## Saturday, December 14, 2013

## Friday, December 28, 2012

### Ramanujan Proved Right After 90 Years

Ramanujan believed that 17 new functions he discovered were "mock modular forms" that looked like theta functions when written out as an infinte sum (their coefficients get large in the same way), but weren't super-symmetric. [...] Emory University mathematician Ken Ono and his team recently proved that these functions indeed mimicked modular forms, but don't share their defining characteristics, such as super-symmetry.

http://www.foxnews.com/science/2012/12/28/mathematician-century-old-secrets-unlocked/

http://www.foxnews.com/science/2012/12/28/mathematician-century-old-secrets-unlocked/

## Wednesday, October 10, 2012

### 2012 Nobel in Physics

The Nobel Prize in Physics 2012 was awarded jointly to Serge Haroche and David J. Wineland

*"for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems"*http://www.nobelprize.org/nobel_prizes/physics/laureates/2012/

## Tuesday, June 19, 2012

### Voyager at Edge of Solar System

Voyager 1 has entered a region of space with a markedly higher flow of charged particles from beyond our solar system. Mission scientists suspect this increased flow indicates that the spacecraft — currently 11.1 billion miles from Earth — may be poised to cross the boundary into interstellar space.

http://www.foxnews.com/scitech/2012/06/18/nasa-voyager-1-spacecraft-nears-interstellar-space/

http://www.foxnews.com/scitech/2012/06/18/nasa-voyager-1-spacecraft-nears-interstellar-space/

## Sunday, January 08, 2012

### A First Course in Loop Quantum Gravity

Same idea as Zwiebach's A First Course in String Theory. I highly recommend both books, whichever side of the intellectual divide you're on, or even if (particularly if?) you are agnostic on the question of the correct way to quantize gravity.

## Saturday, December 31, 2011

### Graduate Physics Education ... Free!

Perimeter Scholars International

The 2011-2012 PSI course series is a condensed program of first and second year graduate physics study including quantum field theory and conformal field theory, quantum information, general relativity, cosmology, the standard model and particle theory, mathematical physics, statistical mechanics and condensed matter physics, string theory, and quantum gravity.

Perimeter Institute Recorded Seminar Archive

The PIRSA website contains the usual collection of advanced graduate courses (together with some unusual but noteworthy choices):

PIRSA:C11003 - Higher Spin Theories

PIRSA:C10018 - Space-time, Quantum Mechanics and Scattering Amplitudes

PIRSA:C10008 - Cosmology Mini Course

PIRSA:C10003 - Quantum Field Theory for Cosmology

PIRSA:C10002 - Foundations and Interpretation of Quantum Theory

PIRSA:C09056 - Quantum Spin Simulations

PIRSA:C09020 - Introduction to Effective Field Theory

PIRSA:C09019 - General Relativity for Cosmology

PIRSA:C08019 - Quantum Field Theory

PIRSA:C08018 - Astrophysics & Cosmology through Problems

PIRSA:C08002 - Advanced General Relativity

PIRSA:C08001 - New Horizons In Fundamental Physics

PIRSA:C07007 - Advanced Topics in Cosmology

PIRSA:C07002 - Introduction to Quantum Groups

PIRSA:C06014 - Introduction to Quantum Information and Computation

PIRSA:C06012 - The Standard Model and Quantum Field Theory

PIRSA:C06001 - Introduction to Quantum Gravity

PIRSA:C05001 - Interpretation of Quantum Theory

as well as a slew of specialized courses on narrower topics.

The 2011-2012 PSI course series is a condensed program of first and second year graduate physics study including quantum field theory and conformal field theory, quantum information, general relativity, cosmology, the standard model and particle theory, mathematical physics, statistical mechanics and condensed matter physics, string theory, and quantum gravity.

