On February 19th, our first day of FSL Math sessions, David Kohler and Natascia Tamburello joined us once again (familiar faces from our quantitative reasoning weeks in September!) Christina Koch, a Master’s student from UBC, also took the time to break several stereotypes surrounding “the mathematician” and to share her versatile version of the profession.
We started off our math sessions last Tuesday by exploring codes. From switching letters and numbers to shiftingletters up or down, we looked at a few simple ways that codes have been used and created. Using David’s spreadsheets, we encrypted and decoded messages in which the letters were shifted up or down 1 to 25 times. This method, called Caesar’s Code – popularized by, you guessed it, Julius Caesar – was used as a basis for German codes in WW2 (for the Enigma machine).
I was most intrigued by the different methods used to guess the key (number to shift the letters) for another group’s message. For example, our messages didn’t have spaces, but if they had, we could have assumed that double letters were vowels often found together (fool, feet) or double consonants (add, guess.) Single letters are also helpful as they are almost always the vowels i or a (as long as there are no numbers.)
Here’s an example:
sghr hr z rdbqds ldrrzfd
Now if you haven’t felt the urge to run away, you can ask…
- Is Z near any vowel that stands alone?
Z is near A
- Is R near any vowel or consonant that is frequently doubled?
R is near S
This method, called frequency analysis, happens to help us with this message. It turns out that Z is shifted 25 times from A (or -1 times) and R is shifted 25 times from S (or -1 times.) We can try shifting the rest of the message back up 25 letters and we get…
this is a secret message
If you decoded the message, congratulations! You would have been quite the asset for Caesar’s army, and it seems many others since.
However creating codes is far from a military-only task. As we explored last Tuesday, the “strength” of your password is entirely based on the how long it takes for a computer to “decipher” the code, if you will, that you have created. If you have few characters and only letters or numbers, your password requires fewer “bits” (small 1s and 0s, on and off switches that hold information.) This means that a computer can find which numbers or letters used quite easily.
The 7 character “password”:
for example, uses just numbers (only 10 possible characters) and requires only 23 bits – a measly sum that most computers would take just over a minute to crack!
Despite the wealth of facts and figures however, the most fulfilling part for me came last and left me with such a valuable wealth of unknown. Not unlike Caesar’s opponents, we were cast into a fray of age old math problems, some with answers just as famous and others famously unanswerable. Yet the wonder of these questions does not lie in how long they have lasted or how long they will endure; instead it lies in the fluttering at the back of my mind as I explore them for the first time. Their value can be found in my abandon at the thought of a possibility and my excited exasperation when that possibility leads no closer to a solution. Our fascination with these enigmas is rooted so deeply in not knowing – in crunched up balls of paper, furrowed brows and sleepless nights when our minds wander just beyond their borders.
David did not give us the answers this week, but it feels as if we were given so much more. We got to jump up and down in frustration and delight, and for one week, we could wonder at all we do not know – without the inconvenience of an answer.
Photo credit: secretcodebreaker.com
About the contributor: AnnieEnergy loves to wonder and ponder, explore and rejoice in finding that she barely understands the tiniest smidgin of what happens in the world and of what is possible. She also enjoys writing, playing and sharing music, laughing in the sun and dancing in the rain.