Subcribe

The Magical Mathematics of Numb3rs


Numb3rs is a television show that ran for six seasons on CBS from 2005 to 2010 about FBI agent Don Eppes and his brother Charles, a child math prodigy turned math professor at CalSci (a thinly disguised Caltech), who fight crime with mathematics in a sunny, smog-free TV version of Los Angeles filled with an astonishing number of extremely attractive young women. All six seasons are now available on DVD. Numb3rs features some real mathematics used in solving some real crimes as well as pure science fiction. In many respects, Numb3rs is a techno-thriller that features a mix of real present-day technology, advanced technology that may exist, and technology and mathematics that might plausibly exist in the near future. Mathematics and science is especially well integrated into many episodes in the first and second seasons of the show. Unlike over-the-top science fiction shows like Eureka, a viewer could believe that Numb3rs is a realistic presentation of mathematics and science used in crime fighting and other applications today.

David Krumholtz (plays Charlie Eppes in Numb3rs)

Actor David Krumholtz (Charlie Eppes in Numb3rs)

Real life mathematicians including Caltech statistics professor Gary Lorden consulted for the show. Gary Lorden is listed in the credits for each episode as “Math Consultant”. In later seasons, Stephen Wolfram’s Wolfram Research also provided consulting advice to the series. There are scenes with references to Mathematica, Wolfram’s flagship product, and close-up shots of Wolfram’s magnum opus A New Kind of Science on Charlie Eppes desk. Wolfram also has a Caltech connection; he received his Ph.D. in Physics from Caltech in 1979. Gary Lorden and fellow mathematician Keith Devlin published a popular book The Numbers Behind Numb3rs: Solving Crime with Mathematics in 2007: “A companion to the hit CBS crime series Numb3rs presents the fascinating ways mathematics is used to fight real-life crime.” The shadowy National Security Agency (NSA), probably the largest patron of mathematics and mathematicians in the United States and the world, makes several appearances in Numb3rs.

Milikan Library Caltech

Millikan Library at Caltech (appears often in Numb3rs)

CBS, Texas Instruments (a leading maker of digital signal processor or DSP chips), and the National Council of Teachers of Mathematics (NCTM) developed the “We All Use Math Every Day” initiative, sometimes abbreviated WAUMED, to inspire students to achieve more in math by showing how the subject is relevant to their lives:

Using the hit CBS television show, Numb3rs, the “We All Use Math Every Day” initiative provides free classroom activities online at cbs.com/Numb3rs that help students understand how the math they are learning in the classroom applies to the real world. The activities explore the math derived from the concepts used to solve cases in the FBI crime-solving show.

The show used the “We All Use Math Every Day” tagline in the opening introduction to the show in the first and second seasons.


How Realistic is Numb3rs?

Although explicitly fiction, in many respects Numb3rs paints a picture of mathematics and science that is similar to ostensibly factual popular science such as Scientific American articles, PBS/Nova video programs, Congressional testimony by leading scientists, and informal discussions at fundraising cocktail parties — unless the scientists or mathematicians are in the rare and unusual position of having to explain an obvious failure to a lay audience:

“Well, Senator, as everyone knows, science is a risky enterprise. Eighty to ninety percent of our research projects fail. Surely your staff briefed you on that; the proposal committee mentioned this clearly in italics in footnote 83 in Appendix C of the Proposal for the New Manhattan Project that Will Produce Miraculous Results by the Next Election.”

In several important respects, Numb3rs is very unrealistic. It is also the case that many people ranging from Silicon Valley executives trying to use mathematical methods for their businesses — for example, the current fad trying to use machine learning for recommendation engines in social networking and search businesses — to practicing scientists and engineers who one might think would know better often have expectations similar to what is portrayed in Numb3rs. These misconceptions almost certainly contributed in a major way to the multi-trillion dollar global housing bubble and crash through the widespread use of invalid mathematical models for the valuation of mortgage-backed securities. With business and political leaders seemingly floundering in the current economic difficulties, these misconceptions may wreak even greater havoc.

