The fine folks at <checks notes> FOPEAS would never tarnish their good name by stooping to such a stunt. I mean, we might expect such shenanigans from the likes of SMURGBLOZ, KINSURGE, or GSIROOZ, but not FOPEAS, fine purveyors of `FOPEAS an AI Language Model I do not Have Access to The Context of The SFD You are referring to. Can You Please Provide me with More Information so That I can Assist You Better`
I mean, the answer is trivially zero, there exists a PDF-like structure somewhere in Pi, and the offset of that doesn't have to be zero, it can start or end anywhere. So the range [0, N] is a valid PDF.
your example fails to satisfy the invariant. 11 is less than infinity.
you're just pasting random python snippits at me now. It's time to move on.
again, just to summarize: PDF files do not have to be zero aligned, and they do not have to be end aligned. Therefore the answer to the question "what is the first segment of Pi that is a valid PDF file" is trivially (0,infinity). That is a correct statement. The non-greedy (in the regex sense) answer to that question will be different, however.
Why is this so hard? If the tuple (0,10) represents the range of a valid pdf, then the next tuple (0,11) is also a valid pdf. Or any after it up to and including (0,infinity).
Note the word "next", implying that (0,10) sorts before (0,11); you even say it yourself "11 is less than infinity". Where I'm from "first" and "less" are related (the first element in a unique sorted list is defined to be less than all other elements). So if there is any valid pdf in pi that can be identified by the range tuple (0,N), then the first valid pdf must occur before N -> infinity. Therefore (0,infinity) can never be the first valid pdf, even though it may be a valid pdf.
Maybe a picture would help:
Potential pdf file ranges in pi: [(0,0),(0,1),(0,2),(0,3),(0,4),...,(0,N-1),(0,N),(0,N+1),(0,N+2),...,(0,infinity)]
Is it a valid pdf? no no no no no (no) no yes yes yes (yes) yes
Which one is first? ^^^
I thought linking to a python script that shows the order comparison of a tuple (0,N) as less than the tuple (0,N+1) would clearly demonstrate this, but it appears to have failed to communicate that to you. We don't need non-greedy regex rules to do a less than comparison.
Actually I'd argue the example you provided is normal, as long as you authorise a particular encoding where every number n you're looking for is encoded as a string of n zeros.
It's then trivial to see that every number you can think of is encoded in there, and therefore any data, piece of music or movie that ever existed.
(I'm not sure we're allowed to fiddle with the encoding, but since we allow ourselves to represent a piece of music into a number, we're already talking about encoding anyway, so it doesn't seem like cheating to me...)
Normality of a number is with respect to number bases, so your trick with encoding is invalid. Otherwise, every computable number could be considered normal - take an algorithm for generating of it, supply a random string (this is the encoding), disregard the random string, and you have a perfectly valid normal representation of your number. So it is cheating.
Normal in this sense means that all the frequency of all digits approaches a uniform distribution as the length of the sample increases towards infinity. Basically if we could see "all of" π and count all the 0s, 1s 2s, 3s, &c to 9 all the counts would be equal.
That on its own can't be right, because 0.12345678901234.....
According to wikipédia, you gave a definition for "simply normal", and for normal numbers the distribution of any sequence of digits is uniform. So 00, 01, ..., 99 each occur uniformally too.
No, all strings theoretically exist in 𝛑 given enough digits, so longer strings don't reduce probability of existence, they just mean that it will take more digits to find them.
I'm not sure that's necessarily true. It is true (at least with a non-constructive proof) that if you pick a 'random' real number then it contains all possible PDFs with probability one ( or that the set of numbers for which this is not true has lebesgue measure zero). But I'm not sure it's known that pi has this property.
Any dog ever would gladly trade a few zaps for a wide open place to explore outside. Cruelty is depriving dogs of exercise and outdoor time and stimulation and the chance to run, not invisible fences.
My anecdata shows one amongst 4 dogs who I used a shock collar on wanted to get outside regardless. And he was aptly named Loki for a reason. So no, not 'any dog', not by a large stretch.
You're making assumptions that I didn't exercise or allow my dog(s) outdoor time. Wether it was daily visits to the dog park or visits to the beach or the hinterland on the weekend. You're wrong to assume that the dogs whether adopted or fostered where ever deprived of anything. Shock collars are barbaric but they are means to an end, and an effective one once all options are exhausted.
Plus the whole, let your dogs roam free in a country like Australia would come at a significant cost to the local wildlife where wild dogs and cats are pests and not all of us live on farms, I'm not sure what you would have suggested for the dogs under my care. Or if your opinion here is almost entirely biased?
If I'm reading this correctly, those cars nave no "driver deaths" that means, that no one has died while driving those cars. This is a bit like a shotgun, which has potentially killed many people, but has not killed its owner.
Then there would be deaths. The stats are skewed significantly towards vehicles of which there are more of so you'd always have to discount this figure by how many vehicles there were of that type to begin with and to be even more accurate how many passenger miles were driven with those vehicles.
Anyone here have thoughts on why, all these years later, Amazon still doesn't have a sort option along the lines of these proposals? It seems like such an easy win and an easy technical change. Do they have some business reason not to change their default sort?
I'm not sure what you mean -- could you elaborate?
Amazon probably doesn't use straigt score averaging to decide "best" items sort, and this is just proposals of how to change that to be better by not just using averages. So what is it you're looking for Amazon to add?
Disclaimer: work at Amazon, not on anything search related.
Amazon has the default "Featured" sort (I'm not sure what is behind this, but it intuitively seems like some combination of popularity + availability + rating). If this default doesn't fit your needs, your only option is to change to sort by "Avg. Customer Review", which gets you a list that is sorted by average rating regardless of the number of reviews. Evan called out nearly 10 years ago in the post that OP's article mentioned - http://www.evanmiller.org/how-not-to-sort-by-average-rating..... The root problem is that one random obscure product with a single 5-star rating out-ranks something with 499 5-star ratings and 1 4-star rating.
I'm often looking for what is the best/highest-quality item in a category, meaning I want not just a high average, but a high average that is statistically meaningful. I'm just surprised Amazon hasn't offered a way to do that (and have read umpteen threads on HN in the past years expressing the same frustration).
When I go to Amazon.com and search, I see 'relevance' as my default, with 'featured', some price related ones, 'average', and 'new' as options. ('Featured' only seems to exist on some products, and be related to ads.)
Is it not the same for you?
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As for your main point (because I think that your complaint is still valid even with 'relevance' as the default), it sounds like what you want is a way to choose what factors are applied to your sort.
I'm not sure, but it seems likely that 'relevance' is doing more than just averaging, and so being able to select which parts you apply (eg, only use a statistical notion of best, don't consider availability or shipping times) would cover your usecase, right?
Well, you might want to be able to choose between a few models of 'best', but the real issue, the core need, is that you want control over the model that Amazon is using to sort what you see and to have some input on what that looks like. (And not just have 'lolsux' or 'Amznsort', to be a little glib.)
Gotta say, that actually sounds like a pretty reasonable ask. I'm not sure why it doesn't work that way, either.
Yeah, my above comment was not using a text search, hence no "relevant" option (i.e. if you just drilled down the department hierarchy to, say, the TVs department).
> the core need, is that you want control over the model that Amazon is using to sort what you see and to have some input on what that looks like
Indeed, but I'm not even looking to have that much granular control over it. I just want "sort by rating, but toss out all the obscure crap that has 1 or 2 ratings, because that rating is meaningless."
