Okay, so just what the hell DID the Mathemagician write to his brother, King Azaz of Dictionopolis? “Why, just last month I sent him a very friendly letter, which he never had the courtesy to answer.”
Here’s the “text” of his letter, printed on page 199 of the trade paperback edition of Norton Juster’s THE PHANTOM TOLLBOOTH:
4738 1919,
The salutation looks to me like “Dear Azaz,” the sign-off is probably “Yours truly,” but the signature is two digits too short to be “Mathemagician.” Maybe some childhood nickname?
Anyone more skilled at ciphering want to translate for me? Or is this letter completely clear to everyone who didn’t goof off in every math class past 6th grade? (Milo seems to be able to have read it, even if Azaz couldn’t.)
I doubt that it actually ciphers into anything. If the “1919” is Azaz, which is a reasonable assumption to make, then there are only ten symbols available to code for ten letters, since the numbers do not pair up to represent one letter. Also, if 1919 is Azaz, 3 different words end with an A, which is unusual in English, and there are more Z’s than one would expect. Additionally, the first “word” (4738) can’t be Dear, since I’m assuming that 1 means A (from the Azaz), not 3.
Of course, if somebody can work out something involving letter pairs, then this is all nonsense (making it rather in the spirit of the book, no?). I don’t think that it works that way, though, for the reasons cited above and because there are “words” with an odd number of numbers in them.
Personally, I always thought that it was just a joke, with no real meaning, with the 1919=Azaz(?) thing thrown in to make it seem slightly more plausible. Why would the Mathemagician bother to use words (even in disguised form) to communicate stuff, when to him, numbers are the be-all and end-all?
This is a kid’s book, right? So I assume it must be a real puzzle, despite GilaB’s misgivings, in case some young reader was interested enough to work it out. So therefore it can’t be terribly difficult. Well now I really feel like an idiot.
I don’t know, Uke - despite the evidence of 1919 = Azaz, it can’t be a simple letter/number substitution. For one thing, the first word of the body would have to start with a double letter, and the only ones I can come up with are “eek” and “ook.” Unless King Azaz is a mouse or a Librarian, this doesn’t make much sense.
And what are those zeros doing there? If we try to develop a scheme where 1 is the beginning and 9 is the end of the alphabet, where does that leave those zeros?
Do we have any other clues to work with? You say “Milo seems to be able to have read it” - does Milo give any indication of what the letter is about? (Sorry, I haven’t read the book.)
Um, forgive me, but to me a translation misses the whole point. The dear Mathemagician is simply stating that numbers are (nearly) universal. The letter is just a list of numbers, each of which can be read by any numerate person on earth.
(Of course, the deeper truth is that math is its own language, or perhaps a lingua franca, easily learned in addition to one’s word-language.)
Yep, I agree the ‘667’ tells us it’s not linear - if it’s anything at all.
I’m sure I read that Juster was a keen amateur mathematician and a former architect so it might well be genuine coding. I think there is some humorous mathematical dimension to this. FWIW, my guess is the coding can only be resolved with the application of a known but somehow discredited equation. And I’m not sure finding the correct way to apply the equation would be straightforward, either.
IMHO, there’s no way of doing this unless you’re totally out there as a code breaker or are ‘in’ on some of the joke.
*“But maybe he [Azaz] doesn’t understand numbers,” said Milo, who found it a little difficult to read himself.
“NONSENSE,” bellowed the Mathemagician. “Everyone understands numbers. No matter what language you speak, they always mean the same thing. A seven is a seven anywhere in the world.”*
This seems like Milo reads it, though with difficulty. And the response confirms xtnj.'s thesis. But why list numbers in a “friendly” message to one’s estranged brother?
I always assumed it was a joke, as GilaB suggests, but I was reading the novel to little 5-year-old Banjo the other day and he insisted that I tell him what the letter said. I held him off by telling him the Mathemagician was inquiring after Azaz’s bunions, but the query led to 4 AM ceiling-staring, and thence to MPSIMS.
FWIW, remember the argument between King Azaz and the Mathemagician? Which is more important, numbers or letters?
I think the Mathemagician was sending a letter to King Azaz in the “language” of mathematics, but which could only be understood in mathematics, it can’t be translated into letters (or English).
Think of it this way; two people who don’t have a common language between them, in fact they speak entirely separate languages; one speaks French, the other Algonquin. The French speaker sends a note off to the Algonquin speaker, which he of course finds totally incomprehensible. Same thing here between the Mathemagician and King Azaz.