Perimeter Institute Recorded Seminar Archive

The PIRSA website contains the usual collection of advanced graduate courses (together with some unusual but noteworthy choices):

PIRSA:C11003 - Higher Spin Theories

PIRSA:C10018 - Space-time, Quantum Mechanics and Scattering Amplitudes

PIRSA:C10008 - Cosmology Mini Course

PIRSA:C10003 - Quantum Field Theory for Cosmology

PIRSA:C10002 - Foundations and Interpretation of Quantum Theory

PIRSA:C09056 - Quantum Spin Simulations

PIRSA:C09020 - Introduction to Effective Field Theory

PIRSA:C09019 - General Relativity for Cosmology

PIRSA:C08019 - Quantum Field Theory

PIRSA:C08018 - Astrophysics & Cosmology through Problems

PIRSA:C08002 - Advanced General Relativity

PIRSA:C08001 - New Horizons In Fundamental Physics

PIRSA:C07007 - Advanced Topics in Cosmology

PIRSA:C07002 - Introduction to Quantum Groups

PIRSA:C06014 - Introduction to Quantum Information and Computation

PIRSA:C06012 - The Standard Model and Quantum Field Theory

PIRSA:C06001 - Introduction to Quantum Gravity

PIRSA:C05001 - Interpretation of Quantum Theory

as well as a slew of specialized courses on narrower topics.

*(This list has been updated to include all courses of interest through 12/31/2011.)*## Tuesday, October 11, 2011

## Tuesday, October 04, 2011

### 2011 Nobel Prize in Physics

The Nobel Prize in Physics 2011 was divided, one half awarded to Saul Perlmutter, the other half jointly to Brian P. Schmidt and Adam G. Riess

http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/

*"for the discovery of the accelerating expansion of the Universe through observations of distant supernovae*."http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/

## Friday, December 31, 2010

### University of Colorado at Colorado Springs Math Video Archive

http://www.uccs.edu/~math/vidarchive.html

Math 448- Mathematical Modeling - Dr. Radu Cascaval

Math 443- Ordinary Differential Equations - Dr. Radu Cascaval

Math 447- Applied Mathematics - Dr. Radu Cascaval

Math 442 - Optimization - Dr. Radu Cascaval

Math 414 - Modern Algebra - Dr. Gene Abrams

Math 533 - Real Analysis - Dr. Rinaldo Schinazi

Math 425 - Chaotic Dynamical Systems - Dr. Greg Morrow

Math 432 - Modern Analysis II - Dr. Bob Carlson

Math 431 - Modern Analysis I - Dr. Rinaldo Schinazi

Math 483 - Linear Statistical Models - Dr. Greg Morrow

Math 535 - Applied Functional Analysis - Dr. Greg Morrow

**Spring Semester 2010**Math 448- Mathematical Modeling - Dr. Radu Cascaval

**Spring Semester 2009**Math 443- Ordinary Differential Equations - Dr. Radu Cascaval

**Fall Semester 2008**Math 447- Applied Mathematics - Dr. Radu Cascaval

**Summer Semester 2008**Math 442 - Optimization - Dr. Radu Cascaval

**Fall Semester 2007**Math 414 - Modern Algebra - Dr. Gene Abrams

Math 533 - Real Analysis - Dr. Rinaldo Schinazi

**Summer Semester 2007**Math 425 - Chaotic Dynamical Systems - Dr. Greg Morrow

**Spring Semester 2007**Math 432 - Modern Analysis II - Dr. Bob Carlson

**Fall Semester 2006**Math 431 - Modern Analysis I - Dr. Rinaldo Schinazi

**Summer Semester 2006**Math 483 - Linear Statistical Models - Dr. Greg Morrow

**Spring Semester 2006**Math 535 - Applied Functional Analysis - Dr. Greg Morrow

### ICTP Diploma Programs in Math & Physics

**High Energy Physics**

Relativistic Quantum Mechanics

Quantum Electrodynamics

Quantum Field Theory

Lie Groups and Lie Algebras

Introduction to Particle Physics

General Relativity

The Standard Model

Susy Field Theory

String Theory

**Condensed Matter Physics**

Advanced Statistical Mechanics

Advanced Quantum Mechanics

Many Body Physics

Solid State Physics

**Graduate Mathematics**

Partial Differential Equations

Topology

Algebraic Topology

Abstract Algebra

Complex Analysis

Real Analysis I and Real Analysis II

Functional Analysis I and Functional Analysis II

Differential Equations and Dynamical Systems

Ergodic Theory

Differential Geometry

Algebraic Geometry

Probability Theory

### Online Physics Video Courses

Everybody knows about MIT OCW and Stanford on iTunes, but here are a few less well known video lectures on advanced physics topics.

