Infinity

[PhatoseAlpha]

It would seem to me there is a basic misunderstanding here. True, infinity doesn't easily correspond to anything in the physical world and exists simply because it's useful.

However, the same is true of all other numbers. Infinity, One, Zero, Fourty-Two. There is no real world correspondence between numbers and reality, except for an arbitrary utilitarian one.

 

[EricMartello]

Originally posted by: Seer
No, wrong again. While its true that a current is being drawn across for an infinite amount of team, the current is asymptotic towards zero, and the integral of current from 0 to t=infinity has a finite amount (which is equal to the energy stored in the capacitor). This is of course ignoring heat dissipation, which would use up an infinite amount of energy if you were to let it run forever. Purely theoretically speaking, however, the energy is most definitely finite, and very much so. Not even high a lot of the time, and often very small.

Ok, so as time progress, it uses less and less energy just as it takes more and more time to charge.

Just as i believe you did not look at my link, you aren't really listening to anyone here. You opened this thread with this statement:

Are you really looking for peoples opinions, or do you just want everybody to nod their head and agree with you?

Anyways, you really should look up nihlism, you'd find it interesting. I fail to see how the existance of infinite scaling suddenly invalidates everything that exists. It simply means our definitions are relative to other things.

Also, the existance of such universal constants as G, c, the planck length, and quantized engergy totally turns your theories on their tales by absolutely specifying an absoluteness to the universe.

I did look at the link, actually, and no I'm not looking for people to agree with me. I actually enjoy talking about this.

In order to understand why infinite scaling can invalidate everything, is the same reason an infinite number line is essentially null. It doesn't matter how far you scale, to or from, nothing ever changes, nothing ever happens, nothing really exists. Just like you could arbitrarily choose 1039 on the infinite number line, that value means nothing because no matter how high or low you count, NOTHING changes.

I don't discount that, within the constraints of our universe (and therefore, infinite scaling would NOT exist), my theory is invalid, but once again, you need to broaden your take. I'm not just talking about "space" as it is in our universe alone, I'm talking about the total space, which includes our universe and spans BEYOND our universe. We can only hope that what works within our universe has some sort of application beyond its boundaries.

 

[EricMartello]

Originally posted by: PhatoseAlpha
It would seem to me there is a basic misunderstanding here. True, infinity doesn't easily correspond to anything in the physical world and exists simply because it's useful.

However, the same is true of all other numbers. Infinity, One, Zero, Fourty-Two. There is no real world correspondence between numbers and reality, except for an arbitrary utilitarian one.

I couldn't agree with you more!

We created math to give structure to understanding. We can create repeatable, verifiable results with math...but to truly understand something, I think that we should not create a cage for it, stuff it in and force it into confinement...for those who want to know the real deal, not just about this universe, but what is beyond it (if anything), then I don't think the answer lies in mathematical formulas and limited theories. Chances are high they wouldn't work "beyond" the Universe anyway.

 

[MrDudeMan]

"WHY" is a question for religion or philosophy. Science seeks to describe what has happened (,is happening, and will happen) -- NOT why.

This mentality is the Achilles heel of of science. It's very arrogant for any person to think that the everything fits into some constraints they create. I always laugh when I see scientists getting all upset that something doesn't fit their model...when they should be making the model fit.

What about you? Do you believe in science?

Actually, you shot yourself in the foot here. Science does not answer the question of why based on how humans invented and defined the word science. Religion attempts to answer why while science attempts to answer how.

I couldn't help but notice you skipped over this:

Also, the existence of such universal constants as G, c, the planck length, and quantized energy totally turns your theories on their tales by absolutely specifying an absoluteness to the universe.

