The Magical Arithmetic of Numb3rs

Numb3rs is a tv present that ran for six seasons on CBS from 2005 to 2010 about FBI agent Don Eppes and his brother Charles, a baby math prodigy turned math professor at CalSci (a thinly disguised Caltech), who struggle crime with arithmetic in a sunny, smog-free TV model of Los Angeles crammed with an astonishing variety of extraordinarily engaging younger ladies. All six seasons at the moment are out there on DVD. Numb3rs options some actual arithmetic utilized in fixing some actual crimes in addition to pure science fiction. In lots of respects, Numb3rs is a techno-thriller that options a mixture of actual present-day expertise, superior expertise that will exist, and expertise and arithmetic which may plausibly exist within the close to future. Arithmetic and science is particularly properly built-in into many episodes within the first and second seasons of the present. Not like over-the-top science fiction reveals like Eureka, a viewer may consider that Numb3rs is a sensible presentation of arithmetic and science utilized in crime combating and different functions at present.

David Krumholtz (plays Charlie Eppes in Numb3rs)

Actor David Krumholtz (Charlie Eppes in Numb3rs)

Actual life mathematicians together with Caltech statistics professor Gary Lorden consulted for the present. Gary Lorden is listed within the credit for every episode as “Math Advisor”. In later seasons, Stephen Wolfram’s Wolfram Analysis additionally supplied consulting recommendation to the sequence. There are scenes with references to Mathematica, Wolfram’s flagship product, and close-up pictures of Wolfram’s magnum opus A New Form of Science on Charlie Eppes desk. Wolfram additionally has a Caltech connection; he obtained his Ph.D. in Physics from Caltech in 1979. Gary Lorden and fellow mathematician Keith Devlin printed a preferred ebook The Numbers Behind Numb3rs: Fixing Crime with Arithmetic in 2007: “A companion to the hit CBS crime sequence Numb3rs presents the fascinating methods arithmetic is used to struggle real-life crime.” The shadowy Nationwide Safety Company (NSA), most likely the biggest patron of arithmetic and mathematicians in america and the world, makes a number of appearances in Numb3rs.

Milikan Library Caltech

Millikan Library at Caltech (seems typically in Numb3rs)

CBS, Texas Devices (a number one maker of digital sign processor or DSP chips), and the Nationwide Council of Lecturers of Arithmetic (NCTM) developed the “We All Use Math Each Day” initiative, generally abbreviated WAUMED, to encourage college students to attain extra in math by exhibiting how the topic is related to their lives:

Utilizing the hit CBS tv present, Numb3rs, the “We All Use Math Each Day” initiative supplies free classroom actions on-line at that assist college students perceive how the maths they’re studying within the classroom applies to the actual world. The actions discover the maths derived from the ideas used to resolve instances within the FBI crime-solving present.

The present used the “We All Use Math Each Day” tagline within the opening introduction to the present within the first and second seasons.

How Practical is Numb3rs?

Though explicitly fiction, in lots of respects Numb3rs paints an image of arithmetic and science that’s just like ostensibly factual common science equivalent to Scientific American articles, PBS/Nova video applications, Congressional testimony by main scientists, and casual discussions at fundraising cocktail events — until the scientists or mathematicians are within the uncommon and strange place of getting to clarify an apparent failure to a lay viewers:

“Nicely, Senator, as everybody is aware of, science is a dangerous enterprise. Eighty to ninety % of our analysis initiatives fail. Absolutely your workers briefed you on that; the proposal committee talked about this clearly in italics in footnote 83 in Appendix C of the Proposal for the New Manhattan Challenge that Will Produce Miraculous Outcomes by the Subsequent Election.”

In a number of essential respects, Numb3rs could be very unrealistic. Additionally it is the case that many individuals starting from Silicon Valley executives attempting to make use of mathematical strategies for his or her companies — for instance, the present fad attempting to make use of machine studying for advice engines in social networking and search companies — to training scientists and engineers who one would possibly suppose would know higher typically have expectations related to what’s portrayed in Numb3rs. These misconceptions virtually actually contributed in a serious option to the multi-trillion greenback international housing bubble and crash by means of the widespread use of invalid mathematical fashions for the valuation of mortgage-backed securities. With enterprise and political leaders seemingly floundering within the present financial difficulties, these misconceptions could wreak even larger havoc.

