Concept of infinity?

[theklng]

put it this way: there is an infinite distance between any two numbers in abstraction.

No. The distance is finite. The possible numbers are infinite.

i deliberately didn't say between two points in a graph or anything in that regard. i meant the distance between any two numbers is infinite.

And you are wrong.
The distance between two finite real numbers a and b with a > b is a - b, using the standard definition of distance (and you'd be hard pressed to find a definition of distance that made the distance between two finite numbers infinite).

Just because you can fit an infinite number of numbers into a finite distance, does not make the distance infinite.

i didn't define real numbers or any mathematical operators for a reason. you're saying i am wrong based on YOUR definitions, not my own. it was very deliberate that i didn't put any confinement on what i said, because it is the only way it can be true. what i mean by distance is not distance as in points in graph, but actual value - because how else would you have distance between numbers (and i mean numbers, not distance between points by which your statement would be true)?

i'm getting tired of these lengthy debates where people try to disprove me on their definitions. it's no use arguing if you start putting boundaries that i never made.

 

[WeedWorm]

I'm thinking that eventually the two lines would be the exact same length, no matter your claims to the contrary

Unless he has an electron-microscope...

 

[Phoenix Arrow]

Watch this. [http://uk.youtube.com/watch?v=HvgwR9ERCBo]
Eat cake.
[/thread]

A very small part of me hates you right now. It may be small, but it hates you alot. I think I can feel my brain trickling out of my ears.

On topic, this is one of those things that I would love to understand even a portion of it, but my tiny little brain can't comprehend it. Maybe if I whack myself over the head with something hard enough and unlock part of my brain that I don't knowingly use...

Hmm. You have to think quite laterally to get it I suppose. I'm lucky that this comes naturally to me. His description of the first 3 dimensions you have to hold in mind when he describes the rest. Think of it as a pattern that repeats itself.

 

[Bolverk]

Hmm. You have to think quite laterally to get it I suppose. I'm lucky that this comes naturally to me. His description of the first 3 dimensions you have to hold in mind when he describes the rest. Think of it as a pattern that repeats itself.

Thats my problem. My brain works on weird tangents, so understand things most other people cant, generally speaking, but I have a hear time understanding some things that involve lateral thinking.

 

[gamshobny]

Eventualy, you would get it right; you can't go any closer then atoms. But I would be bored out of my right mind long before that.

 

[Specter_]

put it this way: there is an infinite distance between any two numbers in abstraction.

No. The distance is finite. The possible numbers are infinite.

i deliberately didn't say between two points in a graph or anything in that regard. i meant the distance between any two numbers is infinite.

Well, the distance between 1 and 2 is 1 (finite), but the possible numbers is infinite. And as long as you don't use infinite as one of the numbers, the distance is always finite.

 

[The_root_of_all_evil]

Watch this. [http://uk.youtube.com/watch?v=HvgwR9ERCBo]
Eat cake.
[/thread]

Well, there's a truth and a failure to come out of this.

On the failure, the concept of dimensions above the 4th is arbitary, because there are many dimensions you can use instead of time; heat, colour, smell.

So for my 4th dimension, I could have a pattern of what range of temperature I am at. Which isn't dependent on time or any other dimensions or conditions.

The secondary failure to this is that to have a dimension above any other, you have to already have something there to fold it. That pre-supposes existence above it.

And the truth lies basically with those 10th Dimension Superstrings. Why not call one of them Jehovah? Then you've scientifically theorised God.

 

[carsenere]

based on the original post i would like to say that you couldnt keep adding zreoes for ever as there is a minimum unit of distance known as the planck length which is equal to
1.6*10^(-35) m and below this units of length are meaningless.

alternatively (and in a classical sence (not using quantumn mech)) you couldn't use a unit smaller than the diameter of an atom.

on the concept of infinity i reccoment brian green elegent universe there a chapter in there on it (or the science bits in science of discworld).

 

[Phoenix Arrow]

Watch this. [http://uk.youtube.com/watch?v=HvgwR9ERCBo]
Eat cake.
[/thread]

Well, there's a truth and a failure to come out of this.

