"The Lost Symbol" - Magic Squares and the Masonic Cipher

Summary

Highlights

• Magic squares, used in "The Lost Symbol," create intrigue through their unique numerical properties. 🔢
• Albrecht Durer's artistic legacy includes a famous magic square from the 1500s! 🎨
• The Masonic Cipher, also known as the Pig Pen Cipher, was a fun way to encode messages! 🕵️‍♀️
• Understanding these historical puzzles gives depth to Dan Brown's narrative. 📖
• The lecture highlighted how math, art, and storytelling interconnect beautifully. 📚

Key Takeaways

• Magic squares are numerical arrangements where rows, columns, and diagonals share the same sum! 🧮
• Dan Brown cleverly uses historical ciphers and puzzles to enrich his storytelling. 📚
• The Masonic Cipher, or Pig Pen Cipher, is a playful way to disguise messages. 🕵️‍♂️
• Benjamin Franklin's magic square, while not perfect, adds an interesting layer to puzzle history. 🧩
• Learning about historical figures like Albrecht Durer enriches our understanding of historical art and math. 🎨

Overview

Chapters

• 00:00 - 00:30: Introduction to The Lost Symbol The opening chapter humorously sets the stage for the quest for the 'lost symbol,' humorously describing a scenario where the symbol was accidentally consumed on a pizza slice. The narrator jokes about the impossibility of Dan Brown's attendance and references the historical figure Albrecht Durer, noting his death in the 1500s.
• 00:30 - 01:30: Dan Brown's Inspirations The chapter titled 'Dan Brown's Inspirations' seems to be a playful introduction, perhaps starting with a humorous note about the absence of historical figures like the inventor of time machines and Benjamin Franklin. The narrator is left to share insights into where Dan Brown drew inspiration for his novel.
• 01:30 - 02:30: Albrecht Durer and His Legacy The chapter introduces Albrecht Durer, suggesting his significance and legacy. It hints at the cultural or historical impact of Durer and encourages readers to further explore his contributions independently. The chapter appears to offer interactive elements, such as games, to engage the audience and deepen their understanding of Durer's work and life.
• 02:30 - 05:00: The Magic Square Concept The chapter titled 'The Magic Square Concept' introduces a character who lived in Germany during the early 1500s. It hints that this person was very exciting, setting the stage for further exploration of their life or contributions, possibly in relation to the magic square concept.
• 05:00 - 09:00: Types of Magic Squares The chapter provides a brief background on the origins of the name 'Durer'. Albrecht Durer's father, who also bore the same name, was from Hungary. The family's original surname was 'Djilt', meaning 'door' in Hungarian. Upon relocating to Germany, the name was translated into 'Tur', the German word for 'door', and eventually evolved into 'Durer'. This etymological transformation highlights the connection between names and cultural identity through language.
• 09:00 - 15:00: Lo Shu - The Divine Turtle The chapter discusses the multifaceted genius of Albert Door, who was renowned across various domains including philosophy, mathematics, sculpture, and painting. One of his notable works mentioned is a wood carving entitled 'Melancholia'.
• 15:00 - 19:00: Contributions to Magic Squares The chapter titled 'Contributions to Magic Squares' discusses the intersection of art and technology. It reflects on the challenges faced by artists, specifically highlighting that having access to various tools does not automatically lead to creativity. The narrative suggests a melancholic artist surrounded by tools but struggling with creativity, illustrating that inspiration and creative breakthroughs are not guaranteed, even with ample resources.
• 19:00 - 23:00: The Brumgnach Strachey Method The chapter titled 'The Brumgnach Strachey Method' discusses an intriguing element found within a picture, specifically a four by four magic square. The speaker notes a sense of sadness in the picture but highlights the significance of this magic square, which caught the interest of both the speaker and an individual named Dan Brown. The chapter focuses on the allure and mystery associated with the magic square.
• 23:00 - 26:00: Magic Square Calculation Program This chapter introduces the concept of a magic square, which is a grid of numbers arranged in such a way that each row, column, and main diagonal have the same sum. This consistent sum feature is the defining characteristic of a magic square.
• 26:00 - 32:00: Benjamin Franklin's Magic Square The chapter 'Benjamin Franklin's Magic Square' explains the formula for calculating the sum of numbers in a magic square. Specifically, it mentions that the sum equals m times m squared plus one divided by two. For a four by four square, the sum is calculated as 4 times 4 squared plus one divided by two.
• 32:00 - 41:00: Introduction to Ciphering The chapter introduces the concept of ciphering by beginning with basic arithmetic operations, such as addition and multiplication, to reach a consistent sum. The example provided involves adding a series of numbers which all result in the same sum, 34. This may be a foundational introduction to a more complex mathematical ciphering or encoding system discussed later in the material.
• 41:00 - 55:00: The Masonic & Pig Pen Ciphers The chapter discusses magic squares, specifically focusing on the Masonic and Pig Pen ciphers. It starts by explaining the concept of a magic square, which is defined by having rows and columns that add up to the same number—in this case, 34 for a four by four square. The chapter further categorizes magic squares into types, highlighting that a four by four square is not only even but also referred to as 'doubly even.'
• 55:00 - 63:00: Magic Squares & Ciphers in The Lost Symbol The chapter discusses the concept of magic squares, highlighting the difference between 'doubly even' and 'singly even' magic squares based on their divisibility by numbers like two and four.
• 63:00 - 72:30: The Complexity of Dan Brown's Ciphers The chapter discusses the concept of magic squares, specifically focusing on singly even and doubly even magic squares. Singly even magic squares are those where the order is divisible by two but not by four, such as six by six squares. In contrast, doubly even magic squares are those that are divisible by both two and four, like four, eight, 12, and 16. In the chapter, there is a focus on explaining these classifications with examples.
• 72:30 - 80:30: Breaking Codes and Understanding Symbols The chapter titled 'Breaking Codes and Understanding Symbols' delves into the concept of 'magic squares', focusing on odd magic squares. It mentions numbers like three, five, seven, and nine as examples of these odd magic squares, noting their longstanding presence and significance.
• 80:30 - 86:30: Concluding Thoughts The chapter discusses the historical significance and intrigue surrounding magic squares, including a mention of the famous Lo Shu magic square.