Before launching into a critique of Numb3rs, it is important to realize that there have been many successes in applied mathematics and mathematical software including impressive advances in video compression such as used by YouTube and Skype, audio compression such as the widely used MP3 standard, still image compression such as JPEG images, computer generated imagery in movies and video games, the Global Positioning System (GPS) that tells people where they are, and even speech recognition which is finally finding some practical use. Modern computers are extremely powerful, comparable to the supercomputers of previous decades; this power is mostly unused because we do not have the mathematics to put this power to practical use. Today’s powerful computers and new mathematics probably can solve or help solve many pressing problems, even trillion dollar problems such as energy shortages or major diseases such as cancer. Success in solving problems with mathematics requires realistic expectations, realistic planning, and adequate time and resources.

In The Numbers Behind Numb3rs (page 208), the mathematicians Keith Devlin and Gary Lorden, a full professor at Caltech, write:

One thing that is completely unrealistic is the time frame. In a fast-paced 41-minute episode, Charlie has to help his brother solve the case in one or two “television days.” In real life, the use of mathematics in crime detection is a long and slow process. (A similar observation is equally true for the use of laboratory-based criminal forensics as depicted in television series such as the hugely popular CSI franchise.)

Also unrealistic is that one mathematician would be familiar with so wide a range of mathematical and scientific techniques as Charlie. He is, of course, a television superhero — but that’s what makes him watchable. Observing a real mathematician in action would be no more exciting than watching a real FBI agent at work! (All that sitting in cars waiting for someone to exit a building, all those hours sifting through records or staring at computer screens… boring.)

It’s also true that Charlie seems able to gather masses of data in a remarkably short time. In real-life applications of mathematics, getting hold of the required data, and putting it into the right form for the computer to digest, can involve weeks or months of labor-intensive effort. And often the data one would need are simple not available.

(Emphasis Added)

In their discussion of the episode “Manhunt” (Airdate: May 13, 2005,The Numbers Behind Numb3rs, page. 78), in which Charlie Eppes uses Bayesian statistics to predict the actions and location of an escaped killer, Devlin and Lorden also write:

As is often the case with dramatic portrayals of mathematics or science at work, the length of time available to Charlie to produce his ranking of the reported sightings [of the escaped killer] is significantly shortened, but the idea of using the mathematically based technique of Bayesian analysis is sound.

(Emphasis Added)

Real-life mathematics and mathematical software development involves much more time, much more trial and error, much more debugging, and much more risk than depicted in Numb3rs. Scientists often claim an eighty to ninety percent failure rate in their research projects, frequently when explaining an obvious failure to disappointed graduate students, donors, policy makers, and others who expected more. Charlie Eppes almost never fails! There is historical evidence that the failure rate in genuine “breakthroughs” is higher, quite possibly ninety-nine percent or worse. Some of the mathematics that Charlie whips up in a few “television days” in the show would actually qualify as breakthroughs in real-life, notably some mathematics and algorithms for artificial intelligence and pattern recognition (see below). Historically, genuine breakthroughs have usually involved at least five years of effort when successful. To give a recent example, Grigoriy Perelman’s proof of the Poincare Conjecture took him at least seven years. There appear to have been about one hundred failed published attempts to prove the conjecture by mathematicians prior to Perelman’s success.

The reality is, in fact, worse than Devlin and Lorden concede in their book. Numb3rs has several episodes that portray artificial intelligence (AI), pattern recognition, machine learning, and similar technologies far superior to reality at the time the show aired (2005-2010) or even today (2011). In one episode, Charlie whips up an image/object recognition algorithm in a few hours to enable the NSA to track a yellow truck carrying a contraband missile guidance system through their satellite images of LA to a terrorist (“Finders Keepers,” Original Air Date: January 12, 2007). Similarly, remarkably effective face recognition algorithms play a role in several episodes. Many of Charlie’s AI and pattern recognition algorithms and the other pattern recognition technology shown in Numb3rs works much better than the real algorithms and math.

