Imaginary Numbers

reply to post by ManFromEurope

we are simply not speaking about numbers at all but about something much more esoterical (with "dimensions", "structures" and complex numbers which are obviously not the usual kind of combined real-part + imaginary-part).

I can see why you are being confused by the terminology, but it's quite simple really. A complex number is a multi-dimensional number because it has two components (making it 2-dimensional) and can be expressed as a vector on a 2D grid. The structure of a complex number is made up of the real part and the imaginary part. Whether you want to call a number which contains multiple dimensions a true number is not quite so clear, I agree with you on that. But for the sake of simplicity lets just say complex numbers are a number just like any other numbers.

I have not had a lot of experience with imaginary numbers, but have come across them in the past. Just seeing how e and pi relate to them was a good WTF, wow moment.

For complex numbers, using a single value can provide better comprehension. For example 80 km/h has a distance part and a time part. There are exceptions where having the data complex helps in allowing other equations and algorithms run through the information. But for arguments sake the vector does boil down to a single value when meeting the imaginary.

As for what the imaginary sign means in relation to the normal sign, not sure. But since that is how the maths adds up, that is how things are.

Too many students get hung up on the 'imaginary' numbers thing.
It's just a convenient convention for working in more than one dimension and it works quite nicely when applied to x vs y in graphical format with x being the horizontal and y being the vertical (or vice versa of you prefer). Y is conventionally the vertical and y coordinates are prefixed with 'j' or 'i' to mark them as different to x axis coordinates (no prefix). Once you get the knack of working in this system converting polar-cartesian and knowing how to process the coordinates in complex equations it's a beautiful thing especially for electrical/electronic engineering but it's applicable to any work in all graphical formats. I'm thinking of my first excursions into working out the star connected equivalent of an assymetrical delta connected load and similar problems that I learnt to perform on a slide rule (there were no calculators back then and such problems consumed a fair amount of ink & paper). Working out the overall power factor of a complex variable load arrangement is another application

I use it often for all sorts of computations and never do I think 'heck I'm working with imaginary numbers'
Real power (watts) are represented on the X axis (real numbers) and 'imaginary' power (vars) are on the Y axis (imaginary numbers). This makes working a power factor for a circuit at a given frequency a trivial exercise which can be solved either mathematically or graphically.

Originally posted by QuantumCounterfeit64
reply to post by ChaoticOrder

 

You said negative numbers cannot exist. Yet. If I owe someone 5 dollars whether I pay them back or not I still have -5 dollars. Because I still owe them until it's paid back. If you have an atom and you take away 5 neutrons and it's supposed to have 10. It is negative 5 neutrons even with the positive 5.

Root point though we can't visually observe negative numbers they do exist.

They are referring to algebraic, not accounting math.

I agree with the OP's later statements. it would seem that we are getting a hint of those other dimensions as shadows in our own reality. That is very interesting. It is ust that sort of thing that leads to a series of breakthroughs. Kind of like after the first exoplanet was "discovered". It just kind of flowed like an avalanche afterwrds.

reply to post by Pilgrum

Yup.

Mathematics can be used to represent some aspects of the real world. That does not mean that mathematics represents reality. There are irrational numbers after all.

reply to post by Phage

There are irrational numbers after all.

Can you prove to me space or time isn't infinite?

reply to post by ChaoticOrder

That has absolutely nothing to do with irrational numbers.

Originally posted by Phage
reply to post by ChaoticOrder

 

That has absolutely nothing to do with irrational numbers.

I don't agree. An irrational number is only so unintuitive because it contains an infinite sequence of digits. It's much like the number system as a whole, which extends into infinity in both directions on the number line. The concept of infinity is the common theme here, of course you're never going to actually see every digit of an irrational number written down on paper, but that doesn't mean irrational numbers have no basis in reality. I personally think the infinite-flat model of the universe is correct and that time is infinite. Irrational numbers are simply one way of representing infinity, and for me the concept of infinity is a very real thing which goes to the heart of reality.

reply to post by ChaoticOrder

An irrational number is only so unintuitive because it contains an infinite sequence of digits.

