolatey estimate for π.

Free #PiDay E-Cards from The Ultimate Quotable Einstein

Send #PiDay Greetings with these free ecards featuring Einstein’s thoughts on birthdays as found in The Ultimate Quotable Einstein, edited by Alice Calaprice.

Pi Day: “Was Einstein Right?” Chuck Adler on the twin paradox of relativity in science fiction

This post is extracted from Wizards, Aliens, and Starships by Charles Adler. Dr. Adler will kick off Princeton’s Pi Day festivities tonight with a talk at the Princeton Public Library starting at 7:00 PM. We hope you can join the fun!

Robert A. Heinlein’s novel Time for the Stars is essentially one long in-joke for physicists. The central characters of the novel are Tom and Pat Bartlett, two identical twins who can communicate with each other telepathically. In the novel, telepathy has a speed much faster than light. Linked telepaths, usually pairs of identical twins, are used to maintain communications between the starship Lewis and Clark and Earth. Tom goes on the spacecraft while Pat stays home; the ship visits a number of distant star systems, exploring and finding new Earth-like worlds. On Tom’s return, nearly seventy years have elapsed on Earth, but Tom has only aged by five.

I call this a physicist’s in-joke because Heinlein is illustrating what is referred to as the twin paradox of relativity: take two identical twins, fly one around the universe at nearly the speed of light, and leave the other at home. On the traveler’s return, he or she will be younger than the stay-at- home, even though the two started out the same age. This is because according to Einstein’s special theory of relativity, time runs at different rates in different reference frames.

This is another common theme in science fiction: the fact that time slows down when one “approaches the speed of light.” It’s a subtle issue, however, and is very easy to get wrong. In fact, Heinlein made some mistakes in his book when dealing with the subject, but more on that later. First, I want to list a few of the many books written using this theme:

• The Forever War, by Joe W. Haldeman. This story of a long-drawn-out conflict between humanity and an alien race has starships that move at speeds near light speed to travel between “collapsars” (black holes), which are used for faster-than-light travel. Alas, this doesn’t work. The hero’s girlfriend keeps herself young for him by shuttling back and forth at near light speeds between Earth and a distant colony world.
• Poul Anderson’s novel, Tau Zero. In this work, mentioned in the last chapter, the crew of a doomed Bussard ramship is able to explore essentially the entire universe by traveling at speeds ever closer to the speed of light.
• The Fifth Head of Cerberus, by Gene Wolfe. In this novel an anthropologist travels from Earth to the double planets of St. Croix and St. Anne. It isn’t a big part of the novel, but the anthropologist John Marsch mentions that eighty years have passed on Earth since he left it, a large part of his choice to stay rather than return home.
• Larris Niven’s novel A World out of Time. The rammer Jerome Corbell travels to the galactic core and back, aging some 90 years, while three million years pass on Earth.

There are many, many others, and for good reason: relativity is good for the science fiction writer because it brings the stars closer to home, at least for the astronaut venturing out to them. It’s not so simple for her stay-at-home relatives. The point is that the distance between Earth and other planets in the Solar System ranges from tens of millions of kilometers to billions of kilometers. These are large distances, to be sure, but ones that can be traversed in times ranging from a few years to a decade or so by chemical propulsion. We can imagine sending people to the planets in times commensurate with human life. If we imagine more advanced propulsion systems, the times become that much shorter.

Unfortunately, it seems there is no other intelligent life in the Solar System apart from humans, and no other habitable place apart from Earth. If we want to invoke the themes of contact or conflict with aliens or finding and settling Earth-like planets, the narratives must involve travel to other stars because there’s nothing like that close to us. But the stars are a lot farther away than the planets in the Solar System: the nearest star system to our Solar System, the triple star system Alpha Centauri, is 4.3 light-years away: that is, it is so far that it takes light 4.3 years to get from there to here, a distance of 40 trillion km. Other stars are much farther away. Our own galaxy, the group of 200 billion stars of which our Sun is a part, is a great spiral 100,000 light-years across. Other galaxies are distances of millions of light-years away.

From our best knowledge of physics today, nothing can go faster than the speed of light. That means that it takes at least 4.3 years for a traveler (I’ll call him Tom) to go from Earth to Alpha Centauri and another 4.3 years to return. But if Tom travels at a speed close to that of light, he doesn’t experience 4.3 years spent on ship; it can take only a small fraction of the time. In principle, Tom can explore the universe in his lifetime as long as he is willing to come back to a world that has aged millions or billions of years in the meantime.

Was Einstein Right?