You stated in another thread that you don't need to understand quantum physics to discuss your thoughts on the issue, but your lack of understanding of the subject area will inhibit you from fully realizing why your initial assertions about infinite scaling invalidating the existence of everything are nonsensical. Energy is released in a "digital" way, not "analog" and that is completely independent of your viewing scale. The above comment by Seer is a good point in that universal constants which are verifiable to extremely high degrees of precision, i.e. the cosmological constant which is accurate to ~120 decimal places, make your claims about infinity inconsequential as they are essentially unfounded and unsupported.

You seem to forget that the all important science you feel is separated from your own personal thoughts is the only basis you have for those thoughts in the first place. You would be unable to comprehend the true complexity of your argument without a basis in science, which limits your ability to actually understand your statements because it places your mental abilities within limitations. The end result is that you are trying to understand a system while inside the confines of the system and there is no known way to escape to another system to observe our current one.

 

[natto fire]

Warning!: HT does not stand for "Heavy Toking".

Just kidding. While you are definitely right about your view on the mindset some scientists can get in, heck Ptolemy and Aristotle were probably considered "scientists" and look how well the geocentric model turned out.
However, the idea of infinite scaling is pretty hard to swallow, in terms of being able to change size. Or are you saying we might already be this small to something else? Because there are obvious physiological problems to shrinking yourself to the size of an atom, or as big as a planet, etc.

 

[CSMR]

Originally posted by: EricMartelloThe concept of infinity

It is a symbol; I wouldn't go so far as to describe it as a concept.

in the context of reality, it is the ultimate negation of any value

Reality is not its context.

regardless of how far you go in either direction, your REAL position never changes.

?

when the line is INFINITE in both directions, there is no middle!

That's right.

but zero is the true definition of an infinite number line - it means nothing.

This is nonsense.

Complex over-my-head math aside, what every scientist seeks to do is to LIMIT their understanding of what they are studying, because only by setting these limits, can they begin to create a system that "works" within these limits. The problem is that the system breaks if it ever needs to be applied to a situation beyond the scientifically imposed limits.

Yes, this is true. Infinity is complex over-your-head maths. What you say about science is also true.

 

[EricMartello]

Originally posted by: MrDudeMan
Actually, you shot yourself in the foot here. Science does not answer the question of why based on how humans invented and defined the word science. Religion attempts to answer why while science attempts to answer how.

The motivation to know HOW something works stems for the curiosity of wondering WHY something works, happens or exists. If this is how you see things, it shows a very narrow mind. Do you really think you can discount something because of its inherent unpredictability, and focus on what works, simply because you find it more convenient? Yeah, you can, but it's not going to lead you anywhere worthwhile.

I couldn't help but notice you skipped over this:

Also, the existence of such universal constants as G, c, the planck length, and quantized energy totally turns your theories on their tales by absolutely specifying an absoluteness to the universe.

Did I?

I don't discount that, within the constraints of our universe (and therefore, infinite scaling would NOT exist), my theory is invalid, but once again, you need to broaden your take. I'm not just talking about "space" as it is in our universe alone, I'm talking about the total space, which includes our universe and spans BEYOND our universe. We can only hope that what works within our universe has some sort of application beyond its boundaries.

But everyone replying has failed to address and answer the direct questions I posed, even the first one using the video game example. Most of the responses have been attempting to correlate what I'm saying directly to accepted scientific theories...the issue here is that I'm trying to get people to think with a blank slate, in a "what if" way.

You stated in another thread that you don't need to understand quantum physics to discuss your thoughts on the issue, but your lack of understanding of the subject area will inhibit you from fully realizing why your initial assertions about infinite scaling invalidating the existence of everything are nonsensical. Energy is released in a "digital" way, not "analog" and that is completely independent of your viewing scale. The above comment by Seer is a good point in that universal constants which are verifiable to extremely high degrees of precision, i.e. the cosmological constant which is accurate to ~120 decimal places, make your claims about infinity inconsequential as they are essentially unfounded and unsupported.

