penteract

This was interesting to read about. I wonder if the 2012 ECJ ruling mentioned here is why various software products switched to a subscription model.

I agree, but I believe the reason for the errors is because people intuitively have a pretty good grasp of the game theory for the situation where someone is trying not to give you something they promised (and it's the sort of thing where IRL you shouldn't believe somebody trying to convince you to change your mind, so it's a useful bias to ignore parts of the problem even when it is fully specified). I believe that the statisticians then try to justify that, and end up making incorrect arguments.

What if he used the knowledge to decide whether or not to open a door and offer you the choice? I think that scenario is why most people instinctively want to not switch (even if they aren't consciously aware of it), so it's a pity to disregard it.

Yes, I am discussing a different problem, and I don't think the original problem formulation gives enough information to distinguish between the 2 problems.

The answer can add assumptions, which is fine. I'm not passing judgement on Marilyn vos Savant. I do object to claims that the problem statement is sufficient to have a single answer, and based on that, I'd object to claims that somebody in that situation would be wrong not to switch doors. I would object on exactly the same grounds to anyone who tells you "you're wrong, there's a 50% chance of getting a car" (I might object further, on the grounds that the most obvious interpretation which gives that answer is inconsistent with this form of the problem statement).

I think we're disagreeing about how much it's reasonable to assume. I'm happier treating it as a self contained problem (in which case I'd say that the form quoted by CrazyStat is underspecified); but if you're familiar with the TV show it's based on, you can reasonably assume that he always opens a door with a goat and gives you a chance to switch.

My objection is to the claim that "most people get it wrong", if most people are being fed the underspecified problem. I think the gut reaction is not to switch, because in most comparable situations across human experience it would be a mistake (imagine a similar situation at a sketchy-looking carnival game rather than a TV show). They then try to justify that formally and make mistakes in their justification, but the initial reaction not to swap is reasonable unless they've been convinced that Monty Hall always opens a door with a goat and gives a chance to switch.

> Nothing about the problem should lead you to believe that the host is an evil genie purposefully trying to trick you.

Is it really unreasonable to assume that the host would like to keep the car? As I see it, that's the economic intuition behind why most people don't switch.

You might live in a world where the host doesn't want to give you the car, and only opens a door and offers you the option of switching if your first choice was the door with the car behind it. In that world, you shouldn't switch. I don't think this form of the problem statement gives you any reason to believe that you aren't in that world.

> And in this particular instance, it makes sense to switch.

Are you are accepting that the host might be someone who only opens a door with a goat when your first choice was the door with a car behind it, and still arguing that you should switch?

Diagonal player movement isn't allowed (from the looks of the article), but wall connections can be diagonal. There's a duality here - if players and enemies could move diagonally, the algorithm could be adapted by only considering horizontal and vertical wall adjacencies (although still looking at the surrounding 8 squares to determine separation of adjacent walls). We're relying on the property "if adding a wall creates an enclosed region, one of the enclosed squares must be move-adjacent to the new wall".

"separated" = "not connected when considering only the 8 neighbors of where you intend to place the new wall; diagonals do count as connections between walls".

In the following example, the walls adjacent to the + are not separated:

    +X
    X.

In the next example, the walls are adjacent to the + are separated:

    X..
    .+.
    ..X

> There was something else in the article that bothered me

Regarding your second point, I think the article changed half way through from assuming the play area is surrounded by a wall to assuming the play area is surrounded by empty space, which I agree is confusing. Either case could be covered by this algorithm - just start with a connected component of wall at the edge of the play area.

Unless I'm missing something, this can be done in O(n) time by tracking the connected components of wall (diagonally touching walls are connected). Placing a new wall creates an enclosed region if and only if it touches 2 separated sections of wall that are part of the same component.

The union-find disjoint sets algorithm can find whether they're in the same component. If a wall is added, it should be unioned with all adjacent walls. If a wall piece is removed, the components it was part of need to be recalculated, but it looks like that shouldn't happen more than once per frame.

In this case, the lookups of the union find algorithm will never take more than O(n) overhead per frame while checking all of up to n possible wall positions.

https://en.wikipedia.org/wiki/Disjoint-set_data_structure

Your conclusion is right, but in bees, sex is determined by Haplodiploidy ( https://en.wikipedia.org/wiki/Haplodiploidy ), not X0. Also, the daughters have the same number of chromosomes as the mother so they share 50%, not 75% of their genes with their mother (they do share an average of 75% of their genes with their sisters).

Here's how to formulate the question in continuous space/time:

Random walks can be defined on continuous space and time as a probability distribution on functions R -> R^n (Brownian motion in n dimensions).

We can then ask whether Brownian motion beginning at the origin will ever revisit it i.e.

Given 2D Brownian motion X such that X(0)=(0,0), the probability that there exists t>0 such that X(t)=(0,0) is 1.

Given 3D Brownian motion X such that X(0)=(0,0,0), the probability that there exists t>0 such that X(t)=(0,0,0) is 0. (This is more clearly true when it doesn't begin at the origin, but it's almost certainly not at the origin at t=1, and you can divide the half open interval (0,1] into a countable number of intervals, each of which have 0 probability of passing through the origin.)

Random walks in 2D are space filling curves; random walks in 3D are not.

Each element of the input array is at least 4 bytes, bringing it to 8GiB.

Having made my own forays into making a structural editor, I'd like to sing the praises of plain text: storing something that has been created by pressing buttons at a keyboard as something very close to the sequence of buttons that have been pressed is a great idea.

The magical ability of plain text is to go back in time and ask "what if I pressed a different button a minute ago/yesterday/last year?". This lets you see and fix mistaken keypresses, and even shapes the kind of mistakes you can make in a moment of confusion into ones that are quickly fixable.