This weird prediction—that clocks run more slowly when traveling close to light speed—has made many people question Einstein’s results. The weirdness isn’t limited to time dilation; there is also relativistic length contraction. A spacecraft traveling close to the speed of light shrinks in the direction of motion. The formulas are actually quite simple. Let’s say that Tom is in a spacecraft traveling along at some speed v, while Pat is standing still, watching him fly by. We’ll put Pat in a space suit floating in empty space so we don’t have to worry about the complication of gravity. Let’s say the following: Pat has a stopwatch in his hand, as does Tom. As Tom speeds by him, both start their stopwatches at the same time and Pat measures a certain amount of time on his watch (say, 10 seconds) while simultaneously watching Tom’s watch through the window of his spacecraft. If Pat measures time ∆t0 go by on his watch, he will see Tom’s watch tick through less time. Letting ∆t be the amount of time on Tom’s watch, the two times are related by the formula

where the all-important “gamma factor” is

The gamma factor is always greater than 1, meaning Pat will see less time go by on Tom’s watch than on his. Table 12.1 shows how gamma varies with velocity.

Note that this is only really appreciable for times greater than about 10% of the speed of light. The length of Tom’s ship as measured by Pat (and the length of any object in it, including Tom) shrinks in the direction of motion by the same factor.

Even though the gamma factor isn’t large for low speeds, it is still measurable. To quote Edward Purcell, “Personally, I believe in special relativity. If it were not reliable, some expensive machines around here would be in very deep trouble”. The time dilation effect has been measured directly, and is measured directly almost every second of every day in particle accelerators around the world. Unstable particles have characteristic lifetimes, after which they decay into other particles. For example, the muon is a particle with mass 206 times the mass of the electron. It is unstable and decays via the reaction

It decays with a characteristic time of 2.22 μs; this is the decay time one finds for muons generated in lab experiments. However, muons generated by cosmic ray showers in Earth’s atmosphere travel at speeds over 99% of the speed of light, and measurements on these muons show that their decay lifetime is more than seven times longer than what is measured in the lab, exactly as predicted by relativity theory. This is an experiment I did as a graduate student and our undergraduates at St. Mary’s College do as part of their third-year advanced lab course. Experiments with particles in particle accelerators show the same results: particle lifetimes are extended by the gamma factor, and no matter how much energy we put into the particles, they never travel faster than the speed of light. This is remarkable because in the highest-energy accelerators, particles end up traveling at speeds within 1 cm/s of light speed. Everything works out exactly as the theory of relativity says, to a precision of much better than 1%.

How about experiments done with real clocks? Yes, they have been done as well. The problems of doing such experiments are substantial: at speeds of a few hundred meters per second, a typical speed for an airplane, the gamma factor deviates from 1 by only about 1013. To measure the effect, you would have to run the experiment for a long time, because the accuracy of atomic clocks is only about one part in 1011 or 1012; the experiments would have to run a long time because the difference between the readings on the clocks increases with time. In the 1970s tests were performed with atomic clocks carried on two airplanes that flew around the world, which were compared to clocks remaining stationary on the ground. Einstein passed with flying colors. The one subtlety here is that you have to take the rotation of the Earth into account as part of the speed of the airplane. For this reason, two planes were used: one going around the world from East to West, the other from West to East. This may seem rather abstract, but today it is extremely important for our technology. Relativity lies at the cornerstone of a multi-billion-dollar industry, the global positioning system (GPS).

GPS determines the positions of objects on the Earth by triangulation: satellites in orbit around the Earth send radio signals with time stamps on them. By comparing the time stamps to the time on the ground, it is possible to determine the distance to the satellite, which is the speed of light multiplied by the time difference between the two. Using signals from at least four satellites and their known positions, one can triangulate a position on the ground. However, the clocks on the satellites run at different rates as clocks on the ground, in keeping with the theory of relativity. There are actually two different effects: one is relativistic time dilation owing to motion and the other is an effect we haven’t considered yet, gravitational time dilation. Gravitational time dilation means that time slows down the further you are in a gravitational potential well. On the satellites, the gravitational time dilation speeds up clock rates as compared to those on the ground, and the motion effect slows them down. The gravitational effect is twice as big as the motion effect, but both must be included to calculate the total amount by which the clock rate changes. The effect is small, only about three parts in a billion, but if relativity weren’t accounted for, the GPS system would stop functioning in less than an hour. To quote from Alfred Heick’s textbook GPS Satellite Surveying,

Relativistic effects are important in GPS surveying but fortunately can be accurately calculated. . . . [The difference in clock rates] corresponds to an increase in time of 38.3 μsec per day; the clocks in orbit appear to run faster. . . . [This effect] is corrected by adjusting the frequency of the satellite clocks in the factory before launch to 10.22999999543 MHz [from their fundamental frequency of 10.23 MHz].

This statement says two things: first, in the dry language of an engineering handbook, it is made quite clear that these relativistic effects are so commonplace that engineers routinely take them into account in a system that hundreds of millions of people use every day and that contributes billions of dollars to the world’s commerce. Second, it tells you the phenomenal accuracy of radio and microwave engineering. So the next time someone tells you that Einstein was crazy, you can quote chapter and verse back at him!

Fantasy Physics: Should Einstein Have Won Seven Nobel Prizes?

This guest post from A. Douglas Stone is part of our celebration of all things Einstein, pi, and, of course, pie this week. For more articles, please click here. Please join Prof. Stone at the Princeton Public Library on March 14 at 6 PM for a lecture about Einstein’s quantum breakthroughs.

