- Good afternoon, ladies and gentlemen. Thank you for coming. We're looking for the lost symbol, but it was on his slice of pizza, and he ate it. It's gone. I tried to get Dan Brown to come, but he couldn't make it. Albrecht Durer is kinda dead from 1500s, so he couldn't make it. Time machine's a little broken. Benjamin Franklin couldn't make it either, so you're stuck with me, so here I am. What I'd like to do with
you is just to show you a few places where this
gentleman, Dan Brown, got his ideas for this novel, and how he kinda put it all together. Hopefully, it will stimulate you, and you will do some
research on your own, okay? There's a few games in
here that are fun to play. First, let me introduce
you to Albrecht Durer. Albrecht Durer was a gentleman, I assume he was, let's see, who lived in Germany in the early 1500s. He was a very exciting person. His father, also named Albrecht Durer, came from Hungary. Their original name was, I believe, Djilt, something like that,
which means door in Hungarian. When they moved to Germany,
he translated it into Tur, which is door, and eventually, it came Durer, which means door. It's Albert Door, there you go. Now, this guy was a genius. He was a philosopher, a mathematician, a sculptor, a painter,
you name it, he did it. You name it, he did it. One of the things that he did was, he made this wood carving, Melancholia. That's right here. You can read all about
it if you want to go on the internet and read it. What you see, it's a comment on art, and technology, and you
see, there's an artist here. He's got all the tools around, and she, I believe, is
very melancholy because, even though you have all
these tools and stuff, creativity doesn't always
come to you, you see. So there's a kind of
sadness to this picture, but what's of interest
to us and to Dan Brown was this little piece back here. This little piece back there
is, it's a magic square. Let's see if I can find it. This is a magic square. It's a four by four magic square. You see it has four rows and four columns. Let me explain to you
what a magic square is. A magic square is an
arrangement of numbers so that each row, each column, and each main diagonal has the same sum. When all the numbers are
added, has the same sum. The value of the sum is always equal to m times m squared plus one over two so that, in his case,
a four by four square, the sum is equal to four
times four times four, is 16, plus one over two, so you
see that, in his case, the sum is equal to, 17
times two, is equal to 34. If you add each row, 16,
three, two, and 13, that's 34. This is 34, this is 34, this is 34. This is 34, this sum is 34,
this sum is 34, this sum is 34. This sum is 34, and this sum is 34. That's a magic square by definition. Now, going a little bit
more into magic squares, there are three types. Obviously, a four by four
is an even magic square. It's called even. Not only even, but it's
called doubly even. The reason it's called doubly even, it's because it's divisible by two, and it's divisible by four. See, four is divisible by two and by four. There is also a singly
even type of magic square. A singly even is divisible by two, but not by four. For example, a six by six is
a singly even magic square because six is divisible by two evenly, but it's not divisible by four. A four, eight, 12, 16,
those are all doubly even, but six, 10, 14, et cetera,
are not divisible by four, so those are singly even. Then there's the odd magic squares. The odd, like three, five,
seven, and nine, et cetera. These magic squares have been around for thousands of years. There are some very famous magic squares. This is one of them. There's another famous magic square, and it's called the Lo Shu magic square. Let me show it to you. This is probably the most famous one, the Lo Shu magic square. Here it is. The story goes that,
thousands of years ago, by the Lo Shu River, they
had some sort of a problem, and they didn't know
exactly how many things to sacrifice in order
for something to happen. Then the answer came on the back of this turtle from the river. You can see the back of
the turtle has one dot, has two dots, has three dots, has four dots, five dots, et cetera. If you look at the way
this thing is arranged you see it's arranged this way. That's a three by three magic square, or The Divine Turtle. This is probably the most famous one. You see that each row, each column, and each main diagonal,
since the order is three, the sum is going to be three
times nine plus one over two. This is 10, 10 over two is five, and five times three is 15. You can see that each horizontal, each vertical, and each
main diagonal adds up to 15. I did some work on the odd magic squares, and the doubly even magic
squares were figured out by Mr. Durer in the early 1500s. The singly even, about 1918, there was a gentleman in England, and his name was Strachey. What he did was, he figured out that you could do the singly even by using combination of odd ones, this hardest one to do,
