Math is racist

[Chesterton]

Bingo.

Use some discrimination. Dont chase down every ridiculous claim that comes your way.

Don't get me wrong, I wasn't accusing you of being prejudiced. Of course you have to decide that it's ridiculous first.

Anyway, FYI, the video was from New Discourses' James Lindsay, one of the authors of the famous "Grievance Studies". Apolitical and very acquainted with what goes on in American academia.

 

[durangodawood]

Don't get me wrong, I wasn't accusing you of being prejudiced. Of course you have to decide that it's ridiculous first.

Anyway, FYI, the video was from New Discourses' James Lindsay, one of the authors of the famous "Grievance Studies". Apolitical and very acquainted with what goes on in American academia.

Let me ask you. Does his conclusion comport generally with your experience of academia? And how broad is your experience?

 

[Chesterton]

Let me ask you. Does his conclusion comport generally with your experience of academia? And how broad is your experience?

I don't really have much experience with academia apart from just sitting in classes in the early '80's. But it was partially formative for me, at a time when I was pretty much a blank slate, and barely knew what the difference between a liberal and a conserative was supposed to be. Outside of math and hard science, the professors were left-leaning, but at the time I just thought they were weird and had bad, wrong ideas. Like, why does the history teacher do nothing but bad-mouth America? Hasn't America done something good once, or twice, sometime? And the teacher who was supposed to be teaching us English, but would do stuff like play Laurie Anderson's "O Superman" song in class, and show us bad video poetry that her girlfriend made. Geez, I paid for an English class, I want my money back. (Plus it's 1983 so why is she dressing like a hippie?)

One anecdote: The drummer in my band lived with his parents, and I was living with them. His mom was a professor of literature. By pure chance I got put in her class at the beginning of a semester. First day of class she gives us four books to read which were hateful, anti-white, anti-male, anti-American garbage. And mostly insipid drivel as far as the writing (imagine a Jesse Jackson speech made into literature). I tried but couldn't read that stuff. I withdrew from the class to get another professor. People were shocked - "you were lucky enough to get a person you live in the same house with for your professor and you withdrew?!" lol But look, I value my mind. You expose your mind to that rot long enough and you can end up thinking 2+2 doesn't equal 4.

 

[bekkilyn]

You know, we can still believe that 2 + 2 doesn't always equal 4 *without* also believing it has anything to do with racism or any other cultural influences. Sometimes it's just a matter of modular mathematics.

 

[durangodawood]

I don't really have much experience with academia apart from just sitting in classes in the early '80's. But it was partially formative for me, at a time when I was pretty much a blank slate, and barely knew what the difference between a liberal and a conserative was supposed to be. Outside of math and hard science, the professors were left-leaning, but at the time I just thought they were weird and had bad, wrong ideas. Like, why does the history teacher do nothing but bad-mouth America? Hasn't America done something good once, or twice, sometime? And the teacher who was supposed to be teaching us English, but would do stuff like play Laurie Anderson's "O Superman" song in class, and show us bad video poetry that her girlfriend made. Geez, I paid for an English class, I want my money back. (Plus it's 1983 so why is she dressing like a hippie?)

One anecdote: The drummer in my band lived with his parents, and I was living with them. His mom was a professor of literature. By pure chance I got put in her class at the beginning of a semester. First day of class she gives us four books to read which were hateful, anti-white, anti-male, anti-American garbage. And mostly insipid drivel as far as the writing (imagine a Jesse Jackson speech made into literature). I tried but couldn't read that stuff. I withdrew from the class to get another professor. People were shocked - "you were lucky enough to get a person you live in the same house with for your professor and you withdrew?!" lol But look, I value my mind. You expose your mind to that rot long enough and you can end up thinking 2+2 doesn't equal 4.