Cross-posted with the Huffington Post.

Albert Einstein never cared too much about receiving awards and honors, and that included the Nobel Prizes, which were established in 1901, at roughly the same time as Einstein was beginning his research career in physics. In 1905, at the age of 25, Einstein began his ascent to scientific pre-eminence and world-wide fame with his proposal of the Special Theory of Relativity, as well as a “revolutionary” paper on the particulate properties of light, his foundational work on molecular (“Brownian”) motion, and finally his famous equation, E = mc2. In 1910, he was first nominated for the Prize and was nominated many times subsequently, usually by multiple physicists, until he finally won the 1921 Prize (awarded in 1922). Surprisingly, he did not win for his most famous achievement, Relativity Theory, which was still deemed too speculative and uncertain to endorse with the Prize. Instead, he won for his 1905 proposal of the law of the photoelectric effect—empirically verified in the following decade by Robert Millikan—and for general “services to theoretical physics.” It was a political decision by the Nobel committee; Einstein was so renowned that their failure to select him had become an embarrassment to the Nobel institution. But this highly conservative organization could find no part of his brilliant portfolio that they either understood or trusted sufficiently to name specifically, except for this relatively minor implication of his 1905 paper on particles of light. The final irony in this selection was that, among the many controversial theories that Einstein had proposed in the previous seventeen years, the only one not accepted by almost all of the leading theoretical physicists of the time was precisely his theory of light quanta (or photons), which he had used to find the law of the photoelectric effect!

In keeping with his relative indifference to such honors, Einstein declined to attend the award ceremony, because he had previously committed to a lengthy trip to Japan at that time and didn’t feel it was fair to his hosts to cancel it. Moreover, when the Prize was officially announced and the news reached him during his long voyage to Japan, he neglected to even mention the Prize in the travel diary he was keeping. He had taken one practical note of it however, in advance. When he divorced his first wife, Mileva Maric in 1919, he agreed to transfer to her the full prize money, a substantial sum, in the form of a Trust for the benefit of her and his sons, should he eventually win.

However, while Einstein himself barely dwelt at all on this honor, it is an interesting exercise to ask how many distinct breakthroughs Einstein made during his productive research career, spanning primarily the years 1905 to 1925, that could be judged of Nobel caliber, when placed in historical context and evaluated by the standards of subsequent Nobel Prize awards. Admittedly, this analysis has a bit in common with fantasy sports, in which athletes are judged and ranked by their statistical achievements and arguments are made about who was the GOAT (“greatest of all time”). Well, why not spend a few pages on this guilty pleasure, at least partly in the service of illuminating the achievements of this historic genius, even if Einstein would not have approved?

Let’s start with the Prize he did receive, which was absolutely deserved, if the committee had had the courage to write the citation, “for his proposal of the existence of light quanta.” The law of the photoelectric effect, which they cited, only makes sense if light behaves like a particle in some important respects, and that is what he proposed in 1905. This proposal came at a time when the wave theory of light was absolutely triumphant and was even enshrined in a critical technology: radio. Not a single physicist in the world was thinking along similar lines as Einstein, nor were all of the important theorists convinced by his arguments for two more decades. Nonetheless, the photon concept was unambiguously confirmed in experiments by 1925, and now is considered the paradigm for our modern quantum theory of force-carrying particles. It is the first in a family of particles known as bosons, most recently augmented by the (Nobel-winning) discovery of the Higgs particle. So the photon is a Nobel slam dunk.

We can move next to two more “no-brainers,” the two theories of relativity, the Special Theory, proposed in 1905, and the General Theory, germinated in 1907 and completed in 1915. These are quite distinct contributions. The Special Theory introduced the Principle of Relativity, that the law of physics must all be the same for bodies in uniform relative motion. An amazing implication of this statement is that time does not elapse uniformly, independent of the motion of observers, but rather that the time interval between events depends on the state of relative motion of the observer. Einstein was the first to understand and explain this radical notion, which is now well-verified by direct experiments. Moreover, Einstein’s concept of “relativistic invariance” is built into our theory of the elementary particles, and so it has had a profound impact on fundamental physics. However, here it must be noted that the equations of Special Relativity were first written down by Hendrik Lorentz, the great Dutch physicist whom Einstein admired the most of all his contemporaries. Lorentz just failed to give them the radical interpretation with which Einstein endowed them; he also failed to notice that they implied that energy and mass were interchangeable: E = mc2. There are also a few votes out there for the French mathematician, Henri Poincare, who enunciated the Principle of Relativity before Einstein, but I can’t put him in the same category as Lorentz with regard to this debate. Einstein would have been happy to share Special Relativity with Lorentz, so let’s split this one 50-50 between the two.