but you can generalize the particular way of doing it. I did some generalization last year, and I added my name to this. We have the Brumgnach Strachey Method. I wrote a paper on these magic squares, and I had a couple of people
from here help me out. What we did was, we
made a computer program. I wrote the paper. Professor Metaxas over
here, he wrote the code, and our technician Steve Trowbridge, he did the layout, and now, you can go on the internet, and you can say things like here, you can go to our website, and you can tell it the
size square you want, and calculate, and there's your square. You want to do a 25 by 25 magic square, well, here it is. Each vertical, each horizontal,
and each main diagonal adds up to 7,825. You guys, if you want to play with this, you're welcome to play. Let's do Durer's square, a four by four, and here it is. See, everything adds up to 34. Benjamin Franklin played
with magic squares, and he did an eight by eight. Here's an eight by eight magic
square by Benjamin Franklin. This is not Benjamin Franklin-- This is a real magic square. The problem with Benjamin
Franklin's square, it's not magic. Why? Well, it does a lot of magical things, but his two main diagonals
don't add up to 260, so by definition, it's not a magic square, because a magic square is
where each vertical sum, each horizontal sum,
and each main diagonal adds up to the same number. His does all sorts of other things, but it doesn't do that. By definition, it's not a magic square. The other concept that I'd
like to introduce you to, besides these magic squares, that Dan Brown used in his
latest novel The Lost Symbol is ciphering, ciphering. How do you write code so that nobody understands what you're writing? There was a movie out called, help me out, something whisperer, during World War II. - [Student] The Navajo. - The Navajo, the Army, the Marines. The Code Talker? - [Student] Code Talker,
I think that's it. - See, the old guys are
remembering all this. It's a story where the military took Native American Indians, and put one of them with each platoon, and they gave them a radio. Then these guys would talk
to one another in Navajo, and the Japanese didn't
understand what was going on. They didn't need a code. They had a built-in code, you see. That's one way of doing symbols. Now, this is a very interesting topic because there's whole
places in the government, the CIA, et cetera, that
tries to break codes that people use, code breakers. I don't know if anybody's
familiar with this, but how do you think we got our symbols, our numerical symbols? If you have these many
items, what do we write? One, well, the original ancient
way of writing one was this. If you have these many
items, what do you write? Two. If you have these many
items, what do you write? The original way they wrote
it was like this, three. If you observe what's going on, they're counting the
number of interior angles. Look at this. Here's one interior angle. Here's two interior angles. Here's one, two, three interior angles. That's why, how many things we got there? Seven. The original way of writing
a seven was like this, and in parts of the world, it still is. Why? Because there's one, two, three, four, five, where's the other two? I don't know, there's seven of them. (laughs) I can't see it. As my students know, the excuse for that is that I'm too close to the board, and I can't see. - [Student] Maybe there's
a line under the seven. - Yes, five, six, seven. Guess what. No interior angles, zero. Whether that's true or not, I don't know, but that's one way of
explaining our symbols to denote a certain number of items. Now, in the 1300s and the 1400s, there was a society called the Masons that wanted to communicate
among themselves without other people
understanding what they wrote. What they did was this. You see, they made an x, and they made-- Let me put it the other way. They made an x, and they made a structure that looks like this. Now, looking from above, this may look like some sort of a farm, and usually, pig pens look like this. That's why this is also
called the Pig Pen Cipher. The idea of a cipher is to use a symbol to denote a concept. What they did here is, they
wrote the alphabet like this, A, B, C, D, E, F, G, H,
I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z. I'm showing off. If you want to refer to the
first letter in that position, you just write it. For example, you see, this would be an A. This would be an I, but
if you want to refer to the second number in the
letter in that position, you draw the symbol. For example, if you want X, it's in here, but it's the second letter,
so you put a dot in there. This is X, all right? Let's write something. I don't know, let's
write something simple. Let's write pig. Pig would be the second letter in here, the first letter here,
