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The complexity of Karatsuba's algorithm, because it's a recursive one that gets "wider" at every level, is dominated by the width of that recursion. The top level always has a small number of operations, so we don't explicitly count them there, but the bottom has the truly huge number of operations that contribute to the algorithm's complexity, because each level of recursion dramatically increases the number of operations. Some number of those operations (most of them, in fact) will be single-digit additions.

Memoizing number-by-digit multiplication doesn't make multiplication O(1) because one must still do an N-digit addition (which is O(N)) for each digit.

Do you write things that you intend other people read?

The value in that writing, one would assume, would include your education, culture, and intelligence.

That's at odds with everything I know about manufacturing robotics, having worked with people doing that work. The complexity of the environment is irrelevant because the robot is programmed to make a specific motion and to adjust that motion in predictable ways based on the appearance of specific features. That is by design, not because (or at least not just because) the robot is incapable of planning its own motion. The whole system is designed to be predictable instead of adaptable because that's what you need to do to do the same thing millions of times.

Sadly, American politics are so absurd now that some people won't recognize you're joking

I am only really confused about this comment. I don't see any shock here, just people discussing the same disappointing state of events you are.

The biggest source of lead exposure in indoor ranges isn't from the chunks of lead shot into targets. It's from the primers. Lead styphnate is still a common ingredient, and the primer is one of those parts of the bullet that ends up mostly in the atmosphere.

I don't understand this comment. The fine article is about a proposed law that would allegedly require the implementation of half-baked censorship systems along the same lines as the DMCA. Are you saying that's not a real issue because the EFF also whines about big tech?

It's also alive and well off the blockchain!

You give a damn about speech. You're publicly criticizing the foundational document of a government, and calling that government a failure. That open criticism is necessary for change to happen and, in the United States, the constitution forbids the government from removing that criticism or punishing you for it.

The constitution is intentionally more difficult to amend than an ordinary law. The entire point is that the government cannot easily remove restrictions on itself. It's not an appropriate place to put, say, housing or employment laws, which should be ordinary laws so they can keep up with a complex and rapidly changing world. It's also not an appropriate place to put a statement that housing is important or that there is a right to housing, because such a statement is unenforceable and would need a separate law designed to enforce that right. There are plenty of countries with a "constitutional right to housing" that still have homelessness because it's such a difficult issue to solve.

Throwing a constitution out and starting over would be even more difficult than amending it and would lose what's already in it. Maybe we need an amendment ending prison labor and private prisons. Maybe we need an amendment extending more rights to immigrants. That doesn't mean that the constitution as it already exists is invalid and worthless.

Eh? More for the rest of us, then!

The U.S. constitution is about the structure of the government and the things it can and cannot do. It's a remarkably short and readable document for what it is and when it was first written. And while it has been amended very slowly, it has been amended all the way up until today.

It seems you have an issue with just one part of it, the bill of rights. Besides property---which doesn't just mean land---that part addresses such other "outdated" concepts as speech, assembly, religion, rights of the individual in criminal investigations and trials, and a number of others. What connects all these ideas together is that they are the rights the people have _against_ government action. Things the government should not do to harm people.

That purpose is really important. The constitution is not, and should not be, a list of good policies or social values. Most of it is a list of specific things the government did in the past---some of them truly heinous things---that it is not allowed to do anymore. There's only one notable exception: the 18th amendment, meant to enforce the social values of the time and which was, ya know, repealed later for being a disaster.

Yes, you are morally responsible for your own actions. But those actions don't happen in a vacuum. They happen in a world that you are able to observe and make predictions about, however imperfect those predictions are. If you don't know that you're enabling the shooter, sure. But if you do know and do it anyway, you are responsible for knowingly enabling the shooter.

This doesn't mean that the shooter doesn't have his own agency and his own responsibility for his actions. It just means that his responsibility for his actions doesn't diminish your responsibility for yours, even if your actions involve him.

It seems to be a common idea that we can just overlook the abuses committed by the other people we deal with, as things "I'm not responsible for", regardless of our actual ability to do something about them. I have no special insight, but I think it's a common idea because it lets us feel better about ourselves while we do nothing. But "feeling good about oneself" isn't a solid way to build or evaluate a moral framework.

Tlön is one of my favorite short stories. Weirdly (and perhaps appropriately) that's despite being unable to remember basically anything about it once I've finished reading.

Who should the unimaginative non-liberals read, and why?

This isn't a forensics class. People are allowed to point out what they think is obvious without having to explain it in detail. And it's rude to insist that they do more than you've done yourself.

The article everyone's commenting on provides numerous examples of things Trump has done, some of which, such as calling for the use of the government against political rivals, are against libertarian ideals. Rather than address any of those directly, you've resorted to handwaving and providing examples of things you personally approve of. That could reasonably be seen as a failure to engage with reality, which would be delusional.

However, I don't know why the specific person you're responding to thinks you're delusional. I am not them.

I will leave aside my own judgment of the things you've listed. I don't agree with all of them, but I do agree with some. My exact opinion doesn't matter here.