Wow. I'm sorry you had such and awful college experience. I went to a place in the late 80s where everyone seem to think the faculty are all left of Castro. But my humanities experiences were excellent. In fact I even revisited an amazing class where the audio of all lectures is posted online. I took podcast "lecture walks" in my neighborhood. But my exposure to academia is way broader than just that......

 

[Chesterton]

Wow. I'm sorry you had such and awful college experience. I went to a place in the late 80s where everyone seem to think the faculty are all left of Castro. But my humanities experiences were excellent. In fact I even revisited an amazing class where the audio of all lectures is posted online. I took podcast "lecture walks" in my neighborhood. But my exposure to academia is way broader than just that......

I remember the title of one of the poems from that English class. It was called Radical Chic, and it was read on video by two well-dressed ladies sipping white wine at a posh cafe, professing their admiration for the Sandinistas or something like that. Now there are at least two ways one could mock radical chic: the way I would do it, or the way my teacher's poet friend did it - by encouraging the ladies to actually become radical.

 

[Radagast]

People like this have been teaching our kids for a couple of generations now, and they're just getting more numerous and more insane.

True, that.

 

[Radagast]

sigh....

This is a better explanation of why a professor would not want their lecture online:

Why do professors refuse to put lecture notes online when copiously convenient? - Quora

Really? "preliminary research, bold hypotheses"? Not in any sensible university and discipline. Undergraduate lectures are (or at least, should be) accepted textbook material.

Most teachers think that if students have the notes, they'll stop coming to class.

And that is indeed a genuine problem; but during Covid-19 that's kind of the whole point.

 

[Radagast]

You know, we can still believe that 2 + 2 doesn't always equal 4

No, 2 + 2 always equals 4.

Sometimes it's just a matter of modular mathematics.

No, it's not. Modulo 3, for example, the following are all true:

• 2 + 2 = 4
• 2 + 2 = 1
• 4 = 1

The numerals here are shorthand for equivalence classes of integers:

• 2 = {..., -4, -1, 2, 5, 8, ...}
• 1 = 4 = {..., -5, -2, 1, 4, 7, ...}

Nothing in modular arithmetic means denying 2+2=4.

 

[bekkilyn]

No, 2 + 2 always equals 4.



No, it's not. Modulo 3, for example, the following are all true:

• 2 + 2 = 4
• 2 + 2 = 1
• 4 = 1

The numerals here are shorthand for equivalence classes of integers:

• 2 = {..., -4, -1, 2, 5, 8, ...}
• 1 = 4 = {..., -5, -2, 1, 4, 7, ...}

Nothing in modular arithmetic means denying 2+2=4.

Try mod 2

 

[Radagast]

Try mod 2

Sigh.

Maybe you should read up on this stuff a little. Modulo 2, the following are all true:

• 2 + 2 = 4
• 2 + 2 = 2
• 2 + 2 = 0
• 4 = 2
• 2 = 0
• 4 = 0

The numerals here are shorthand for equivalence classes of integers (that's what "modular" means):

• 0 = 2 = 4 = {..., -4, -2, 0, 2, 4, 6, ...}
• 1 = 3 = 5 = {..., -5, -3, -1, 1, 3, 5, ...}
• 0 + 0 = 1 + 1 = 0
• 0 + 1 = 1 + 0 = 1

Nothing in modular arithmetic means denying 2+2=4.

 

[bekkilyn]

Sigh.

Maybe you should read up on this stuff a little. Modulo 2, the following are all true:

• 2 + 2 = 4
• 2 + 2 = 2
• 2 + 2 = 0
• 4 = 2
• 2 = 0
• 4 = 0

The numerals here are shorthand for equivalence classes of integers:

• 0 = 2 = 4 = {..., -4, -2, 0, 2, 4, 6, ...}
• 1 = 3 = 5 = {..., -5, -3, -1, 1, 3, 5, ...}

Nothing in modular arithmetic means denying 2+2=4.

