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File: 1613405748934.jpg ( 209.61 KB , 900x899 , 589f51682de7eb28660186206c….jpg )

Is any of Engels' math in Anti-Dühring wrong, or outdated (wrong to a lesser extent)? I showed my STEMlord friend some of these quotes and they didn't understand what they meant:

>It is for example a contradiction that a root of A should be a power of A, and yet A^(1/2) = square root of A.

> 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 the 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?

>We have already noted that one of the basic principles of higher mathematics is the contradiction that in certain circumstances straight lines and curves may be the same. It also gets up this other contradiction: that lines which intersect each other before our eyes nevertheless, only five or six centimetres from their point of intersection, can be shown to be parallel, that is, that they will never meet even if extended to infinity. And yet, working with these and with even far greater contradictions, it attains results which are not only correct but also quite unattainable for lower mathematics.

>It is for example a contradiction that a root of A should be a power of A, and yet A^(1/2) = square root of A.

> 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 the 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?

>We have already noted that one of the basic principles of higher mathematics is the contradiction that in certain circumstances straight lines and curves may be the same. It also gets up this other contradiction: that lines which intersect each other before our eyes nevertheless, only five or six centimetres from their point of intersection, can be shown to be parallel, that is, that they will never meet even if extended to infinity. And yet, working with these and with even far greater contradictions, it attains results which are not only correct but also quite unattainable for lower mathematics.

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>>4999

>They said "so is (-i)^2 positive is it

Uh…

(-i)^2 = (-1 * i)^2

(-1 * i)^2 = (-1)^2 * i^2

(-1)^2 * i^2 = 1 * i^2

1 * i^2 = i^2

I don't think they understand the basic math going on here.

The i is what makes the result negative. The minus sign gets canceled.

>>4997

>Is any of Engels' math in Anti-Dühring wrong, or outdated (wrong to a lesser extent)

He's not saying that math is wrong. He spells out what he means later in what you quoted:

<And yet, working with these and with even far greater contradictions, it attains results which are not only correct but also quite unattainable for lower mathematics.

He's saying that "lower mathematics" is a simpler way of understanding math and that just because something is contradictory within a particular system, that doesn't mean that it's actually contradictory or false. It may be that the system is just too simple. Math is a little abstract though, so let's use a more concrete example. Newton's version of physics is pretty good and gets the job done in a lot of cases, but without Einstein's more advanced additions you can't understand things like time dilation. If you try to explain those things within Newton's model you get "contradictions" where the velocity of an object are difficult to make sense of. This doesn't matter for cases where Newton is enough, like constructing a building that won't collapse, but if you want to build a GPS satellite, you need to understand relativity so they can stay properly synchronized at speeds where time dilation is a factor. By the same token, you don't need to understand quantum mechanics to build a GPS satellite, but you do if you build a quantum computer, and Einstein himself was skeptical of conclusions involved in quantum physics because they apparently contradict certain physical principles of simpler physics.

tl;dr

The map is not the territory.

>They said "so is (-i)^2 positive is it

Uh…

(-i)^2 = (-1 * i)^2

(-1 * i)^2 = (-1)^2 * i^2

(-1)^2 * i^2 = 1 * i^2

1 * i^2 = i^2

I don't think they understand the basic math going on here.

The i is what makes the result negative. The minus sign gets canceled.

>>4997

>Is any of Engels' math in Anti-Dühring wrong, or outdated (wrong to a lesser extent)

He's not saying that math is wrong. He spells out what he means later in what you quoted:

<And yet, working with these and with even far greater contradictions, it attains results which are not only correct but also quite unattainable for lower mathematics.