General Relativity on the other hand is all Albert. Like the photon, no one on the planet even had an inkling of this idea before Einstein. Einstein realized that the question of the relativity of motion was tied up with the theory of Gravity: that uniform acceleration (e.g. in an elevator in empty space) was indistinguishable from the effect of gravity on the surface of a planet. It gave one the same sense of weight. From this simple seed of an idea arose arguably the most beautiful and mathematically profound theory in all of physics, Einstein’s Field Equations, which predict that matter curves space and that the geometry of our universe is non-Euclidean in general. The theory underlies modern cosmology and has been verified in great detail by multiple heroic and diverse experiments. The first big experiment, which measured the deflection of starlight as it passed by the sun during a total eclipse, is what made Einstein a worldwide celebrity. This one is probably worth two Nobel prizes, but let’s just mark it down for one.

Here we exhaust what most working physicists would immediately recognize as Einstein’s works of genius, and we’re only at 2.5 Nobels. But it is a remarkable fact that Einstein’s work on early atomic theory, what we now call quantum theory, is vastly under-rated. This is partially because Einstein himself downplayed it due to his rejection of the final version of the theory, which he dismissed with the famous phrase, “God does not play dice.” But if one looks at what he actually did, the Nobels keep piling up.

The modern theory of the atom, quantum theory, began in 1900 with the work of the German physicist, Max Planck, who, in what he called “an act of desperation,” introduced into physics a radical notion, quantization of energy. Or so the textbooks say. This is the idea that when energy is exchanged between atoms and radiation (e.g. light), it can only happen in discrete chunks, like a parking meter that only accepts quarters. This idea turns out to be central to modern atomic physics, but Planck didn’t really say this in his work. He said something much more provisional and ambiguous. It was Einstein in his 1905 paper—but then much more clearly in a follow-up paper on the vibrations of atoms in solids in 1907—who really stated the modern principle. It is not clear if Planck himself accepted it fully even a decade after his seminal work (although he was given credit for it by the Nobel Prize committee in 1918). In contrast, Einstein boldly applied it to the mechanical motion of atoms, even when they are not exchanging energy with radiation, and stated clearly the need for a quantized mechanics. So despite the textbooks, Einstein clearly should have shared Planck’s Nobel Prize for the principle of quantization of energy. We are up to 3.0 Nobels for Big Al.

The next one in line is rarely mentioned. After Einstein proposed his particulate theory of light in 1905, he did not adopt the view that light was simply made of particles in the ordinary sense of a localized chunk of matter, like a grain of sand. Instead, he was well aware that light interfered with itself in a similar manner to water waves (a peak can cancel a trough, leading to no wave). In 1909, he came up with a mathematical proof that the particle and wave properties were present in one formula that described the fluctuations of the intensity of light. Hence, he announced that the next era of theoretical physics would see a “fusion” of the particle and wave pictures into a unified theory. This is exactly what happened, but it took fourteen years for the next advance and another three (1926) for it all to fall into place. In 1923, the French physicist Louis de Broglie hypothesized that electrons, which have mass (unlike light) and were always previously conceived of as particles, actually had wavelike properties similar to light. He freely admitted his debt to Einstein for this idea, but when he got the Nobel Prize for “wave-particle” duality in 1929, it was not shared. But it should have been. Another half for Albert, at 3.5 and counting.

From 1911 to 1915 Einstein took a vacation from the quantum to invent General Relativity, which we have already counted, so his next big thing was in 1916 (he didn’t leave a lot of dead time in those days). That was three years after Niels Bohr introduced his “solar system” model of the atom, where the electrons could only travel in certain “allowed orbits” with quantized energy. Einstein went back to thinking about how atoms would absorb light, with the benefit of Bohr’s picture. He realized that once an atom had absorbed some light, it would eventually give that light energy back by a process called spontaneous emission. Without any particular event to cause it, the electron would jump down to a lower energy orbit, emitting a photon. This was the first time that it was proposed that the theory of atoms had such random, uncaused events, a notion that became a second pillar of quantum theory. In addition, he stated that sometimes there was causal emission, that the imposition of more light could cause the atom to release its absorbed light energy in a process called stimulated emission. Forty-four years later, physicists invented a device that uses this principle to produce the purest and most powerful light sources in nature, the LASER (Light Amplified by Stimulated Emission of Radiation). The principles of spontaneous and stimulated emission introduced by Einstein underlie the modern quantum theory of light. One full Prize please—now at 4.5.

After that 1916-1917 work, Einstein had some health problems and became involved in political and social issues for a while, leading to a Nobel batting slump for a few years. (He did still collect some hits, like the prediction of gravitational waves (a double) and the first paper on cosmology and the geometry of the Universe using General Relativity (a triple)). But he came out of his slump with a vengeance in 1924 when he received a paper out of the blue from an unknown Indian, physicist Satyendranath Bose. It was yet another paper about particles of light, and although Bose did not state his revolutionary idea very clearly, reading between the lines, Einstein detected a completely new principle of quantum theory, the idea that all fundamental particles are indistinguishable. This is the standard terminology in physics, but it is actually very misleading. Here, indistinguishability is not the idea that humans can’t tell two photons apart (like identical twins); it is the idea that Nature can’t tell them apart, and in a real sense interchanging the two photons doesn’t count as a different state of light.