"The Lost Symbol" - Magic Squares and the Masonic Cipher Transcription

• 00:00 - 00:30 - 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,
• 00:30 - 01:00 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,
• 01:00 - 01:30 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,
• 01:30 - 02:00 who lived in Germany in the early 1500s. He was a very exciting person.
• 02:00 - 02:30 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.
• 02:30 - 03:00 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.
• 03:00 - 03:30 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.
• 03:30 - 04:00 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.
• 04:00 - 04:30 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.
• 04:30 - 05:00 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,
• 05:00 - 05:30 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.
• 05:30 - 06:00 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.
• 06:00 - 06:30 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,
• 06:30 - 07:00 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,
• 07:00 - 07:30 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
• 07:30 - 08:00 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,
• 08:00 - 08:30 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
• 08:30 - 09:00 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.
• 09:00 - 09:30 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.
• 09:30 - 10:00 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,
• 10:00 - 10:30 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.
• 10:30 - 11:00 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.
• 11:00 - 11:30 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,
• 11:30 - 12:00 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
• 12:00 - 12:30 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.
• 12:30 - 13:00 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,
• 13:00 - 13:30 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,
• 13:30 - 14:00 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,
• 14:00 - 14:30 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,
• 14:30 - 15:00 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
• 15:00 - 15:30 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?
• 15:30 - 16:00 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.
• 16:00 - 16:30 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.
• 16:30 - 17:00 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,
• 17:00 - 17:30 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.
• 17:30 - 18:00 - 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.
• 18:00 - 18:30 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--
• 18:30 - 19:00 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,
• 19:00 - 19:30 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,
• 19:30 - 20:00 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,
• 20:00 - 20:30 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.
• 20:30 - 21:00 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.
• 21:00 - 21:30 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?
• 21:30 - 22:00 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,
• 22:00 - 22:30 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,
• 22:30 - 23:00 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.
• 23:00 - 23:30 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.
• 23:30 - 24:00 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,
• 24:00 - 24:30 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,
• 24:30 - 25:00 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,
• 25:00 - 25:30 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.
• 25:30 - 26:00 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,
• 26:00 - 26:30 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,
• 26:30 - 27:00 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,
• 27:00 - 27:30 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
• 27:30 - 28:00 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.
• 28:00 - 28:30 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?
• 28:30 - 29:00 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,
• 29:00 - 29:30 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,
• 29:30 - 30:00 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,
• 30:00 - 30:30 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,
• 30:30 - 31:00 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
• 31:00 - 31:30 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.
• 31:30 - 32:00 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,
• 32:00 - 32:30 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.
• 32:30 - 33:00 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.
• 33:00 - 33:30 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,
• 33:30 - 34:00 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.
• 34:00 - 34:30 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.
• 34:30 - 35:00 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.
• 35:00 - 35:30 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,
• 35:30 - 36:00 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.
• 36:00 - 36:30 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?
• 36:30 - 37:00 - [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?
• 37:00 - 37:30 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.
• 37:30 - 38:00 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.
• 38:00 - 38:30 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.
• 38:30 - 39:00 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.
• 39:00 - 39:30 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,
• 39:30 - 40:00 and number seven is here, and number eight is this position. Nine, it's here, 10, 11, and 12, and then 13, and 14,
• 40:00 - 40:30 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,
• 40:30 - 41:00 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.
• 41:00 - 41:30 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.
• 41:30 - 42:00 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.
• 42:00 - 42:30 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."
• 42:30 - 43:00 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.
• 43:00 - 43:30 Thank you very much. (students clap)