Alice and the Frog of Destiny (1/3)
A short story about Convolutional Neural Networks
Alice awoke to find herself on a beach, guarded by three friendly looking pirates.
“Who are you?” she asked, cautiously. The three replies came one after the other,
Gathering herself together, Alice looked around. “And where am I?”
Before the pirates could answer, there was a puff of smoke, and a wizard appeared, holding a staff and wearing a pointy hat that folded over at the top.
“Hello Alice — sorry to startle you. My name is Bacchus Propagus. You’re on an island in the middle of the Sea with No Name. Or Sea-NN for short. Can I help you?”
“Yes — I’m not sure I should be here. How do I get home?”
The wizard looked bemused. “You’ll need to find the Frog of Destiny of course. He lives in a cave on one of these islands and can fly you home”
Alice had so many questions. “A flying frog? How will I know that I’ve found the Frog of Destiny? And on which island does he live?”
“Well, many islands have a cave that contains a frog, but the Frog of Destiny is the only one that wears sunglasses. You can’t miss him,” began Bacchus. “As for which island he lives on…I’m afraid I don’t know.”
Alice’s heart sank. “You don’t know? But there must be thousands of islands in this sea! I’ll never be able to find him…”
“Arr! Gee! Bee!” the pirates chorused again.
“I think we may still be able to help you.” Bacchus motioned to the pirates. “Arr, Gee, Bee — fetch the maps!”
The pirates shuffled off into the trees, still calling their names out at the tops of their voices and returned carrying heaps of paper, which they dumped at the feet of the wizard.
“You have maps of the islands?” Alice began to feel more hopeful.
“Yes, three maps of each island to be precise — one drawn by Arr, one drawn by Gee and one drawn by Bee.”
Bacchus thumbed through the piles and found the three maps for Tomato Island. Pointing at the maps, he continued,
“Conveniently, each island is a square, with each coast measuring exactly 32 miles in length. Arr, Gee and Bee have spent many hours scouring the terrain and have each independently produced a score, from 0 to 1 for each square mile. The complete grid of 1024 scores is shown on their map of the island.”
“But the scores don’t match between corresponding squares on the three maps?” Alice noticed.
“There’s no guarantee that the pirates will agree on the scoring for each square mile of an island. In fact, it’s a terrible sign if they do — it means all the inhabitants have the skin disease greyscale, so I wouldn’t venture there.”
Alice still wasn’t following. “Arr is scoring most of Tomato Island very highly, whereas Bee and Gee don’t seem to like it at all! What do the scores even mean?”
“That’s just the thing — nobody knows for sure,” replied the wizard. “However, we do know that each island has exactly one cave and that the scores on the maps give an indication of what’s inside it. For example, an island with many square miles rated highly by Arr is more likely to contain a tomato cave and an island with many areas favoured by Gee is more likely to contain a frog cave.”
“Frogs! Well that’s great — I’ll just look through these maps for one that’s rated highly by Gee…”
“No so fast…” the wizard interrupted. “Unfortunately, the islands rated particularly highly by Gee are also more likely to contain snake caves or even worse, Brussels sprouts caves.
“Eurgh!” Alice grimaced. “So these maps are useless then?”
“Not quite…” Bacchus sighed. “It’s rumoured that there exist mythical beasts who can look at the pirates’ maps of an island and tell instantly what’s inside the island’s cave. We call them ‘hyumans’, but no-one has ever seen one.”
“So even you can’t interpret the maps?”
Bacchus shook his head. “No…it’s all just a sea of numbers of me. However, I’ve been working on an intricate contraption that mimics the magical powers of a hyuman. Do you want to see it?”
“Yes of course!” Alice knew that the machine may be her only hope of finding the island with the cave containing the Frog of Destiny.
Alice and Bacchus walked to the old dilapidated shed that sat in one corner of the perfectly square island, accompanied by the three pirates, each carrying their collection of maps.
Once inside Bacchus opened a cabinet and took out what looked like twenty identical silver kaleidoscopes. Each was rectangular and had a window on one side, through which Alice could see dozens of tiny lenses. Before she could ask the wizard what these odd-looking objects were, she was startled by a small, squeaky voice, that appeared to come from one of the kaleidoscopes.
“How are you today Bacchus?”
“Very well thank you. Yourself?”
“Never been better. I must say, I like that hat — where did you get it?”
“I can’t remember actually — I keep meaning to send it back as it keeps flopping over at the top…”
“They talk?!” Alice asked, astounded.
“Oh yes,” replied the wizard. “Each one is a real conversational revolution — a conver-lution, you might say…that’s why I called this machine in front of us the conver-lution layer””
Alice was intrigued. She looked from the maps to the talking kaleidoscopes and on to the rest of the machine that stretched out across the shed.
“So tell me…how does it all work?”
To be continued…. for part 2, click here
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