Am I infinitely stupid?

[n0mad23]

I suggested earlier to look in the direction of the infinitely small hoping you might spot the solution to the paradoxical nature of infinity.

Like its strange cousin eternity, it's not a 3d construction. Space isn't a mathematical artifice, or even an artifact.

It is Naught. Capital "N" nothing. But luckily for us there's a lot of that 3d stuff occupying it, moving through and rippling time, so it's only disturbing when used for contemplative purposes.

At least, that's how I deal with this one. I realize it's a pretty heretical position to occupy, but this abstraction has kept me from getting to sleep in the past. No wonder you're having a tough time pinning the question down.

 

[V8Li]

Am I infinitely stupid?

If you're just a bit smart that would mean you're ... wait for it ... infinitely smart SO you can't be infinitely stupid :speakcool: .

 

[agentgonzo]

Infinite just means: No borders. Nothing else.

Not true. Infinite things can have bounds. Think of the natural numbers. They are bounded at one but they are still infinite in number. Finite things are bounded on all sides.

If they were infinite, taking up all space in the universe, you couldn't be there to try and count the pages as there would be no room in space.

Again, not true. You can have an infinite number of infinitely sized objects coexisting and not overlapping in an infinite space. Think of a cylinder 1m in diameter but infinitely tall. It is infinite in size (and again has a bound, but still infinite) but you can stack an infinite number of these next to eachother in an infinite universe.

 

[Urwumpe]

Not true. Infinite things can have bounds. Think of the natural numbers. They are bounded at one but they are still infinite in number. Finite things are bounded on all sides.

Well, then rename it: Not enough borders.

 

[jedidia]

I hope no one gets mad if I throw a theological example in. The reason for this is because theology has a concept of "infinite" (or rather called "eternal") that has quite some similarities with the mathemathical one, but is a bit more easy to grasp to the mind, since practical examples lie closer.

I'll take the example of "eternal life" and "eternal god". While both are infinite, only the second is omnipresent. The "eternal life" will start at some point after the end of the world. hence this life is not part of it. It is not present nor evident nor anything at the moment, it is yet to start. Once it started, it will be infinite. So this is an infinity that does not take up all time. It has a defined starting point, but no end. It is infinite, but is not present in every moment in time.

God on the other hand is infinite too, however the duration of his existence is infinitly longer than the infinite duration of the eternal life, because while said has not even begun yet, God allready existed for an infinite amount of time.

Let's be heretic and say God would some day end - die, whatever - He still would be "eternal", because he has been around for an infinite amount of time before his death. However, he would not be omnipresent, because there also is a moment he would no longer exist.

I think this is the best I can do to explain the difference between "infinite" and Omnipresent". Martin said about the same in more abstract mathemathical terms, maybe I was able pull the concept to a level where it can be grasped more easily. Or maybe not.

 

[agentgonzo]

God on the other hand is infinite too, however the duration of his existence is infinitly longer than the infinite duration of the eternal life, because while said has not even begun yet, God allready existed for an infinite amount of time.

Jedidia, a very good example and very easy to read. I salute you.

However, I will pull you up on this one point. Apologies if this is against the scripture (I'm an atheist, so don't really know what's written and taught), but I'm commenting from a mathematical point of view here. At any given point in time, God will have existed for an infinite amount of time more than a mortal with eternal life. However, the duration of their existence is the same - that is, an infinite amount of time, even though it would appear that God's duration should be longer.
See my post on this topic for more explanation.

 

[Andy44]

Head....hurting....drink.

 

[jedidia]

However, I will pull you up on this one point. Apologies if this is against the scripture (I'm an atheist, so don't really know what's written and taught),

Well, we ARE disputing maths here, after all. The scriptures don't generally tell much about it

However, the duration of their existence is the same - that is, an infinite amount of time, even though it would appear that God's duration should be longer.

In other words, infinity equals infinity - 1?

doesn't sound very logical to me, but I'm far from being at home with mathemathical dogmatics, so I take your word for it... :hmm:

 

[agentgonzo]

In other words, infinity equals infinity - 1?

Correct. Isn't maths fun!

 

[Eagle]

If anyone else wants their head exploded we can get into infinities that are more infinite than other infinities. Or one infinity divided by another can result in a finite number. Or Ka'spaaat!!

 

[cjp]

Well, the question about existence has been asked. Does infinity "exist"?

You might as well ask whether the number 42 exists. Can you see 42 anywhere? Sure, you can see the number in this forum post, but that's just pixels on your screen. I can also tell you about a friend of me with the name Arthur, but that doesn't mean that person actually exists.

