ChaiTRex [none/use name]

You can't play every game because some only support Windows/Mac, but yes, Steam has a lot of games that have native Linux versions. For those games without Linux versions, the Windows version will sometimes work on Linux.

Ubuntu LTS is the best for getting used to Linux. You get more supported software (when companies release a Linux version of software, they don't always provide technical support for all distributions; Ubuntu is generally the most supported). There are also lots of forums where you can get free help with it, like Ask Ubuntu.

If you have an older machine, Xubuntu LTS is an official Ubuntu variation, so it has the same benefits as Ubuntu, and it uses a lightweight desktop that goes easier on older machines.

There are also a lot of Steam games that have Linux versions.

If either of you is 45 or under in the USA, you can get an HPV vaccine if you didn't get it already. Good even if you've had HPV to protect you against some types of HPV you didn't get yet.

Here's an archive of the post: https://archive.is/YqlM3

a resilient grid that keeps America safe

So, one of the national grids?

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Some therapists offer reduced fees for people who have lower income. Ask them if they offer sliding scale pricing.

I'm voting for the Jurassic Park T. rex.

I don't care what you acknowledge. I can see that a function can take a set of positions and produce a set of positions, and that's good enough for me.

It doesn't quite matter how absurd it appears to you. What matters is that it fulfills the definition of function you said it didn't.

You mean to write the infinite set of ordered pairs of infinite sets? No, I can't quite do that, as it would take infinite time.

Sure.

As for how, the first element of the ordered pair is a set of starting positions. The second element of the ordered pair is a set of ending positions. ({start_0, ...}, {end_0, ...}). The function is, of course, a set of these ordered pairs where each ordered pair's first element is unique in the set.

The X in your definition of function is the same set as Y: the set of sets of positions.

As for why, just to demonstrate that the statement was incorrect.

As far as why I personally proposed that formalism, it was because you claimed that multiple positions implied a non-function relation, which isn't necessarily the case.

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As far as how it could be done in that hypothetical world: you move each position according to how far the velocity says it would move and you return the set of results.

[Edited because this webpage is wildly closing the editing field and either deleting or submitting the contents of it]

As far as why? Generality for the theory. No one cares what kinematics says about the movement of particular dust particles on a particular exoplanet, but it's nice to know that kinematics works generally. The same would be true for dialectics.

The point of dialectics is what can be predicted usefully from it, I think. I'm still new to it, so I'm still waiting to see what that is. The thing about motion isn't that useful, it's more a thing about making the theory general, but there should be results that are useful.

I agree. I earlier thought by 'unique', you meant unique in the sense that no other input produced the same output, but I see that I was mistaken. Since I see what you mean, I don't know why you said it, because I never implied that a function could give different outputs for the same input. The same output set would always be produced for the same input set in what I said.

Now that we're agreed that a function can output a set, a set of positions at a point in time can be transformed by a function into a set of positions at a later time, meaning that it's theoretically possible for kinematics of a more complicated variety to handle the motion of particles with multiple simultaneous positions.

As far as the uncertainty principle, I may or may not be wrong about it, but my main point stands: empirically, we don't know whether moving particles have unique instantaneous positions or not because we can't measure to the exactness needed to determine that. Theoretically, this seems to be the case as well, which is why I mentioned the Planck length.

One possible alternative would be that it could be that the particle occupies all the positions of a too-small-to-measure segment along the direction of travel, for example. I'm not saying that this is the case. I'm merely trying to give the benefit of the doubt to Engels. I don't want to summarily dismiss his work just because it doesn't meet my preconceptions of how kinematics work.

You are apparently unaware that sets can contain sets, so the element of set Y in your definition can itself be a set, so the output of a function can be a set.

The position of an arbitrary particle can't empirically be known as exactly as you want because there are limitations to measuring devices, as you are apparently also unaware.

Sure, but you’re changing what he is saying.

Engels isn't a mathematician. To demand that he get correct every detail of a proof he may have heard once and that he has no training to reproduce is a bit overblown when the conclusion is correct and the true proof that he's obviously referencing would have been produced historically.

Functions by definition produce a single unique output for a given input. To say that something is in two places at one is to say that you can’t describe motion as a function of time, which is the opposite result of kinematics. See the second image in the linked section.

This is blatantly incorrect. Function outputs don't have to be unique. That's an injective function. If functions produce one output, that one output doesn't have to be a single number, it can be a single set of positions. You can have a function that takes in the starting set of positions and produces the resulting set of positions.

That’s not what Heisenberg’s uncertainty relation says. And wouldn’t matter anyway because epistemic uncertainty is different than ontological non-existence. Not knowing the exact position doesn’t not proscribe the existence of an exact position.

You must be having an argument with someone else in your head, because my point was that we can't know for sure whether or not particles have single positions, not that single positions are proscribed.

The denial of a unique instantaneous position for a given time t flies in the face of pretty much all of kinematics.

The linked essay has another example of a supposed impossibility, though the proof needs a bit of filling in:

It is a contradiction that a negative quantity should be the square of anything, for every negative quantity multiplied by itself gives a positive square. The square root of minus one is therefore not only a contradiction, but even an absurd contradiction, a real absurdity. And yet square root of minus one is in many cases a necessary result of correct mathematical operations. Furthermore, where would mathematics — lower or higher — be, if it were prohibited from operation with square root of minus one?

In its operations with variable quantities mathematics itself enters the field of dialectics, and it is significant that it was a dialectical philosopher, Descartes, who introduced this advance. ...

It's correct that there are no real numbers that are the square root of negative real numbers. It's a real proof by contradiction if it's filled out properly.

How would it have been if they'd said to Descartes that complex numbers flew in the face of pretty much all of arithmetic? Because I know that complex numbers had opposition after they were invented.

(because multiple positions at time t indicates the relation is not a function)

A function can in fact take a set of positions (or some other type of thing containing multiple positions) and produce a new set of positions. Perhaps it's merely a useful simplification to say that there's a unique position.

We know that we can never find out exactly where a particle is due to the uncertainty principle and we know that we can't distinguish things that are separated by less than a Planck length, so is it possible even in principle to empirically determine for sure whether or not particles have a single instantaneous position?

Engels said, "Motion itself is a contradiction."

How is motion itself a contradiction? What things contradict each other?