Classical Mechanics at McGill University

Computational Physics at Oregon State University

Foundations of Theoretical Physics at USC

General Relativity at McGill University

Quantum Physics A, B & C at UCSD

Mathematical Physics I & II at University of New Mexico

Quantum Mechanics I & II at University of New Mexico

Quantum Field Theory I & II at University of New Mexico

Classical Mechanics at McGill University

Computational Physics at Oregon State University

Foundations of Theoretical Physics at USC

General Relativity at McGill University

Quantum Physics A, B & C at UCSD

Mathematical Physics I & II at University of New Mexico

Quantum Mechanics I & II at University of New Mexico

Quantum Field Theory I & II at University of New Mexico

## Wednesday, December 22, 2010

### Here's someone else who shouldn't be trying to do math

http://www.thebigquestions.com/2010/12/22/a-big-answer-2/

The correct answer is 1/2. In statistical notation, he is asking us to calculate E[G]/E[B+G], the expected proportion of females in the total population. However, he turns it into the different question E[G/(B+G)], the expected proportion of females in an average family, which is not generally equal to the first expression (since families are of different sizes) and which in this case gives the incorrect answer of 30.6%. The guy is impervious to all the good arguments that have been posted to his blog pointing out his error.

His argument is exactly the same as if headed down to the roulette tables in Vegas and placed bets on black, just making sure that at each session I stop when black hits. According to his "math", that strategy should provide a 69.4% win rate (slightly less once we account for 0 and 00, but still well above 50%). A sure-fire way to beat the house!

The correct answer is 1/2. In statistical notation, he is asking us to calculate E[G]/E[B+G], the expected proportion of females in the total population. However, he turns it into the different question E[G/(B+G)], the expected proportion of females in an average family, which is not generally equal to the first expression (since families are of different sizes) and which in this case gives the incorrect answer of 30.6%. The guy is impervious to all the good arguments that have been posted to his blog pointing out his error.

His argument is exactly the same as if headed down to the roulette tables in Vegas and placed bets on black, just making sure that at each session I stop when black hits. According to his "math", that strategy should provide a 69.4% win rate (slightly less once we account for 0 and 00, but still well above 50%). A sure-fire way to beat the house!

## Tuesday, November 30, 2010

### String Theory Tested, Fails Black Hole Predictions

Back in 2006 there was a lot of talk of testing String Theory. Well, today CERN released a statement for the Compact Muon Solenoid Experiment. The short of it is simply that as far as they could tell, 'No experimental evidence for microscopic black holes has been found.' The long statement indicates that since the highly precise CMS detector found no spray of sub-atomic particles of normal matter while LHC smashed particles together, the hypothesis by string theory that micro black holes would be formed and quickly evaporated in this experiment was incorrect. These tests have given the team confidence to say that they can exclude a 'variety of theoretical models' for the cases of black holes with a mass of 3.5-4.5 TeV. While you may not be able to run around claiming that string theory is dead and disproved, evidently there are some adjustments that need to be made. (Source: Slashdot)

## Saturday, October 09, 2010

### 2010 Nobel in Physics

http://nobelprize.org/nobel_prizes/physics/laureates/2010/

The Nobel Prize in Physics 2010 was awarded jointly to Andre Geim and Konstantin Novoselov

The Nobel Prize in Physics 2010 was awarded jointly to Andre Geim and Konstantin Novoselov

*"for groundbreaking experiments regarding the two-dimensional material graphene."*## Thursday, September 30, 2010

### World's Worst Physicist?

University of Central Florida physics professor Costas Efthimiou's work debunks pseudoscientific ideas, such as vampires and zombies, in an attempt to enhance public literacy. Legend has it that vampires feed on human blood and once bitten a person turns into a vampire and starts feasting on the blood of others. Efthimiou's debunking logic: On Jan 1, 1600, the human population was 536,870,911. If the first vampire came into existence that day and bit one person a month, there would have been two vampires by Feb. 1, 1600. A month later there would have been four, and so on. In just two-and-a-half years the original human population would all have become vampires with nobody left to feed on. If mortality rates were taken into consideration, the population would disappear much faster. Even an unrealistically high reproduction rate couldn't counteract this effect.

