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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 [19]

Ivan from Nevada

The barber paradox isn't so much self-conflicting as it is incomplete. It is oversimplified as an expression. Asking "Who shaves the barber? Is like asking: Where does it rain? We would first need to know When or, under what laundry list of conditions, does it rain? Once you have a correct and complete laundry list, you have a complete and valid construct (Rain). You can solve the pieces for an outcome or analyze the outcome in front of you. With the present approach you can't possibly be expected to come up with a valid answer except by chance. I am admitedly not a mathematician but as you present in the earlier Muppet Chronicles, Math is comprised of the symbols that represent instances of event or item occurrence. Even Mathematics can't generate, in and of itself, items that don't exist in a situation or equation to begin with. So, the flaw isn't the math, it's the the construct. You can't answer the question who shaves the barber until you answer the question when is it time to shave the barber. More particularly, What happens when the barber get shaved.
For the question of rain, a scientific (cause and effect) explanation would include all procedural, elemental and temporal parts to account for each item requisite for the phenomenon to take place. It therefore exists in the empirical world. The barber paradox is a cute story but like the big bad wolf, it is a fantasy construct where we can't figure out how the wolf blows down the house of brick because there isn't enough cause and effect data to validate the existence of such an event. So either we've missed something or it's fantasy (invalid in it's qualifications for achieving the "critical mass" for being a "reality event" or, non-existent as being empirically perceptible). It's the wrong question (at the least, in it's generality of scope and/scale) yoked to a contrived outcome (for the record, in no way do I mean to suggest it was intentional, it's just that human history, including the human present, is replete with conceptual miscoupling. It's
something we fall into alot.). Neither of the to sets shaves the barber and there's not enough data to know what else happens The fact that he's the only one that's part of both groups makes him unique. He's like salt. The rules prevent him from being one thing or the other so he must be something else but what? Either one of the hosts or someone else want to help out a fellow Wonderer? P.S. Not adverse to a little math :-) Be warned, I am slow.

Sep. 01 2014 09:17 PM

i may be out on a limb to call this a paradox, but this segment reminded me of the debate whether or not..
"Christ either deceived mankind by conscious fraud, or He was Himself deluded and self-deceived, or He was Divine. There is no getting out of this trilemma. It is inexorable."

Aug. 31 2014 03:00 AM
Margaret Nahmias

Even with God one must accept some mysetry.

Aug. 30 2014 07:02 PM

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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