Earlier than launching right into a critique of Numb3rs, it is very important understand that there have been many successes in utilized arithmetic and mathematical software program together with spectacular advances in video compression equivalent to utilized by YouTube and Skype, audio compression such because the broadly used MP3 customary, nonetheless picture compression equivalent to JPEG pictures, pc generated imagery in films and video video games, the World Positioning System (GPS) that tells individuals the place they’re, and even speech recognition which is lastly discovering some sensible use. Trendy computer systems are extraordinarily highly effective, similar to the supercomputers of earlier many years; this energy is generally unused as a result of we don’t have the arithmetic to place this energy to sensible use. At this time’s highly effective computer systems and new arithmetic most likely can clear up or assist clear up many urgent issues, even trillion greenback issues equivalent to power shortages or main illnesses equivalent to most cancers. Success in fixing issues with arithmetic requires sensible expectations, sensible planning, and enough time and sources.

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

One factor that’s utterly unrealistic is the timeframe. In a fast-paced 41-minute episode, Charlie has to assist his brother clear up the case in a single or two “tv days.” In actual life, the usage of arithmetic in crime detection is an extended and gradual course of. (An analogous statement is equally true for the usage of laboratory-based felony forensics as depicted in tv sequence such because the vastly common CSI franchise.)

Additionally unrealistic is that one mathematician can be accustomed to so large a variety of mathematical and scientific methods as Charlie. He’s, in fact, a tv superhero — however that’s what makes him watchable. Observing an actual mathematician in motion can be no extra thrilling than watching an actual FBI agent at work! (All that sitting in vehicles ready for somebody to exit a constructing, all these hours sifting by means of data or watching pc screens… boring.)

It’s additionally true that Charlie appears in a position to collect lots of knowledge in a remarkably brief time. In real-life functions of arithmetic, getting maintain of the required knowledge, and placing it into the correct type for the pc to digest, can contain weeks or months of labor-intensive effort. And sometimes the information one would wish are easy not out there.

(Emphasis Added)

Of their dialogue of the episode “Manhunt” (Airdate: Might 13, 2005,The Numbers Behind Numb3rs, web page. 78), through which Charlie Eppes makes use of Bayesian statistics to foretell the actions and site of an escaped killer, Devlin and Lorden additionally write:

As is usually the case with dramatic portrayals of arithmetic or science at work, the size of time out there to Charlie to provide his rating of the reported sightings [of the escaped killer] is considerably shortened, however the thought of utilizing the mathematically primarily based strategy of Bayesian evaluation is sound.

(Emphasis Added)

Actual-life arithmetic and mathematical software program growth entails way more time, way more trial and error, way more debugging, and way more danger than depicted in Numb3rs. Scientists typically declare an eighty to ninety % failure price of their analysis initiatives, ceaselessly when explaining an apparent failure to upset graduate college students, donors, coverage makers, and others who anticipated extra. Charlie Eppes virtually by no means fails! There may be historic proof that the failure price in real “breakthroughs” is greater, fairly presumably ninety-nine % or worse. A few of the arithmetic that Charlie whips up in just a few “tv days” within the present would truly qualify as breakthroughs in real-life, notably some arithmetic and algorithms for synthetic intelligence and sample recognition (see beneath). Traditionally, real breakthroughs have often concerned not less than 5 years of effort when profitable. To provide a latest instance, Grigoriy Perelman’s proof of the Poincare Conjecture took him not less than seven years. There seem to have been about 100 failed printed makes an attempt to show the conjecture by mathematicians previous to Perelman’s success.

The truth is, actually, worse than Devlin and Lorden concede of their ebook. Numb3rs has a number of episodes that painting synthetic intelligence (AI), sample recognition, machine studying, and related applied sciences far superior to actuality on the time the present aired (2005-2010) and even at present (2011). In a single episode, Charlie whips up a picture/object recognition algorithm in just a few hours to allow the NSA to trace a yellow truck carrying a contraband missile steering system by means of their satellite tv for pc pictures of LA to a terrorist (“Finders Keepers,” Authentic Air Date: January 12, 2007). Equally, remarkably efficient face recognition algorithms play a task in a number of episodes. Lots of Charlie’s AI and sample recognition algorithms and the opposite sample recognition expertise proven in Numb3rs works significantly better than the actual algorithms and math.