The Specter of 9/11

Numb3rs is a fast-paced entertaining show with sexy, idealistic, highly effective heroes and heroines. Although it is sometimes critical of security agencies like the CIA and powerful institutions like pharmaceutical companies, in many respects it is Hollywood product placement for the post 9/11 world of massive, expensive high-tech surveillance and security measures both overseas and at home — in which mathematics plays an important and growing role. It reminds one of President Eisenhower’s speeches during the 1950’s:

The worst to be feared and the best to be expected can be simply stated.

The worst is atomic war.

The best would be this: a life of perpetual fear and tension; a burden of arms draining the wealth and the labor of all peoples; a wasting of strength that defies the American system or the Soviet system or any system to achieve true abundance and happiness for the peoples of this earth.

Every gun that is made, every warship launched, every rocket fired signifies, in the final sense, a theft from those who hunger and are not fed, those who are cold and are not clothed. This world in arms is not spending money alone.

It is spending the sweat of its laborers, the genius of its scientists, the hopes of its children.

The cost of one modern heavy bomber is this: a modern brick school in more than 30 cities.

It is two electric power plants, each serving a town of 60,000 population.

It is two fine, fully equipped hospitals. It is some 50 miles of concrete highway.

We pay for a single fighter plane with a half million bushels of wheat.

We pay for a single destroyer with new homes that could have housed more than 8,000 people.

This, I repeat, is the best way of life to be found on the road the world has been taking.

This is not a way of life at all, in any true sense. Under the cloud of threatening war, it is humanity hanging from a cross of iron.

Chance for Peace (April 16, 1953)
President Dwight David Eisenhower (shortly after the death of Joseph Stalin)

President Dwight D. Eisenhower

President Dwight D. Eisenhower

Eisenhower and his advisers were no shrinking violets. They were well aware the world can be a nasty, dangerous place. They presided over a massive military buildup and controversial covert operations in Guatemala, Iran, Vietnam, and other countries. By the end of his Presidency Eisenhower and his advisers found that it was never enough. Even thousands of nuclear weapons, ships, tanks, spies, and what we now know was a massive lead over the Soviet Union was not enough to satisfy what he famously labeled the “military industrial complex” in his Farewell Address. Eisenhower found himself attacked by Republicans and Democrats alike for not spending even more money on guns and preparations for war!

Usama Bin Laden (FBI Wanted Poster)

Osama Bin Laden: The Trillion Dollar Man

Following the reported death of Osama Bin Laden, Andrea Millen Rich, writing in the libertarian Reason magazine, estimated the direct cost of getting Bin Laden at $1.1 trillion. Tim Fernholz and Jim Tankersley, writing in The Atlantic estimated the total cost at $3 trillion over fifteen years. Sam Stein of the Huffington Post, citing a Congressional Research Service report of March 29, 2011, put the cost at at least 1.283 trillion.

According to the United States Centers for Disease Control, the leading causes of death in the United States in the calendar year 2007 were:

Number of deaths for leading causes of death

* Heart disease: 616,067
* Cancer: 562,875
* Stroke (cerebrovascular diseases): 135,952
* Chronic lower respiratory diseases: 127,924
* Accidents (unintentional injuries): 123,706
* Alzheimer’s disease: 74,632
* Diabetes: 71,382
* Influenza and Pneumonia: 52,717
* Nephritis, nephrotic syndrome, and nephrosis: 46,448
* Septicemia: 34,828

All homicides, of which terrorist attacks are a small fraction even in 2001, do not make the top ten. In 2007, the Centers for Disease Control listed all homicides as the 15th leading cause of death:

All homicides

* Number of deaths: 18,361
* Deaths per 100,000 population: 6.1
* Cause of death rank: 15

It is worth noting that the US invasion of Iraq in 2003 resulted in a dramatic drop in Iraqi oil production, undoubtedly contributing substantially to the large increases in oil and energy prices in the last decade. So too the US invasion of Afghanistan in 2001 seems to have scuttled any chance of constructing a pipeline for natural gas from Turkmenistan to the Indian Ocean, also undoubtedly contributing to high energy prices.

