120 karma · joined April 18, 2023
> So you can never close the case on even one candidate, let alone all of them at once, which means the lower bound stays sealed.
Which is simply not true. The specifics depends on what language you use, but let's take Turing machines as an example. Many candidates are easily disproven: ones that halt immediately, ones that have no rule for writing a "1", ones that have no rule for halting and so on. It's impossible to write a program that can handle every possible candidate though.
And if your string is short enough, let's say the string you are investigating is "0011" then you CAN sit down and check all Turing machines of size 4 and lower. This is essentially what the https://bbchallenge.org/ project did.
For Turing machines we have determined if they halt or not for all machines up to 5 states. It is very computationally hard to push this limit further, but we don't know where the theoretical limit is. We have some large upper bound where a Turing machine computes something that we know is independent of ZFC (see Scott Aaronson for more details), but many suspect that the limit is way lower.
I've never heard this before. I thought UBI would be very freeing and without much control. If it is universal then there needs to be no control of who gets it or not. What am I missing?
Scala 3 is much more mainstream and has path dependent types. I've only used Scala 2, and there the boilerplate for dependent types was frustrating imo, but I've heard its better in 3.
You want to read about "conservation of etendue" for a technical explanation. For an easier explanation, look for xkcd's excellent "Fire from Moonlight".
In the graphic from the example we would keep track like this:
low: - high -
low: 11 high: -
low: 23 high: -
low: 23 high: 26
Error: now we see item 13, but that is not inside our span!How can we detect PHBs if they exist? If they existed in large numbers, would we notice them? The paper says that you would notice a PHB if it went through you, since you would likely die. We are not noticing people dying by mysterious gunshot-like wounds without guns in any large amounts, so there can not be that many PHBs around.
The paper is (weak) evidence against a large amount of PHBs. The paper is also slightly funny.
Someone malicious doesn't care about laws anyway. If they get caught today, couldn't they could just deny that they were there? I don't understand what would change in that case.
If you have a non-null returning function that you need to change so it can return null, then your typechecker will tell you all the places where you now need to handle the new null return.
It doesn't need to be a very large codebase before this becomes a very useful tool to help when refactoring.
Here is a direct link: https://github.com/bevyengine/bevy
The book is clearly very unfinished still, but what exists is very good. Got my mind spinning on what a good statically typed language running on a VM could look like.