Wow! Leaving aside that his work debunking pseudoscience is NOT what we as a society expect our well-paid physicists to be working on, let's look at his own pseudoscientific work...

536,870,911 - really? and he knows this how? Has he ever heard of significant digits?

"once bitten a person turns into a vampire" - false; anybody with even a passing understanding of the vampire myth knows this to be wrong; dude needed to do some basic research

He's essentially assuming (a) vampires are immortal and (b) vampires must feed at least once a month on a human. These assumptions are mutually contradictory. If vampires were immortal then they would not have to feed every month to stay alive. If they must feed every month to stay alive then the well-known predator-prey model (based on the Lotka-Volterra differential equation) can predict all sorts of end-states, including extinction of humans, extinction of vampires, equilibrium, oscillation, or chaotic swings in the vampire and human populations, depending on the various parameters that can be used in the equations. Seriously, what on earth was this guy thinking when he tackled this problem? I wonder how long he worked on his "solution"? I've seen better thought-out logic on freshman physics papers.

Actually, on second thought, maybe it's better that this guy isn't doing physics. That could be dangerous!

Wow! Leaving aside that his work debunking pseudoscience is NOT what we as a society expect our well-paid physicists to be working on, let's look at his own pseudoscientific work...

536,870,911 - really? and he knows this how? Has he ever heard of significant digits?

"once bitten a person turns into a vampire" - false; anybody with even a passing understanding of the vampire myth knows this to be wrong; dude needed to do some basic research

He's essentially assuming (a) vampires are immortal and (b) vampires must feed at least once a month on a human. These assumptions are mutually contradictory. If vampires were immortal then they would not have to feed every month to stay alive. If they must feed every month to stay alive then the well-known predator-prey model (based on the Lotka-Volterra differential equation) can predict all sorts of end-states, including extinction of humans, extinction of vampires, equilibrium, oscillation, or chaotic swings in the vampire and human populations, depending on the various parameters that can be used in the equations. Seriously, what on earth was this guy thinking when he tackled this problem? I wonder how long he worked on his "solution"? I've seen better thought-out logic on freshman physics papers.

Actually, on second thought, maybe it's better that this guy isn't doing physics. That could be dangerous!

## Wednesday, August 11, 2010

### Peer review

Breakthroughs from the second tier

Peer review isn't perfect - meet 5 high-impact papers that should have ended up in bigger journals.

by the Scientist staff

I hate your paper

Many say the peer review system is broken. Here's how some journals are trying to fix it.

by Jef Akst

Peer review and the age of aquarius

It's time to reinvent the system that validates scientific discovery.

by Sarah Greene

Peer pressure

What should we do with peer review? Tell us in our new poll.

by Richard Grant

Peer review isn't perfect - meet 5 high-impact papers that should have ended up in bigger journals.

by the Scientist staff

I hate your paper

Many say the peer review system is broken. Here's how some journals are trying to fix it.

by Jef Akst

Peer review and the age of aquarius

It's time to reinvent the system that validates scientific discovery.

by Sarah Greene

Peer pressure

What should we do with peer review? Tell us in our new poll.

by Richard Grant

## Thursday, April 08, 2010

## Tuesday, April 06, 2010

### My nominee for the decade's worst scientific reporting

http://www.foxnews.com/scitech/2010/04/05/freaky-physics-proves-parallel-universes/?test=faces

2) The "time travel to the future and back again" idea is completely idiotic. I find it hard to believe that Richard Gott actually said that. My bet is the reporter got it wrong. (If not, then shame on Richard Gott.)

3) None of this has anything to do with the actual discovery, which is that researchers at UCSB appear to have found a macro-system that exhibits quantum superposition.

4) The headline is that this proves parallel universes exist. I'm still trying to figure out wtf that even means in the context of this story.