Quantum theory is a theory, and that is a seperate topic. Anyway, there is an issue where, with all respondents, who are not thinking beyond what they've been taught, or beyond what they may be able to readily perceive. Nothing you have stated really discounts my theory, in fact, you failed entirely to understand what I am saying. It may be that I'm not doing a good job of explaining it, or it could just be over your head. I don't know. The highly precise cosmological constant, great for working with things IN this universe...but not so great when you're trying to understand everything.

You seem to forget that the all important science you feel is separated from your own personal thoughts is the only basis you have for those thoughts in the first place. You would be unable to comprehend the true complexity of your argument without a basis in science, which limits your ability to actually understand your statements because it places your mental abilities within limitations. The end result is that you are trying to understand a system while inside the confines of the system and there is no known way to escape to another system to observe our current one.

I'm not the one suggesting we keep science and philosophy separated, am I? If anything, my theory blends the two. The irony of your statement about understanding a system while being within a system is that by choosing to only accept science and reject the philosophical elements, you create a system that further limits the potential for understanding.

 

[EricMartello]

Originally posted by: CSMR
(infinity)
It is a symbol; I wouldn't go so far as to describe it as a concept.
Reality is not its context.

Once you start talking about reality, you are talking about something entirely subjective. You really can't say it's *not*. It would certainly be nice if "reality" was a globally definable value that does not change...but the fact is, reality is perhaps the most ambiguous human concept ever.

regardless of how far you go in either direction, your REAL position never changes.

?

If you are on an infinite number line, no matter how far you go in either direction, your real position never changes. The number system fails here, as you may be able to see.

but zero is the true definition of an infinite number line - it means nothing.

This is nonsense.

This of course assumes you consider the line as infinite. If you are using "infinite" merely to allow for unexpectedly high values that may push previously established bounds further, that is a different situation - and you're still working within defined limits. When you work without limits, most equations fall apart, and the infinite number line gives us an easy way to visualize how the number system can be irrelevant in some situation.

Yes, this is true. Infinity is complex over-your-head maths. What you say about science is also true.

Infinity is as much of a philosophical idea as it is a mathematical concept, though many people choose to ignore one or the other in favor of keeping things simple.

 

[EricMartello]

Originally posted by: Captain Howdy
Warning!: HT does not stand for "Heavy Toking".

Just kidding. While you are definitely right about your view on the mindset some scientists can get in, heck Ptolemy and Aristotle were probably considered "scientists" and look how well the geocentric model turned out.
However, the idea of infinite scaling is pretty hard to swallow, in terms of being able to change size. Or are you saying we might already be this small to something else? Because there are obvious physiological problems to shrinking yourself to the size of an atom, or as big as a planet, etc.

It's not so much about changing physical size, like "Honey I Shrunk the Kids" or something. It's more about considering the possibility that perspective along the scale can change what is readily defined as "reality".

Within our universe, there are rules that we can identify, and these rules create our bounds for understanding it. But with infinite scaling, you can shift your perspective to a vantage point that is outside of our universe.

Now, everything changes. For example, our universe may actually be the size of an atom, if our vantage point is that of being outside of it. Size may not even exist, beyond the confines of this universe, therefore it's not even something we can measure.

I can see why no pure scientist would want to "go here"...there a lot of room for the arbitrary. Albert Einstein already took a shot at understanding "everything" with his "theory of everything" and it didn't compute. I think that he ultimately realized what I am saying now - that you can't approach something this grandiose with preconceived notions or expectations. He said something to the effect of "God wouldn't create such an unorganized thing." So the great scientist conceded in the divine...but there are plenty of people today who think they have the answer, or are onto something. Good luck to them, I say.

 

[MrDudeMan]

Originally posted by: EricMartello

snip

You are way off course now, so I don't really know how to respond at this point. I never once said science should be completely separate from philosophy, but they most definitely are different in principle. No one here is really understanding what you are saying because it doesn't make sense. You appear to have no point.

