Not sure I care overly much about the fate of the amoral corporation getting fucked over by the fascist regime. They’re both juggernauts, and I would love to see them damage each other.

Remember, the falling out wasn’t about the morality of the unsupervised spicy autocomplete killing people, it was about who had the liability when the AI went inevitably wrong. Had the DoD accepted the liability, I’m certain Anthropic would have sold the the stupidest version of skynet imaginable.

https://jmail.world/thread/0f7fac62a94c1d9a989c769d770dbb1a?view=inbox

Smh Tom. You should have known better.

https://youtube.com/watch?v=BKJ90uXkGdE

Is… that a reference to Frankie and Johnny’s???

Um… Hello, fellow person who grew up in or around New Orleans in the 1990s. How are things? Where did you wind up after Katrina? I have no idea how to handle someone just randomly referencing commercials I had completely forgotten about.

That’s a deep cut reference. 👏

Anyway, to prove this is a metric we must prove that it satisfies the 4 laws of metrics.

1. The distance from a point to itself is zero. 🍊 (🍎, 🍎) = 0

This can be accomplished by simply observing that |🍎 (x) - 🍎 (x)| = 0 ∀x ∈ [a,b], so its sup = 0.

2. The distance between any two distinct points is non-negative.

If 🍎 ≠ 🍌, then ∃x ∈ [a,b] such that 🍎 (x) ≠ 🍌 (x). Thus for this point |🍎 (x) - 🍌 (x)| > 0 and the sup > 0.

3. 🍊 (🍎, 🍌) = 🍊 (🍌, 🍎) ∀(🍎, 🍌) in our space of functions.

Again, we must simply apply the definition of 🍊 observing that ∀x ∈ [a,b] |🍎 (x) - 🍌 (x)| = |🍌 (x) - 🍎 (x)|, and the sup of two equal sets is equal.

4. Triangle inequality, for any triple of functions (🍎, 🍌, 🍇), 🍊 (🍎, 🍌) + 🍊 (🍌, 🍇) ≥ 🍊 (🍎, 🍇)

For any (🐁, 🐈, 🐕) ∈ ℝ³ it is well known that |🐁 - 🐕| ≤ |🐁 - 🐈| + |🐈 - 🐕|, (triangle inequality of absolute values).

Further, for any two nonnegative functions 🍍, 🍑 we have sup({🍍 (x) : x ∈ [a, b]}) + sup({🍑 (x) : x ∈ [a, b]}) ≥ sup({🍍 (x) + 🍑 (x) : x ∈ [a, b]})

Letting 🍍 (x) = |🍎 (x) - 🍌 (x)|, and 🍑 (x) = |🍌 (x) - 🍇 (x)|, we have the following chain of implications:

🍊 (🍎, 🍌) + 🍊 (🍌, 🍇) = sup(🍍 (x) : x ∈ [a, b]}) + sup({🍑 (x) : x ∈ [a, b]}) ≥ sup({🍍 (x) + 🍑 (x) : x ∈ [a, b]}) ≥ sup({🍎 (x) - 🍇 (x)| : x ∈ [a, b]) = 🍊 (🍎, 🍇)

Taking the far left and far right side of this chain we have our triangles inequality that we seek.

Because 🍊 satisfies all four requirements it is a metric. QED.

QED stands for 👸⚡💎, naturally

What happened to 🍇 and 🍍?