On the failure, the concept of dimensions above the 4th is arbitary, because there are many dimensions you can use instead of time; heat, colour, smell.

So for my 4th dimension, I could have a pattern of what range of temperature I am at. Which isn't dependent on time or any other dimensions or conditions.

The secondary failure to this is that to have a dimension above any other, you have to already have something there to fold it. That pre-supposes existence above it.

And the truth lies basically with those 10th Dimension Superstrings. Why not call one of them Jehovah? Then you've scientifically theorised God.

True. I really only see it as a model if you know what I mean. It isn't as if the dimensions from 4 up arbitarily time and so on, but it's showing the pattern and similarites between how you view world around you in shapes and such and how the universe works in time. It's basically just saying a point in time is no different to a point on a piece of paper with the posibilities of different shapes you could have equal to the possible decisions and outcomes etc and just calling it the 4th dimension as an illustration.

His statement about the 10th dimension is very theoritical though. To be able to prove or disprove the string theory we would need to know a lot more about the behaviour of quarks and their makeup than we do now and possibly than we can do for a very long time. Also, for this theory to have a chance of being valid then you would need to prove various other theories such as the big bang theory. So, if God is a being in the 10th (or 11th) dimension, then you would need to disprove Christianity to prove God. But then God wouldn't be a physical thing but rather a collection of these "strings".

 

[The_root_of_all_evil]

So, if God is a being in the 10th (or 11th) dimension, then you would need to disprove Christianity to prove God. But then God wouldn't be a physical thing but rather a collection of these "strings".

"I refuse to prove I exist says God. Proof denies faith, and without faith I am nothing."

These "strings", as you call them, are the total possibilities of this and every possible universe and all the inhabitants in them though. If we call them Buddha, Allah and Jehovah; we've actually managed to appease both Science and Religion. How's that for a mexican standoff? Deny one and you've denied the other.

 

[Phoenix Arrow]

So, if God is a being in the 10th (or 11th) dimension, then you would need to disprove Christianity to prove God. But then God wouldn't be a physical thing but rather a collection of these "strings".

"I refuse to prove I exist says God. Proof denies faith, and without faith I am nothing."

These "strings", as you call them, are the total possibilities of this and every possible universe and all the inhabitants in them though. If we call them Buddha, Allah and Jehovah; we've actually managed to appease both Science and Religion. How's that for a mexican standoff? Deny one and you've denied the other.

Hmm. A very good point. What it does do is kill the typical view on religion and God to the extent that most of the deeply religious types would refuse to accept on the grounds of it being too different. Also, how come Jesus never bought String Theory up at one of his surmons? Would've saved us so much time and money in research.

 

[The_root_of_all_evil]

Also, how come Jesus never bought String Theory up at one of his surmons? Would've saved us so much time and money in research.

Well, there wasn't much call for strings, super or not, in Jerusalem. Most of them used hemp.

As for Religion, " Many will say to Me on that day, 'Lord, Lord, did we not prophesy in Your name, and in Your name cast out demons, and in Your name perform many miracles?' And then I will declare to them, 'I never knew you. Depart from Me, you who practice lawlessness.'"

 

[Bofus Teefus]

If I had an electron microscope and quite a bit of patience I could verify that I had drawn a line identical in length to yours. You cheating bastard.

The resolution of an electron microscope is 30 angstroms (A), or 0.000000003m, so there would still be some ambiguity. Someone else already pointed out that this is a math question and not so much a real, measurable one.

 

[exocel]

i think the old phrase "over the next hill" is a very rough analogy for infinity. its out of your field of vision, past what you see and know, but its still there. but if you go over the hill theres another one, with infinity behind that one. its all perspective.


-and everything rests on the back of a space turtle, and its turtles all the way down.

 

[exocel]

So, if God is a being in the 10th (or 11th) dimension, then you would need to disprove Christianity to prove God. But then God wouldn't be a physical thing but rather a collection of these "strings".

technically, its spaghetti.