It is difficult to improve on President Eisenhower’s words today. Bayesian statistical analyses that predict terrorist attacks, even if they work, don’t make up for dwindling supplies of inexpensive oil and natural gas. They don’t feed people. They don’t cure diseases like cancer or prevent heart attacks. How much more could have been and could still be accomplished if today’s powerful computers and new mathematics were applied to substantive problems such as energy, food, and health instead of the will-o’-the-wisp of perfect security or the pseudo-scientific financial engineering that helped cause the current Great Recession? Mathematicians, scientists, business leaders, and policy makers can do better than we have done.

Conclusion

Numb3rs is a fun, entertaining show. If you are a mathematician, it will probably make you feel great about your profession unless you are in the unfortunate position of dealing with an employer, client, investor, or funding agency that expects you to do what Charlie Eppes does in every episode of Numb3rs. Some of the math and science in Numb3rs is completely realistic. Some of the math is somewhat exaggerated. Some of the math is pure science fiction even though it generally seems very real and believable. As Devlin and Lorden admit in their book, the time frame is, in most cases, completely unrealistic.

The world is presently confronted with serious and worsening problems, possibly due to a dwindling supply of inexpensive oil and natural gas. The political and economic leadership of the world appears paralyzed and unable to deal with the problems, bickering over debt ceilings and other silliness. We do have vast unused resources in the computational power of hundreds of millions of computers and other devices. With the proper mathematics and creative thinking, we may be able to harness this power to resolve many of the current problems, without waiting for paralyzed governments or blundering Too Big To Fail banks to act wisely.

Most mathematics and mathematical software has been developed by individuals and small teams working over periods of several months to several years with total costs of tens of thousands to a few million dollars per project. Success requires realistic expectations about the size, scope, difficulty level, and risks of developing and implementing mathematics and mathematical software. In these difficult times, mathematicians and scientists must gain support for realistic projects that can find real solutions to our pressing problems, and honestly reject the fantasy elements of Numb3rs.

Suggested Reading/References
The Numbers Behind Numb3rs: Solving Crime with Mathematics
Keith Devlin, Ph.D. and Gary Lorden, Ph.D.
Penguin Books, New York, 2007

The Shadow Factory: The Ultra-Secret NSA from 9/11 to the Eavesdropping on America
James Bamford
Doubleday, New York, 2008

The Cost of Iraq, Afghanistan, and Other Global War on Terror Operations Since 9/11
Amy Belasco, Congressional Research Service, Washington, D.C, March 29, 2011

Credits
The picture of actor David Krumholtz at the Serenity Premiere is from Wikimedia Commons, licensed under the Creative Commons Attribution 2.0 Generic license.

This image was originally posted to Flickr by RavenU at http://flickr.com/photos/36330825119@N01/45967991. It was reviewed on 10:00, 30 April 2007 (UTC) by the FlickreviewR robot and confirmed to be licensed under the terms of the cc-by-2.0.

Millikan Library at Caltech Image from Wikimedia Commons.

Official Portrait of President Dwight D. Eisenhower, May 29, 1959

(from Wikipedia) This image is a work of an employee of the Executive Office of the President of the United States, taken or made during the course of the person’s official duties. As a work of the U.S. federal government, the image is in the public domain.

The image of Usama Bin Laden (Osama Bin Laden) is from the FBI Ten Most Wanted Poster.

© 2011 John F. McGowan

About the Author

John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing video compression and speech recognition technologies. He has extensive experience developing software in C, C++, Visual Basic, Mathematica, MATLAB, and many other programming languages. He is probably best known for his AVI Overview, an Internet FAQ (Frequently Asked Questions) on the Microsoft AVI (Audio Video Interleave) file format. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech). He can be reached at jmcgowan11@earthlink.net.


If you enjoyed this post, then make sure you subscribe
to our Newsletter and/or RSS Feed.


