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Comments

• [1] Jennifer F from Sacramento, CA October 07, 2009 - 06:40PM

  This episode was totally engrossing. I only wish I'd ever turned any of my random, maddening numbers obsessions into a "law."

  Thanks for this show - loved it.

  
  
• [2] Chris Reyes from Sebastopol, CA October 12, 2009 - 04:20PM

  Hello Mark Migrini, don't forget about this possibility: If you see a low amount on another gas pump, it *could* be from a cash-strapped teenager, but it could also be a motorcycle that needs only a fraction of what an automobile needs.

  Oh, and be careful for motorcycles and bicycles. I ride both...

  
  
• [3] Paula Caraballo from Queens, New York October 12, 2009 - 05:26PM

  I really enjoyed this program. I find math fascinating and scary. I am currently enrolled in college (online)and have a remedial math class so naturally, your talk caught my attention. I agree that you cannot live without numbers I have focused on getting jobs based on how much math I needed to know. I worked in some aspect of bookeeping/accounting for the first four years of my professional life. At age 49 I am trying to beat my fear of math which reduces my mind to chaotic confusion until I just give up and just guess the answers. But I have managed to pass some math classes post high school and even understand your basic accounting. Paul Erdos and Benfords law will probably find their way into my class at some point.

  
  
• [4] Steve from Morristown October 16, 2009 - 04:01PM

  I've used Benfords Law as a bundled application in some powerful data mining software to discover payroll fraud.

  
  
• [5] Akenji Ndumu from Bowie, MD October 22, 2009 - 02:34AM

  This was a fantastic show. My father is a mathematician, and during the Erdos segment, it hit me, I have no idea what this man does! No idea of what the heat kernels or eigenvalues of 3 spheres he speaks of are. As a first step towards that understanding, I think I am going to try to find his Erdos number....

  
  
• [6] David Pearce from Washington, D.C. October 25, 2009 - 06:53PM

  I'm still listening to the show here in D.C., at 6:47 p.m. and I thought you were going to relate the Bendford Rule and the Erdos number, but I don't think you are.

  However, it seems to my VERY untrained ear as if the Erdos numbers do sort of follow the Benford Rule.

  I.E., at first the numbers are big, though not in order (one is not bigger than two, etc.). By the five and six numbers, the amount of these is very large, i.e., robust.

  And yet the numbers after six (I think) go down, which goes against the "robustness" of the lower Erdos numbers, yet seems to follow the Benford Rule.

  Will someone comment to set me straight?

  
  
• [7] David Pearce from Washington, D.C. October 25, 2009 - 06:55PM

  I like the Wiki quote which notes that Alfréd Rényi said, "a mathematician is a machine for turning coffee into theorems"

  
  
• [8] Stephen Grimes from Philadelphia November 17, 2009 - 03:43PM

  David, I think there's every reason to belief that the distribution of Erdős numbers follows Benford's Law. However, the trouble in verifying this is that people with Erdős numbers greater than 6 either can't calculate it, don't wish to report it, are embarrassed it isn't lower, or are in a profession so distant from mathematics they have no reason to care! Hence in practice only a non-random subset of Erdős numbers are ever reported.

  By the way Radio Lab, it's Erdős, not Erdös!! I enjoyed the show!

  
  
• [9] Angus from Davis, California November 24, 2009 - 06:57PM

  Referring to the use of Benford's law to discover fraud. In order for this to work, numbers generated through purposeful human deception (i.e. me making up a fake salary), and those generated through more genuine means (i.e. the real salary that my boss decides to give me) must be fundamentally different. I am aware that consciously forged numbers probably differ from Benford's law, and possibly approach actual randomness. However, wouldn't all the permutations that occur on any tax form (subtract paid taxes, consider dependents, adding in other income, etc) eventually make my "fake" salary follow Benford's law?

  
  
• [10] Avi Burstein from NYC December 01, 2009 - 08:48PM

  Great episode. I really enjoyed it. But I don't really agree with the notion that everyone with an Erdös number was "influenced" by the man. Just because I collaborate with someone who collaborated with him means that now I'm influenced by him, or connected to him? Why? Working with someone who worked with someone else doesn't make one influenced by the original person in any way, and surely not as the chain is expanded further.