When Bose applied this principle to light he didn’t get anything radically new; it was just a different way of thinking about Planck’s original discovery in 1900. But Einstein then took the principle and applied it to atoms for the very first time, with amazing results. He discovered that a simple gas of atoms, if cooled down sufficiently, would cease to obey all the laws that physicists and chemist had discovered for gases over the centuries, and to which no exception had ever been found. Instead, all gases should behave like a weird liquid or super-molecule known as a Bose-Einstein condensate. But remember, Bose had no clue this would happen; he didn’t even try to apply his principle to atoms. It turns out that Einstein condensation underlies some of the most dramatic quantum effects, such as superconductivity, which is needed to make the magnets in MRI machines and has been the basis for five Nobel Prizes. No knowledgeable physicist would dispute that Einstein deserved a full Nobel Prize for this discovery, but I am sure that Einstein would have wanted to share it with Bose (who never did receive the Prize).

So we are at 5.0 “units” of Nobel Prize but seven trips to Stockholm. And this leaves out other arguably Nobel-caliber achievements (Brownian motion as well as the Einstein-Podolsky-Rosen effect, which underlies modern quantum information physics). And wait a minute—when someone shares the Nobel Prize do we refer to them as a “half- Laureate”? No way. Even scientists who get a “measly” third of a Prize are Nobel Laureates for life. Thus by the standard we apply to normal humans, Einstein deserved at least seven Nobel Prizes. So next time you make your fantasy scientist draft, you know who to take at number one.

A. Douglas Stone is author of Einstein and the Quantum: The Quest of The Valiant Swabian.

The complete line up for Princeton’s Pi Day Celebration

As noted earlier, we are partnering with the Princeton Public Library and the Princeton Tour Company on some author presentations this week. In fact, Chuck Adler is the kick-off for the entire weekend with a talk on Wizards, Aliens, and Starships at the Princeton Public Library on Thursday evening. Physicist Doug Stone will then present about Einstein’s under acknowledged contributions to quantum theory and quantum mechanics on Pi Day proper. We hope you will join the library in welcoming our authors and that you will check out the other fantastic, fun events scheduled over the weekend.

To really give you a sense of what to expect, read this excellent preview from the Princeton Packet.

An Infinitely Delightful Number of Events Planned for the 2014 Pi Day Princeton & Einstein Birthday Party Celebrations!

Thursday, 3.13.14             PI DAY EVE

7:00 p.m.

Academic Celebrity Pi Day Event with Charles Adler at Princeton Public Library

Friday, 3.14.14                 PI DAY & EINSTEIN’S BIRTHDAY

11:00 a.m.

Walking Tour of Einstein’s Neighborhood begins at 116 Nassau Street (the U-Store)

1:59 p.m.

Deadline to submit International Pi Day Princeton Video Contest

3:14 p.m.

Walk a Pi Event at YMCA

3:14 p.m.

Pizza Pi Competition at Princeton Pi – Mayor & Superintendent of Princeton Schools are judges!   Winner receives free pizza for a year!  (Email here to register your middle school aged competitor.)

3:14 p.m.

6:00 p.m.

Academic Celebrity Pi Day Event with famed physicist A. Douglas Stone at Princeton Library

8:00 p.m.

Princeton Light Up The Night Event - Courtesy of Princeton University, Princeton Township and Princeton Pedestrian/Bicyclist Advisory Committee

8:00 p.m.

Outerbridge Ensemble, led by pianist, Steve Hudson at Arts Council of Princeton

Saturday, 3.15.14            OUR UNREAL CELEBRATION DAY

9:00 a.m.

Pie Eating Contest at McCaffrey’s at Princeton Shopping Center and moderated by Princeton comedic celebrity, Adam Bierman. Winner gets bragging rights and all the pie they can eat first thing in the morning!

10:00 a.m.

Kids’ Violin Exhibition at Princeton Library by Princeton Symphony Orchestra (Email here to register your 3yr – 6yr old child)

11:00 a.m.

Einstein Look A Like Contest at Princeton Library. Winner of 13yrs and younger category receives \$314.15  (Email here to register your child.)

11:00 a.m.

“Happy Birthday Einstein!” party at Historical Society of Princeton (Email here to register your child)

12:00 p.m.

International Puzzle Celebrity Guest: Tetsuya Miyamoto, inventor of KENKEN at Princeton Library

12:00 p.m.

Dinky Rides with Einstein at Dinky Station

12:00 p.m

Academic Celebrity Book Signing with Jennifer Berne at Jazams

1:00 p.m.

KENKEN Tournament for Teens (and other teen-spirited humans) at Princeton Library

1:00 p.m.

Pi Recitation Contest at Princeton Library. Winner of Youth Category (aged 7yrs – 13 yrs) receives \$314.15  (Email here to register your child.)

1:30 p.m.

Finding Pi – hands on activities for children 5yrs and up at Princeton Library

2:00 p.m.

Celebrity Book Party with Laura Overdeck at Labyrinth Books

2:15 p.m.

Rubik’s Cube Interactive Demonstration at Princeton Library

2:45 p.m.

