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.
> A design (or implementation) cannot ever be declared “correct” on its own. It can only ever be “correct with respect to a given specification.” Whether the formal specification correctly describes the problem to be solved is a separate issue.
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?
I thought the point of index funds weighting by market cap is that they don't require rebalancing, because the weight of stocks in the index exactly tracks price movements. You just keep holding the exact same number of shares, and more valuable stocks automatically take up more of your portfolio.
If you pick stocks with the correct weight to track the index, you're effectively running an index fund. And so you don't have to rebalance to keep tracking the index.
You can add stocks whenever you put money in. Whether that's because you got your paycheck or a dividend or some other income is kind of irrelevant. And you can remove stocks when you take money out. But you probably shouldn't start selling one stock to buy another just because their prices moved, unless you have information that lets you time the market.
But then you wind up with a portfolio that isn't balanced and isn't tracking like an index fund. An index fund doesn't simply buy a flat amount of stock and hold it, they buy stock in proportion to the relative weight of the exchange. Which is always moving
Market cap weighting is special. If company A has 500 shares, company B 500 also, than a fund that has 5 shares of A and 5 of B is market cap weighted.
And what happens if company A issues more stock? Company B is delisted? Company C is now listed? Company A and C merge? Company A spins off it's most valuable side business into it's own independent listing company?
500 shares of company A is worth 100% of the market cap of company A.
500 shares of company B is also worth 100% of the market cap of company B.
So if you have 5 shares of each, you'll have 1% of the market cap of each, even if one of those companies finds the cure for cancer or turns out to be a money furnace.
What are you talking about? Those index fund are constantly rebalancing. This is why you buy an index fund, so you don’t have to constantly rebalance your portfolio.
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.
1.1% is about 15% of the typical returns for a year in the S&P500, from a single stock. Folks and funds invest here for diversity precisely to limit such impacts.
It’s a big risk and that’s why there’s a big fuss right now to keep these guys out of the index.
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.
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.
It is not about stateless nature of LLMs. The problem of time-series A versus B is that our mathematical constructions just cannot describe the perception of time flow or at least for over 100 years nobody managed to figure out how to express it mathematically. As such any algorithms including LLMs remains just a static collection of rules for a Turing machine. All the things that consciousness perceives as changes including state transitions or prompt responses in computers are not expressible standalone without references to the consciousness experience.
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.
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."