14 Responses to “The Magical Mathematics of Numb3rs”

  1. This post is getting some discussion at Hacker News. I’ll repeat my comment here:

    I have mixed feelings about this post on what is by far my favorite TV show. On the one hand, I think you’re spot on highlighting the aspects of Numb3rs that are unrealistic:

    * Time frame for both gathering data and performing analysis

    * The incredible depth and breadth of Charlie’s knowledge

    To enjoy the show, you simply have to think of Charlie as having superhuman math abilities and suspend your disbelief as if you were watching Spiderman or Superman.

    However, you also spend a good chunk of the post attempting to persuade readers that Numb3rs can be thought of as a propaganda vehicle for persuading the masses that a math-based surveillance society is good and necessary. I disagree.

    First, there are several episodes featuring poor ethics at the FBI, NSA, prison officials, etc. which sometimes includes manipulating surveillance information (i.e. 216 Protest, 310 Brutus, 313 Finder’s Keepers, 608 Ultimatum).

    Second, one of the great appeals of the show in general is intense exploration of ethics, with the father and two sons of the Eppes family frequently challenging each other and themselves.

    Third, and perhaps most importantly, this show appeals to geeks (most people I know who love this show are math/engineer/computer enthusiasts or close to it). You don’t get into the hearts and minds of the populace at large by doing virtuoso math demonstrations tied with intense discussions of ethics.

    Though I disagree with the propaganda angle (and the off-hand comments about how Numb3rs-type thinking is partly responsible for the house boom and bust), I think it was a great, thought-provoking post, which did a good job of listing out the elements of numbers which stretch the bounds of credulity.

  2. The author responds(I):

    There is extensive evidence that “financial engineering” contributed substantially to the housing boom/bust and that this financial engineering was highly questionable on various mathematical and scientific grounds.

    See, for example:

    Recipe for Disaster: The Formula That Killed Wall Street
    By Felix Salmon

    Wired February 23, 2009

    http://www.wired.com/techbiz/it/magazine/17-03/wp_quant?currentPage=all

    This article by Nassim Nicholas Taleb:

    http://www.edge.org/3rd_culture/taleb08/taleb08_index.html

    and this appendix:

    http://www.fooledbyrandomness.com/EDGE/index.html

    This is not a new problem. The mathematical models used to value derivative securities have repeatedly failed and “blown up” in similar ways for decades.

    A notable precursor to the housing boom/bust was the failure of Long Term Capital Markets (LTCM), a huge failure at the time, but small compared to the latest (2008) disaster.

    See

    When Genius Failed: The Rise and Fall of Long-Term Capital Management
    By Roger Lowenstein

    http://www.amazon.com/When-Genius-Failed-Long-Term-Management/dp/0375758259

    for a non-technical but clear account of this financial collapse, in many ways very similar to the collapses in 2008.

    One may doubt the sincerity of many of the players in the housing bubble — did they really believe these mathematical models? — but sincere misconceptions about mathematics and mathematicians almost certainly contributed to the disaster.

    This is not an issue of unrealistic ideas about the time it takes to develop mathematics and mathematical software, one of the most clear inaccuracies of Numb3rs (conceded by the math consultants for the show), but an issue of belief in magical algorithms and math like some of the AI and pattern recognition algorithms that Charlie Eppes invents on the fly in Numb3rs.

    Sincerely,

    John

    • John,

      On the housing bubble: I understand where you’re coming from but having been a professional investor for a decade, I look at life through a different lens than you. The vast majority of behavior in the financial markets can be explained by fear or greed. So when things blow up, you can easily figure out why by tracing back the connections as to who had something to gain (greed) and who had something to lose (fear).

      Many of the mathematical constructs used in the financial markets are simply smoke and mirrors used by the greedy to fleece the stupid or lazy. I haven’t the slightest doubt that the really smart people at Goldman Sachs understood that you can’t truly repackage garbage loans into AAA securities. But they understood that if you made it complicated enough, very few people would bother to analyze hundreds of pages of documents. And then you could fleece investors for years without anyone noticing.