It’s been a while since I read TPT (which means it’s time for me to dig it out again). But I do recall I found much of it capricious. It has a latter-day Lewis Carroll feel to it, and seemed to have nonsense for nonsense’s sake at times. Just a bit of leavening for the serious nonsense in there, you understand.
I think that this falls into that category. The text of the letter is actually of no consequence to the plot, true? So knowing it was a “friendly letter” is more important than knowing precisely what it said. And the follow-up argument (“numbers are numbers all over the world”) is more important than what he said with those numbers.
It’s tougher to come up with meanings for a string of numbers than it is for The White Knight’s song, though, as we usually think and communicate in words rather than numbers. Yet we want to make sense of it (ie, translate it into words) because that’s what the characters in the book do. But I think it’s a red herring.
It can’t be something as simple as a cipher with one number standing for a letter. And it’s not written in equation form, so it can’t result in a sum. Anything more complicated than that could very well be lost on young readers who try to solve the puzzle. It’s also a little ridiculous to think of a string of numbers (which represent amounts) as being “friendly” in the same way words are (since words are names given to feelings, things, and which communicate emotion). Math is actually dispassionate, unlike language. In the words of Foghorn Leghorn, “It’s a joke, son. Don’tcha get it? (aside) Nice kid but a little slow.”
Which reminds me of one thing that bugged me when I first read the book myself, as a kid.
The Mathemagician, the Dodecahedron, and the other residents of Digitopolis communicate with Milo, Tock, and the Humbug with…words.
Earlier, Azaz tells Milo, “Never mention numbers here. Only use them when we absolutely have to.” Numbers rarely come up in the Dictionopolis chapters (and in bizarre ways, suck as Milo’s six million year prison sentence). But in Digitopolis, the use of despised words is an everyday given.
The Mathemagician, the Dodecahedron, and the other residents of Digitopolis communicate with Milo, Tock, and the Humbug with…words.
Earlier, Azaz tells Milo, “Never mention numbers here. Only use them when we absolutely have to.” Numbers rarely come up in the Dictionopolis chapters (and in bizarre ways, suck as Milo’s six million year prison sentence). But in Digitopolis, the use of despised words is an everyday given.**
I agree with your point, but then, how would you effectively show the people in Digitopolis communicating without thoroughly confusing the reader? Reality is “bent” at this point to allow for the flow of the story.
I don’t have time to work on it now, but it seems quite possible that the message does translate. It is probably something like the old telephone cipher, where each number stands for one of the three letters with it on a telephone keypad. Unfortunately, it couldn’t be that exactly, since ‘Z’ doesn’t appear on telephones. Usually, the cipher uses one and zero for ‘Q’ and ‘Z’, since they don’t have letters on the phone.
So, if 1919 is ‘Azaz’, it can’t be the telephone cipher, at least not in its simplest form.
It’s incorrect to say 1919 “is” Azaz in this particular case; it’s better to say 1919 “means” Azaz.
The numbers are individual units that by and large have no individual meaning, but can be grouped together to form strings that label objects and/or concepts. Exactly like letters and words. All that’s going on here is that numbers are being made to conform to the patterns of language.
So why does 1919 mean Azaz? Simple - A and Z are the first and last letters in the alphabet, and 1 and 9 are the first and last numbers in the basic cardinal numeric system. It’s just a similarity of patterns rather than a direct correspondence.
I know, I know, it doesn’t explain the presence of zeroes, but this is just a theory anyway.
You guys are completely forgetting the possibility that each set of numbers is a character, a la Chinese characters. While the individual numbers in “1919” don’t correspond to the individual letters of “Azaz”, It could be that each set of numbers equal a different word. For all we know, “4” could mean “abracadabra.” And in my world, “4” DOES mean “abracadabra.”
My copy of The Phantom Tollbooth is now in a box of my children’s books in my attack back in Kentucky. However, I actually remember spending some time thinking about this puzzle. I seem to remember that the numbers were not printed in straight lines. In each line, some letters were higher or lower than others. Could somebody please get out their copy and check whether this is true?
This is true in my copy, but it doesn’t have anything to do with the code. The numbers are like that because of the typeface they used to print the book. I’ve seen a lot of books where the numbers are printed like that.
Two books I MUST force the kids to read. TFT and " The 21 Balloons".
Is TFT still in print, or do I have to get on the Glinternet?
Uke, ya cut a mean figure in that jacket mah man. And, nice decoder ring. What happens if you spin the bezel on your Captain Midnight Watch in a dextrorotary fashion instead of a levulorotary fashion??
And, nice decoder ring. What happens if you spin the bezel on your Captain Midnight Watch in a dextrorotary fashion instead of a levulorotary fashion??