Fair to Things You Have Forgotten
Pick six items uniformly from a stream of unknown length while holding only six. The items you threw away had exactly the same chance as the one in your hand.
Page 6 of 9
Days 44 to 33
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Faster Forever
A click track that speeds up without limit, built out of a nine-second loop that repeats exactly.
sound - 42
One Bit Too Many
Huffman coding is provably optimal and famously within one bit of entropy. On the right source that one bit is a twelve-fold overhead.
- 41
Modes That Stop Being Harmonic
Twelve masses on springs. The first few modes are the harmonics you would expect. The last few are nowhere near.
sound - 40
The Shape Decides
The convex hull of n random points has far fewer than n vertices. How many fewer depends on the shape they came from, not on n.
- 39
A Tone in Neither Ear
The same noise in both ears, with one narrow band phase-inverted on the right. Each ear alone is featureless. Together they produce a pitch.
sound - 38
Every Boundary Is All Three
Newton's method on z³ − 1 has three basins. Pick any point on any boundary between them and all three are arbitrarily close.
- 37
The Wheel Goes Backwards
Two wheels on one shaft, one seen continuously and one at 24 frames a second. Half of all speeds make the second wheel spin the wrong way.
- 36
A Filter That Lies
A Bloom filter's false-positive rate has a famous closed-form formula. The formula is right about filters in general and wrong about yours.
- 35
Which Half Matters
A Fourier transform splits an image into sizes and offsets. Throw away the sizes and you can still read it. Throw away the offsets and you cannot.
- 34
Cloth
No springs, no stiffness, no forces between the threads. Just moving the links back to the right length, over and over.
- 33
The Best Fraction
22/7 is not just close to π. Nothing with a smaller denominator is closer, and there is a machine that finds such fractions.