Wolf says that time - at least in quantum mechanics - doesn't move straight like an arrow. It zig-zags, and he thinks it may be possible to build a machine that lets you bend time. Consider Sergei Krikalev, the Russian astronaut who flew six space missions. Richard Gott, a physicist at Princeton University, says Krikalev aged 1/48th of a second less than the rest of us because he orbited at very high speeds. And to age less than someone means you've jumped into the future - you did not experience the same present. In a sense, he says, Krikalev time-traveled to the future - and back again!1) Writer switches from QM to relativity in a completely unwarranted manner.

2) The "time travel to the future and back again" idea is completely idiotic. I find it hard to believe that Richard Gott actually said that. My bet is the reporter got it wrong. (If not, then shame on Richard Gott.)

3) None of this has anything to do with the actual discovery, which is that researchers at UCSB appear to have found a macro-system that exhibits quantum superposition.

4) The headline is that this proves parallel universes exist. I'm still trying to figure out wtf that even means in the context of this story.

## Tuesday, March 30, 2010

## Thursday, February 11, 2010

### Get your geek on!

For those (like myself) who wanted to play with Mathematica but couldn't justify the price ... there's now Mathematica Home Edition!!

http://www.wolfram.com/products/mathematicahomeedition/qa.html

(The functionality is exactly the same as in the full edition; it's just the licensing that is more restricted.)

http://www.wolfram.com/products/mathematicahomeedition/qa.html

(The functionality is exactly the same as in the full edition; it's just the licensing that is more restricted.)

## Monday, January 04, 2010

## Saturday, October 10, 2009

### Undergraduate Physics Education ... Free!

iTunes U has a free downloadable course by Stanford's Leonard Susskind called The Theoretical Minimum. It consists of 57 video lectures covering almost an entire undergraduate physics education - Classical Mechanics, Quantum Mechanics, Statistical Mechanics, Special Relativity & Electromagnetism, General Relativity, even Cosmology.

## Tuesday, October 06, 2009

### 2009 Nobel in Physics

This year's Nobel Prize in Physics is awarded for two scientific achievements that have helped to shape the foundations of today's networked societies. They have created many practical innovations for everyday life and provided new tools for scientific exploration.

In 1966, Charles K. Kao made a discovery that led to a breakthrough in fiber optics. He carefully calculated how to transmit light over long distances via optical glass fibers. With a fiber of purest glass it would be possible to transmit light signals over 100 kilometers, compared to only 20 meters for the fibers available in the 1960s.

In 1969 Willard S. Boyle and George E. Smith invented the first successful imaging technology using a digital sensor, a Charge-Coupled Device. Digital photography has become an irreplaceable tool in many fields of research. The CCD has provided new possibilities to visualize the previously unseen. It has given us crystal clear images of distant places in our universe as well as the depths of the oceans.

In 1966, Charles K. Kao made a discovery that led to a breakthrough in fiber optics. He carefully calculated how to transmit light over long distances via optical glass fibers. With a fiber of purest glass it would be possible to transmit light signals over 100 kilometers, compared to only 20 meters for the fibers available in the 1960s.

In 1969 Willard S. Boyle and George E. Smith invented the first successful imaging technology using a digital sensor, a Charge-Coupled Device. Digital photography has become an irreplaceable tool in many fields of research. The CCD has provided new possibilities to visualize the previously unseen. It has given us crystal clear images of distant places in our universe as well as the depths of the oceans.

## Wednesday, August 26, 2009

### Loop Quantum Gravity

I attended a lecture today by Professor Abhay Ashtekar (of the Institute for Gravitation at Penn State University) about Loop Quantum Gravity at Georgia Tech. Apparently recent work has made considerable progress towards solving the infrared problem (i.e., proving agreement of LQG with classical General Relativity at low densities). Also, a density cutoff (of approximately 41% of the Planck density) has appeared naturally out of the formalism, instead of being imposed arbitrarily as an additional condition.