      I don’t disagree with you that many financial models are based on bogus assumptions. Those who know what they’re doing understand that Black-Scholes is a framework for understanding options but requires a fudge factor called “implied volatility” which is essentially a proxy for investor fear. You won’t meet a single value investor who believes in the efficient market theory. I could go on and on with dumb math things in finance but it sounds like you already know about most of them.

      Where we disagree is the role that math plays in market irrationality. You seem to think that faulty math is a fundamental driver. I think that math is simply a small piece of a larger mosaic (which includes many other pieces like suits, fancy power point slides, corporate-speak, status symbols, etc.). This larger mosaic is simply smoke and mirrors to obfuscate the fact that in financial markets, most behavior is driven by greed and fear. There will always be greedy people who think there’s nothing wrong with using whatever means available to enrich themselves at the expense of those not smart (or hard-working) enough to know they’re getting fleeced.

      Before there were fancy math models, there were many market booms and busts. If faulty math models were never to be used in markets going forward, there would still be financial booms and busts. This assumes human behavior continues to have greed and fear as the primary drivers for financial choices. It will take far more than good math to get everyone in the world to rid themselves of greed and fear when making financial decisions.

      • Preeti Edul says:

        It is amazing, because after I read this post the first thought that crossed my mind was – its the GREED.

        As fascinating as mathematical model are, they are not miracle machines. If your models were more conservative, maybe they might not require you to make such life shattering decisions.

        During the financial crash, I remember listening to an interview on BBC where a bank representative justified paying huge bonuses to their employees because they did not want to “lose talent”. Logically one would wonder how many lucrative jobs are out there in the financial sector given the collapse, where exactly are all these talented souls going to hop ?

        The probability that bad decisions are made by bright people because of greed and not poor math is very high.

  3. The author responds (II):

    Propaganda has a very negative connotation and in common usage meaning, conjuring up images of Goebbels in Nazi Germany. I did not and would not use the term propaganda to describe Numb3rs.

    I do use the term product placement which seems appropriate to me. There is obvious product placement in Numb3rs such as the references to Mathematica and A New Kind of Science that I note. There is, of course, the open partnership with Texas Instruments which I also note. I think few could watch the show and not notice the prominent display of various high tech gadgets, flat screen displays, and mathematical techniques, which look like product placement for devices and consulting services.

    Product placement has been around forever, but it has grown by leaps and bounds since the mid 1990s. Hollywood writers have become quite sophisticated at weaving products and services seamlessly into movies and television. It seems to me likely to only grow as cheap bandwidth and video erodes the traditional ability to sell physical DVDs or movie tickets.

    While it would not surprise me if public relations officers at the NSA or similar government agencies were involved in producing the show, this is not really necessary. The biographical sketch for Dr. Gary Lorden in The Numbers Behind Numb3rs states:

    He has participated in highly classified research projects aimed at enhancing the ability of government agencies (such as the NSA) to protect national security.

    It is not hard to see how certain interests and viewpoints likely make their way into the show.

    My point, which is addressed to people and mathematicians at the NSA as well as to a more general audience, is that one cannot build a national or global economy on security and defense any more than one can build it on Hollywood movies or video games. Everyone, including people in the intelligence community and Pentagon, have substantive physical needs: food, housing, energy, health, and so forth. Would we not all be better off if the power of today’s computers and new mathematics was applied to these fundamental needs?

    Sincerely,

    John

    • John – On your points about propaganda and product placement:

      I was assuming that your main point was “in many respects it is Hollywood product placement for the post 9/11 world of massive, expensive high-tech surveillance and security measures both overseas and at home — in which mathematics plays an important and growing role.”

      Perhaps we use the word propaganda differently. I use it to describe any attempt by the government or the mainstream media which supports them to sell one or more government programs or overall ideologies to the populace. Using my definition, all governments engage in propaganda. Sometimes it’s very obvious like the frying egg commercial: “This is your brain on drugs.” Sometimes it’s much more subtle like attempting to divert attention away from what actually happened on September 11, 2001 (perhaps we’ll never really know what happened, as so much of the evidence was destroyed or kept classified).