I wasn't at all suggesting that modular arithmetic *denies* 2+2=4, but that 2+2 does not always equal 4. Sometimes it is equal to other numbers, such as 0 in mod 2, since 4 is outside of the allowed range of (0,1). Even a statement that 4=0 still shows that 2+2 can be equal to something other than 4.

 

[Radagast]

I wasn't at all suggesting that modular arithmetic *denies* 2+2=4, but that 2+2 does not always equal 4

No, 2+2 always equals 4. In modular arithmetic, it also equals other things as well.

And you seem a little confused on what the word "deny" means. Saying "2+2 does not always equal 4" means denying that "2+2=4" is always true.

since 4 is outside of the allowed range of (0,1)

That remark suggests to me a misunderstanding of how modular arithmetic works. Please read my post again.

 

[bekkilyn]

No, 2+2 always equals 4.

In modular arithmetic, it also equals other things as well.

And you seem a little confused on what the word "deny" means.

If it equals other things as well, that means the result is not always 4 but can be one of those other numbers. I'm not confused and I know exactly what you are saying and if I was looking at the example from only your perspective, I would agree with you, but I'm looking at it from a different perspective. If we can only have a result of 0 or 1 then we cannot have a result of 4 EVEN IF 4=0 in which 2+2 must be equal to a number other than 4. If 2+2 is a number other than 4, then it is not always 4.

That remark suggests to me a misunderstanding of modular arithmetic. Please read my post again.

Are you suggesting that the remainders of mod 2 arithmetic can be other than 0 or 1?

 

[Radagast]

I'm not confused and I know exactly what you are saying

No, you don't.

If we can only have a result of 0 or 1

Firstly, that reflects a serious misunderstanding of how modular arithmetic works, and secondly, if all you have is 0 and 1, how can you be adding 2 and 2?

Are you suggesting that the remainders of mod 2 arithmetic can be other than 0 or 1?

That reflects a serious misunderstanding of how modular arithmetic works. Please read my post again (or pick up a textbook: https://books.google.com/books?id=rLZjBAAAQBAJ&pg=PA6).

 

[bekkilyn]

No, you don't.

Yes, I do. You are simply unable to see from my perspective because you are fixed on "proper math" rather than being out of the box.

Edit: The point here isn't to show that 2+2 is not equal to 4, but to show that 2+2 can be equal to something *other* than 4, which using mod 2 easily shows. While a 4 and a 0 might be equal to one another by your demonstration, they are not the *same* number, just like two sides of any other equation may be equal, but they are not the *same*.

Firstly, that reflects a serious misunderstanding of how modular arithmetic works, and secondly, if all you have is 0 and 1, how can you be adding 2 and 2?

Because we're talking about the result of adding 2 + 2. If you get a result other than 0 or 1, then is it still mod 2 or something else?

That reflects a serious misunderstanding of how modular arithmetic works. Please read my post again (or pick up a textbook).

I'm not sure how having a result of either 0 or 1 reflects a serious misunderstanding of how modular arithmetic (in mod 2) works. What other remainder are you going to get after dividing a number by 2? It's not going to be 4.

 

[Radagast]

Yes, I do. You are simply unable to see from my perspective because you are fixed on "proper math"

The only math is "proper math." And in "proper math," 2+2=4.

The point here isn't to show that 2+2 is not equal to 4

Now you've changed your claim, which was, and I quote, that "2+2 does not always equal 4."

While a 4 and a 0 might be equal to one another by your demonstration, they are not the *same* number

Modular arithmetic deals with equivalence classes, not numbers. Modulo 2, the equivalence classes 0 and 4 are indeed the same equivalence class. That's why we can write 0 = 4 (in case you hadn't noticed, I'm using underlines for equivalence classes, because CF doesn't give me overbars as an option).

Because we're talking about the result of adding 2 + 2. If you get a result other than 0 or 1, then is it still mod 2 or something else?

