twiceaday

Lean is like a statically typed programming language and validity is guaranteed if it compiles. The only room for errors is in translating a non-Lean theorem into Lean, so that you are not proving what you think you are proving.

"And the trees are all kept equal / By hatchet, axe, and saw"

And the relative values of those stocks will shift requiring rebalancing. You might be able to do that with new dollars for a while but hopefully, eventually, the swings are much more than new dollars and then what? Pay capital gains tax on sales to rebalance? Convince yourself the new random allocation is fine?

Value is tied to how people assess value. They used to assess it on the performance or potential of the company whose ownership you were taking a part of. Now speculation plays a much bigger role. This seems predictably correlated with distance to last deep crash.

Tesla is currently 2.2% of S&P 500. If it halves, losing $800,000,000,000 usd market cap, the index will go down by 1.1%. What big risk?

How about every value appears 0 mod n times except one which appears 1 mod n times? :)

Solution: xor is just addition mod 2. Write the numbers in base n and do digit-wise addition mod n (ie without carry). Very intuitive way to see the xor trick.

You assume the goal is to dominate the EV market. It seems pretty clear that this hasn't been Teslas revealed preference for a long time. The goal is to keep raising the stock price. If that involved selling fewer EVs Elon would do it. He turned Teslas humble beginnings as an EV company into just the first stage in $TSLAs booster rocket to the moon, one that it already separated from.

All of us trained our human "LLM" in the same environment (a human baby body) so it's easy for us to agree. I think once we have LLM-like entities that are always on and output a constant stream of thoughts, lines are going to get real blurry. Things that always used to be coupled and so had one name might need to be split. I think consciousness is one of those. Consciousness does not have a single definition as far as I am aware but one definition is something like the feeling of a potential future I am passively predicting happening and becoming the past. Riding that "now" wave. This definition seems extremely substrate specific. What if this sensation is just an implementation detail of an evolved intelligence in an Earth animal? The feeling of information being processed. I suspect this is just what consciousness feels like, not what it is. I don't know what you're feeling but from observing and interacting with you I assume and act like you are conscious. You are "functionally conscious." I don't see why AIs couldn't be functionally conscious. I further assume that you are human and so I extend even more consideration to how I talk to you. I assume you have feelings that you like to feel and those you don't and I prefer to trigger the former and avoid the latter, not simply because I don't want to take the conversation there but because as a fellow animal I care about your feelings. But I can see how there could be entities in the future that are conscious "functionally" but do not have the accompanying human feelings. They would speak human, since thats useful to humans, but wouldn't "be" human. I don't think we need to understand how / why humans feel conscious for that to happen.

The stateless/timeless nature of LLMs comes from the rigid prompt-response structure. But I don't see why we cant in theory decouple the response from the prompt, and have them constantly produce a response stream from a prompt that can be adjusted asynchronously by the environment and by the LLMs themselves through the response tokens and actions therein. I think that would certainly simulate them experiencing time without the hairy questions about what time is.

This is a critique of basketed index funds not total stock market index funds like FSKAX. When that observation is applied to FSKAX it reads like this

"An index fund, by its nature, must occasionally dump stock I like and buy stock I don't like simply because the entire stock market dumped the stock I like and bought the stock I don't like."

Seems more of a 'how' than 'why.' Good stated reason that lets you keep the actual reason private.

Math is a purely logical tool. None of it "exists." That makes no sense. Some of it can be used to model reality. We call such math "physics." And I think physics is significantly closer to math than to reality. It's just a collection of math that models some measurements on some scales with some precision. We have no idea how close we are to actual reality.

I do not understand the framing of "translating math concepts directly into reality." It's backwards. You must have first chosen some math to model reality. If you get "bad" numbers it has nothing to do with translating math to reality. It has to do with how you translated reality into math.

This phone has the highest screen area to weight ratio except for the Galaxy S25 Edge.

This is naive. The problem is that there are enough people with enough power who want house prices to keep going up. The solution must involve making them upset that they cannot get their way. Anything that doesn't have this shape is a stalling tactic in their favor.