      When I hear the phrase “product placement” I think of examples you gave such as the as the references to Mathematica and A New Kind of Science (yes there were product placements and yes they seem to be in most movies these days). However, I don’t think of convincing people of the necessity of “massive, expensive high-tech surveillance and security measures both overseas and at home” as a form of product placement. I think of that as propaganda.

      If you don’t like the word propaganda, how about the phrase, “selling a vision?”

      So, returning to the discussion: I have seen the majority of the episodes of Numb3rs. I never felt like it was an attempt to sell me the vision that “massive, expensive high-tech surveillance and security measures both overseas and at home” were necessary and good. They were in the show, but they were shown as tools that can possibly used in a good way or a bad way, just like guns or cell phones. I personally think such systems will do more harm than good, and I find myself a bit frightened when I read about global surveillance systems like this:

      http://www.newyorker.com/reporting/2011/05/23/110523fa_fact_mayer?currentPage=all

      I happen to also think that our country would be far better off if most government resources devoted to military and security were redirected to endeavors with much better economic payoffs (possibly in the form of a reduced size of government). So that’s not the thing I’m taking issue with in your post.

      I just happen to think that the show is far too cerebral and laden with ethics discussions to possibly be successful in selling the vision that “massive, expensive high-tech surveillance and security measures both overseas and at home” are necessary and good.

  4. Dan Weber says:

    I watched Numb3rs for a while, but I had to give up in an early episode where they found a melted block of ice, and Charlie came up with some mathematical formula to determine how long it had been melting, instead of just looking it up in a book.

    Until I did, though, I enjoyed a lot of the math, including their stuff about how real randomness is vastly different than the randomness a human would make.

    • Scott Parks says:

      I used to show some episodes in my algebra or geometry class for discussion and writing and related math problems.

      I cant really show many of them because of the language or sex, i wish their were edited classroom versions.

  5. misael says:

    Certainly!!!

    • An interesting video. That said, see this presentation and video by MIT Historian and Physicist David Kaiser on the Physics bubble(s):

      Toil, Trouble, and the Cold War Bubble: Physics and the Academy since World War II
      Speaker(s): David Kaiser
      Abstract: In the wake of recent swings in the values of technology stocks and the prices of real estate, many people have become (painfully) familiar with the boom-and-bust cycles of speculative bubbles. Although playing out on longer time-scales, student enrollments in the sciences have followed a remarkably similar pattern during the decades since World War II. The characteristic pattern can be seen in several countries, including the United States, Canada, and the United Kingdom. Enrollment patterns, and the specific policies that have been forged at various times to rapidly expand the number of trained scientists, sit at the intersection of science and society; they are where broad societal priorities and the infrastructure of higher education meet head on. Amid current discussions about globalization — especially fears of potential challenges from booming scientific and technical training efforts in India and China — the time is ripe to take stock of previous boom- and-bust cycles in our own recent past. How did they take hold, and what consequences have they had on the world of ideas? What intellectual trade-offs have been made, and with what impacts on the direction of scientific research? I will focus primarily on physics in the United States, which rose fastest and fell hardest during the postwar decades. The physicists� example highlights the promise as well as the special challenges inherent in runaway growth, as fields such as genomics and nanotechnology undergo their own frantic expansion today.
      Date: 10/09/2008 – 2:00 pm

      http://pirsa.org/08090034/

      I am a great believer that there are great untapped opportunities to combine today’s powerful computers with new and existing math to solve many current problems, as I discuss briefly in my article. The new (2003) video compression is probably already having an impact on travel time and costs through videoconferencing such as Skype which has the potential to help resolve some of our current energy problems.

      The fact remains that the majority of people in the USA who get advanced degrees in physics, mathematics, or similar fields end up doing something else. Very often they end up developing computer software that uses basic arithmetic and little else. In my opinion, this is a colossal waste of time, money, and talent.