What matters is this: you can agree that Trump has done good things and still think he's done horrible things as well. A shit sandwich is still a shit sandwich. You shouldn't eat it just because the bread's edible.

We can chuck the entire concept of rights out the window and come up with agreements surrounding social behavior that actually reflect the society and culture we have today or want tomorrow.

What, exactly, do you think a right even is, if not an agreement that something cannot be done to people or cannot be taken away from them?

Americans don't do this, though. They don't demand better. They accept shitty governance and say "at least I voted". And frankly I don't think they ever will.

That is an obviously wrong statement even if we only look at protests within the past 5 years.

The reason you don't see "free speech" used for those causes isn't because they don't rely on free speech. It's because advocacy for them is so clearly protected as free speech that it isn't even a question. There have been times when that protection was a question in the U.S., like when protesting wars or segregation laws.

Without the right to say something, there is no legal way to organize or to demand any other right.

Edited to remove an unwarranted statement at the beginning of this comment.

Donald Trump is currently doing immense damage to the personal liberty of some and to the free expression of all. Every one of the numerous things listed in the article is something that actually happened. I don't know nor do I care whether you believe what you're saying. Donald Trump, a man petty enough to punish a news organization for not saying "gulf of America" and cruel enough to send people to a foreign prison without trial, clearly doesn't.

It wouldn't be an ordinary law, it would be a constitutional amendment, so that wouldn't be an issue. It's probably not going to happen, though. Amending the U.S. constitution is incredibly difficult.

Sharpening and bandwidth-limiting have the exact same effect, because the maximum sharpness of an image (like any other signal) depends on its bandwidth. There is no difference in the type of artifact produced. That's why the artifact from both has the same name of "ringing".

I am unsurprised that the author would hold a video distribution company which supposedly pays good money for experts to a higher standard than the average hobbyist blogger. I don't think it's hating for the sake of hating.

It's the exact same phenomenon in both. Not sure where you're making the distinction.

This is what's so terrifying about uses of "AI". People's idea of accuracy being "tell me what I think is there", not "tell me what's there". The can in this image probably says "coconut milk", but the image certainly doesn't.

I'm saying it's moot because, if you're just flagging things for review, there's already a more direct and reliable way to do that. The OCR classifier itself outputs a confidence score. The naieve way of just checking that confidence score will work. The OCR classifier has less overall information than an LLM, but the information it has is much more relevant to the task it's doing.

When I have some time in front of a computer, I'll try a side-by side comparison with some actual images.

This is moot anyway if the LLM is only used as part of a review process. But the most valuable documents to digitize are, almost by definition, those that don't have widely-known information that an LLM is statistically likely to guess. There's no way to get around that.

I am working with printed documents. Maybe LLMs currently make a difference with handwriting recognition. I wasn't directly responding to that. It's outside the little bit that I know, and I didn't even think of it as "OCR".

I'm not saying that I need high accuracy (though I do), I'm saying that the current accuracy (and clarifying that this is specifically for printed text) is already very high. Part of the reason it's so high is because the old complicated character-by-character classifiers have already been replaced with neural networks that process entire lines at a time. It's already moving in the direction you're saying we need.

You are thinking of a fully automated process, not of the human verification through `diff ocr_output llm_corrected`.

Fair, and I'm aware that that makes a huge difference in how worthwhile an LLM is. I'm glad you're not doing the annoyingly common "just throw AI at it" without thinking through the consequences.

I'm doing two things to flag words for human review: checking the confidence score of the classifier, and checking words against a dictionary. I didn't even consider using an LLM for that since the existing process catches just about everything that's possible to catch.

I am using LSTM-based engines . . .

I'm using Tesseract 5.5. It could actually be that much better, or I could just be lucky. I've got some pretty well-done scans to work with.

It's the opposite: for the numbers it could go (implicitly) "are you sure, I have a different figure for that" . . .

I honestly don't know what you mean. Are you saying that an LLM would know that a reference to "page 311" should actually be a reference to "page 317" based on context?

I think the example you've given makes a lot of sense if you're just using an LLM as one way to flag things for review.

As someone who's learning how to do OCR in order to re-OCR a bunch of poorly digitized documents, this will not work with modern OCR. Modern OCR is too good.

If you're able to improve the preprocessing and recognition enough, then there's a point at which any post-processing step you do will introduce more errors than it fixes. LLM's are particularly bad as a post-processing step because the errors they introduce are _designed to be plausible_ even when they don't match the original text. This means they can't be caught just by reading the OCR results.

I've only learned this recently, but it's something OCR experts have known for over a decade, including the maintainers of Tesseract. [1]

OCR is already at the point where adding an LLM at the end is counterproductive. The state of the art now is to use an LSTM (also a type of neural network) which directly recognizes the text from the image. This performs shockingly well if trained properly. When it does fail, it fails in ways not easily corrected by LLM's. I've OCR'ed entire pages using Tesseract's new LSTM engine where the only errors were in numbers and abbreviations which an LLM obviously can't fix.

[1] https://tesseract-ocr.github.io/docs/Limits_on_the_Applicati...