The Specter of 9/11

Numb3rs is a fast-paced entertaining present with horny, idealistic, extremely efficient heroes and heroines. Though it’s generally vital of safety companies just like the CIA and highly effective establishments like pharmaceutical firms, in lots of respects it’s Hollywood product placement for the put up 9/11 world of large, costly high-tech surveillance and safety measures each abroad and at house — through which arithmetic performs an essential and rising function. It reminds one among President Eisenhower’s speeches throughout the 1950’s:

The worst to be feared and one of the best to be anticipated might be merely acknowledged.

The worst is atomic warfare.

The perfect can be this: a lifetime of perpetual worry and stress; a burden of arms draining the wealth and the labor of all peoples; a losing of power that defies the American system or the Soviet system or any system to attain true abundance and happiness for the peoples of this earth.

Each gun that’s made, each warship launched, each rocket fired signifies, within the last sense, a theft from those that starvation and should not fed, those that are chilly and should not clothed. This world in arms just isn’t spending cash alone.

It’s spending the sweat of its laborers, the genius of its scientists, the hopes of its kids.

The price of one fashionable heavy bomber is that this: a contemporary brick faculty in additional than 30 cities.

It’s two electrical energy crops, every serving a city of 60,000 inhabitants.

It’s two effective, absolutely geared up hospitals. It’s some 50 miles of concrete freeway.

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

We pay for a single destroyer with new properties that might have housed greater than 8,000 individuals.

This, I repeat, is one of the simplest ways of life to be discovered on the highway the world has been taking.

This isn’t a lifestyle in any respect, in any true sense. Underneath the cloud of threatening warfare, it’s humanity hanging from a cross of iron.

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

President Dwight D. Eisenhower

President Dwight D. Eisenhower

Eisenhower and his advisers had been no shrinking violets. They had been properly conscious the world generally is a nasty, harmful place. They presided over an enormous army buildup and controversial covert operations in Guatemala, Iran, Vietnam, and different international locations. By the tip of his Presidency Eisenhower and his advisers discovered that it was by no means sufficient. Even 1000’s of nuclear weapons, ships, tanks, spies, and what we now know was an enormous lead over the Soviet Union was not sufficient to fulfill what he famously labeled the “army industrial advanced” in his Farewell Deal with. Eisenhower discovered himself attacked by Republicans and Democrats alike for not spending much more cash on weapons and preparations for warfare!

Usama Bin Laden (FBI Wanted Poster)

Osama Bin Laden: The Trillion Greenback Man

Following the reported dying of Osama Bin Laden, Andrea Millen Wealthy, writing within the libertarian Motive journal, estimated the direct price of getting Bin Laden at $1.1 trillion. Tim Fernholz and Jim Tankersley, writing in The Atlantic estimated the overall price at $3 trillion over fifteen years. Sam Stein of the Huffington Put up, citing a Congressional Analysis Service report of March 29, 2011, put the fee at not less than 1.283 trillion.

Based on america Facilities for Illness Management, the main causes of dying in america within the calendar yr 2007 had been:

Variety of deaths for main causes of dying

* Coronary heart illness: 616,067
* Most cancers: 562,875
* Stroke (cerebrovascular illnesses): 135,952
* Persistent decrease respiratory illnesses: 127,924
* Accidents (unintentional accidents): 123,706
* Alzheimer’s illness: 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 assaults are a small fraction even in 2001, don’t make the highest ten. In 2007, the Facilities for Illness Management listed all homicides because the fifteenth main reason for dying:

All homicides

* Variety of deaths: 18,361
* Deaths per 100,000 inhabitants: 6.1
* Reason behind dying rank: 15

It’s value noting that the US invasion of Iraq in 2003 resulted in a dramatic drop in Iraqi oil manufacturing, undoubtedly contributing considerably to the big will increase in oil and power costs within the final decade. So too the US invasion of Afghanistan in 2001 appears to have scuttled any probability of developing a pipeline for pure fuel from Turkmenistan to the Indian Ocean, additionally undoubtedly contributing to excessive power costs.