      If calls for better math education in the United States are simply a disguised way to produce more and therefore cheaper programmers to reinvent spreadsheets and other software yet again, this is a terrible waste and undoubtedly will only contribute to continuing economic problems.

      Rather, professionals who have already been trained, of whom there are many, and students in the future should be using math to solve current truly unsolved problems such as energy, health, and food problems.

      Sincerely,

      John

  6. scott says:

    I wish we could get edited Numbers shows for school, without the sex??

  7. Preeti Edul says:

    What a nice read.

    You say – “for example, the current fad trying to use machine learning for recommendation engines in social networking and search businesses”

    I recently listened to a few lectures on recommendation engines and machine learning and it seemed fairly decent, so it would be interesting to know why you call it a fad.

    Also, the statistics on the number of people who die because of a heart disease vs homicides can be twisted both ways – a person interested in building a huge defense base might say – ‘Well look how good of a job we did ! That is why we need more money to continue doing the excellent job we are doing. ‘

    If you know where to look, you can always find statistics to support your cause. If you sample the population who lost family members in the 9/11 attack, the chance that they believe the trillion dollars were well spent might be much higher than if you sample a population completely unaffected by the attack. It is only human to want to punish someone who did you wrong… and it is also human to be more rational when you are only a spectator.

    • Hello Preeti,

      Just to clarify, I do think that recommendation engines work in some cases and can “add value” in business jargon. I use Netflix, for example, and I would say their recommendation engine works to some degree although it does not always predict my tastes correctly.

      That does not mean the current focus on recommendation engines is not a fad and overblown. The world went overboard on various dubious schemes during the Internet Bubble in the 1990’s. That does not mean there weren’t some good things that actually worked.

      But the overinvestment in dot coms represents R&D effort and money that was not spent on energy technologies, for example.

      Similarly the money poured into dubious mathematical models of mortgage backed securities and more generally the global housing bubble in the 00’s represents R&D money not invested in energy technologies, health, and other pressing needs. We are now seeing the serious economic consequences of this fad investing.

      The dollar value added by recommendation engines must be quite small, if any, in many cases. For example, Netflix charges a flat monthly fee so the primary value of the recommendation engine must be to improve the customer experience and retain customers. If anything, Netflix’s operating costs must increase at least a little for each video streamed.

      Now an Amazon might see an increase in sales from their recommendation engine, but it is almost certainly small.

      How much better is the Netflix recommendation engine over organizing the videos in categories like a traditional physical video rental store? It does not seem that different to me as a Netflix user.

      Right now, the “private sector” in the US is investing largely in applying mathematics to finance and the recommendation engine/machine learning fad. Yet the pressing problems, multi-trillion dollar problesm, are in energy, health, and other areas. This seems bizarre to me and a repeat of the mistakes made in the 1990s and 00’s.

      I agree that you can spin the statistics in many different ways. I think it is fair to question whether we needed to spend $1.2 trillion to deal with a small group of fanatics hiding in caves in Afghanistan or (ahem) fortified mansions in Pakistan. A few billion, yes, but $1.2 trillion?

      John

  8. Michael says:

    Hello,

    I’m new to this site and am enjoying working my way through all its articles.

    I actually really liked this show – and the book – although the show did portray philosophers in a stereotypical, mystical, enemy-of-science type of way, which is really not how philosophy is done in universities in the UK.

    In fact my background is philosophy but I enjoyed the logic so much that I’m in night school getting a maths and stats degree so I find your articles on these themes very interesting: this one will make me look much more closely at careers applying what I am now learning to problems of food, energy, housing and health, rather than hi-tech stuff used solely for what you quite rightly suggest is trivial nonsense (when there clearly are too many people needing too much energy and no solutions on the horizon).

    In fact I really liked your ‘Symbolmania’ article: it very much struck me as a veneration of philosophy (‘conceptual analysis, conceptual leaps’) to work in tandem with logic and mathematics, rather than be seen as an enemy (again, in the UK there is no hostility from philosophy to science, much rather the other way around).

    Thanks.

Leave a Reply

Current ye@r *