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3 months agoArguably a lot of these tools are designed specifically to reduce the effort a human has to put in to create the art they want to make too.
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There are some subtleties to this particular topic that are worth mentioning. I would be careful to distinguish between constructing vs defining here.
The usual definition of the irrationals works roughly like this:
You have a set of numbers R which you call the real numbers. You have a subset of the real numbers Q which you call the rational numbers. You define a real number to be irrational if it is not a rational number.
This is perfectly rigorous, but it relies on knowing what you mean by R and Q.
Both R and Q can be defined “without” (a full) construction by letting R be any complete ordered field. Such a field has a multiplicative identity 1 by definition. So, take 0 along with all sums of the form 1, 1+1, 1+1+1 and so on. We can call this set N. We can take Z to be the set of all elements of N and all additive inverses of elements of N. Finally take Q to be the set containing all elements of Z and all multiplicative inverses of (nonzero) elements of Z. Now we have our R and Q. Also, each step of the above follows from our field axioms. Defining irrationals is straightforward from this.
So, the definition bit here is not a problem. The bigger issue is that this definition doesn’t tell us that a complete ordered field exists. We can define things that don’t exist, like purple flying pigs and so on.
What the dedekind cut construction shows is that using only the axioms of zfc we can construct at least one complete ordered field.
So its a case of it not working on irrational numbers, its just that we cant prove it because we cant calculate the multiplication of 2, right?
The issue is the proving part. We can’t use repeated addition trickery (at least not in an obvious way) to show a product of two irrational negative numbers is positive. It’s definitely still true that a product of two negative numbers is positive, just that proving it in general requires a different approach.
Somehow, my mind has issues with the e*pi = ke. Id say that ke = e * pi is impossible because k is an integer and pi isnt, no? It could never be equals, i think.
Yes this is correct. The ke example is for a proof by contradiction. We are assuming something is true in order to show it forces us to be able to conclude something ridiculous/false. Since the rest of our reasoning was correct, then it must have been our starting assumption that was wrong. So, we have to conclude our starting assumption was wrong/false.
Multiplying two negative irrational numbers together will still give you a positive number, it’s just that you can’t prove this by treating multiplication as repeated addition like you can multiplication involving integers (note that 3 is an integer, 3 is not irrational, the issue is when you have two irrationals).
So, for example with e * pi, pi isn’t an integer. No matter how many times we add e to itself we’ll never get e * pi.
Try it yourself: Assume that we can add e to itself k (a nonnegative integer) times to get the value e * pi. Then e * pi = ke follows by basic properties of algebra. If we divide both sides of this equation by e we find that pi=k. But we know k is an integer, and pi is not an integer. So, we have reached a contradiction and this means our original assumption must be false. e * pi can’t be equal to e added to itself k times (no matter which nonnegative integer k that we pick).
Copy pasted from my other comment:
This doesn’t work if you have to deal with multiplication of numbers that are not integers. You can adjust your idea to work with rational numbers (i.e. ratios of integers) but you will have trouble once you start wanting to multiply irrational numbers like e and pi where you cannot treat multiplication easily as repeated addition.
The actual answer here is that the set of real numbers form a structure called an ordered field and that the nice properties we are familiar with from algebra (for ex that a product of two negatives is positive) can be proved from properties of ordered fields.
This doesn’t work if you have to deal with multiplication of numbers that are not integers. You can adjust your idea to work with rational numbers (i.e. ratios of integers) but you will have trouble once you start wanting to multiply irrational numbers like e and pi where you cannot treat multiplication easily as repeated addition.
The actual answer here is that the set of real numbers form a structure called an ordered field and that the nice properties we are familiar with from algebra (for ex that a product of two negatives is positive) can be proved from properties of ordered fields.
Don’t confuse the wording “set of real numbers” here, this is just the technical name for the collection of numbers people use from elementary algebra on through to calculus.
Machine learning techniques are often thought of as fancy function approximation tools (i.e. for regression and classification problems). They are tools that receive a set of values and spit out some discrete or possibly continuous prediction value.
One use case is that there are a lot of really hard+important problems within CS that we can’t solve efficiently exactly (lookup TSP, SOP, SAT and so on) but that we can solve using heuristics or approximations in reasonable time. Often the accuracy of the heuristic even determines the efficiency of our solution.
Additionally, sometimes we want predictions for other reasons. For example, software that relies on user preference, that predicts home values, that predicts the safety of an engineering plan, that predicts the likelihood that a person has cancer, that predicts the likelihood that an object in a video frame is a human etc.
These tools have legitamite and important use cases it’s just that a lot of the hype now is centered around the dumbest possible uses and a bunch of idiots trying to make money regardless of any associated ethical concerns or consequences.
1·1 year agoIf you’re talking about having family photos pirated, there’s a privacy issue, not a property issue.
It’s pretty clear that I’m talking about more than just family photos. It’s also pretty clear that what I’m saying is that privacy problems are one of possibly many issues with copying data without permission. My actual point here from the start has been that it’s not always ethical to copy other people’s data without permission.
Everyone talking about media in privacy talks about distributable media. If you want to include other things, that’s on you, but you’ll be yapping in the void as that isn’t what the conversation is about. Not secrets, or private documents.
