Why mathematics is neither absolutely nor objectively "right."

[Emily Lake]

Like I already explained 2 + 2 isn't always 4. If we base on calculations on the integers modulo 3 (Z
3), then 2 + 2 = 1.

No, it doesn't.

If you're using modulo 3, then 2+2 = 11. And in modulo 4, 2+2 = 10.

Your error here is akin to you saying that Z10 9+9 = 8.

 

[Emily Lake]

2+2=4. This is true. No matter what modulus you choose, what notation you use.
Binary, decimal, hexidecimal, octal. Roman numerals, Arabic numerals or Aztec numerals. Anything else does not work in real world operations. If you want a deeper understanding of this, we have the Peano axioms, Cantor's set theory. Russell and Whitehead, Frege and others to explain to you why this works. Underlying mathematics is logic.

Hey, even a course in Number Theory would clear up his misconceptions.

 

[Emily Lake]

There is no "objective math," and it's very suspicious that any engineer would think so. The mathematics I've been citing on this thread, which you appear to be completely ignorant of, is known as modular arithmetic. As a reference, I'm using Linear Algebra: A Modern Introduction 3rd Edition by David Poole, pages 13-14. So the math I'm using is math that is standard and commonly accepted by mathematicians.

<Removed> I AM a mathematician! Or at least, given that I have a masters in applied mathematics, I can reasonably refer to myself as a mathematician.

In reality, however, I'm an actuary. I've forgotten more math than you have yet attained. Let me assure you that your understanding is sophomoric and shallow. You're taking something that you don't understand well... and you're applying some pomo philosophizing on top of it. <Removed>

And I guarantee that Steve has considerably more depth of knowledge when it comes to math than you do. <Removed>

 

[Emily Lake]

Steve, I think I'm going to rest my case. I've tried my best to explain my position to you on this issue, but you don't seem to be getting it.

That would be because your position is untenable and demonstrably wrong.

 

[Emily Lake]

The problem for you is I have used modulo arithmetic, as well as most of general applied math. Most of us electrical engineers are applied mathematicians.

Fun factoid - I end up using modular math when I'm doing crochet


ETA: I love crochet, it's math made tactile.

 

[Unknown Soldier]

It's very popular these days to see mathematics as one truth we can know is objectively and absolutely right. I must disagree. A common example of this supposed absolute and objective truth is the equation 2 + 2 = 4. We are told that for all times and places, 2 + 2 = 4, no matter what! If human beings went extinct, then 2 + 2 = 4 still holds as true. If the dinosaurs had the brains, then they would have known 2 + 2 = 4. If there's an advanced civilization of extraterrestrials in the Andromeda galaxy, then they know 2 + 2 = 4.

It's not true that 2 + 2 is absolutely 4. Depending on the rules mathematicians are using, 2 + 2 = 0 might be the case. In modular arithmetic, 2 + 2 might not even be defined at all much less true. For example, in binary there is no 2.

So the truth of 2 + 2 = 4 depends on what arbitrary set of rules you are using. No absolute or objective truth can be so arbitrary. Hence in general, mathematics is neither absolutely nor objectively "right."

You're not even wrong here.

And you clearly have no understanding of how modular mathematics work. Regardless of the modulo of your system, and regardless of the terms you use for your numbers... the relationships ALWAYS hold.

FALSE!!!!!

Here's an online Modular arithmetic calculator. Just enter 2 + 2 modulus 2. The result is 0, not 4.

 

[Cheerful Charlie]

And the Earth is flat and is the center of the Universe.

 

[bilby]

It's very popular these days to see mathematics as one truth we can know is objectively and absolutely right. I must disagree. A common example of this supposed absolute and objective truth is the equation 2 + 2 = 4. We are told that for all times and places, 2 + 2 = 4, no matter what! If human beings went extinct, then 2 + 2 = 4 still holds as true. If the dinosaurs had the brains, then they would have known 2 + 2 = 4. If there's an advanced civilization of extraterrestrials in the Andromeda galaxy, then they know 2 + 2 = 4.

It's not true that 2 + 2 is absolutely 4. Depending on the rules mathematicians are using, 2 + 2 = 0 might be the case. In modular arithmetic, 2 + 2 might not even be defined at all much less true. For example, in binary there is no 2.

So the truth of 2 + 2 = 4 depends on what arbitrary set of rules you are using. No absolute or objective truth can be so arbitrary. Hence in general, mathematics is neither absolutely nor objectively "right."

You're not even wrong here.

And you clearly have no understanding of how modular mathematics work. Regardless of the modulo of your system, and regardless of the terms you use for your numbers... the relationships ALWAYS hold.

FALSE!!!!!

Here's an online Modular arithmetic calculator. Just enter 2 + 2 modulus 2. The result is 0, not 4.

I find your faith in the Internet... disturbing.

 

[Unknown Soldier]

And the Earth is flat and is the center of the Universe.

I absolutely LOVE to show you guys up!

 

[Unknown Soldier]

Like I already explained 2 + 2 isn't always 4. If we base on calculations on the integers modulo 3 (Z
3), then 2 + 2 = 1.

