Welcome, Guest. Please login or register.
Did you miss your activation email?
December 19, 2014, 11:31:08 pm
HomePredMockPollEVCalcAFEWIKIHelpLogin Register
News: Please delete your old personal messages.

+  Atlas Forum
|-+  General Discussion
| |-+  Religion & Philosophy (Moderator: Gustaf)
| | |-+  Do you believe in √(-1)?
« previous next »
Pages: [1] 2 Print
Poll
Question: Do you believe in √(-1)?
Yes   -19 (70.4%)
No   -5 (18.5%)
I'm agnostic   -3 (11.1%)
Show Pie Chart
Total Voters: 27

Author Topic: Do you believe in √(-1)?  (Read 3356 times)
A18
YaBB God
*****
Posts: 23836
Political Matrix
E: 9.23, S: -6.35

View Profile
« on: May 22, 2009, 09:34:06 pm »
Ignore

Discuss.
Logged
incredibly specific types of post-punk music
BRTD
YaBB God
*****
Posts: 73022
United Kingdom


View Profile
« Reply #1 on: May 22, 2009, 09:35:46 pm »
Ignore

No.
Logged




01/05/2004-01/10/2014
IDS Judicial Overlord John Dibble
John Dibble
YaBB God
*****
Posts: 18786
Japan


View Profile
« Reply #2 on: May 22, 2009, 09:46:21 pm »
Ignore

The letter i is merely a concept, much like the invisible pink unicorn, the flying spaghetti monster, zombie Jesus, or the Teenage Mutant Ninja Turtles. It also isn't nearly as cool as any of those things, so that makes me believe in it even less. Seriously, it's so damn boring.
Logged

memphis
YaBB God
*****
Posts: 15477


View Profile
« Reply #3 on: May 22, 2009, 10:58:19 pm »
Ignore

It's just a place holder much like zero is. No need to get all fussy about it.
Logged

I cannot do anything good under my own power. 
I don't want my women talking to people
dead0man
YaBB God
*****
Posts: 22786
United States


Political Matrix
E: 6.84, S: -4.52

View Profile
« Reply #4 on: May 23, 2009, 12:43:02 am »
Ignore

It was at this point in my math learning career that I started to get frustrated.  The f of X sh**t was the end.
Logged

Tik
ComradeCarter
YaBB God
*****
Posts: 5043
United States


View Profile
« Reply #5 on: May 23, 2009, 01:05:49 am »
Ignore

In the same way that I believe in the idea of ghosts - impossible, but good for scaring people.
Logged

I don't wanna think about it all, I'm tired.
The Mikado
Moderators
YaBB God
*****
Posts: 14584


View Profile
« Reply #6 on: May 23, 2009, 01:12:09 am »
Ignore

It's true in the same way a corporation being a "person" is true.  Strictly speaking, it's a nonsense mathematical term, but in a broader sense, it's a necessary fiction to make everything else work.
Logged

Snowstalker   mikado is content with only questions
23:03   Snowstalker   questions never helped anyone
23:03   Snowstalker   only answers
GMantis
Dessie Potter
YaBB God
*****
Posts: 5271
Bulgaria


View Profile
« Reply #7 on: May 23, 2009, 02:38:39 am »
Ignore

Imaginary numbers, despite their name, have actually real life application in modern physics, so yes.
Logged

realisticidealist
YaBB God
*****
Posts: 6854
Vatican City State


Political Matrix
E: -0.13, S: 4.52

View Profile
« Reply #8 on: May 23, 2009, 01:34:18 pm »
Ignore

i is the most awesome number ever. Give it a break.
Logged

"The greatest thing you'll ever learn is just to love and be loved in return."
muon2
Moderators
YaBB God
*****
Posts: 8943


View Profile
« Reply #9 on: May 23, 2009, 02:34:35 pm »
Ignore

When I was young, I found Isaac Asimov's rebuttal to the unreality of imaginary numbers one of the most compelling. The story has stayed with me throughout my academic career, but I am afraid I might not get it all verbatim. So, I found this rendition of it from his later autobiography, In Memory Yet Green (1979):

Quote
    On September 27, 1938, I registered for my fourth year at Columbia. I was taking integral calculus now and Sidney was taking more sociology while I was doing that. After calculus, I would go around to the sociology class, where the professor held court after the lecture was over. When that was done, Sidney and I would have lunch.

    It made for dull listening, generally, for I never have been impressed by the soft sciences. On October 10, I found the sociology professor (his name was Casey) had made a table on the board in the course of his lecture in which he divided people into rationalists and mystics. Under mystics he had listed mathematicians.

    I studied that for a while and then, even though I was not a class member, I interrupted the postlecture session by saying, “Sir, why do you list mathematicians as mystics?”

    He said, “Because they believe in the reality of the square root of minus one.”

    I said, “The square root of minus one is perfectly real.”

    He said, “Then hand me the square root of minus one piece of chalk.”

