All the letters lived together on islands in the Alphabet Archipelago in the Symbol Sea. Certain groups of letters knew each other very well. A,B,C were close as were X,Y, and Z. The letters lived at different addresses. The island addressing system was binary. A was 1 so he lived at 00001, and B was 2 so he lived at 00010, and so on. The distance between islands was the smallest number of bits that had to be flipped. So for example, A and B were not next to each other but lived 2 spaces apart, C at 00011 was the neighbor between them. The 00000 island was reserved for space.
The letters actually did not travel often from their islands. Numbers travelled more quickly than letters so the letters had developed a standard of communication. Messages were of the form X:Y where X was a string of bits that were the addresses of islands and Z was a string of bits that was converted into a message. What about punctuation like the : in the message? It was taken from the Symbol Sea. Numbers made up the atmosphere and could be grabbed from the air.
One night M, was gazing across the Symbol Sea, quiet as an ellipsis, and the reflection of the Moon added to her thoughts. “What if there was an M just like me, an M-prime, but different across the sea looking at the Moon reflecting?” She sent a letter to her friend J.
J: DO YOU THINK THERE ARE LETTERS JUST LIKE US THAT LIVE ON THE OTHER SIDE OF THE SEA? – M
M: I DON’T KNOW. LET ME ASK Z. – J
Some time later Z responded.
J,M: IF YOU TURN AROUND THAT IS THE WHOLE WORLD. – Z
M: Z TOLD ME THAT YOU THINK THAT THE WORLD IS REFLECTED BECAUSE YOU ARE M. – J
This annoyed M. Though by this point as Z pontificated to R about his thoughts, and R told his view to his friends, all the other letters had begun to discuss the matter. E was partial to M’s view whereas S was partial to Z’s.
E and S started to collaborate, and with the help of a few other letters they invented a ship. One day they showed up on M’s shore. They had made the voyage okay, E traveling to S, and then together to M. Over those several days, the sea was calm full of periods and commas and no roiling exclamations. M wanted to travel across the sea and look for her reflection. In order to settle the matter, E and S agreed on the voyage and that M could borrow their ship, but first they explained the operation of the craft.
E began, “The ship has two methods of propulsion. It has an adder and a flipper.” The adder was a propeller attached to a windmill whereas the flipper was a set of fins that used currents of exclamation.
“The way the adder works is through binary addition. For example, if you are at space, 00000, you can use the adder to add 1, to get to 00001, A, and again to get to 00010, B, as the 1 adds to 1 giving the result that carries to the next spot.”
“The way the flipper works is that you can flip any bit at any position for example M, at your island, you can visit J, if you flip the bit in the 1s place, so we’ll travel from 01011 to 01010, not accounting wind.”
“Yes, the wind” said S with import.
S began, “Once we got out to Sea, we discovered that the wind blew our craft to and fro over the symbols. Through careful observation, we discovered that if you are at position 01010 or at J’s island, there is a 1/2 probability of getting blown over to T’s island 10100, and a 1/2 probability of going to E’s island 00101. Curiously, if you are at space 00000, the wind doesn’t seem to have any effect.”
“What happens if you are at A, 00001, and the wind blows you over to the right or over to the left?” asked M.
“That’s a very interesting question,” said S “What happens is that the location truncates so you end up at space, so 00001 becomes 00000. If you are blown to the left, a 0 is tacked onto the end, so 00001 becomes 00010. So what the wind does, is that it shifts the entire binary location to the left or right, each with a probability of 1/2, with truncation occurring to digits that go beyond the first bit. As the atmosphere is made of numbers there is a constant inequality, < or >. This difference is the source of the wind.”
“Every day you can use either the adder or flipper,” said E.
“And every day the wind blows,” said S.
M accompanied E and S back to their homes, and then she propelled her way forward, first flipping her way to the different islands of the Alphabet Archipelago, sometimes a lucky shift sending her to her destination and other times closer to space.
M reasoned that since the letters lived in a 5-bit system, her reflection would live within 10-bits. So if her address was 01011, then her reflection lived at 1101000000. In between lay the Symbol Sea.
After putting together her supplies and receiving a message from the letters wishing her good luck, she started out.
M's Log
Each day there is a head or tail wind and an operation.
headwind or tailwind
f11 flip 11th bit
a add 1
00000 Start M' 10110|01101 M 00000 Finish
0 01101
1 00111 a,T
2 0100000011 f10,T
3 101000000110 f11,H
4 1011000001100 f9,H
5 001100000110 f13,T
6 0110000010 f2,T
7 1011000001 f11,T
8 0101100001 a,T
9 10110000 f1,T Almost
10 101110000 f4,H
11 10110000 f5,T
12 1101100000 f10,H
13 1011000000 f10,H
After 9 days of travel she saw land, but the wind swept her away, and on the 13th day, after circling her destination, she made it to 1101000000 where she made landfall. There lived on the island, the letter, m. M was so happy to meet m! M and m were quick friends. As M explained herself, m made mango lassi, and m told M about all the letters that lived around, and M told m about her friends. Although between their two descriptions, they had some trouble following each other. It was as if you learned the story of a long lost twin, and saw in his or her life similarities to your own, but all the same a difference. m produced some letters.
“These are from a game of chess that I am playing with p.”
m: 1. e4
m showed M the board so that she understood. M exclaimed, “That’s very peculiar. We write that as P-K4.” After comparing the systems of notation, m understood.
Just then, a letter came. m opened it.
m: i just saw a vessel coming in your direction, what is it? – z
“Take a look at this,” m passed the letter to M. M read the letter, it looked mostly the same, though letters were connected in places they were not, more curvy, smaller and connected. She understood its meaning. m wrote z. Together M and m visited other lowercase letters.
Eventually M went back home. When she arrived, she told all the uppercase letters of her travels and showed them this new way of writing the letters. It was a great discovery and work began on creating new vessels and means of communication. It was agreed between the upper and lower case letters that an extra bit would be used to distinguish between upper and lower case letters. Until this point, both letter systems were using the same way of encoding messages, on each set of islands 00001 were both A and a. So for the lower case letters, their islands did not correspond with their writing. In the new system, 00001 was A and 100001 was a, 00010, B, and 100010, b, and so on. Though mostly, communication stayed the same. Between all the letters the meaning was clear and bonds of friendship were formed from a to Z and z to A.
ThE eNd