I seriously don't get the idea behind daily challenges unless you want to keep users hooked to extract some value from them, but that doesn't seem to be the case here, as there are no ads.
That's fine. So these kind of games aren't for you, then. Remember crosswords in newspapers? Yeah, think of it like that. You don't get hooked until you cannot let go, you get a limited chunk served each day. Same with Wordle.
I remember buying a magazine full of crosswords and similar puzzles when I was in the mood.
And when there were sites with unlimited Wordle, I played a few in a row.
On the internet, unlike with newspapers, you're not limited to how many levels/games you can make per day. Making it once per day doesn't make any sense whatsoever. It's condescending to the users and feels like a power trip.
> It's condescending to the users and feels like a power trip.
condescending (adjective): having or showing an attitude of patronizing superiority.
I don't really see how a once-a-day puzzle is condescending, unless it's a "You can't be trusted to regulate yourself so I'll do it for you" type thing. Adding a dictionary definition like above, however, probably is condescending :)
But I like the one-a-day format because, as other comments have said, you can spend an entire day with just one puzzle feeling important (relative to things that are important).
You can freely make levels and browse other people's levels. The complaining about power trips seems as uncharitable a perspective as you could possibly conceive of, not to mention a bit theatric.
> you want to keep users hooked to extract some value from them
Ironically, that's what I initially liked about the daily puzzles like Wordle: they forcibly prevented you from sinking too much time into them. It was sort of like, "hey here's something cool, and I'm going to make sure it's a positive addition to your life by preventing you from succumbing to your own addictive impulses". You could call that condescending or infantilizing, but to me it's just part of the look and feel of a thing. Especially if the author isn't charging money, they get to use whatever tools are at their disposal to craft the users' experience of it. Wordle Over And Over Again is a different game than Wordle Once Daily. (And WOAOA done properly would probably have a progression of difficulties, or themes, or something, whereas WOD makes more sense with pure randomness.)
I assume that "all the different levels" might not exist yet. The author is probably creating them a bit in advance, and will keep going as long as they're motivated. Having a regular schedule for new releases helps, and doing it daily seems as sensible as any other schedule.
If it's AI-generated, it should be legal - regardless of whether the person consented for their image to be used and regardless of the age of the person.
You can't have AI-generated CSAM, as you're not sexually abusing anyone if it's AI-generated. It's better to have AI-generated CP instead of real CSAM because no child would be physically harmed. No one is lying that the photos are real, either.
And it's not like you can't generate these pics on free local models, anyway. In this case I don't see an issue with Twitter that should involve lawyers, even though Twitter is pure garbage otherwise.
As to whether Twitter should use moderation or not, it's up to them. I wouldn't use a forum where there are irrelevant spam posts.
With apps like Signal, installed via apk, without going through Google on a de-Googled phone, I receive notifications in real time. What's the point of having all notifications go through Google, except to save some battery life and data?
Also, can Google read push notifications going through FCM?
Why can I only play #736? What's up with games nowadays that only give you 1 puzzle per day? IIRC the original Wordle was like that. Is it designed to make you bookmark the URL and visit it every day? I doubt most people would do that.
I haven't dealt with statistics for a while, but what I don't get is why squares specifically? Why not power of 1, or 3, or 4, or anything else? I've seen squares come up a lot in statistics. One explanation that I didn't really like is that it's easier to work with because you don't have to use abs() since everything is positive. OK, but why not another even power like 4? Different powers should give you different results. Which seems like a big deal because statistics is used to explain important things and to guide our life wrt those important things. What makes squares the best? I can't recall other times I've seen squares used, as my memories of my statistics training is quite blurry now, but they seem to pop up here and there in statistics relatively often, it seems.
It has nothing to do with being easier to work with (at least, not in this day and age). The biggest reason is that minimizing sum of squares of residuals gives the maximum likelihood estimator if you assume that the error is iid normal.
If your model is different (y = Ax + b + e where the error e is not normal) then it could be that a different penalty function is more appropriate. In the real world, this is actually very often the case, because the error can be long-tailed. The power of 1 is sometimes used. Also common is the Huber loss function, which coincides with e^2 (residual squared) for small values of e but is linear for larger values. This has the effect of putting less weight on outliers: it is "robust".
In principle, if you knew the distribution of the noise/error, you could calculate the correct penalty function to give the maximum likelihood estimate. More on this (with explicit formulas) in Boyd and Vandenberghe's "Convex Optimization" (freely available on their website), pp. 352-353.