Slides covering material very similar to his Georgia Tech lecture can be found at

http://universe2009.obspm.fr/fichiers/Recherche/Friday-3/ashtekar.pdf

Possible ramifications of this work:

1) Help resolve the well-known horizon problem

2) Provide a mechanism for propagation of "seeds" for creating structure in the universe

3) Predicts a period of super-inflation, which could have implications for gravitational waves

4) Cause quantum corrections to the cosmic microwave backround radiation

#3 and #4 might provide testable predictions unlike superstring theory

Slides covering material very similar to his Georgia Tech lecture can be found at

http://universe2009.obspm.fr/fichiers/Recherche/Friday-3/ashtekar.pdf

Possible ramifications of this work:

1) Help resolve the well-known horizon problem

2) Provide a mechanism for propagation of "seeds" for creating structure in the universe

3) Predicts a period of super-inflation, which could have implications for gravitational waves

4) Cause quantum corrections to the cosmic microwave backround radiation

#3 and #4 might provide testable predictions unlike superstring theory

## Saturday, August 01, 2009

## Thursday, April 23, 2009

## Tuesday, April 21, 2009

## Monday, December 15, 2008

## Thursday, December 11, 2008

### Baez's Classical Mechanics Website

As long as I'm posting these Goldstein solutions, I should definitely point out one of the best classical mechanics websites out there.

http://math.ucr.edu/home/baez/classical/

http://math.ucr.edu/home/baez/classical/

## Wednesday, December 10, 2008

## Tuesday, October 07, 2008

### 2008 Nobel Prize in Physics

Yoichiro Nambu, who discovered the mechanism of spontaneous symmetry breaking, and Makoto Kobayashi and Toshihide Maskawa, who discovered the origin of the broken symmetry that predicts the existence of at least three families of quarks in nature, are announced as winners of the 2008

**Nobel Prize in Physics**.## Wednesday, September 10, 2008

## Saturday, May 17, 2008

### The Monty Hall Problem

Let's start with a very standard probability question (the Monty Hall problem) that was put to Marilyn vos Savant.

Q: Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?

A: Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here's a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what's behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You'd switch to that door pretty fast, wouldn't you?

Now, I understand that the immediate instinct is to think that door #1 and door #2 each have a 50-50 chance of having the car. However, if you think about it for a few minutes (and I would certainly expect you to do so before writing Ms. vos Savant to tell her she's wrong), you should pretty quickly realize that the host will always open the door from 2,3 that does NOT have a car, and therefore the probability of the remaining door is 2/3 as opposed to 1/3 for the original door #1. I would certainly expect a PhD in math to come to this conclusion in short order. Even if they couldn't do it on their own, this is a standard problem covered in dozens of introductory statistics textbooks (hell, it's so well understood it's got a freakin' name), so I would at least expect a PhD in math to LOOK IT UP! However, I guess my expectations would be sadly shattered, not once but nine times (the names have been bolded to call out the guilty)...

Since you seem to enjoy coming straight to the point, I'll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. As a professional mathematician, I'm very concerned with the general public's lack of mathematical skills. Please help by confessing your error and in the future being more careful. -- Robert Sachs, Ph.D., George Mason University

DUH, we're not talking about quantum tunnelling.

You blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I'll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. There is enough mathematical illiteracy in this country, and we don't need the world's highest IQ propagating more. Shame! -- Scott Smith, Ph.D., University of Florida

And you have a 0% chance of being correct with this reasoning. I didn't know so much of the mathematical illiteracy in this country resided in mathematics faculties.

May I suggest that you obtain and refer to a standard textbook on probability before you try to answer a question of this type again? -- Charles Reid, Ph.D., University of Florida

Preferably not the one that he uses to teach.

I am sure you will receive many letters on this topic from high school and college students. Perhaps you should keep a few addresses for help with future columns. -- W. Robert Smith, Ph.D., Georgia State University

And with future lectures at GSU.

You are utterly incorrect about the game show question, and I hope this controversy will call some public attention to the serious national crisis in mathematical education. If you can admit your error, you will have contributed constructively towards the solution of a deplorable situation. How many irate mathematicians are needed to get you to change your mind? -- E. Ray Bobo, Ph.D., Georgetown University

Apparently the necessary number of IRATE mathematicians is n where n>9. To get her to change her mind, she needed to hear from exactly 1 CORRECT mathematician.