Firstly, that reflects a serious misunderstanding of how modular arithmetic works, and secondly, if all you have is 0 and 1, how can you be adding 2 and 2?

Modulo 2, the only sums you can have
are 0 + 0 = 1 + 1 = 0
and 0 + 1 = 1 + 0 = 1

I'm not sure how having a result of either 0 or 1 reflects a serious misunderstanding of how modular arithmetic (in mod 2) works.

Because in modular arithmetic we deal with equivalence classes of integers that have the same remainder.

See this textbook: https://books.google.com/books?id=rLZjBAAAQBAJ&pg=PA6

And I'm really unsure why you think that the denial of 2+2=4 needs such an elaborate (albeit misguided) defence in the first place.

 

[bekkilyn]

The only math is "proper math."

Now you've changed your claim, which was, and I quote, that "2+2 does not always equal 4."

Modular arithmetic deals with equivalence classes, not numbers. Modulo 2, the equivalence classes 0 and 4 are indeed the same equivalence class. That's why we can write 0 = 4 (in case you hadn't noticed, I'm using underlines for equivalence classes, because CF doesn't give me overbars as an option).

Firstly, that reflects a serious misunderstanding of how modular arithmetic works, and secondly, if all you have is 0 and 1, how can you be adding 2 and 2?

Modulo 2, the only sums you can have
are 0 + 0 = 1 + 1 = 0
and 0 + 1 = 1 + 0 = 1

Because in modular arithmetic you deal with equivalence classes of integers that have the same remainder.

See this textbook: https://books.google.com/books?id=rLZjBAAAQBAJ&pg=PA6

I understand all of what you are saying, and have studied equivalence classes, but it doesn't at all negate that 2+2 does not always equal 4.

Sometimes 2+2 can equal 0.

Sometimes 2+2 can equal some other number. And we haven't even brought in the possibilities of different measurement scales.

So while 0 = 4 can be a true statement based on equivalence classes and everything you're presented in order to complicate things since there is no need here to go into the theory behind modular arithmetic, 0 is not the same as 4.

2+2=4 and 2+2=0 are not the same equation. 2+2=4 is not the same as 2+2=0. Perhaps they can be shown to be equivalent, but it still doesn't mean that they are the same.

I see your perspective just fine and I'm not saying it's incorrect, but your perspective is not the only way to see things. 2+2 does not always equal 4. Sometimes 2+2 is equal to 0. Sometimes 2+2 is equal to some other number. All may be correct based on how it's determined. All may be equivalent. But all are not the same. You are too fixed to the textbook to be able to see my perspective, but it is still easy enough for even a child to visually see that a 0 and a 4 are not the same regardless of whether or not they are equal, equivalent, or congruent, or display lines on the top or bottom.

We could even look at it in terms of money. There used to be $2 bills for a short time. Well on the surface using two of those bills 2+2 would be equal to 4 right, but what if there was deflation, then 2+2 would be some number less than 4, or if they grow in value, then 2+2 may be 1,250 in terms of money.

There are many examples we can use to show that 2+2 is not always equal to 4.

Still of course doesn't mean it has anything to do with racism. It's just that mathematics isn't meant to be contained within a neatly defined box with one and only one possible result.

 

[Radagast]

I understand all of what you are saying, and have studied equivalence classes, but it doesn't at all negate that 2+2 does not always equal 4.

I'm sorry, but 2+2=4 is a necessary truth. It is indeed always true.

So while 0 = 4 can be a true statement based on equivalence classes and everything you're presented in order to complicate things since there is no need here to go into the theory behind modular arithmetic

You were the one that wanted to bring in modular arithmetic. If we're going to do that, let it be by the textbook.

0 is not the same as 4

Modulo 2, we have 0 = {..., -4, -2, 0, 2, 4, 6, ...}
and 4 = {..., -4, -2, 0, 2, 4, 6, ...}
The equivalence classes 0 and 4 are exactly the same.