    I said, “The cardinal numbers are used for counting. The so-called imaginary numbers, like the square root of minus one, have other functions. If you had me a one-half piece of chalk, however, I’ll hand you a square root of minus one piece of chalk.”

    Whereupon Casey promptly broke a piece of chalk in half and handed it to me with a smile. “Now your turn,” he said.

    “Not yet,” I said. “That is one piece of chalk you’re handing me.”

    “It is half a regulation length of chalk.”

    “Are you sure?” I said. “Will you swear it is not 0.52 times a regulation length or 0.48 times that?”

    By now Casey realized it was time for hard logic if he was to win the argument, so he decided that since I was not a member of the class, I would have to leave the room at once. I left, laughing rather derisively, and after that I waited for Sidney in the hall.

Mathematics deals in abstract quantities that include thing like zero, negative numbers, variables, functions, groups, vector spaces, algebras, and a host of other concepts. One of them happens to be complex numbers which includes the square roots of -1, and for historical reasons they were dubbed imaginary numbers. They are no more imaginary than any of the other abstract objects in mathematics.
Logged


Partial solar eclipse of October 23, 2014 with a cloud and large sunspot.
A18
YaBB God
*****
Posts: 23836
Political Matrix
E: 9.23, S: -6.35

View Profile
« Reply #10 on: May 23, 2009, 03:26:44 pm »
Ignore

I'm shocked that you didn't mention infinitesimals.
Logged
Stranger in a strange land
strangeland
YaBB God
*****
Posts: 6373
United States


View Profile
« Reply #11 on: May 23, 2009, 05:13:42 pm »
Ignore

Imaginary numbers, despite their name, have actually real life application in modern physics, so yes.
Logged

Gustaf
Moderator
YaBB God
*****
Posts: 26997


Political Matrix
E: 0.39, S: -0.70

View Profile
« Reply #12 on: May 24, 2009, 08:45:36 am »

Yes. But I am religious. Wink

Seriously though I think some of these concepts are mystic by nature. The human mind (or at least my mind) cannot comprehend many of the concepts used in modern matehmatics and physics. Sure, I can follow the proofs and I can use it (I owned imaginary numbers back when we had exams on it) but I can't really wrap my mind around it and get it. It is about as mystic to me as God. Tongue
Logged

This place really has become a cesspool of degenerate whores...

Economic score: +0.9
Social score: -2.61

In MN for fantasy stuff, member of the most recently dissolved centrist party.
Citizen James
James42
YaBB God
*****
Posts: 2554


Political Matrix
E: -3.87, S: -2.78

View Profile
« Reply #13 on: May 27, 2009, 02:05:38 am »
Ignore

I believe in i.

I also believe in pi, although it is irrational.
Logged

We do what we must
because we can.
For the good of all of us.
Except the ones who are dead.
But there's no sense crying over every mistake.
You just keep on trying till you run out of cake.
Tetro Kornbluth
Gully Foyle
YaBB God
*****
Posts: 11632
Ireland, Republic of


View Profile
« Reply #14 on: June 02, 2009, 06:09:24 pm »
Ignore

i is just an abstraction of an abstraction. If you accept the existence of 'two' then you should probably accept the existence of i.
Logged



Quote
Keith R Laws ‏@Keith_Laws  Feb 4
As I have noted before 'paradigm shift' is an anagram of 'grasp dim faith'
Tonberry
Jr. Member
**
Posts: 59
United States


View Profile
« Reply #15 on: June 02, 2009, 09:34:25 pm »
Ignore

i do.
Logged
Gustaf
Moderator
YaBB God
*****
Posts: 26997


Political Matrix
E: 0.39, S: -0.70

View Profile
« Reply #16 on: June 03, 2009, 10:59:29 am »

No.  Imaginary numbers are, by definition, imaginary, i.e. products of the imagination.  Therefore, they are not real; if they were, they would be real numbers.  Since the square root of -1 is clearly not a real number but an imaginary number, then by its very definition it cannot exist.

All abstractions are products of the imagination.
Logged

This place really has become a cesspool of degenerate whores...

Economic score: +0.9
Social score: -2.61

In MN for fantasy stuff, member of the most recently dissolved centrist party.
muon2
Moderators
YaBB God
*****
Posts: 8943


View Profile
« Reply #17 on: June 03, 2009, 07:21:30 pm »
Ignore

No.  Imaginary numbers are, by definition, imaginary, i.e. products of the imagination.  Therefore, they are not real; if they were, they would be real numbers.  Since the square root of -1 is clearly not a real number but an imaginary number, then by its very definition it cannot exist.

The name has little to do with its meaning and more to do with its history. That would be like saying a strange quark has less reality than an electron because of its fanciful name.

