Math is harder than social science

>u cand ave comblex nomberz

complex numbers are an analogy for rotation in the same way negative numbers are an analogy for debt

>just a naming convention, right?
no because i can have 5 apples but not 5 square root of -1 apples

You also can't have root(2) apples, what's your point? If your criterion for what's real is based on apples then even Wildberger would think you're being a bit excessive. But gave a decent explanation, one way of thinking about complex numbers is a way of describing 90 degree rotations.

>You also can't have root(2) apples
1 apple + almost half an apple
jesus, how retarded are you?
>one way of thinking about complex numbers
lol your thought experiments doesn't make it less made up

You can have a sqare foot of land tho.

Yes, because that's not an imagniary (cheat) number retard

All numbers are imaginary. Or do you think there's numbers floating in space or something?

>he thinks maths is the science of "real" numbers and not the deductive, logical reasoning behind any set of axioms/postulates
get a load of this p.leb

>1 apple + almost half an apple
That's still not sqrt(2) apples, only close to it.

Now another example, can you have -2 apples?

Have you ever thought about the possibility that they do exist but that our interpretation of math is retarded?
i.e There is a function that extends the plane horizontally, but it's not something as absurd as [math]\sqrt{-1}[/math] and the reason it is absurd is because the foundations it is defined over are absurd and flawed as well.

Maybe. But you can't have 5. In of itself, "5" doesn't exist.
>inb4 platonists come and start whining

This DESU. If we were alive in 500 BC retards like OP would say irrational numbers cannot exist. It's just an argument that's logical conclusion is that anything but natural numbers are bullshit.

if math is made up then philosophy is also made up, except philosophy is only useful in convincing people to do things based on their ethics (also made up) but math is used to convince people to do things based on the results you can derive from applying math to situations. wield both and you are a powerful adversary to your enemies.

>Now another example, can you have -2 apples?

Why couldn't you owe someone two apples? What are you smoking?

>You also can't have root(2) apples

liquify an apple
pour the liquified apple into a cylindrical beaker
measure the depth of the liquid in that beaker
now build a new cylindrical beaker with the same diameter, but sqrt(2) times longer than the depth of the liquid in the first beaker (this is a trivial construction)
liquify two apples
fill the newly constructed beaker with apple pulp
throw the excess apple pulp away
you now have sqrt(2) apples
add several mg of cyanide to the beaker and drink it

Consider then a noncomputable real number of apples.

no such number exists

You mean like chaitin's constant or the BB function, both which are rigorously defined and produce noncomputable real number.

You can't "produce" a "noncomputable" number. You can't even manipulate such a number in the way that all other numbers can be manipulated.

I wouldn't consider myself a hard platonist. Numbers are abstract concepts, like pieces in a game that can be moved around according to rules. Noncomputable reals can't be moved by any rules. They're not numbers. You could rigorously define how many angels can stand on the head of a pin and say it was "a noncomputable real". But that's isomorphic to saying "at least zero".

Negative numbers aren’t easy. Imagine you’re a European mathematician in the 1700s. You have 3 and 4, and know you can write 4 – 3 = 1. Simple.

But what about 3-4? What, exactly, does that mean? How can you take 4 cows from 3? How could you have less than nothing?

Negatives were considered absurd, something that “darkened the very whole doctrines of the equations” (Francis Maseres, 1759). Yet today, it’d be absurd to think negatives aren’t logical or useful. Try asking your teacher whether negatives corrupt the very foundations of math.

What happened? We invented a theoretical number that had useful properties. Negatives aren’t something we can touch or hold, but they describe certain relationships well (like debt). It was a useful fiction.

Rather than saying “I owe you 30” and reading words to see if I’m up or down, I can write “-30” and know it means I’m in the hole. If I earn money and pay my debts (-30 + 100 = 70), I can record the transaction easily. I have +70 afterwards, which means I’m in the clear.

The positive and negative signs automatically keep track of the direction — you don’t need a sentence to describe the impact of each transaction. Math became easier, more elegant. It didn’t matter if negatives were “tangible” — they had useful properties, and we used them until they became everyday items. Today you’d call someone obscene names if they didn’t “get” negatives.

But let’s not be smug about the struggle: negative numbers were a huge mental shift. Even Euler, the genius who discovered e and much more, didn’t understand negatives as we do today. They were considered “meaningless” results (he later made up for this in style).

It’s a testament to our mental potential that today’s children are expected to understand ideas that once confounded ancient mathematicians.