 

[sao123]

Originally posted by: EricMartello

Originally posted by: ADDAvenger
Of course it's just an example, it's impossible to show infinity on a finite computer screen

http://i129.photobucket.com/albums/p237/addavenger/boxes.jpg

Yeah, I see what you mean now. Here's my take on this.

If you say this 2D grid is infinite in all directions, it would make sense to say the blue dots are 2 x infinity. But the thing about infinity is that it invalidates any number other than zero (which is also a concept, incidentally - we cannot imagine true nothingness any better than we can fathom infinity), so instead of 2 x infinity for the blue dots, you still just have an "infinite" number of dots. You can multiply infinity by any number other than zero, the result doesn't change - it's still infinity, just as anything multiplied by zero is nothing.

To make it easier to think of this problem, separate the dots from the boxes. You have an infinite number of dots, and an infinite number of boxes. Whether the dots are "in" the boxes or not is irrelevant in this context.

fortunately we already know there are different levels of infinity....

1 How many distinct decimal numbers are there between 0 & 1? infinite.
2 how many distinct integers are there? infinite.

3 How many distinct decimal numbers are there between all of the integers? infinite.

Is the third number larger than the first 2? Could you also imagine the answer to 3 being (infinity squared)?


You should be able to see that item 3 is infinately larger than items 1 or 2.

 

[PowerEngineer]

Originally posted by: EricMartello

Originally posted by: PowerEngineer
You start this thread (and this response) by observing that definable beginnings and ends make more sense to you than infinites, and then you seem to take exception to the suggestion that the universe had a beginning. Are you now arguing that time goes back infinitely far after all? And in closing you seem to say the space is infinite too. Are you arguing for or against the physical existence of infinities?

Of course they make more sense to me, I am human...my brain understands things much easier when there are defined limits! But the nice thing about the human mind is that it doesn't need to constrain itself to any one type of thinking or reasoning. It's not so much that I have trouble with the universe beginning, it's what was there BEFORE the universe ever came to be. SOMETHING must have been there, right? Otherwise, the universe is born of nothingness.

If we restrict our thoughts and analysis to within our universe, things work fine...I'm trying to figure out the whole picture, though. I would agree that our universe has bounds, but what is beyond those bounds? Not even a guess? Humor me, please.

What makes you so sure that "SOMETHING" must have been there? Isn't it conceivable that the universe was born from nothingness? Science, by its very definition, has to restrict its scope to the observable (i.e. sensible) universe. Going outside those bounds becomes baseless conjecture and is the province of religion/philosophy.

Originally posted by: EricMartello

Originally posted by: PowerEngineer
I will agree that measurement of length in a physical dimension requires some sort of ruler (and time some sort of clock). The presense or absense of other objects (e.g. just one star) does not mean that the star does not have physical dimensions (expressed perhaps in wavelengths of light generated by a particular electron transition for a hydrogen atom).

In order to properly understand my example, you need to disregard what you may already know about stars. If all that exists is empty space, with a single star, that is all you can possibly know. I never stated what "size" you are relative to the star, did I? For all you know, the relative size of the star to you could be microscopic, or it could be "heavenly body" sized. You just assumed that, based on what you know now, that the star is going to be pretty big, pretty hot and pretty massive. Preconceived notions cloud true understanding, in my opinion.

Don't call something a star if you don't want someone to think you mean a star. Please note that I made no assumption about the size of a star, did I? I assumed that the star gave off light, and therefore using the wavelength of light as a measuring device. I'm only guilty of accepting your description of the object in your example as a "star".

Originally posted by: EricMartello

Originally posted by: PowerEngineer
"WHY" is a question for religion or philosophy. Science seeks to describe what has happened (,is happening, and will happen) -- NOT why.

This mentality is the Achilles heel of of science. It's very arrogant for any person to think that the everything fits into some constraints they create. I always laugh when I see scientists getting all upset that something doesn't fit their model...when they should be making the model fit.

What about you? Do you believe in science?

