S03 Ep12: The Psychic Vortex

Hey Kids!  “Math Doesn’t Suck.”  That’s what we learned in tonight’s episode.

First, Sheldon takes us on a visit in his mind to Flatland.  Flatland is a small book written over 100 years ago about a people living in a world with only two space dimensions. Its inhabitants call their two directions  North/South and East/West.  They are unconcerned with our own three-dimensional world that includes a third direction; Up/Down.  Its a book that nearly every one of my physics friends, as well as those in math, engineering and computer science read as a teenager.   Except me…Flatland was the Moby Dick to my Zelig.

So the episode shamed me into finally reading Flatland.  I figured that by now it wouldn’t have anything new about dimensionality I hadn’t picked up somewhere else.   But I was wrong.  Something I had never considered is that being from a world that is one dimension larger allows you to peer inside everything in a world one dimension smaller.  For example, here is a picture of a Flatlander’s house:

A typical house in Flatland.

Since the Flatlanders (not to be confused with The Flatlanders) have no concept of  covering the “top” and “bottom” of their houses, we can see right inside their rooms and even their cabinets.    More abstractly put, we can see the inside of circles, which they cannot.  Similarly a four-dimensional being could see right inside one of our spheres. Four-dimensional people could see right inside every part of our bodies, organs and even cells as if they were all laid out on paper.

But one page in Flatland really blew me away.   Gravity cannot point “down” for them because they have no concept of down.  It points South in Flatland.   It is never explained, but this could be achieved by tilting Flatland relative to the Earth.  Flatland would be tilted in a dimension they cannot even comprehend.  Also gravity is much stronger in some regions of Flatland than others.   So it seems that Flatland is not so flat at all…it must  not only be tilted, but curved space  like so:

Flatland is really tilted and curved. Flatlanders just don't know it.

The increased “steepness” on one end means gravity has a stronger effect there.  Because Flatlanders have no idea of Up/Down, they have no concept of “steepness” either.  Therefore they have no explanation for the variation of gravity in their land.   In the language of modern mathematics we can say that Flatland is a two dimensional world, but it is “embedded” in a three dimensional one.  It would be decades after this book was published that  Albert Einstein described the possibility of gravity in our own world being related to curvature of space.   Like many science fiction writers,  Flatland’s author, Edwin Abbot, was a step ahead of the physicists.

Little books like this can give a pre-teenager or teenager a taste for mathematics that lasts a lifetime.   Which brings us the the second bit of mathematics in the episode:

I am sure the viewers noticed a bit of mathematics “stunt casting”.   At a university mixer, Raj meets Abby who is played by Danica McKellar.  Yes, she is the McKellar of the Chayes-McKellar-Winn Theorem   (“Percolation and Gibbs States Multiplicity for Ferromagnetic Ashkin-Teller Models on Z²”).   She wrote this paper while still an undergraduate math major (at my university, U.C.LA.)    Basically her theorem tells you how magnets must behave if you put them in a particular configuration.

Danica McKellar proceeded to write a wonderful set of books for pre-teen and teenage girls about mathematics, Math Doesn’t Suck followed by Kiss my Math about algebra and pre-calculus respectively.  A third book is on the way.

Mathematician Danica McKellar guest-starred as Abby in tonight's episode. Her books are terrific for middle school girls.

I bought them to take a look, and will be sending to my niece.  These are terrific books with real-world examples that connect directly to mathematics curricula.  They are fun and quirky.   But make no mistake…The content is serious math.  For example, she explains prime factorization,  in terms of a middle-school crush.  She gives little tricks to conquer the dreaded “word problems”.   She warns against common mistakes: 33 is not 9.  She includes testimonials from her friends,  women who used math to succeed, such as  a petroleum engineer and the finance director of a style magazine.   Other times she just gives friendly advice about growing up such as explaining why young women should not try to dumb themselves down to be popular.  The  first book leads up to and includes algebra. The second gives the reader all she needs for pre-calculus.  Somehow it still all looks fun.  I will see if my niece agrees.

The examples are intended  to resonate with young women.  I was having dinner with two female friends last month who remembered math from middle school.  They pointed out to me that many of the examples in middle-school math books use examples like football, that would  more likely interest boys than girls.  No one would accuse Danica McKellar of doing that in these books.

As we saw from Sheldon’s childhood love of Flatland, a small book can make a big impact on the  life of a pre-teen future mathematician, physicist or engineer.  So consider picking up Danica McKellar’s books for the tweenager you know.  Even if you don’t know any young women, you can click here and Danica McKellar  will send books to the library or school of your choice and send you an autograph.

24 Responses to “S03 Ep12: The Psychic Vortex”

1. Ashish Says:

I don’t think of installing OS’s as nerdy. Any kid today can do that. However, if you really have to incorporate computers, please do something related to algorithms/machine learning/compilers/complexity theory. Plus, somehow I think the nerd content is going down. Its now a love story of 2 + love story of a guy who’s scared of girls + a story of a guy who doesn’t care about girls. Please include more Maths/Physics/Psychology/Computer Science.

