This blog is about Simon, a young gifted mathematician and programmer, who had to move from Amsterdam to Antwerp to be able to study at the level that fits his talent, i.e. homeschool. Visit https://simontiger.com
Simon keeps thoroughly enjoying Brilliant’s approach to intelligence and learning (even though he sometimes dislikes the way the daily challenges are formulated). His latest stats:
From the courses he has done most I conclude he’s mostly into Computer Science and real world problem solving at the moment:
Below are some screen shots of the daily challenges he was especially curious about lately and also excerpts of his taking part in Brilliant’s discussions:
I noticed it’s a cyclic quadrilateral and I know that the opposite angles of a cyclic quadrilateral have to add up to 180 degrees. At first I thought: How am I even going to go about doing it, because it’s so cryptic and so full of information. But once I solved it, it actually became quite easy to draw!
The end of 2019 was packed with logic. Simon even started programming an AI that would solve logical puzzles, here is the beginning of this unfinished project (he switched to programming a chess AI instead). In the two vids below, he explains the puzzle he used as an example and outlines his plan to build the AI (the puzzles come from Brilliant.org):
And here are some impressions of Simon working on the puzzles and showing them to his sis:
Simon working on a simplified version of a search engine, including just a few documents, and performing calculations to determine how many searches one should do to make creating an index of all the documents efficient (something he has picked up in Brilliant.org’s Computer Science course.
This is an example of the learning style that Simon enjoys most. He really likes doing the daily challenges on Brilliant.org. He later sometimes discusses them with other participants or even writes wikis!
While in Southern France, Simon really enjoyed solving this puzzle (he originally saw in a Brilliant.org vid). He was so happy with his solution he kept drawing it out on paper and in digital apps, and later shared the puzzle on Twitter. This sparked quite a few reactions from fellow math lovers, encouraged Brilliant to tweet new puzzles and now Brilliant follows Simon on Twitter, how cool is that!
Had great fun learning how to crack codes using Python! Simon is currently following the Programming with Python course on Brilliant.org and showed me how to see whether an encrypted piece is gibberish or a real text is hidden behind it.
A Caesar Shift is a simple cipher, which was a standard in Roman times. It works like this: shift every character by some fixed amount in the alphabet. Something like this:
Example: Suppose some professor writes his name on his board:
It’s encoded with a caesar shift. Because it’s a professor’s name, it probably starts with “Dr.”, so it’s probably a shift that turns D into E, and R into S. So we can work backwards from that shift, and get:
That was an easy one, so let’s do something more complex with code.
One of the messages below is a real text, encoded using a Caesar Shift, the other one is just a random sequence of letters. Can you tell which one is which?
Simon has explained a way to see whether the encrypted piece contains meaningful (real) text: one can plot the frequency of each letter as it’s used in the encrypted piece. If all letters have generally similar frequency, it’s not a real text, because in real texts, certain letters are encountered much more often than others. Below are the frequency plots Simon made for the texts above, using a Python package called matplotlib:
Frequencies for text 1:
Frequencies for text 2:
As you can see, the second plot depicts a greater variety in frequencies. “For example, o appears the most, but g does not appear that much. And t does not appear at all!” Simon showed me.
As it turned out, we could actually use our knowledge about which letters naturally appear more frequently in English-language texts to crack the code! “Which letter is the most frequent one in English writing?” Simon asked me. “Letter e!” I guessed. “So now we know that the letter o in the encrypted text stands for e in the real text!” Simon exclaimed. “All we have to do to decode it now is simply shift the letters by 10 letters back, because e is 10 letters behind the o!”
So, what is the message about? Simon tweaked Brilliant’s code to make sure it shifted by the amount of 10…
I met a traveller from an antique land Who said: “Two vast and trunkless legs of stone Stand in the desert . . . Near them, on the sand, Half sunk, a shattered visage lies, whose frown, And wrinkled lip, and sneer of cold command, Tell that its sculptor well those passions read Which yet survive, stamped on these lifeless things, The hand that mocked them, and the heart that fed: And on the pedestal these words appear: ‘My name is Ozymandias, king of kings: Look on my works, ye Mighty, and despair!’ Nothing beside remains. Round the decay Of that colossal wreck, boundless and bare The lone and level sands stretch far away.”
So, it’s about Archeology! This is the poem Ozymandias by Percy Shelley (1818).
Encoder / Decoder:
alphabet = "abcdefghijklmnopqrstuvwxyz"
# convert between letters and numbers up to 26
# How to encode a single character (letter or not)
def caesar_shift_single_character(l, amount):
i = letter_to_number(l)
if i == -1: # character not found in alphabet:
return "" # remove it, it's spaces or punctuation
return number_to_letter(i + amount) # Caesar shift
# How to encode a full text
def caesar_shift(text, amount):
shifted_text = ""
for char in text.lower(): # also convert uppercase letters to lowercase
shifted_text += caesar_shift_single_character(char, amount)
### MAIN PROGRAM ###
message = """
paste the text here
code = caesar_shift(message, 2)
Code for Plots:
import matplotlib.pyplot as plt
alphabet = "abcdefghijklmnopqrstuvwxyz"
code = """
paste the text here
letter_counts = [code.count(l) for l in alphabet]
letter_colors = plt.cm.hsv([0.8*i/max(letter_counts) for i in letter_counts])
plt.bar(range(26), letter_counts, color=letter_colors)
plt.xticks(range(26), alphabet) # letter labels on x-axis
plt.tick_params(axis="x", bottom=False) # no ticks, only labels on x-axis
plt.title("Frequency of each letter")
Simon loves challenging other people with math problems. Most often it’s his younger sister Neva who gets served a new portion of colourful riddles, but guests visiting our home also get their share, as do Simon’s Russian grandparents via FaceTime. Simon picks many of his teaching materials in the Mathematical Fundamentals course on Brilliant.org, and now Neva actually associates “fundamentals” with “fun”!
Sunday at the beach, Simon was reenacting the 5 doors and a cat puzzle (he had learned this puzzle from the Mind Your Decisions channel). The puzzle is about guessing behind which door the cat is hiding in as few guesses as possible, while the cat is allowed to move one door further after every wrong guess.
“Here’s a fun fact!” Simon said all of a sudden. “If you add up all the grains of sand on all the beaches all over the world, you are going to get several quintillion sand grains or several times 10^18!” He then proceeded to try to calculate how many sand grains there might be at the beach around us…
In the evening, while having a meal by the sea, Simon challenged Dad with a Brilliant.org problem he particularly liked:
Simon’s explanation sheet (The general formulas are written by Simon, the numbers underneath the table are his Dad’s, who just couldn’t believe Simon’s counterintuitive solution at first and wanted check the concrete sums. He later accepted his defeat):