He's saying that "lower mathematics" is a simpler way of understanding math and that just because something is contradictory within a particular system, that doesn't mean that it's actually contradictory or false. It may be that the system is just too simple. Math is a little abstract though, so let's use a more concrete example. Newton's version of physics is pretty good and gets the job done in a lot of cases, but without Einstein's more advanced additions you can't understand things like time dilation. If you try to explain those things within Newton's model you get "contradictions" where the velocity of an object are difficult to make sense of. This doesn't matter for cases where Newton is enough, like constructing a building that won't collapse, but if you want to build a GPS satellite, you need to understand relativity so they can stay properly synchronized at speeds where time dilation is a factor. By the same token, you don't need to understand quantum mechanics to build a GPS satellite, but you do if you build a quantum computer, and Einstein himself was skeptical of conclusions involved in quantum physics because they apparently contradict certain physical principles of simpler physics.

tl;dr

The map is not the territory.

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>>5002

I don't see how that point would be relevant to the rest of his argument, he says

>But even lower mathematics teems with contradictions. It is for example a contradiction that a root of A…

after some stuff about higher maths. I don't get what "fractional powers are only allowed in higher maths" is meant to prove or anything.

I don't see how that point would be relevant to the rest of his argument, he says

>But even lower mathematics teems with contradictions. It is for example a contradiction that a root of A…

after some stuff about higher maths. I don't get what "fractional powers are only allowed in higher maths" is meant to prove or anything.

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>>5003

>(they were pointing out (-1)^2 being negative as a counterexample to Engels)

Your friend has it backward. Engels didn't say you can't square a negative ie (-1)^2. He said a negative can't*be* a square ie i^2 = -1. Totally different concepts.

>>5004

Well that part wasn't in the original post. IDK how that's meant as a contradiction then, might just be a change in the way they teach math like when "new math" was introduced.

>(they were pointing out (-1)^2 being negative as a counterexample to Engels)

Your friend has it backward. Engels didn't say you can't square a negative ie (-1)^2. He said a negative can't

>>5004

Well that part wasn't in the original post. IDK how that's meant as a contradiction then, might just be a change in the way they teach math like when "new math" was introduced.

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>>5000

>He's not saying that math is wrong.

To clarify, I was wondering if Engels' mathematical knowledge or theory itself was wrong, because I/my friend didn't understand what the root contradiction was and how counter examples don't apply to his point about positive squares. Are you saying that, 'removing the concept of i from the conversation', his point about positive squares is a valid observation of a contradiction, and furthermore that the because it is "contradictory within a particular system, that doesn't mean that it's actually contradictory or false"? That makes more sense to me.

>He's not saying that math is wrong.

To clarify, I was wondering if Engels' mathematical knowledge or theory itself was wrong, because I/my friend didn't understand what the root contradiction was and how counter examples don't apply to his point about positive squares. Are you saying that, 'removing the concept of i from the conversation', his point about positive squares is a valid observation of a contradiction, and furthermore that the because it is "contradictory within a particular system, that doesn't mean that it's actually contradictory or false"? That makes more sense to me.

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>>5007

Doesn't change the point. A minus sign is canceled by squaring it. The i isn't because it's the square root of a negative, not a negative itself.

>>5006

>Are you saying that, 'removing the concept of i from the conversation', his point about positive squares is a valid observation of a contradiction, and furthermore that the because it is "contradictory within a particular system, that doesn't mean that it's actually contradictory or false"?

More or less.

The number i (and complex numbers in general) do fall outside "lower math" and particularly the kind of math you can apply to objects directly. It's obvious what one apple is, what half an apple is, even what a fractional or negative apple is. What does i apples look like though? The "lower math" framework has certain assumptions based on how people intuitively understand numbers based on our experience. Complex/imaginary numbers are a later addition to math that violate the rules laid out in the more basic version. Imaginary numbers are of course real though, both in the sense of the abstract math and in their real-world applications to science and technology.

Doesn't change the point. A minus sign is canceled by squaring it. The i isn't because it's the square root of a negative, not a negative itself.

>>5006

>Are you saying that, 'removing the concept of i from the conversation', his point about positive squares is a valid observation of a contradiction, and furthermore that the because it is "contradictory within a particular system, that doesn't mean that it's actually contradictory or false"?

More or less.