In fact, modulo 2, there are only two equivalence classes,
with 1 = {... -3, -1, 1, 3, 5, ...} being the other one.

And there are only four possible sums:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0

I see your perspective just fine and I'm not saying it's incorrect, but your perspective is not the only way to see things.

Mathematics is not a matter of perspective. You may "feel" that 2+2 is 3 or 5 or 17½. But what you feel doesn't matter. In mathematics, there is only one right answer.

You are too fixed to the textbook

In mathematics, you can't be "too fixed to the textbook." Mathematics is not poetry. You don't get to just make up random stuff.

to be able to see my perspective

I see your perspective fine. You're just wrong.

it is still easy enough for even a child to visually see that a 0 and a 4 are not the same regardless of whether or not they are equal, equivalent, or congruent, or display lines on the top or bottom

If you're going into it at that childish level, then ••+••=•••• (Mayan) or II+II=IV (Roman) or β+β=δ (Greek) or 2+2=4 (modern) or 10+10=100 (binary) indeed all look like totally different statements.

But to see only the symbols, and not understand their meaning, is to totally misunderstand what mathematics is about.

It's just that mathematics isn't meant to be contained within a neatly defined box with one and only one possible result.

That's exactly what mathematics is meant to be.

That is why Mayan, Roman, Greek, Egyptian, Babylonian, Indian, and Chinese mathematicians came up with the same answers to the same questions. Because there really is "one and only one possible result," which does not depend on culture.

 

[bekkilyn]

I'm sorry, but 2+2=4 is a necessary truth. It is indeed always true.

While it's already been agreed that 2+2=4 is true (though how do we really know that it is *always* true rather than a hypothesis that we have simply decided is true?), we also know that 2+2 is not always equal to 4.

You were the one that wanted to bring in modular arithmetic. If we're going to do that, let it be by the textbook.

Nope, never said anything about being by any textbook. While 4 and 0 may be equivalent, they are not the same, and 2+2=4 and 2+2=0 are both true.

Modulo 2, we have 0 = {..., -4, -2, 0, 2, 4, 6, ...}
and 4 = {..., -4, -2, 0, 2, 4, 6, ...}
The equivalence classes 0 and 4 are exactly the same.

But the numbers 0 and 4 are not the same. They don't even look the same.

In fact, modulo 2, there are only two equivalence classes,
with 1 = {... -3, -1, 1, 3, 5, ...} being the other one.

Are you sure there aren't 4 equivalence classes?

Mathematics is not a matter of perspective. You may "feel" that 2+2 is 3 or 5 or 17½. But what you feel doesn't matter. In mathematics, there is only one right answer.

False. There is plenty of ambiguity in mathematics.

Devlin's Angle: Most Math Problems Do Not Have a Unique Right Answer

In mathematics, you can't be "too fixed to the textbook." Mathematics is not poetry. You don't get to just make up random stuff.

Mathematics is a language, much closer to poetry than you might think.

I see your perspective fine. You're just wrong.

If you saw my perspective, you wouldn't be misunderstanding it.

If you're going into it at that childish level, then ••+••=•••• (Mayan) or II+II=IV (Roman) or β+β=δ (Greek) or 2+2=4 (modern) or 10+10=100 (binary) indeed all look like totally different statements.

Indeed, they are different statements.

But to see only the symbols, and not understand their meaning, is to totally misunderstand what mathematics is about.

Not at all. Meanings are one way of seeing. Symbols are another way of seeing. Some combination of both are yet more ways of seeing, and there are other ways of seeing as well. Mathematics isn't so limited as you seem to wish to believe.

That's exactly what mathematics is meant to be.

That is why Mayan, Roman, Greek, Egyptian, Babylonian, Indian, and Chinese mathematicians came up with the same answers to the same questions. Because there really is "one and only one possible result," which does not depend on culture.

Never said anything about culture, but your conclusion here is false.