Pie Judging Event at Nassau Inn Yankee Doodle Tap Room by Real Possibilities Accounting Firm  First 50 participants to arrive will decide the Best Apple Pie among select Princeton bakeries!

3:14 p.m.

Pie Throwing Event at Palmer Square Green

3:14 p.m.

World Premiere & Announcement of International Video Contest Winner on Facebook . Winning Middle School receives \$314.15

3:30 p.m.

Guided Einstein Tour with Mimi Omiecinski of Princeton Tour Company  begins at Library

4:00 p.m.

“Happy Birthday Einstein!” party at Historical Society of Princeton (Email here to register your child)

4:00 p.m.

Mega Chess Champion Demo & Free Style Play featuring chess champion David Hua

5:00 p.m.

Pi Social & Concert at Princeton Library

ADVANCED REGISTRATION for Pi Day Competitions and EARLY ARRIVAL are preferred to guarantee participation.  All contests are free and open to the public.  Arts Council Performance and Historical Society Birthday Parties require a nominal fee.  See website for additional details.

A detailed description, rules and addresses for Pi Day 2014 Events can be found here!

Pi Day and Princeton as perfect as…well…pie

As you can well imagine, Einstein is kind of a big deal in Princeton. So, it’s not too surprising that Pi Day, the annual celebration of Einstein’s actual birthday on March 14 (3.14!) that has morphed into a celebration of all things scientific and mathematical, is practically a town-wide holiday. Princeton University Press is partnering with Princeton Public Library on some very exciting events with our authors.

Chuck Adler will kick things off at 7 PM on Pi Day Eve (yes, I may have just invented a new holiday) at the Princeton Public Library with a discussion of his new book Wizards, Aliens, and Starships. Chuck’s specialty is looking at the mathematical underpinnings of some of our favorite works of science fiction and fantasy literature. Why is Hogwart’s always so dark? Could the Weasleys’ flying car really exist? How much longer do we have to wait for Star Trek-style teleportation and/or space elevators? Chuck answers these questions and more with fun, accessible math.

The following day, Doug Stone headlines the Pi Day festivities with a talk about Einstein and the Quantum: The Quest of the Valiant Swabian, a new book that argues that Einstein’s contributions to science have not been fully realized. While we acknowledge Einstein as the father of relativity, we haven’t really understood the scope of the work he did on quantum theory and why he ultimately turned his back on this area of inquiry. Join Doug at the Princeton Public Library at 6 PM as he fills in the gaps and presents a more complete portrait of Einstein’s career than ever available before.

For a complete list of PiDay events in Princeton, including a mysterious pizza pi competition and Einstein walking tours, please visit the official Pi Day Princeton web site.

PUP News of the World, February 14, 2014

Each week we post a round-up of some of our most exciting national and international PUP book coverage. Reviews, interviews, events, articles–this is the spot for coverage of all things “PUP books” that took place in the last week. Enjoy!

With George Washington’s birthday approaching, it seems fitting that we start off this week with a look at good ol’ G.W. We depend on George Washington every day — on the front of the dollar, of course. For PUP author Eswar Prasad, it is all about the dollar. The U.S. dollar’s dominance seems under threat. The near collapse of the U.S. financial system in 2008-2009, political paralysis that has blocked effective policymaking, and emerging competitors such as the Chinese renminbi have heightened speculation about the dollar’s looming displacement as the main reserve currency. Yet, as The Dollar Trap powerfully argues, the financial crisis, a dysfunctional international monetary system, and U.S. policies have paradoxically strengthened the dollar’s importance. This week, the New York Times ran a review of The Dollar Trap in the Sunday Business section. Want to preview the book? You can view the preface and Chapter One. Professor Prasad is also included in this week’s edition of BBC World Service Business Matters.

Has the mindless skimming of your Facebook and Instagram feeds gotten you down? We have the perfect, stimulating read for you to begin this weekend. Bernard Williams was one of the most important philosophers of the last fifty years, but he was also a distinguished critic and essayist with an elegant style and a rare ability to communicate complex ideas to a wide public. Essays and Reviews is the first collection of Williams’s popular essays and reviews, many of which appeared in the New York Review of Books, the London Review of Books, and the Times Literary Supplement. In these pieces, Williams writes about a broad range of subjects, from philosophy and political philosophy to religion, science, the humanities, economics, socialism, feminism, and pornography.

The Shanghai Daily‘s Wan Lixin reviewed Essays and Reviews, saying of the book:

[A] stimulating read for anyone who cares about the condition of the world. With characteristic clarity, insight, and humor, the author tackles a wide range of topics as diverse as philosophy, religion, science, the humanities, and pornography.

“Start spreading the news…” We reading today. We know you’d like to be a part of it — our new book on old New York. We’re channeling our inner Sinatra as we present our next book in this week’s News of the World: The New York Nobody Knows.