Your answer to the question is in error. But if it is any consolation, many of my academic colleagues have also been stumped by this problem. -- Barry Pasternack, Ph.D., California Faculty Association

You're in error, but Albert Einstein earned a dearer place in the hearts of people after he admitted his errors. -- Frank Rose, Ph.D., University of Michigan

I have been a faithful reader of your column, and I have not, until now, had any reason to doubt you. However, in this matter (for which I do have expertise), your answer is clearly at odds with the truth. -- James Rauff, Ph.D., Millikin University

You made a mistake, but look at the positive side. If all those Ph.D.'s were wrong, the country would be in some very serious trouble. -- Everett Harman, Ph.D., U.S. Army Research Institute

Serious trouble indeed! What a sad state of affairs that not only can't these nine PhD's not get the correct answer on their own, but they can't even recognize the correct answer when it is put before them in excruciating detail. I am so sad for their students, more so than for the country!

[Thanks to WM for the link]

Q: Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?

A: Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here's a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what's behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You'd switch to that door pretty fast, wouldn't you?

Now, I understand that the immediate instinct is to think that door #1 and door #2 each have a 50-50 chance of having the car. However, if you think about it for a few minutes (and I would certainly expect you to do so before writing Ms. vos Savant to tell her she's wrong), you should pretty quickly realize that the host will always open the door from 2,3 that does NOT have a car, and therefore the probability of the remaining door is 2/3 as opposed to 1/3 for the original door #1. I would certainly expect a PhD in math to come to this conclusion in short order. Even if they couldn't do it on their own, this is a standard problem covered in dozens of introductory statistics textbooks (hell, it's so well understood it's got a freakin' name), so I would at least expect a PhD in math to LOOK IT UP! However, I guess my expectations would be sadly shattered, not once but nine times (the names have been bolded to call out the guilty)...

Since you seem to enjoy coming straight to the point, I'll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. As a professional mathematician, I'm very concerned with the general public's lack of mathematical skills. Please help by confessing your error and in the future being more careful. -- Robert Sachs, Ph.D., George Mason University

DUH, we're not talking about quantum tunnelling.

You blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I'll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. There is enough mathematical illiteracy in this country, and we don't need the world's highest IQ propagating more. Shame! -- Scott Smith, Ph.D., University of Florida

And you have a 0% chance of being correct with this reasoning. I didn't know so much of the mathematical illiteracy in this country resided in mathematics faculties.

May I suggest that you obtain and refer to a standard textbook on probability before you try to answer a question of this type again? -- Charles Reid, Ph.D., University of Florida

Preferably not the one that he uses to teach.

I am sure you will receive many letters on this topic from high school and college students. Perhaps you should keep a few addresses for help with future columns. -- W. Robert Smith, Ph.D., Georgia State University

And with future lectures at GSU.

You are utterly incorrect about the game show question, and I hope this controversy will call some public attention to the serious national crisis in mathematical education. If you can admit your error, you will have contributed constructively towards the solution of a deplorable situation. How many irate mathematicians are needed to get you to change your mind? -- E. Ray Bobo, Ph.D., Georgetown University

Apparently the necessary number of IRATE mathematicians is n where n>9. To get her to change her mind, she needed to hear from exactly 1 CORRECT mathematician.

Your answer to the question is in error. But if it is any consolation, many of my academic colleagues have also been stumped by this problem. -- Barry Pasternack, Ph.D., California Faculty Association

You're in error, but Albert Einstein earned a dearer place in the hearts of people after he admitted his errors. -- Frank Rose, Ph.D., University of Michigan

I have been a faithful reader of your column, and I have not, until now, had any reason to doubt you. However, in this matter (for which I do have expertise), your answer is clearly at odds with the truth. -- James Rauff, Ph.D., Millikin University

You made a mistake, but look at the positive side. If all those Ph.D.'s were wrong, the country would be in some very serious trouble. -- Everett Harman, Ph.D., U.S. Army Research Institute

Serious trouble indeed! What a sad state of affairs that not only can't these nine PhD's not get the correct answer on their own, but they can't even recognize the correct answer when it is put before them in excruciating detail. I am so sad for their students, more so than for the country!

[Thanks to WM for the link]

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