2. jg Says:

…”horoscope inside?” Did the cover really say that?

3. Chuk Says:

Haven’t seen the second book but the first one is definitely good. My math phobic daughter didn’t seem to interested in it (but then they started doing Algebra and she loves that).

4. Wilson Fowlie Says:

Even if you don’t know any young women, you can click on the links above and Danica McKellar will send an autographed copy to the school library of your choice.

I can’t find that offer. Can you point to that more specifically, please?

• David Saltzberg Says:

I put a link now in the text to the webpage. Actually the webpage says she will send the books to the library or school of your choice and will send an autographed sticker to you. However you can probably ask them to put the stickers in the books you are sending to the library or school.

5. Greg Says:

I loved that episode of Big Bang Theory. In fact, I like all of them. My Dad gave me a copy of the book back in the 60s. Have you seen the feature length, computer animated film at http://www.flatlandthefilm.com/ It’s been modernized to reflect the current times. It’s brilliant.

6. Nyc Psychic Says:

Haven’t seen the second book but the first one is definitely good. My math phobic daughter didn’t seem to interested in it (but then they started doing Algebra and she loves that

7. Wilson Fowlie Says:

Here’s an interesting study on a possible part-cause as to why girls may think they don’t do math as well as boys:

http://www.cbc.ca/technology/story/2010/01/26/tech-math-female-teachers.html

8. bugys Says:

great blog is very informative..

9. John Says:

There was a young-adult book by William Sleator called “The Boy Who Reversed Himself” that caused me to read Flatland when I was a kid. The main character had the ability to move at a right angle to our world. The interesting side effect was that sometimes he would come back “flipped” (the same way a 2d Flatland creature would have a 50% chance of landing backwards if she were somehow temporarily removed from her 2d world). If I remember correctly, the story describes how he has trouble tasting food correctly since molecules aren’t oriented correctly (from his perspective). It’s worth checking out and potentially recommending to younger readers, especially if they have a natural curiosity of science.

10. Alec Says:

I think there might be a problem with your picture. In Flatland, the further North you get the more strongly gravity pulls you South. (Correct me if I’m wrong, I haven’t read the book in 4 years). So, in your picture, this makes me assume that the Northern side of Flatland is held in your right hand, where gravity in our 3D world most greatly affects the curved 2D Flatland. But this increasing force would pull the flatlanders further North, rather than South!

• David Saltzberg Says:

Hi,

Here’s the quote from the book (chapter 2):

“By a law of Nature there is a constant attraction to the South…in temperate climates this is very slight…”

So in other, less temperate, regions, it must be larger. But as far as I can tell the book does not say where the attraction is stronger relative to the N-S/E-W directions. If you find it somewhere else in the book let me know.

But even if it does, I presume you don’t know what direction is North in my office so I am not sure how the picture could be wrong.

There is a kind of sequel to the book called “Sphereland”. I have not read it, but from the reviews it sounds like it addresses this issue. I’ll check it out.

David

• David Saltzberg Says:

Just finished reading “Sphereland”. While the author does propose that Flatland is curved, he does it differently. More about this later, since we’ll have an upcoming post on non-Euclidean (Riemannian) geometry in a few weeks.

11. Greg Says:

Even if you don’t know any young women, you can click here and Danica McKellar will send books to the library or school of your choice and send you an autograph.

That’s not exactly it, perhaps they’ve recently changed it, but *you* have to buy 5 books and donate them to a library, she’ll send you a signature in return.

12. dirk alan Says:

etch a sketch

13. Jonathan Says:

Winnie Cooper. Sigh.

I’m intrigued by four-dimensional beings. It’s hard to wrap my head around the concept of being able to look through something as easily as we three-dimensional beings can look down or up at something. It’s equally difficult for me to imagine not being able to look down or up at something, but that just might be my dyscalculia.

Basically, what I’m asking is just how would a four-dimensional being ‘see’? Or for that matter, how do they ‘see’ things? I’m attempting a science fiction novel for Young Adults that will involve a four-dimensional being, and this would be very useful to know.

14. Naomi Says:

Another interesting book is Einstein’s Dreams by Alan Lightman. It discusses what if time were a place, what if time flowed backward, what if time were circular, etc and many other ideas.

15. sohcahtoa Says:

I didn’t know Flatland was its own story! I just remember it from watching the series Cosmos when I was a kid.

16. Tradução: “S03E12: The Psychic Vortex (O Vórtice Psíquico)” « The Big Blog Theory (em Português!) Says:

[…] feita a partir de texto extraído de The Big Blog Theory, de autoria de David Saltzberg, originalmente publicado em 11 de Janeiro de […]