and the first letter here. That's pig. You can write anything you want like this. That's cool, but what's the problem now? Well, everybody knows this,
so what's the big deal? What's the secret? If you know I'm writing like this, all you gotta do is do that, and you know what I said. How do I make it hard
for you to figure it out? - [Student] Scramble it. - Yeah, you can simply put in a key. For example, don't start with A. We're going to communicate, however, I'm going to start like this. I'm going to start with
another word in here, key, and then A, B, C, D, E, F,
G, H, I, J, K, L, M, N, O, P, Q, R, but what's the problem? Well, I used it already. You see, so you can't. I used the K, the E, and the Y. A, B, C, D, E, F, E is no good, so you can't use these again. You can only use them once. We have to remember the
K, the E, and the Y. It's A, B, C, D, no E, F, G, H, I, J, no K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z. If I want to write pig now, I would have to write it this way. I would have to write P, I, and G. It's pig. This is P-I-G. Now, you see, it's harder because, if you know I'm writing this way, with a key in front, and you can put whatever word you want in there, as long as the receiver knows that word, they can figure out what the code is, what is being said. That's nice, but Dan Brown
wasn't happy with this. Says, "Yeah, that's cool, that's good," but it wasn't happy. What he did is, he took
Durer's magic square, he took Durer's magic square, the one from his Melancholia. Let's see, let's try to
go back here and find it. His magic square looks like this, one, and then here, 14, 15, four. Then he has nine, six, seven, 12. Then he has, I believe that's a five, five, 10, 11, eight. The top line is 16, 3, 2, 13. Now, at this point, let me show you how to make this four by four magic square according to Durer's directions. Durer said that, for a
four by four magic square, all you have to do, and this is guaranteed that it comes out every time, you have to start either here or here, and think of the two main diagonals. You start counting, but you
only write down the number if it falls on the main diagonal. If I doesn't fall on the main diagonal, then you keep the count, but you don't write down the number. For example, you would write, and you can start either here or here. Let's, one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16. You only write down the number if it falls on the main diagonal. Then you go backwards,
and you fill in the rest. One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16. Guaranteed, everything adds up to 34, but this carving, he did in 1514. If you look at the magic square
that he has in the carving, you see that, cleverly, he arranged it so that the date of the carving is the middle two numbers in the last row, which is very clever. This guy was pretty sharp. Let's see how he did this. There are other ways of
doing Durer's magic square. The way he did this was the following. He started over here, and he went this way, this
way, and this way going up. Here's the main diagonals. He wrote one, two, three, four,
and then he went that way, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, okay? Then, coming back, he went this way, the same way, this way,
this way, and this way. Coming back, he went,
one, two, three, four, five, six, seven, eight, nine,
10, 11, 12, 13, 14, 15, 16. This also is a magic square because each row, each column, and each main diagonal adds up to 34. But, very cleverly, he
made the middle two numbers of the bottom row come out with the date that he did this carving. This is the extra complication that Dan Brown put in his novel, so instead of putting in a key, he left this the way it was. However, he arranged the
letters in here, this way. He arranged the letters in here so that you would put
the first letter here, the second here, the third
here, the fourth here, fifth, sixth, seven, eight, so you had to know where the letters are. You see, they're scrambled,
definitely scrambled. That's another extra complication. Not only that, but he added a
third layer of complication. The message, after you
unscramble all the stuff, if you read the book, you'll see it, the message didn't mean anything. Why? It was in Latin. After your figured out that they use the Masonic cipher, or the Pig Pen Cipher, and it was arranged in this format of Durer's four by four magic square, and you figured out what the letters were in the proper order, you
now had to know Latin to figure it out. That's the story here. You have here a nice novel. If you like chase scenes, this is good. He's got all sorts of
symbols and stuff like that, and he claims this is
the lost symbol here. I don't know, that's a zero. No interior angles. It's a very interesting novel, and this is where he got all
these ideas from, you see, the magic squares, the ciphering, plus the extra complication that, after you've figured out