Is this supposed to be in response to what I said? This "mentality" recognizes the limits of science (and of religion/philosophy). It has nothing to do with arrogantly thinking that everything must fit theory. To the contrary, good scientists become excited when facts do not fit into accepted theories! These are openings to discoveries and greater understanding.

Originally posted by: EricMartello

Originally posted by: PowerEngineer
Let me suggest that what you (and every other human observer) have come to think of as "reasonable" based on the inputs from our senses can not necessarily to extrapolated into scales of time and space that are many orders of magnitude larger or smaller than what our senses can grasp. Our senses bauk at the idea that nothing can go faster then the speed of light; anyone who has tried to wrap their brains around Einstein's general relativity understands how its concepts run counter to our "common sense". And quantum physics is at least as unsettling when we get down to looking at the subatomic world. We must therefore proceed with caution when deciding what "makes sense" and what doesn't.

Where is it written or stated that anything needs to make sense, tho? Why does everything have to work out neatly or predictably, other than it's what works for us. Some people may be content sticking with what works...my quest is for true understanding, and I keep my mind open to many possibilities.

Where did I write that it did need to make sense? My point was precisely the opposite.

Originally posted by: EricMartello

Originally posted by: PowerEngineer
Which leads me to:

I do not want to look up anything because I prefer to formulate my own conclusions with as little external influence as possible.

The Greeks also believed that they could discern the nature of the world through thought alone. To their way of thinking, it was obvious that heavier objects fell faster than lighter ones -- so obvious that this belief went untested until Galileo conducted physical experiments that proved otherwise. My point is that you always need to check your conclusions against the harshness of reality.

Of course, observation is the first step, testing it is the next...as far as our physical reality is concerned, but what I'm trying to understand is what's beyond our senses, our universe and possibly us. Remember that tou can't really say reality IS anything other than what your senses tell you it is...can you? Even if you bust out fancy tools and math, it's still just something you're understanding using some combination of your senses...it's more likely that our senses are there to LIMIT us, rather than to allow us to experience the true nature of existence.

Again, science is by definition limited to the observable universe. Your "quest for true understanding" through thoughts unconstrained by the limits of reality is purely religion/philosophy. But I suspect you know this and are just baiting us here.

 

[EricMartello]

Originally posted by: sao123
fortunately we already know there are different levels of infinity....

1 How many distinct decimal numbers are there between 0 & 1? infinite.
2 how many distinct integers are there? infinite.

3 How many distinct decimal numbers are there between all of the integers? infinite.

Is the third number larger than the first 2? Could you also imagine the answer to 3 being (infinity squared)?


You should be able to see that item 3 is infinately larger than items 1 or 2.

This is somewhat of a paradox, for lack of a better word. In my infinite number line example, I stick to whole numbers just to keep it simple. You're right, there is an infinite number of fractional numbers between each whole number, but they are just as irrelevant as the whole numbers on the infinite number line.

There is not any difference between position 3 or position 3.1308532801351593735, neither really exist because when you are talking about infinity, you are talking about two fundamentals intertwined - everything and nothing.

Originally posted by: PowerEngineer
What makes you so sure that "SOMETHING" must have been there? Isn't it conceivable that the universe was born from nothingness? Science, by its very definition, has to restrict its scope to the observable (i.e. sensible) universe. Going outside those bounds becomes baseless conjecture and is the province of religion/philosophy.

Again, science is by definition limited to the observable universe. Your "quest for true understanding" through thoughts unconstrained by the limits of reality is purely religion/philosophy. But I suspect you know this and are just baiting us here.

Baiting for what? It's just a discussion. Now that you said this: Isn't it conceivable that the universe was born from nothingness? Yes, it is...but how do you explain that? If you could consider this as a valid possibility, doesn't that beg the question what caused it to just manifest out of nothingness?

I'd like some answers, even if they are hypothetical, to these questions:

- It is probable that our Universe has physical bounds that limit its size. What might be BEYOND those bounds?