It’s troublesome to enhance on President Eisenhower’s phrases at present. Bayesian statistical analyses that predict terrorist assaults, even when they work, don’t make up for dwindling provides of cheap oil and pure fuel. They don’t feed individuals. They don’t treatment illnesses like most cancers or stop coronary heart assaults. How way more may have been and will nonetheless be completed if at present’s highly effective computer systems and new arithmetic had been utilized to substantive issues equivalent to power, meals, and well being as a substitute of the will-o’-the-wisp of excellent safety or the pseudo-scientific monetary engineering that helped trigger the present Nice Recession? Mathematicians, scientists, enterprise leaders, and coverage makers can do higher than now we have completed.


Numb3rs is a enjoyable, entertaining present. If you’re a mathematician, it is going to most likely make you are feeling nice about your occupation until you’re within the unlucky place of coping with an employer, consumer, investor, or funding company that expects you to do what Charlie Eppes does in each episode of Numb3rs. A few of the math and science in Numb3rs is totally sensible. A few of the math is considerably exaggerated. A few of the math is pure science fiction although it typically appears very actual and plausible. As Devlin and Lorden admit of their ebook, the timeframe is, typically, utterly unrealistic.

The world is presently confronted with critical and worsening issues, presumably because of a dwindling provide of cheap oil and pure fuel. The political and financial management of the world seems paralyzed and unable to take care of the issues, bickering over debt ceilings and different silliness. We do have huge unused sources within the computational energy of lots of of thousands and thousands of computer systems and different units. With the correct arithmetic and inventive pondering, we could possibly harness this energy to resolve lots of the present issues, with out ready for paralyzed governments or blundering Too Large To Fail banks to behave properly.

Most arithmetic and mathematical software program has been developed by people and small groups working over intervals of a number of months to a number of years with whole prices of tens of 1000’s to a couple million {dollars} per undertaking. Success requires sensible expectations concerning the dimension, scope, issue degree, and dangers of creating and implementing arithmetic and mathematical software program. In these troublesome occasions, mathematicians and scientists should achieve assist for sensible initiatives that may discover actual options to our urgent issues, and actually reject the fantasy parts of Numb3rs.

Instructed Studying/References
The Numbers Behind Numb3rs: Fixing Crime with Arithmetic
Keith Devlin, Ph.D. and Gary Lorden, Ph.D.
Penguin Books, New York, 2007

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

The Price of Iraq, Afghanistan, and Different World Warfare on Terror Operations Since 9/11
Amy Belasco, Congressional Analysis Service, Washington, D.C, March 29, 2011

The image of actor David Krumholtz on the Serenity Premiere is from Wikimedia Commons, licensed beneath the Inventive Commons Attribution 2.0 Generic license.

This picture was initially posted to Flickr by RavenU at[email protected]/45967991. It was reviewed on 10:00, 30 April 2007 (UTC) by the FlickreviewR robotic and confirmed to be licensed beneath the phrases of the cc-by-2.0.

Millikan Library at Caltech Picture from Wikimedia Commons.

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

(from Wikipedia) This picture is a piece of an worker of the Govt Workplace of the President of america, taken or made throughout the course of the particular person’s official duties. As a piece of the U.S. federal authorities, the picture is within the public area.

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

© 2011 John F. McGowan

Concerning the Creator

John F. McGowan, Ph.D. solves issues utilizing arithmetic and mathematical software program, together with creating video compression and speech recognition applied sciences. He has intensive expertise creating software program in C, C++, Visible Fundamental, Mathematica, MATLAB, and lots of different programming languages. He’s most likely finest recognized for his AVI Overview, an Web FAQ (Incessantly Requested Questions) on the Microsoft AVI (Audio Video Interleave) file format. He has labored as a contractor at NASA Ames Analysis Heart concerned within the analysis and growth of picture and video processing algorithms and expertise. He has printed articles on the origin and evolution of life, the exploration of Mars (anticipating the invention of methane on Mars), and low-cost entry to area. He has a Ph.D. in physics from the College of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Know-how (Caltech). He might be reached at [email protected].