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Paradoxical sign Paradoxical sign (Arenamontanus/flickr/CC-BY-2.0)

In the late 1800's, mathematicians fantasized about a machine that could answer any math question at all. But Steve Strogatz explains -- by way of Sesame Street and a thought experiment involving a conflicted barber -- that their dreams were dashed by a scrawny little German guy. Then, theoretical physicist Janna Levin at Barnard tells us how Kurt Godel's maddeningly loopy theorem revealed the limits of math, and the infinite depths of our ignorance.

And for our final loop, we talk with author Melanie Thernstrom who has been living with pain every day for fifteen years. Neuroscientist Sean Mackey explains that she is caught in a crossfire of signals between her body and her brain. Sean showed Melanie how to enter that loop and ultimately take control of her pain... for a while.


Janna Levin, Sean Mackey, M.D., Ph.D., Steve Strogatz and Melanie Thernstrom

Comments [16]


It's not so much that two primes (excepting 2) make an even number--that's a given. What we don't know is if <b>every</b> even number can be made by the sum of two primes. If we get high enough, are there even primes any more? There's not an end to numbers (that we know of), so we have no way of knowing.

Oct. 10 2013 11:06 AM
Peter Keegan

Fair point, but 2 is the only even prime number. All others must necessarily be odd; even numbers except 2 are by definition divisible by 2, making them composite (with the exception of 2). Plus, the fact that 2 is a prime number may help my case. I'm not a mathematician, but I would venture to guess that 2 being a prime number has some involvement in the fact that all even numbers are the sum of two primes.

May. 21 2012 03:16 AM

Not all prime numbers are odd. The number 2 is a prime number.
Please see

May. 20 2012 11:25 PM
Peter Keegan

Godels's theorem should be provable (or disprovable), if you think about it: any two odd numbers when added together make an even number, and prime numbers are always odd. That in itself shows that two prime numbers when added together will make an even number. Furthermore, prime numbers, though mathematically not proven to be predictable, logically should be indirectly predictable in that they are the only numbers that cannot be directly predicted in some way. So to prove or disprove the theorem, what is needed is to find a formula to predict prime numbers by predicting the two numbers above and below the prime, similar to the way black holes are visible only when in the midst of visible material. In this manner, the intervals of prime numbers can be predicted, meaning that the theorem can be fully tested. (I do admit that my logic could be flawed; feel free to tell me if it is.)

May. 20 2012 05:47 PM

Melanie describes a festival she saw in Singapore as a Hindi festival. It is in fact a Tamil festival - Thai Poosam - celebrated to honor the Tamil God Murugan

Hindi on the other hand is a language spoken in the northern parts of India :-)

Jan. 30 2012 11:04 AM
Bethany from Peoria, IL

There's a great comic book (graphic novel) about Bertrand Russel and his foundational quest and life, called _Logicomix_. My 2 and 4 year old **love** it, and it tells the story and explains the math bits really nicely. And my 4 year old can tell you the Barber Paradox, and name all the mathematicians in the story. Highly recommended.

Nov. 12 2011 10:47 AM
Vin from Brunswick, Maine

In Melanie Thernstrom's story, she refers to a "Hindi" festival and becoming a religious "Hindi." Come on now. Does she want to become a "Hindu" or does she want to speak "Hindi"? Anyone who knows the word "analgesic" should know better. Grr.

Oct. 28 2011 12:13 PM


The piece playing in the background is the 5th movement from Edward Lalo's Symphonie Espagnole. Great episode!


Oct. 19 2011 10:58 PM
Thomas Cook from Peachtree City, GA

Great show. Does anyone know what is the name of the classical piece that plays whenever things get mathematical and pretty? I know I should know it . . .

Oct. 17 2011 09:37 PM

before it started... the song is from The Octopus project. The album "Hello, Avalanche" the song is "I saw the bright shinies"

One of the members play this machine called a Theremin, which i believe is the only instrument that you play that you don't need to touch. Its a form of synth.

One of my most favorite of bands. :).

Oct. 12 2011 04:03 PM

Dear 7.830hz from Yukon -

Which song are you wondering about?


Oct. 11 2011 12:35 PM
7.830hz from Yukon

Can anyone tell me that name of the song played in the background during this segment? Thanks.

Oct. 10 2011 12:51 AM
Greg Jackson from North Platte, NE

I too am somewhat miffed as is "dean from atlanta re: Barber Paradox" I'm not seeing a true paradox. references two: The Barbershop Paradox (with 3 barbers) and The Barber Paradox (one barber).
The Barber Paradox was proposed by Lewis Carroll but attributed to Bertrand Russell. Every man keeps himself clean-shaven by doing one of two things: shaving himself, or going to the barber. Another way to state this is: The barber shaves only those men in town who do not shave themselves.

" The question is, does the barber shave himself? In this form the contradiction is not very difficult to solve. Bertrand Russell, The Philosophy of Logical Atomism

I am in total agreement with Russell's statement above(but not sure why):

List of paradoxes

Oct. 09 2011 01:17 AM

@Sidola If I'm not mistaken, that's known as a "Brazilian".

What? The paradox doesn't specify "face".

Oct. 08 2011 10:58 PM

@Sidola I actually saw that as an answer in a quiz in a math book I read through some years ago.

Oct. 08 2011 07:28 PM

What if the barber was a woman?

Oct. 05 2011 11:30 AM

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