It doesn't really have anything to do with being "unintuitive". It's simply a value that cannot be expressed as of ratio between two integers. Quite different concept than i.

But my comment was more of a joke. Is reality irrational? Is it insane? Is there no order to it all?

reply to post by Phage

It's simply a value that cannot be expressed as of ratio between two integers.

Yes, which implies it must have an infinite series of digits.

Is reality irrational? Is it insane? Is there no order to it all?

I don't think the term irrational and insane are interchangeable in the way you have used them. Something being "irrational" doesn't make it insane or completely unordered. A better question: is reality infinite?

reply to post by ChaoticOrder

i've never understood the position that the universe is infinite. what would you say to expansion and entropy?

the biggest problem i have with it is that an infinite quantity cannot exist within time, though i would like to hear your views and i'm open to reassessing my opinions.

reply to post by ChaoticOrder

Yes, which implies it must have an infinite series of digits.

Right. But numbers aren't reality (unless you are counting things) anyway.

I don't think the term irrational and insane are interchangeable in the way you have used them.

In punnery all words can be considered interchangeable.

reply to post by Bob Sholtz

i've never understood the position that the universe is infinite. what would you say to expansion and entropy?

The concept of expansion within an infinite universe is the first thing I had trouble understanding when I first learnt about the infinite-flat model (which is now the most widely accepted model of the universe). There is complicated math which explains how more space can be added to infinite space but honestly I don't claim to understand it properly myself. Using infinity in mathematics is a tricky business but mathematicians do it all the time and know it works.

reply to post by Phage

Right. But numbers aren't reality (unless you are counting things) anyway.

Or unless you're dealing with quantum mechanics, at which point the line between reality and numbers is blurred to the degree where a strong argument for an artificially generated reality can be made (and has been made by many intelligent people).

Originally posted by Phage
reply to post by ChaoticOrder

 

An irrational number is only so unintuitive because it contains an infinite sequence of digits.

It doesn't really have anything to do with being "unintuitive". It's simply a value that cannot be expressed as of ratio between two integers. Quite different concept than i.

But my comment was more of a joke. Is reality irrational? Is it insane? Is there no order to it all?

edit on 6/13/2013 by Phage because: (no reason given)

So couldn't an irrational number represent the distance between us by using some very tiny incremental scale of measurement? like how many subatomic particle lengths are between us? Or the amount of time you have been alive in the smallest measurement of time? I may be wrong, just trying to think of potential representations of irrational values in reality

reply to post by ChaoticOrder

perhaps i worded my statement wrong, it isn't that i am unable to comprehend the idea of adding space to an infinite quantity (infinity +1 is still infinity, as is infinity -1, demonstrating that the concept "infinity" means unending, yet not necessarily all inclusive), but rather the problem of an infinite quantity existing in time.

i can see how the math would work and can be understood on paper, as an irrational number can be understood, yet physically expressing an irrational number perfectly inside a space that has time cannot be done.

reply to post by ChaoticOrder

Or unless you're dealing with quantum mechanics

But quantum mechanics does not really deal with irrational numbers. A quantum is a single unit. An integer.


Quantum mechanics does however deal with uncertainty but that is not the same thing as irrationality. And it may or may not be reality, depending on how you look at it....literally.

reply to post by ImaFungi

So couldn't an irrational number represent the distance between us by using some very tiny incremental scale of measurement?

Well the smallest level of measurement you could probably get down to is the planck scale, so you wouldn't need an infinite amount of precision, so the result would never be an irrational number.

reply to post by Phage

But quantum mechanics do not really deal with irrational numbers. A quantum is a single unit. An integer.

That's a valid point, but I wasn't saying irrationals numbers are involved in quantum calculations, I was just pointing out how the line between numbers and reality is blurred when it comes to quantum mechanics. But my point about infinity still holds.

reply to post by ChaoticOrder

Not sure what that point was. But what does it have to do with imaginary numbers which do not represent reality in and of themselves?