All of the types of media and data I’m talking about are distributable in a colloquial sense. This conversation is about the fact that copying data without permission isn’t always ethical. The data we’re talking about here absolutely includes secrets, private documents and so on.
As for the term of taking, it’s clear what taking means when you try to erroneously conflate piracy with stealing. It doesn’t mean the same as taking a shit either,
I don’t think that’s what’s happening. I’m talking about the ethics of copying data. Perhaps sometimes copying data can be considered theft, but whether or not copying data is theft, has nothing to do with my point. A thing being called theft doesn’t make that thing morally wrong or right. The term theft itself has little to do with the actual issue we’re talking about.
Also, I’ve never actually claimed piracy is theft. I’m also not claiming piracy is morally wrong, or even that theft is inherently morally wrong for that matter (a person can be justified in stealing in some cases).
it has nothing to do with personal definitions, merely the accepted definitions when talking about either piracy, or stealing.
Lets assume you’re right and that literally everybody in the world uses these words the way you do (they don’t). I don’t think arguing “but that word means…” makes a very good argument against the fact that copying data from other people just isn’t always morally right. The fact that you don’t like how I use certain words is just not a good argument against what I’m saying. If you understand what I mean and you disagree with what I’m saying, then why not argue against my point instead of complaining about the fact that you don’t like HOW I use certain words? If you understand what I’m saying and you agree that sometimes it’s wrong to copy other peoples data without permission, then why are we still discussing this?
I’m imposing that property on it because for the overwhelming majority of media that is absolutely the case.
I don’t see why this is such a necessary property of media? Arguably there could be more media inside peoples private homes and hard-drives that is not for sale than media that is for sale. On top of that, this kind of thing depends on how we define media, we can take more or less inclusive definitions of this term.
It should also be clear that the kinds of things that I’m talking about in my original post refers to more than just movies, music, games and software (despite me using “media” as a convenient example in my previous post).
If it’s for sale it’s something you do not mind other people seeing. My documents I do not sell because I don’t want people seeing it. If I were to sell them, clearly I don’t mind people seeing it.
I don’t agree. I’d bet a lot of people are willing to sell plenty of ordinarily private things given a high enough price. I don’t think the notion that something is for sale all of a sudden makes that thing magically not private? When you sell something you don’t always make the thing you’re selling available to the public, just to the buyer, and until the sale is complete you’re not typically giving anybody full access to the thing. If it were public/not private the minute you made it for sale, then what is the point in selling it?
Making it for sale means you intend to share it, even if conditionally. Also “taking it” doesn’t apply, making a copy isn’t taking anything.
This isn’t true either. Sometimes people make things for sale with no actual intent of selling. And the intent to share, does not make something all of a sudden not private either. You might share something (perhaps a secret) with a friend, that doesn’t mean the thing you are sharing suddenly becomes not private/public, but that the scope of people you’re will to share this thing privately with has increased by a small amount.
I also disagree with the notion that making a copy just inherently isn’t “taking” things. This is also a matter of definitions, but people actively use the word “taking” to encompass more than just physical things. Phrases like “he took my idea”, “she took my credit card information” and so on are examples of this. Obviously people do consider “taking” to include acts of copying in some cases. If you mean something else by taking, that’s fine, but your personal definition for taking isn’t really relevant when the point I’m making regards a more inclusive notion.
I’ll take your approach. No, that’s not what “taking something” means, because clearly the definition they’re using for that is more inclusive.
Keep telling yourself that champ.
its not piracy. this is /c/piracy
The ethics of data reproduction have been discussed in piracy communities for decades. It’s a central topic to communities centered around data reproduction. Pretending otherwise is stupid.
you dont need my permission you are just making a fool of yourself by trying to call piracy what is not piracy again in /c/piracy
Am I? Or are you arguing in bad faith on a topic you didn’t bother to read the context of?
Feel free to clarify why? At what point does my example become what we’re talking about? Is it the number of people the content is sold for? Is it the amount of money the content is sold for? Enlighten me.
I feel like many people would disagree with you.
I don’t see why I need your permission? I feel like talking about when it is and isn’t ethical to reproduce data is appropriate in this sort of community.
making a copy of Frozen is not.
I feel like I’ve been pretty clesr that this sort of example is not what I’m talking about…
piracy is distributing copies of publicly available media.
Arguably software, films and music aren’t “publically available” in the sense that they’re only conditionally available to the public (ignoring piracy).
But okay, lets take the pornographic example. Say they occasionally sell nude photos to acquaintances too. Now the photos are in some sense “publicly available” in the sense that some people can buy them. Is it now suddenly okay to pirate this media? If so, then why?
accessing a private device and making copies of personal content inside is illegal and unethical.
Did you not read my very first example where I claimed almost exactly that. What have you been thinking I was talking about?
Operating System Concepts by Silberschatz, Galvin and Gagne is a classic OS textbook. Andrew Tanenbaum has some OS books too. I really liked his OS Design and Implementation book but I’m pretty sure that one is super outdated by now. I have not read his newer one but it is called Modern Operating Systems iirc.