You might be able to go to a parking lot and count the number of cars. At a certain moment of time, you might count exactly 42 cars. Does this mean that 42 exists? I guess you can say that those cars exist, but I think that 42 is more like an abstract concept in your mind, to help you in counting things. You can say that it does not exist as a physical object, but it exists in mathematics. You can define it, e.g. as the integer following 41, and examine all its properties. By definition, you know it is an integer number, but you can also find out that it is 6 times 7.

Now, I think it's just the same thing with infinity. Just like the number 42, it is an abstract concept, and it too might help you in thinking about the physical reality. Maybe the universe is infinitely large. In reality this simply means that no matter how far you travel, you'll never hit a border, nor return to your point of departure (like when traveling around the earth).

In mathematics, you have to realize that infinity is not a number, just like 42 is not a physical object. In mathematics, you are allowed to use infinity in place of a number, but only in very special circumstances. Technically, infinity is just a "limit" situation. For instance, it might help to know that when x goes to infinity (becomes bigger and bigger), 1 + 1/x approaches 1 (the difference with 1 becomes arbitrarily small). But you can't say anything about things like infinity / infinity, or infinity - infinity.

 

[Urwumpe]

it is also the same with complex numbers... a very abstract thing, but very useful... complex numbers don't exist in nature, but you can use complex numbers well for modeling natural processes.

 

[jedidia]

You might as well ask whether the number 42 exists. Can you see 42 anywhere? Sure, you can see the number in this forum post, but that's just pixels on your screen.

Pythagoras would disagree! :lol:

 

[Eagle]

Pythagoras would disagree! :lol:

Perhaps not. 42 is just a quantifier, meaningless without a context. The question is 42 what?

42 cars? 42 inches?

But of course we run into a problem with the infinites.
"Can you have infinite cars?"
"No, you can't."
"Aww."

I guess similar things can be said about zero.
"Can I have zero hamburgers?"
"Technically you already do, assuming you don't have any hamburgers. But I'm not sure you can actually have nothing.":dry:
"Please...":sorry:
"Shut up."

 

[Urwumpe]

Is appetite for a hamburger equal to 1E-30 hamburgers?



Zero is a special number and the most important number in mathematics - without a absolute or relative zero, all other numbers would be without values.

 

[Kaito]

Well, the question about existence has been asked. Does infinity "exist"?

You might as well ask whether the number 42 exists. Can you see 42 anywhere? Sure, you can see the number in this forum post, but that's just pixels on your screen. I can also tell you about a friend of me with the name Arthur, but that doesn't mean that person actually exists.

You might be able to go to a parking lot and count the number of cars. At a certain moment of time, you might count exactly 42 cars. Does this mean that 42 exists? I guess you can say that those cars exist, but I think that 42 is more like an abstract concept in your mind, to help you in counting things. You can say that it does not exist as a physical object, but it exists in mathematics. You can define it, e.g. as the integer following 41, and examine all its properties. By definition, you know it is an integer number, but you can also find out that it is 6 times 7.

Now, I think it's just the same thing with infinity. Just like the number 42, it is an abstract concept, and it too might help you in thinking about the physical reality. Maybe the universe is infinitely large. In reality this simply means that no matter how far you travel, you'll never hit a border, nor return to your point of departure (like when traveling around the earth).

In mathematics, you have to realize that infinity is not a number, just like 42 is not a physical object. In mathematics, you are allowed to use infinity in place of a number, but only in very special circumstances. Technically, infinity is just a "limit" situation. For instance, it might help to know that when x goes to infinity (becomes bigger and bigger), 1 + 1/x approaches 1 (the difference with 1 becomes arbitrarily small). But you can't say anything about things like infinity / infinity, or infinity - infinity.

I feel like this has been done to me: :chair:
I tried, i really did. No my head hurts because i tried TO hard. *head throbs* ow....ow....ow

 

[Talon1]

Well, my bottom line description for infinity is that it means no end, no borders etc.
Oh, and I also feel the same way Kaito does:chair: *Head throbbing..ow..ow..ow..

 

[bujin]

Just to throw something "infinite" into the mix:

A triangle has three vertices. A square has four vertices. A pentagon has five, hexagon six, etc...

How many vertices are there in a circle? A perfect circle is made up of an infinite number of vertices, is it not?

 

[Linguofreak]

That also means there would be an infinite nuimber of people ready to shhh! Shoosh? (How do you spell that?)

The verb meaning "to say 'shhhh'" or "to command someone to be quiet," is "to shush."

Oddly enough the "to" form of a verb (to shush, to be, not to be, etc.), is called an infinitive.

 

[Eagle]

How many vertices are there in a circle? A perfect circle is made up of an infinite number of vertices, is it not?

Zero verticies. You can approximate as a regular polygon as the number of sides approaches infinity, but that's not a circle.

Closed arc of constant radius from a single point.