 

[Eclectic Dreck]

I was really bored today, and I started thinking about the whole concept of time and stuff. So for example, lets take the concept of time. Some say that the concept of time has extended forever back, and will go on forever as well. So on a seperate note, let's say that I drew a line, and told you to draw a line exactly as long as the one I just drew. You could get as close as you want, but I could keep saying that you were 0.1 mm off, then 0.01 mm, and keep going on and adding zeros no matter how close you got. However, If you have infinite time to do this task, what would happen? It's sorta like infinite time to complete infinite scenarios I guess. I may have worded this in a real crap way, but if you understand what I'm trying to say, kinda makes you think... I think

Infinity, for much of a persons math learning is expressed as nothing more than a vague concept that is, quite naturally, incomprehensible. Everything anyone ever does, or sees, or thinks about etc all works on the concept of limits (yes, infinity can be a limit, not relevant), and thus when pondering the infinite you are quite simply wrestling with a concept that describes something you simply cannot understand outside of very simple terms.

That said, as an example of what you're asking, look at the function: f(x) = cos(1\x). Obviously, there is a point at which the equation is undefined, when x = 0 (you cannot divide by zero). However, though there is a defininte point at which that function ceases to exist, that point is infinitely small. More interesting, if you graph the function, as it approaches zero from the period (the space between the wave tops) grows progressively shorter, and the distance between waves becomes infinitely small. It's an example of a function that demonstrates two different qualities that deal with the concept of infinity.

 

[Beetlejooce]

Infinity is infinite(yeah obvious but you know it's the simple truth)

Read this somewhere - 'If infinite rednecks fired infinite shotguns at infinite roadsigns, then all the great literary works of the world would eventually be created in braille'

 

[theklng]

Well, the distance between 1 and 2 is 1 (finite), but the possible numbers is infinite. And as long as you don't use infinite as one of the numbers, the distance is always finite.

that's the thing: you're counting in a more defined system than i am. i'm not counting in base 10 real numbers. what you said about the possible numbers is actually what i mean by this.

the point i'm also trying to make here (apart from the claim that i've made) is that you people don't see things from an abstract enough perspective. you still say think a distance is 'where-from, where-to', when in fact a distance does not need end points, or interfere with points at all. i am speaking strictly numeric, yet you try and superimpose it on graphical functions such as a distance function. if anything, this proves that you do not have an understanding of the level of abstraction i am speaking of, and that by defining you're going down in levels of abstractions in favor of comparing objects to something you already know. this leads me to the assumption that you do not grasp the concept of infinity.

 

[Mr Fatherland]

Time was invented by humanity. Think about it, Humans made the rules of time. Minutes, hours, weeks, years, they don't actually exist. We invented them.

 

[Maze1125]

put it this way: there is an infinite distance between any two numbers in abstraction.

No. The distance is finite. The possible numbers are infinite.

i deliberately didn't say between two points in a graph or anything in that regard. i meant the distance between any two numbers is infinite.

And you are wrong.
The distance between two finite real numbers a and b with a > b is a - b, using the standard definition of distance (and you'd be hard pressed to find a definition of distance that made the distance between two finite numbers infinite).

Just because you can fit an infinite number of numbers into a finite distance, does not make the distance infinite.

i didn't define real numbers or any mathematical operators for a reason. you're saying i am wrong based on YOUR definitions, not my own. it was very deliberate that i didn't put any confinement on what i said, because it is the only way it can be true. what i mean by distance is not distance as in points in graph, but actual value - because how else would you have distance between numbers (and i mean numbers, not distance between points by which your statement would be true)?

i'm getting tired of these lengthy debates where people try to disprove me on their definitions. it's no use arguing if you start putting boundaries that i never made.

If you didn't put any boundaries on then you are automatically wrong, due to all the times that distances aren't infinity.
An unbounded statement is a general statement, and it is certainly not true that distances are infinity in general, or even in general on the real numbers.

And if you don't want to be caught out over definitions, maybe you should learn some before you start spouting random claims that rely on definitions.