Enter Imaginary Numbers
Imaginary numbers have a similar story. We can solve equations like this all day long:

If you could go back in time and rename imaginary numbers, what would you call them?

\displaystyle{x^2 = 9}
The answers are 3 and -3. But suppose some wiseguy puts in a teensy, tiny minus sign:

\displaystyle{x^2 = -9}

Uh oh. This question makes most people cringe the first time they see it. You want the square root of a number less than zero? That’s absurd! (Historically, there were real questions to answer, but I like to imagine a wiseguy.)

It seems crazy, just like negatives, zero, and irrationals (non-repeating numbers) must have seemed crazy at first. There’s no “real” meaning to this question, right?

Wrong. So-called “imaginary numbers” are as normal as every other number (or just as fake): they’re a tool to describe the world. In the same spirit of assuming -1, .3, and 0 “exist”, let’s assume some number i exists where:

\displaystyle{i^2 = -1}

That is, you multiply i by itself to get -1. What happens now?

Well, first we get a headache. But playing the “Let’s pretend i exists” game actually makes math easier and more elegant. New relationships emerge that we can describe with ease.

You may not believe in i, just like those fuddy old mathematicians didn’t believe in -1. New, brain-twisting concepts are hard and they don’t make sense immediately, even for Euler. But as the negatives showed us, strange concepts can still be useful.

I dislike the term “imaginary number” — it was considered an insult, a slur, designed to hurt i‘s feelings. The number i is just as normal as other numbers, but the name “imaginary” stuck so we’ll use it.

betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/

"Noncomputable real number" is a very thin subject which requires care. Do you mean "a number which exists in arithmetic but cannot be represented in a concrete formal model"?

These are noncomputable functions for Turing machine. The numbers themselves are well-defined.

nonstandard numbers
this would become outdated as their usage became standard, but it's less offensive and mystical than "imaginary"

hyper-real numbers, or extra-real numbers

Co-reals?

that's much better, i'll admit

positive discrete cardinals, discrete cardinals, continuous cardinals, directionals

take 5 apples, rotate them 90 degrees

Then you're willing to let go of pretty much all real numbers, the set of computable real numbers has measure zero, in fact it's countable, while the set of noncomputable real number is uncountable, throwing away those numbers or saying they "don't exist" means essentially scraping the real line itself. Also yes you can produce a noncomputable real number, I just gave you two examples of numbers that are noncomputable, and yes you can "move" noncomputable real numbers, they are well defined real numbers that cannot be constructed physically but are still exist on the real line, in fact they are most of the real line, if you reject complex numbers on the basis that there is no "physical" analogue then you reject the existence of pretty much the entire real line.

I posted both of those, and yes, that's what I meant by noncomputable real number.

>lol. Natural scientists work with NATURAL things

I'm gonna start using this now.

>I posted both of those, and yes, that's what I meant by noncomputable real number.
Well, guess what. They do exist. You van construct them, just not in certain formal models of mathematics. You CAN construct and verify each and every busy beaver number. Yes, you can't define some reals in, say, countable models of arithmetic. But we are doing math "above" formal logic, not inside it. They all can physically be constructed.

why when this is clearly better? co-reals doesn't do anything more to describe their function than "imaginary"

N, Z, R, C, respectively

3+5
this makes sense
3-5
this makes sense, although less intuitively
[math]5*\sqrt{(-3)}[/math]
I can conceive of a way in which this makes sense
[math]\frac{\Omega_n}{t(BB-n)}[/math] where [math]\Omega_n[/math] is the product of n different halting probabilities and t(BB-n) is the average execution time of n trials of whatever the fuck program the Busy Beaver algorithm is supposed to be on n machines
This does not make sense in any context and you will never tell me what this ratio is in any capacity.

I don't have to scrap the set of reals by ignoring the noncomputable reals. There are more than enough reals left over. And considering that the only reals I'll ever use are the rational approximations to reals, that should be good enough for anyone. And if I ever need to say that there's an unbroken continuum down the number line I can use the hyperreals or the surreals, but that would be approaching peak autism.

The problem with 'imaginary' it's misleading and has a negative connotation. It's the whole reason OP made this thread. Co-real is much more representative of what they actually are.

And directionals are complex numbers, not imaginary numbers.

I think the biggest problem is saying that i equals to [math]\sqrt {-1}[/math], when root is a set-valued function.

>Co-real is much more representative of what they actually are.
great justification there, i'm totally convinced. i don't really have the inclination to join your circle-jerk though.

directional is perfect for complex, but "co" real indicates that they're separate from the traditional reals. they aren't, because if they are, then you'd be suggesting that the x axis is somehow inherently separate from the y-axis when they are independent.