what the letters were, unless you knew Latin,
it had no meaning to you. That's basically it. Now, in another part of the book, he also uses Benjamin Franklin's square. This is Durer's square. He used Durer's magic square. He used the Masonic cipher. Then the message was
then written in Latin, so you had to know Latin. Then there was another
complication to the whole thing where he used an eight by eight
square by Benjamin Franklin. Let me go find this square for you here. Of course, we know that it's
not a magic square because, you see, here is the square, but the two main diagonals do
not add up to the magic sum. Now, just to see if that works, an eight by eight should add up to eight times eight squared
plus one divided by two. This should be the sum. That's a two, 64 plus one is 65, and that's a four, and
65 times four is 260. The sum here of each
row, each column, is 260, but the two main diagonals are not 260, so by definition, it's not a magic square, but look what else this thing does. It's amazing. If you add these, these, these, or these position, those are 260. This and the two corners are 260, this and this, you see, these arrows, these two corners are 260, this four corners are 260, the four corners and the
four middle ones are 260. Yes? - [Student] Did Franklin know that? - Yeah, yeah, yeah, he knew this. Then he made a 16 by 16 magic square. That, I did not check if it's true or not, but the eight by eight isn't. Mr. Brown stops here, says
eight by eight is okay. Although it's not a true
magic square, he uses it. Now he calls these bent
rows and stuff like that. The reason I'm showing you
these on the internet is, I hope people will go look, go look at all these
ideas of magic squares, and Masonic ciphers. As a matter of fact, there are websites where you can get the Masonic cipher as a font, you can install
it on your computer, and that's how I wrote
this little note for you. Then you can type in Masonic
cipher or Pig Pen Cipher. Now, what did I write here? Well, let's see. What did I write? Should I tell you? - [Student] What did you use as the key? - I don't know, let me see. I don't remember. That's why, every time you use a key, you should write it down. This is like having many passwords. The only person that
you're excluding from there is probably you because you forgot what password you used. Let's see, what did I write here? I wrote this. Now, one way that codebreakers use to break codes is that they try to figure out what language
it was written for. Then they look at the language, and they figure out which letter occurs most often in that language. For example, in English,
it may be the letter E. Then they look at the message, and they check which
symbol occurs more often. That's probably the E. Then they go from there. They try to break the code, but what is this? Notice, the first hint here is that it's laid out in a four
by four arrangement. That's one hint because, probably, probably, we introduce
this level of difficulty, or this one, or this one, but it's probably something to do with a four by four square. Probably, I'm gonna have
to read it this way. This is gonna be number one. This is number two, this is number three. This is number four. I'm sorry, number four is down here, if I'm using this one. Then number five is here,
number six is over here, and number seven is here, and
number eight is this position. Nine, it's here, 10, 11, and 12, and then 13, and 14, and 15, and 16. That's the arrangement of the symbols. Now, that's number one,
and according to this, this would be an E. Okay? If I did that, and I figured out, I'm gonna get gibberish. That's where the extra
complication comes in, and he mentioned it, maybe
there's a key to this. If you don't know the key, you don't know where to start. Well, since you're all my pals here, the key is the word key, just like I did over here. That's my key, the word key. This, which is the number one, is really a B. That's a B. Here's the number two. Number two, I'm over here now, that's an E. It's the second letter in that position. Here's the number three, and that is the first
letter in this position. That's a Y. Where's number four? Here it is, that's number four. Number four is the second letter here, you see, because it's got a dot. The number five is this,
which you see is N. Then the number six is
this symbol, which is D. Oh, look at that, beyond. If you decipher everything else, it says, "Beyond Dan Brown
and The Lost Symbol." That's the little presentation. I hope we didn't put you to sleep. I hope you enjoy the pizza, and read the book, and hope we brought you a little bit of entertainment, a little bit of insight
into symbols, ciphers, magic squares, and languages. Thank you very much. (students clap)
Very awesome! I've been curious about Masonic ciphers for a while. If you can keep up, it's a good watch.