No, it doesn't.

If you're using modulo 3, then 2+2 = 11. And in modulo 4, 2+2 = 10.

Your error here is akin to you saying that Z10 9+9 = 8.

Did you try the online Modulo calculator I linked to that demonstrates that I'm right and you're wrong?

 

[steve_bank]

The problem for you is I have used modulo arithmetic, as well as most of general applied math. Most of us electrical engineers are applied mathematicians.

Fun factoid - I end up using modular math when I'm doing crochet


ETA: I love crochet, it's math made tactile.

Ah in time saves nine.

 

[steve_bank]

The problem for you is I have used modulo arithmetic, as well as most of general applied math. Most of us electrical engineers are applied mathematicians.

Fun factoid - I end up using modular math when I'm doing crochet


ETA: I love crochet, it's math made tactile.

Ah in time saves nine.

Oopa.

A stich in time saves 9.

 

[steve_bank]

Modular arithmetic - Wikipedia

en.wikipedia.org

2 + 2 = 4 means a linear addition of objects.

Modulo arithmetic does not represent linear addition.

4 mod 3 + 4 mod 2 = 1

 

[Alcoholic Actuary]

Like I already explained 2 + 2 isn't always 4. If we base on calculations on the integers modulo 3 (Z
3), then 2 + 2 = 1.

No, it doesn't.

If you're using modulo 3, then 2+2 = 11. And in modulo 4, 2+2 = 10.

Your error here is akin to you saying that Z10 9+9 = 8.

mod vs. base

aa

 

[Unknown Soldier]

2 + 2 = 4 means a linear addition of objects.

Actually, 2 + 2 = 4 modulo 5 too. Try this modular arithmetic calculator. Just enter 2 + 2 and modulus 5.

Modulo arithmetic does not represent linear addition.

4 mod 3 + 4 mod 2 = 1

That's about right. What 2 + 2 equals depends on the rules being employed by the mathematician. It's what I've argued from the OP.

 

[steve_bank]

2 + 2 = 4 means a linear addition of objects.

Actually, 2 + 2 = 4 modulo 5 too. Try this modular arithmetic calculator. Just enter 2 + 2 and modulus 5.

Modulo arithmetic does not represent linear addition.

4 mod 3 + 4 mod 2 = 1

That's about right. What 2 + 2 equals depends on the rules being employed by the mathematician. It's what I've argued from the OP.

I had limited use for mod arithmetic when doing analysis. Differential equations, complex variables,.

Curl, the divergence theorem were very important and of practical utility. Control systems.

 

[Unknown Soldier]

2 + 2 = 4 means a linear addition of objects.

Actually, 2 + 2 = 4 modulo 5 too. Try this modular arithmetic calculator. Just enter 2 + 2 and modulus 5.

Modulo arithmetic does not represent linear addition.

4 mod 3 + 4 mod 2 = 1

That's about right. What 2 + 2 equals depends on the rules being employed by the mathematician. It's what I've argued from the OP.

I had limited use for mod arithmetic when doing analysis. Differential equations, complex variables,.

Curl, the divergence theorem were very important and of practical utility. Control systems.

That's a good resume, but please understand my main point that I highlighted in bold.

 

[steve_bank]

Bold text makes all the fiffernve.

Not an impressible resume, quite ordinary as engineers go.

 

[Jarhyn]

I believe U.S. thinks that the fact that there are limits to applied mathematics - like trying to add clouds as quanta - makes his "point" that 2+2≠4.

Well, I think it's rather explanatory that 2+2 is not always 4, especially when "standard" algebra does not describe the group one is working with.

One has to select appropriate operations and sets in order to get a useful answer.

It's not a limit to applied mathematics, it's a limit owing only to a misapplication of mathematics.

When you use the wrong algebra on a problem obviously you end up with wrong answers!

When dealing with "clouds" for example, one would have to move boolean algebra, where the operators are different. Or quantify cloud by some measure of volume and mass.

Indeed attempts to do math on quanta can easily require bizarre algebra to answer questions about them, wherein 2+2 does not evaluate to 4, trying to fit the triangle peg in the square hole, as it were, and wondering why it doesn't seem to work out for them.

It is not about the rules applied by the mathematician, but about the mathematician correctly applying the set of rules that corresponds to the problem. The set of rules to apply is not arbitrary and Soldier needs to realize that.

 

[Jimmy Higgins]

2 + 2 = 4 means a linear addition of objects.

Actually, 2 + 2 = 4 modulo 5 too. Try this modular arithmetic calculator. Just enter 2 + 2 and modulus 5.

Modulo arithmetic does not represent linear addition.

4 mod 3 + 4 mod 2 = 1

That's about right. What 2 + 2 equals depends on the rules being employed by the mathematician. It's what I've argued from the OP.

I had limited use for mod arithmetic when doing analysis. Differential equations, complex variables,.

Curl, the divergence theorem were very important and of practical utility. Control systems.

That's a good resume, but please understand my main point that I highlighted in bold.

You mean the objective and absolute rules?