But I would claim the imaginary numbers to be just as functional as any real number. If you believe that a line segment can be rotated in a plane then you have worked with imaginary numbers, just not in their algebraic form. For instance, consider the line segment in the 2-dimensional plane from (0,0) to (3,4). A 90 degree rotation around the origin takes the other end to (-4,3). But this is just multiplying the 2-dimensional point by the imaginary unit i. If I wrote it with algebra it would read (3+4i)i = (-4+3i), and I would have used imaginary numbers.
Logged


Partial solar eclipse of October 23, 2014 with a cloud and large sunspot.
Magic 8-Ball
mrk
YaBB God
*****
Posts: 3725
Czech Republic


View Profile
« Reply #18 on: June 03, 2009, 10:37:04 pm »
Ignore

I am faithful.
Logged
pbrower2a
YaBB God
*****
Posts: 10489
United States


View Profile
« Reply #19 on: June 07, 2009, 12:55:46 pm »
Ignore

i is an answer; one can debate the relevance of the answer.

We have a hierarchy of genuineness of numbers. First we have the natural numbers that one counts with. Add the number "zero" for completeness through the inclusion of the concept of "nothingness" or a void.

The ancient Egyptians and Greeks hardly accepted zero as a number, perhaps suggesting that "nothingness" had no significance. Neither did they have the mirror image of the whole numbers, the negative integers, which with the whole numbers and zero comprise the integers, the "complete" numbers. 

The Egyptians found fractions -- "broken numbers" useful, as did the Greeks. Add to such numbers as 3/8  and 2/5  such inverses as 8/3 and 5/2 and one has all the broken, if sensible "rational" numbers -- if one allows 1 as a divisor. Zero is of course prohibited as a divisor.

Trouble arose with numbers that could not be seen as fractions -- like the square roots of 2 or 23, or the cube roots of 4 or 25. They could only be approximated with fractions, but they were solutions. The Egyptians knew well of the 3-4-5 right triangle and perhaps 5-12-13, 7-24-25, 8-15-17, 9-40-41, and 11-60-61 ... but the great Euclid could prove that the diagonal of a right triangle with rational sides could never be expressed precisely as a fraction. Such numbers didn't seam quite 'reasonable', so they were called 'irrational'. The weird constant π created its own problems.

Some cultures discovered zero -- our use of zero derives from Indian practice. They had the concept of the void and nothingness and had a number to express it. The Arabs found it useful, and we learned it from the Arabs.

In the Renaissance, people started trying to solve equations that supposedly had no answers -- like x^4 =1. "1" and "-1" are solutions, but so are "i" and "-i"; after all, i^4 =1. Numbers involving i were thus "imaginary" even if three-dimensional mathematics is  a sane proposition. But they were algebraic, establishing them as solutions of polynomial equations.  One could do about everything but establish order among them.

Numbers like π and the frequently-used e (base of the natural logarithms, and heavily in use) could later be proved impossible to find polynomial equations with π or e (among other numbers) from which one can find a root. Such numbers are called transcendental -- as they "go beyond" computation as they are un-algebraic.
« Last Edit: June 18, 2009, 08:05:57 pm by pbrower2a »Logged



Your political compass

Economic Left/Right: -7.00
Social Libertarian/Authoritarian: -5.49
Mechaman
YaBB God
*****
Posts: 14162
Jamaica


View Profile
« Reply #20 on: June 07, 2009, 05:11:23 pm »
Ignore

√(-1) is dead.
Logged



17:20   bore   the point of atlasia is to achieve things which you can then use as pick up lines
realisticidealist
YaBB God
*****
Posts: 6854
Vatican City State


Political Matrix
E: -0.13, S: 4.52

View Profile
« Reply #21 on: June 07, 2009, 08:31:25 pm »
Ignore

√(-1) is dead.

You killed him, you monster. Angry
Logged

"The greatest thing you'll ever learn is just to love and be loved in return."
Mechaman
YaBB God
*****
Posts: 14162
Jamaica


View Profile
« Reply #22 on: June 07, 2009, 11:56:27 pm »
Ignore

√(-1) is dead.

You killed him, you monster. Angry

That wasn't a nice thing to say. A real gentleman of your persuasion would've said "you bastard."
« Last Edit: June 08, 2009, 12:19:47 am by Mechaman »Logged



17:20   bore   the point of atlasia is to achieve things which you can then use as pick up lines
Storebought
YaBB God
*****
Posts: 3084
View Profile
« Reply #23 on: June 08, 2009, 09:33:06 pm »
Ignore

No. I believe in quaternions.
Logged
muon2
Moderators
YaBB God
*****
Posts: 8943


View Profile
« Reply #24 on: June 09, 2009, 12:19:58 am »
Ignore

No. I believe in quaternions.

Hamilton's greatest achievement. Too bad we quit teaching and using them in favor of vector and matrix formalism. Matrices always work as a representation, but the beauty of simple elements like quaternions directly shows symmetry.
Logged


Partial solar eclipse of October 23, 2014 with a cloud and large sunspot.
Pages: [1] 2 Print 
« previous next »
Jump to:  


Login with username, password and session length

Logout

Powered by SMF 1.1.20 | SMF © 2013, Simple Machines