Edit: I remembered another reason. Least squares fits are also popular because they are what is required for ANOVA, a very old and still-popular methodology for breaking down variance into components (this is what people refer to when they say things like "75% of the variance is due to <predictor>"). ANOVA is fundamentally based on the pythagorean theorem, which lives in Euclidean geometry and requires squares. So as I understand it ANOVA demands that you do a least-squares fit, even if it's not really appropriate for the situation.
The mean minimizes L2 norm, so I guess there's some connection there if you derive OLS by treating X, Y as random variables and trying to estimate Y conditioned on X in a linear form. "L[Y|X] = E[Y] + a*(X - E[X])"
If the dataset truly is linear then we'd like this linear estimator to be equivalent to the conditional expectation E[Y|X], so we therefore use the L2 norm and minimize E[(Y - L[Y|X])^2]. Note that we're forced to use the L2 norm since only then will the recovered L[Y|X] correspond to the conditional expectation/mean.
I believe this is similar to the argument other commenter mentioned of being BLUE. The random variable formulation makes it easy to see how the L2 norm falls out of trying to estimate E[Y|X] (which is certainly a "natural" target). I think the Gauss-Markov Theorem provides more rigorous justification under what conditions our estimator is unbiased, that E[Y|X=x] = E[Lhat | X=x] (where L[Y|X] != LHat[Y|X] because we don't have access to the true population when we calculate our variance/covariance/expectation) and that under those conditions, Lhat is the "best": that Var[LHat | X=x] <= Var[Lh' | X=x] for any other unbiased linear estimator Lh'.
Also, quadratics are just much easier to work with in a lot of ways than higher powers. Like you said, even powers have the advantage over odd powers of not needing any sort of absolute value, but quartic equations of any kind are much harder to work with than quadratics. A local optimum on a quartic isn't necessarily a global optimum, you lose the solvability advantages of having linear derivatives, et cetera.
To put it very simplistically, from mostly a practical view:
abs: cannot be differentiated around 0; has multiple minima; the error space has sharp ridges
power 4: way too sensitive to noise
power 3: var(x+y) != var(x) + var(y)
A power of 1 doesn’t guarantee a unique solution. A simple example has 3 points:
(0,0), (1,0), (1,1)
Any y = a × x with a between zero and one gives you a sum of errors of 1.
Powers less than 1 have the undesired property that they will prefer making one large error over multiple small ones. With the same 3-point example and a power of ½, you get:
- for y = 0, a cumulative error of 1
- for y = x/2, a cumulative error of 2 times √½. That’s √2 or about 1.4
- for y = x, a cumulative error of 1
(Underlying reason is that √(|x|+|y|) < √|x| + √|y|. Conversely for powers p larger than 1, we have *(|x|+|y|)^p > |x|^p + |y|^p)
Odd powers would require you to take absolute differences to avoid getting, for example, an error of -2 giving a contribution of (-2)³ = -8 to the cumulative error. Otherwise they would work fine.
For linear models, least squares leads to the BLUE estimator: Best Linear Unbiassed Estimator. This acronym is doing a lot of work with each of the words having a specific technical meaning.
Fitting the model is also "nice" mathematically. It's a convex optimization problem, and in fact fairly straightforward linear algebra. The estimated coefficients are linear in y, and this also makes it easy to give standard errors and such for the coefficients!
Also, this is what you would do if you were doing Maximum Likelihood assuming Gaussian distributed noise in y, which is a sensible assumption (but not a strict assumption in order to use least squares).
Also, in a geometric sense, it means you are finding the model that puts its predictions closest to y in terms of Euclidean distance. So if you draw a diagram of what is going on, least squares seems like a reasonable choice. The geometry also helps you understand things like "degrees of freedom".
Because the Euclidean norm is defined as the square root of a sum of squares. You can drop the square root and calculate everything as a least squares optimization problem. This problem in turn can be solved by finding where the derivative of the quadratic function is zero. The derivative of a quadratic function is a linear function. This means it is possible to find a matrix decomposition, say QR decomposition, and solve the problem directly.
If you want non linear optimization, your best bet is sequential quadratic programming. So even in that case you're still doing quadratic programming with extra steps.
Least squares is guaranteed to be convex [0]. At least for linear fit functions there is only one minimum and gradient descent is guaranteed to take you there (and you can solve it with a simple matrix inversion, which doesn't even require iteration).
Intuitively this is because a multidimensional parabola looks like a bowl, so it's easy to find the bottom. For higher powers the shape can be more complicated and have multiple minima.