>cosine is on the real axis
>sine is on the co-real axis
I dislike this idea

You mean sinus and cosinus, of course.

>That's still not sqrt(2) apples
yes it is
yes it does
when you peel away at the second apple it will eventually reach exactly sqrt(2) -1
Q:E:D FAGGOT!!!!

you're slime like co-mucus

Do negative objects exist?

No, and yet you use negative numbers every day.

>but "co" real indicates that they're separate from the traditional reals. they aren't,

They're the orthogonal complement of R in C. Co-real is perfect for that.

All the good social science is coming from fields like network science, systems science, and ecology. Social science as an independent field was eaten by ecology anyhow.

If the algorithms defining these numbers have no finite extinction time then how can we physically construct them? Even if busy beaver doesn't yield the proper example how can ALL noncomputable numbers be physically constructed by some computer? I see no problem constructing these things in some mental or abstract model but in real life by some computer? The reason I keep focusing on computers is that op's insistence there exists no physical analogue of complex numbers, well if there exists no physical analogue or construction of these numbers by some computer than you'd have to reject them in a similar fashion. So I was referring to the impossibility of constructing noncomputable numbers via computers, or maybe I should say turing machines.
The set of computable reals has measure zero, in fact it's countable, so yeah, you are scrapping most of the real line. Also the real line is contained within the surreals or hyperreals and you have noncomputable reals there again, hell you'll still have that the set of computable reals in those number systems has measure zero. Also the concept of rational approximation requires the use of closure of the rationals which generates the irrationals, however the complex numbers are simply the algebraic closure of the reals, the step from rationals to irrationals is the same from the reals to the complex, why is one fine but the other not?

I just realized that there may be some confusion in what I meant by noncomputable numbers, I simply meant those that cannot be computed with arbitrary accuracy in a finite time by an algorithm.

This.

I stopped caring about math when I was introduced to the concept of imaginary numbers. What a crock of shit. If your equation can only be solved by inventing numbers that can't exist, like some kind of math deity , then you are fucking wrong and the math is flawed. Same for algebra solutions that basically say "the correct answer is whatever the correct answer is". Thats what the math said transcribed to words but god forbid if i wrote in down in english instead of the ancient math runes the teacher word mark me wrong.

Math is logical and numbers never lie my ass. Math is just as flawed as any other human construct.

rotational numbers

>If the algorithms defining these numbers have no finite extinction time then how can we physically construct them?
So you think 1/3 cannot be constructed?

1/3 is a computable number, in fact all rationals are, what's your point?

Chicken.
youtube.com/watch?v=oENQ2jlHpfo

if you can't compute a number to arbitrary accuracy then it's not a number. [math]\Omega[/math] is somewhere between 0 and 1, exclusive, but that doesn't really mean anything, like how [math]\frac{0}{0}[/math] doesn't mean anything. Furthermore, I don't understand how you can imply that I'm scrapping "most" of the real line if the entire set of reals has measure zero. The set of computable reals are the only attainable subset of the reals; the rest are functionally irrelevant. You're assigning some sort of importance to numbers which all have a trivially indeterminate form, as evidenced by the fact that you cannot calculate any of them to even 0% accuracy.

>shitty bait thread
>tons of replies

God jesus fucking christ oh my god holy FUCK why do you people fall for such simple bait. This fucking thread is bait

>the entire set of reals has measure zero
??

numbers are symbols to represent a quantity

imaginary numbers are symbols that represent a hypothetical nonexistent subject

>matters of philosophy and mathematics are bait to the uninitiated.

It models some physical phenomena well, that's enough justification for the use of complex numbers, if you're one of those fags that believe that math for maths sake isn't worth it
4/10 bait

Say I owe you one square meter of land. Supposing that I owe you a square plot of land, the land that I owe is i meters to a side.

Numbers are whatever the fuck we define them to be.

Social science is way harder than math. That's why we don't know shit about it.

>numbers are symbols to represent a quantity

Numbers can represent anything.

>imaginary numbers are symbols that represent a hypothetical nonexistent subject

They represent a phase shift in voltage or current. Those two are very real things.

Exactly. Anyone who has taken a DSP or higher level circuits class knows that complex numbers are amplitude + phase angle, I don't see how this is such a difficult concept to grasp.

>Math is logical and numbers never lie my ass. Math is just as flawed as any other human construct
ever heard of Godel, nigger?