  
  
• [11] Patrick McFadden from Seattle December 02, 2009 - 01:44PM

  The Erdös number is fun, but what starts making it really interesting is when you look at the Erdös-Bacon number.

  http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Bacon_number

  
  
• [12] Mitch Shively from Delaware, OH December 02, 2009 - 02:50PM

  Fascinating show. I was really engrossed by the Benford's Law stuff...tested it out on a few of my recent expense reports (sample size of 34 and 49 numbers) and it roughly approximated Benford.

  Then I found this really great link to a video that does a great job of illustrating Benford's law with some large data sets, and shows numbers (such as rankings) that do not follow Benford: http://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/

  Jad and Robert, please do keep up the great work!

  
  
• [13] Josh from Rockford, MI December 03, 2009 - 03:15PM

  to David in DC:

  The Erdős number distribution seems to be more of a bell curve. Go about half way down this page:

  http://www.oakland.edu/enp/trivia/

  under 'The distribution of Erdös numbers'

  Lots of data sets do conform to Benford, but many don't. To see the battle between Benford and the bell curve, we'll have to hope for a Radiolab short.

  
  
• [14] Jim Sutphen from Charlottesville, Va December 04, 2009 - 04:19AM

  I loved this episode too. I was absolutely captivated by the computerized music that followed this episode. There was a piece that ended the episode that was a series of chimes the pulsated and moved laterally outward through the stereo. It was like a musical mantra. Does anyone know the composer?

  
  
• [15] Jobe Bernier from Missoula, Montana December 09, 2009 - 04:21PM

  As stated by Benford's law not all lists universally apply to this law. I enjoy that the occurrences of people's Erdős number is inversely proportional to Benford's law (at least if you focus on the first few natural numbers).

  
  
• [16] Tim Wright from Ann Arbor, MI December 11, 2009 - 09:39PM

  I also enjoyed the show. However, I felt that the segment on Benford's law a little confusing so I looked it up. I was confused why proper accounting numbers follow the law but bad accounting does not. It seems a little weird. Both are sets of data. I looked in wikipedia and its links. As for accounting, it is really emperical. Somebody analyzed a lot of data and showed that cooked books do not follow it and non cooked books follow the law. The next question is do mathematician's empirically show a data set to follow the law or can it be proven analytically?

  
  
• [17] barry p skeist from United States December 11, 2009 - 11:16PM

  I was a bit disappointed that there was no significant effort to explain benford's law. To me it seems fairly intuitive, so here goes.

  If you are counting something that "grows" out of something else, then the "energy" needed to grow a certain amount will be more related to the percent increase, not the absolute amount.

  If I make 80,000, it is far more likely that I will get to 90,000, than if I make 110,000 that I will get to 200,000. so I stay in "low 6 figures" for much longer time and I will have more company. If a city street needs to be lengthened (adding more addresses) Same percentage growth in the city will go much quicker from the 700's to the 800's and 900's than doubling the entire length from 1000 to 2000.

  
  
• [18] Tal Tversky from Austin, TX December 27, 2009 - 01:58AM

  I love the show, but it's a shame you didn't tie together Benford's law with the previous segment on infant's understanding of numbers. They fit together perfectly. Once you've explained logarithms, you can easily explain Benford's law.

  It's exactly because we live in a logarithmic world that Benford's law holds true. If you pick a random number on a logarithmic number line, you'll get lead digits following Benford's law. Some might also argue that it's because the world has logarithmic properties that infant's judgements seem to follow a logarithmic scale. They are understanding something fundamental about the world.

  
  
• [19] A person from Boulder January 05, 2010 - 02:16AM

  Love this Radiolab show on Numbers. Those who enjoyed this will probably also love a series of short programs on BBC Radio called "5 numbers", "Another 5 numbers" and "A Further 5 Numbers". Check them out.

  http://www.bbc.co.uk/radio4/science/5numbers.shtml