As a kid growing up in Manhattan, William Helmreich played a game with his father they called “Last Stop.” They would pick a subway line and ride it to its final destination, and explore the neighborhood there. Decades later, Helmreich teaches university courses about New York, and his love for exploring the city is as strong as ever. Putting his feet to the test, he decided that the only way to truly understand New York was to walk virtually every block of all five boroughs–an astonishing 6,000 miles. His epic journey lasted four years and took him to every corner of Manhattan, Brooklyn, Queens, the Bronx, and Staten Island. Helmreich spoke with hundreds of New Yorkers from every part of the globe and from every walk of life, including Mayor Michael Bloomberg and former mayors Rudolph Giuliani, David Dinkins, and Edward Koch. Their stories and his are the subject of this captivating and highly original book.

Professor Helmreich wrote an op-ed for the Daily News this week. The piece, entitled “I was on your block; here’s what I learned,” addresses what he sees as the “often underappreciated norm” of New York City’s tolerance for differences. He writes:

How is it, I wondered, that immigrants from more than 100 countries speaking more than 170 languages can coexist in relative peace and harmony, while European cities like Paris, Frankfurt and Amsterdam have far greater difficulty integrating their racial, ethnic and religious groups?

Wonder what he has discovered about the Big Apple? Read Helmreich’s conclusions in the full Daily News article. You can read Chapter One here and tweet your thoughts to us using #NYNobodyKnows.

In Princeton, our fingers are crossed for an end to the cold and a start to spring. With the return to the outdoors on our minds, we present one of our new titles, Ten Thousand BirdsThis new book by Tim Birkhead, Jo Wimpenny & Bob Montgomerie provides a thoroughly engaging and authoritative history of modern ornithology, tracing how the study of birds has been shaped by a succession of visionary and often-controversial personalities, and by the unique social and scientific contexts in which these extraordinary individuals worked. The New Scientist has published a review of Ten Thousand Birds. Adrian Barnett calls the book “lovingly well-researched and beautifully written..” as well as “..definitive, absorbing and highly recommended.” You can preview this beautifully illustrated book here.

Looking for your weekly political science fix? We have a book for you. Why do democracies keep lurching from success to failure? The current financial crisis is just the latest example of how things continue to go wrong, just when it looked like they were going right. In The Confidence Trap, a wide-ranging, original, and compelling book, David Runciman tells the story of modern democracy through the history of moments of crisis, from the First World War to the economic crash of 2008. A global history with a special focus on the United States, The Confidence Trap examines how democracy survived threats ranging from the Great Depression to the Cuban missile crisis, and from Watergate to the collapse of Lehman Brothers. Check out the reviews of The Confidence Trap in the the Sydney Morning Herald and the Tablet. John Keane, of the Sydney Morning Herald, writes that “Runciman is a good writer and brave pioneer….The picture he sketches is agreeably bold.” The Tablet‘s Chris Patten states that the book is ‘..excellent and interesting..’ as well as  ‘…admirable and very well written…’ Want to read more? You can view the introduction here.

If you have been following our News of the World series, then you are familiar with Angela Stent, a former officer on the National Intelligence Council and the author of The Limits of Partnership. This new book offers a riveting narrative on U.S.-Russian relations since the Soviet collapse and on the challenges ahead. It reflects the unique perspective of an insider who is also recognized as a leading expert on this troubled relationship.

New this week, Professor Stent sits down with PBS Newshour and the Economist to discuss her views of the tense relationship between the U.S. and Russia as well as her personal interactions with Russia’s President Vladimir Putin. Check out these two videos:

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The Mystery of Snowfall Explained

The view from my backyard.

We’re still in the midst of a blizzard — indeed Princeton University Press is actually closed for the day as we huddle down at home with 8-10 inches and counting on the ground. But what better time to share this opinion piece from Ian Roulstone, meteorologist and author of Invisible in the Storm. While we’re waiting for an opportunity to get out there and shovel, we hope you will enjoy this article about the strange world of snowfall prediction and why it can’t be more accurate:

A snow-covered landscape is one of the classic images showcasing the beauty of weather on Earth. We are awed by the grandeur of white-capped mountains and the almost magical quality of snow-covered trees. We are also frustrated when the tempests of winter reach far and wide, striking as they have done this year in America’s southern states.

When it comes to forecasting the likelihood of a blizzard, the weather anchors know what to say. But when asked to predict how much snow will actually accumulate, they will give estimates. Why?

Read the rest of the story at CNN.com.

“Tea, Earl Gray, Hot” or the most energy ineffecient cuppa ever

This is crossposted from Chuck Adler’s new blog called Wizards, Aliens, and Starships where he will be posting about physics and math found in our favorite science fiction and fantasy tv shows, films, and books. Here, he reveals the most inefficient way to make a cup of tea.

Sometimes the best things in life are the simplest ones. Perhaps my favorite holiday gift ever was an electric kettle, a device whose only purpose in life is to boil water — but boil it efficiently, in a fraction of the time it would take for a kettle on the stove, and for a fraction of the energy, too. It’s simplicity itself — it has a coil which a current runs through. The coil gets hot, heats water in a chamber sitting above it, and voila! Boiling water. By my estimates, the electricity costs are about a tenth to a fifth of a cent for every cup of tea I brew.