But I guess these arguments are more about making the problem easy to solve. There could be applications where higher powers are worth the extra difficulty. You have to think about what you're trying to optimize.
L1 (abs linear difference) is useful as minimizing on it gives an approximation of minimizing on L0 (count, aka maximizing sparsity). The reason for the substitution is that L1 has a gradient and so minimization can be fast with conventional gradient descent methods while minimizing L0 is a combinatoric problem and solving that is "hard". It is also common to add an L1 term to an L2 term to bias the solution to be sparse.
I haven't done it in a while, but you can do cubes (and more) too. Cubes would be the L3 norm, something about the distance between circles (spheres?) in 3d space? I need to read about norms again to tell you why or when to choose that, but I know the Googlable term is "vector norms"
I remember one is Manhattan distance, next is as-the-crow-flies straight line distance, next is if you were a crow on the earth that can also swim in a straight line underwater, and so on
It all boils down to the fact that mean and variance give a good approximation of a probability distribution.
In the same way that things typically converge to the average they converge even more strongly to a normal distribution. So estimating noise as a normal distribution is often good enough.
The second order approximation is just really really good, and higher orders are nigh impossible to work with.
One way to think of it is that each point in your data follows your model but with gaussian iid noise shifting them away. The likelihood is then product of gaussians mean shifted and rescaled by variance. Minimize the log-likelihood then becomes reducing the sum of (x-mu)^2 for each point, which is essentially least squares.
An easy solution - open the package when the delivery person comes or when you pick it up from the delivery office. The delivery person can take a photo and act as a witness. If you take the package from the local delivery office, there are cameras and staff, so I can't just swap a ripe apple for a rotten one.
Where I live we don't have the habit of just putting the delivery on the porch for a few reasons. First, it's ridiculous if you think about it - no one signed for it, so how could you mark it as delivered? I don't get the US in that regard. Secondly, most of the houses have fences, so the delivery person can't come to the house even if they wanted to. You're basically required to meet the delivery person.
>An easy solution - open the package when the delivery person comes
That would massively slow down delivery times, especially if the packaging is non-trivial to open/inspect. Not to mention that not everyone works a comfy remote job where they're at the door the entire day.
I'm at home most of the time, yet I prefer to go to the delivery office to pick up my packages. It's a 5 minute walk, as they're all over the city. Might not work well for big car-first American cities, though. I prefer going to the delivery office because I hate waiting for a delivery person to show up and wondering if I have time to go to the bathroom or not.
But I agree that not everything is easy to inspect. Most things seem to be, though. Another issue is not wanting third parties from seeing what you've purchased.
I've tested a few microwaves from different manufacturers with my phone a few years ago. I think I looked at some file in my router (OpenWRT), but I can't recall. I got a lot of dropped packets each time. The amount of degradation was similar for the different microwaves.
I had to put the phone close to the microwave to detect this. The degradation was obviously stronger when the phone was closer.
If your friend experiences noticeable degradation regardless of the distance within the room, it might be worrisome.
But I think it's normal to have some interference. That doesn't necessarily mean enough of the 2.4 GHz radiation escapes the microwave to be harmful to an animal, as Wi-Fi, Bluetooth and so on are very weak, comparatively.
Funny thing is, after putting my phone inside a closed turned off microwave, it got Wi-Fi, although very weak. I didn't try that with all the microwaves, but with 2 or 3 of them.
I think the Faraday cage around the microwave was built to be good enough for safety, but it wasn't built with Wi-Fi interference in mind.
Disclaimer: I might be wrong, as I don't have enough background to make any bold claims.
> If your friend experiences noticeable degradation regardless of the distance within the room, it might be worrisome.
Probably not. I recall calculating it once, and the legal requirements for microwave oven shielding still allow it to produce a few watts of 2.4Ghz leakage. This is contrasted to 50mW typical WiFi AP power, and 5-50mW BlueTooth powers.
A few watts is totally non-dangerous to humans, especially diffused across the entire door.
> - Telling him I suspect he has dyslexia. I'm not a doctor.
You don't have to be a doctor to tell him he might have dyslexia or something related. If he goes to a doctor to diagnose it, he'll be better off because of you. Either he'll have dyslexia and he'll know his problem or he won't and he'll start considering other causes.
People nowadays seem reluctant to offer medical advice of any kind. It's one thing to just hand him some pills, it's another to suggest he goes to see a doctor.
Just show all the different levels at once.
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