The number i (and complex numbers in general) do fall outside "lower math" and particularly the kind of math you can apply to objects directly. It's obvious what one apple is, what half an apple is, even what a fractional or negative apple is. What does i apples look like though? The "lower math" framework has certain assumptions based on how people intuitively understand numbers based on our experience. Complex/imaginary numbers are a later addition to math that violate the rules laid out in the more basic version. Imaginary numbers are of course real though, both in the sense of the abstract math and in their real-world applications to science and technology.

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>>5008

Okay, I sort of understand it. I still don't see how the maths works though.

(-sqrt(-1))*(-sqrt(-1)) = -1 which is a negative number

Can you explain like I'm an idiot why that doesn't fit Engels' set-up and contradict his assertion? Or does it not make sense to give a counter-example that involves i because of what you said in your post (excluding them)? What does "gives a positive square" mean?

If it's because you exclude them, I think that makes much more sense to me but that would seem to suggest that i is really a concept invented to "hide" this contradiction that exists at the simple level of maths. I have no idea if that is an accurate portrayal of i though, haven't studied maths properly yet.

Okay, I sort of understand it. I still don't see how the maths works though.

(-sqrt(-1))*(-sqrt(-1)) = -1 which is a negative number

Can you explain like I'm an idiot why that doesn't fit Engels' set-up and contradict his assertion? Or does it not make sense to give a counter-example that involves i because of what you said in your post (excluding them)? What does "gives a positive square" mean?

If it's because you exclude them, I think that makes much more sense to me but that would seem to suggest that i is really a concept invented to "hide" this contradiction that exists at the simple level of maths. I have no idea if that is an accurate portrayal of i though, haven't studied maths properly yet.

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>>5010

>Or does it not make sense to give a counter-example that involves i because of what you said in your post (excluding them)?

This. i was invented to resolve the contradiction.

>What does "gives a positive square" mean?

The square is the number B you get by multiplying the number A by itself. The square of 2 is 4. Etc.

It's often mixed up with square root, which is the reverse - the number B you must multiply by itself to get the number A. The square root of 4 is 2.

It just so happens that both the square and square root of 1 are also 1, because 1 is the identity quantity. I think this may be part of the confusion.

A "positive square" means a positive number you get from multiplying two numbers together. Unless you include i (and by extension the complex numbers), you can only have a positive square, because a negative times a negative cancels to being a positive.

>If it's because you exclude them, I think that makes much more sense to me but that would seem to suggest that i is really a concept invented to "hide" this contradiction that exists at the simple level of maths.

It's only a "contradiction" because the system was constructed assuming that this was impossible. Basically, the assumption that because we don't know any "real" number that can be squared and give a negative, there is no such thing. But the fact that you can express the idea of a square root of a negative makes it possible to make a mathematical construct representing that. Once you have that much you can extend the math. The fact that complex numbers are pretty widely applicable IRL means that the "contradiction" was more like a limit on the original model.

>Or does it not make sense to give a counter-example that involves i because of what you said in your post (excluding them)?

This. i was invented to resolve the contradiction.

>What does "gives a positive square" mean?

The square is the number B you get by multiplying the number A by itself. The square of 2 is 4. Etc.

It's often mixed up with square root, which is the reverse - the number B you must multiply by itself to get the number A. The square root of 4 is 2.

It just so happens that both the square and square root of 1 are also 1, because 1 is the identity quantity. I think this may be part of the confusion.

A "positive square" means a positive number you get from multiplying two numbers together. Unless you include i (and by extension the complex numbers), you can only have a positive square, because a negative times a negative cancels to being a positive.

>If it's because you exclude them, I think that makes much more sense to me but that would seem to suggest that i is really a concept invented to "hide" this contradiction that exists at the simple level of maths.

It's only a "contradiction" because the system was constructed assuming that this was impossible. Basically, the assumption that because we don't know any "real" number that can be squared and give a negative, there is no such thing. But the fact that you can express the idea of a square root of a negative makes it possible to make a mathematical construct representing that. Once you have that much you can extend the math. The fact that complex numbers are pretty widely applicable IRL means that the "contradiction" was more like a limit on the original model.

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