The direct representation of buttons pressed also really helps with teaching/learning: With plain text, for mechanical questions on the level of "What buttons do I press to make a program that looks like that?", the answer is obvious for anyone who knows how to type. Try the editor discussed in the article to appreciate how different answering that question can be in a structural editor. Seeing and explaining how someone got where they did is also straightforward ("you missed a semicolon", "you misspelt a variable name"). Ideally, those are problems that don't happen in a structural editor, but people who press a slightly wrong sequence of buttons will probably still exist.

These arguments get much weaker when you aren't using a physical keyboard; I think this is the reason the article starts by talking about writing programs on a phone and a TV. In those environments structural editing has much more to offer.

With 2 clean buttons, there are 4x2 ways for only 1 to repeat, giving 14 combinations in total.

I've encountered a Matrix server/Element client that doesn't always present the same options for providers, making it very difficult to log in on a second machine.

I believe it's not that collisions (and gravitational interactions) don't happen when it's in a disk, but the galaxy as a whole has an overall rotational momentum about some axis, and collisions within the galaxy can't change that. This means that it can flatten along the axis, but it can't shrink in the perpendicular plane.

If everything were twice as close to the axis (as gravity would like it to be), it would need to be moving twice as fast to conserve rotational momentum, but that's faster than the velocity of a circular orbit at the new radius (assuming everything was in a circular orbits to begin with).

The same principle is why almost everything in the solar system approximately lies within a plane.

The relevant part being near the bottom:

> These images are a composite of separate exposures acquired by the James Webb Space Telescope using the MIRI instrument. Several filters were used to sample wide wavelength ranges. The color results from assigning different hues (colors) to each monochromatic (grayscale) image associated with an individual filter. In this case, the assigned colors are: Blue: F770W, Green: F1130W, Red: F1280W.

Chasing some numbers up, it looks like they've made the wavelengths around 20 times shorter to bring the picture into the visible spectrum.

I think that was intended to be read as "how all wars must end" rather than "because all wars must end".

Such a waste of faces :). Give a tetrahedron's faces 0,1,2, and 4 pips and throw it into a v-shaped groove so that it lands on an edge. (This is also a solution to numbering the corners of a cube).

I'd add that "waters" doesn't need to mean more than one body of water. It can be used somewhat poetically to refer to water in a single body. First example I could find: https://biblehub.com/joshua/3-8.htm

Doesn't most geothermal heat come from radioactive decay and gravitational potential energy of the planet as it formed, rather than reactions involving multiple particles? I'd have agreed if you'd said "radioactive substances" rather than "fission reactions".

Some earlier blog posts by the same author give more detail.

https://www.sligocki.com/2021/07/17/bb-collatz.html is one that covers the analysis of a particular machine in great detail, including explaining what definitions like "M(n) = 0^inf < A 1^n 0^inf" mean.

> Human morality has no meaning if humans aren't special.

What part of this argument would fail if you identified as a belonging to a particular religion, culture or race, or as an intelligent being more than you identified as human?

I believe I should treat humans well (beyond self-interest) because I believe they have minds somewhat like mine, despite the impossibility of proving that by direct experience. I could imagine extending that to other species of animal or aliens or artificial minds. I would view them as more worthy of empathy than a braindead human, even one with a function reproductive system which would appear to satisfy your criteria.

You don't explicitly exclude AIs being seen as equals; so perhaps we mostly agree, and your rejection of the idea of superior AIs comes from the same place as a reluctance to call some humans superior to others that I share?

I think you've got the first claim wrong - for a church numeral N, (N b g f) appears to give the composition of g and f with f taking N arguments.

    2 b = (λf x.f (f x)) b
        ~> λx.b(b x)
        = λx.(λgfy.(g (f y))) (λabc.(a (b c)) x)
        ~> λx.(λfy.(λabc.(a (b c)) x) (f y))
        ~> λxfy.(λbc.(x (b c))) (f y)
        ~> λxfy.(λc.(x ((f y) c)))
        = λxfyc.(x (f y c))
    
    (3 b) ~> λihgfx.i (h g f x)

Does "remits" mean reduces here, along the lines of https://en.wikipedia.org/wiki/Remittitur? It was an unfamiliar term to me and I'm not sure I've found the right meaning.

> what about the billions of uneducated rural people today that get along fine without treated water and don't drink wine or beer?

Less than 1 billion now without reliable nearby access to clean water[0], and "get along fine" is dubious - an estimated 1.4 million people died in 2019 from unsafe drinking water, sanitation and hygiene (more than 500000 from drinking water specifically) [1].

[0] https://www.wateraid.org/uk/what-we-do/water [1] https://www.who.int/publications/i/item/9789240075610

Germ theory wasn't widespread throughout the time period we're talking about, so they wouldn't have been able to give the reasoning that we would about why clean water is important or how alcohol acts as a disinfectant.

However, the Small beer Wikipedia page says that very large quantities of these drinks were consumed

> It was common for workers who engaged in laborious tasks to drink more than ten imperial pints (5.7 litres) of small beer a day to quench their thirst

And that it was believed to be good for people

> "For the drink of the more robust children water is preferable, and for the weaker ones, small beer"

The fact that aqua vitae means "water of life" is also evidence for this.

That's something that's different between X11 and Wayland - in Wayland, windows are responsible for their own decoration (I presume Xwayland handles decoration for X11 windows running through Wayland). This makes it quite a bit harder to hide all decorations on Wayland - various UI toolkits have ways that the end-user can tell them to hide bits, but they all operate differently and don't cover everything.

Nice find, I think it would.