The 23rd-century designers of the USS Enterprise seem to have lost this technology. To get a cup of tea, Captain Jean-Luc Picard stands next to a little box in his room, says “Tea, Earl Gray, hot”, and a cup of tea is beamed in. It seems to be an offshoot of transporter technology: you’re either beaming a cup made before from somewhere else, or assembling it whole from “pure energy” (whatever that means.) Either way, it seems to be a damn-fool way to make a cuppa.

E=mc squared, right? Each kilogram of matter takes 90,000 trillion joules of energy to create. The water in a cup of tea has a mass of about one-third of a kilo, so this is 30,000 trillion joules. But no technology is perfect: if the replicator is only 99.99% efficient, we are wasting 30 trillion joules into heat – enough to heat 100 million kilograms of water for tea… Just why are we doing it this way, again?

For more math and physics from Star Trek, Harry Potter, Dresden Files, 2001: A Space Odyssey, and more, check out Chuck’s new book: Wizards, Aliens, and Starships: Physics and Math in Fantasy and Science Fiction

Interested in Einstein?

EVENT

On Wednesday 29th January, A.Douglas Stone will be giving a talk at Blackwell’s Bookshop, Oxford, one of Britain’s best loved and most famous bookshops.

Einstein’s development of Quantum theory has not really been appreciated before. Now A.Douglas Stone reveals how he was actually one of the most important pioneers in the field.  Einstein himself famously rejected Quantum mechanics with his “God does not play dice” theory, yet he actually thought more about atoms and molecules than he did about relativity. Stone’s book ‘Einstein and the Quantum‘, which was published in November by Princeton University Press, outlines Einstein’s personal struggle with his Quantum findings as it went against his belief in science as something eternal and objective. Professor Stone will be happy to take questions and sign copies at the end of his talk.

Wednesday, January 29th at 19:00

Tickets cost £3 and are available from Blackwell’s Customer Service desk in the shop; by telephoning 01865 333623; by emailing events.oxford@blackwell.co.uk

New Mathematics Catalog!

Be among the first to browse and download our new mathematics catalog!

Of particular interest is Undiluted Hocus-Pocus: The Autobiography of Martin Gardner. Gardner takes readers from his childhood in Oklahoma to his college days at the University of Chicago, his service in the navy, and his varied and wide-ranging professional pursuits. Before becoming a columnist for Scientific American, he was a caseworker in Chicago during the Great Depression, a reporter for the Tulsa Tribune, an editor for Humpty Dumpty, and a short-story writer for Esquire, among other jobs. Gardner shares colorful anecdotes about the many fascinating people he met and mentored, and voices strong opinions on the subjects that matter to him most, from his love of mathematics to his uncompromising stance against pseudoscience. For Gardner, our mathematically structured universe is undiluted hocus-pocus—a marvelous enigma, in other words. Undiluted Hocus-Pocus offers a rare, intimate look at Gardner’s life and work, and the experiences that shaped both.

Also be sure to note Wizards, Aliens, and Starships: Physics and Math in Fantasy and Science Fiction by Charles L. Adler. From teleportation and space elevators to alien contact and interstellar travel, science fiction and fantasy writers have come up with some brilliant and innovative ideas. Yet how plausible are these ideas—for instance, could Mr. Weasley’s flying car in the Harry Potter books really exist? Which concepts might actually happen, and which ones wouldn’t work at all? Wizards, Aliens, and Starships delves into the most extraordinary details in science fiction and fantasy–such as time warps, shape changing, rocket launches, and illumination by floating candle—and shows readers the physics and math behind the phenomena.

And don’t miss out on Beautiful Geometry by Eli Maor and Eugen Jost. If you’ve ever thought that mathematics and art don’t mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important and beautiful branches of mathematics.

Even more foremost titles in mathematics can be found in the catalog. You may also sign up with ease to be notified of forthcoming titles at http://press.princeton.edu/subscribe/. Your e-mail address will remain confidential!

If you’re heading to the Joint Mathematics Meeting in Baltimore, MD, January 15th-18th, come visit us at booth 407. We’ll be hosting the following book signings:

The 5 Elements of Effective Thinking, Edward B. Burger and Michael Starbird
Wednesday, January 15th 4:30-5:30 p.m.

Wizards, Aliens, and Starships: Physics and Math in Fantasy and Science Fiction, Charles L. Adler
Thursday, January 16th 11:00 a.m.-12:00 p.m.

Also stop by 629, the Martin Gardner Centennial Booth. Staffed by a team of enthusiasts who have long been inspired by Gardner, there will be interactive activities and different handouts and puzzles to enjoy each day. Don’t miss ”Martin Gardner’s Outreach in His Centennial Year: Mathematics Awareness Month 2014,” a short talk by Colm Mulcahy, Bruce Torrence, and Eve Torrence, Saturday, January 18th at 1:00 p.m. in Convention Center room 346.

Follow @MGardner100th on Twitter for more updates throughout the year, and #JMM14 and @PrincetonUnivPress for updates and information on our new and forthcoming titles throughout the meeting. See you there!