- Is it possible for there to be absolute nothingness, not even space? What would we call that state?

- Doesn't infinite scaling make more sense if you consider our universe a point on an infinite number line, rather than a container for that number line?

Ok, that last one, not really necessary to answer...but the other two, I'd like to hear some best guesses.

 

[StopSign]

1. I can't say if it's probable or not because for probability to exist, we must know the composition of the whole set of possibilities. I'm just going to say it's possible that boundaries exist. What might be beyond the boundaries if they do exist? I'm not even going to make guesses because I'm inside the universe and therefore cannot observe what's outside, if there is an outside.

2. Singularity? Well actually that's an infinitely small portion of space so it doesn't quite qualify as nothingness.

3. Not really sure what you're asking. The universe can't be a point.

 

[sao123]

Originally posted by: EricMartello

Originally posted by: sao123
fortunately we already know there are different levels of infinity....

1 How many distinct decimal numbers are there between 0 & 1? infinite.
2 how many distinct integers are there? infinite.

3 How many distinct decimal numbers are there between all of the integers? infinite.

Is the third number larger than the first 2? Could you also imagine the answer to 3 being (infinity squared)?


You should be able to see that item 3 is infinately larger than items 1 or 2.

This is somewhat of a paradox, for lack of a better word. In my infinite number line example, I stick to whole numbers just to keep it simple. You're right, there is an infinite number of fractional numbers between each whole number, but they are just as irrelevant as the whole numbers on the infinite number line.

There is not any difference between position 3 or position 3.1308532801351593735, neither really exist because when you are talking about infinity, you are talking about two fundamentals intertwined - everything and nothing.

It is neither paradoxal nor incorrect. Set theory would indicate that your thinking is incorrect. Research the difference between the "small" infinite set called Aleph 0, and the "large" infinite set Aleph 1.

http://mathworld.wolfram.com/CountablyInfinite.html

Any set which can be put in a one-to-one correspondence with the natural numbers (or integers) so that a prescription can be given for identifying its members one at a time is called a countably infinite (or denumerably infinite) set. Once one countable set is given, any other set which can be put into a one-to-one correspondence with it is also countable. Countably infinite sets have cardinal number aleph-0. Examples of countable sets include the integers, algebraic numbers, and rational numbers.

Georg Cantor showed that the number of real numbers is rigorously larger than a countably infinite set, and the postulate that this number, the so-called "continuum," is equal to aleph-1 is called the continuum hypothesis. Examples of nondenumerable sets include the real, complex, irrational, and transcendental numbers.

Both sets are infinite in size, yet one is clearly larger than the other.

 

[EricMartello]

Originally posted by: sao123
It is neither paradoxal nor incorrect. Set theory would indicate that your thinking is incorrect. Research the difference between the "small" infinite set called Aleph 0, and the "large" infinite set Aleph 1.

http://mathworld.wolfram.com/CountablyInfinite.html

Both sets are infinite in size, yet one is clearly larger than the other.

Citing another theory and claiming it invalidates another is pretty much bunk. A theory is essentially a guess, and while one may have a higher probability of being "correct", in this case, it really doesn't sway things one way or another.

Here's what I understand you to be saying:

Between 0 and 1 there is an infinite number of fractional numbers.
Between 0 and infinity are also an infinite number of numbers.
0 to infinity, including fractional numbers between the integers is also infinite.

Once you create a SET, you impose limits. You are grouping all numbers, including decimals, between 0 and 1...0 and 1 are the boundaries there...while the potential values WITHIN the set are infinite, there are clearly defined start and endpoint values, which limit the numerical value of the set to <= 1 and >= 0.

The second two sets imply an infinite ray, with 0 as the starting point...this works fine conceptually, and can be used in certain calculations, but has no basis in this discussion...because the starting point is essentially a limit, and true "infinity" has no starting point. There is a difference between infinite precision, and infinity as a numerical concept...just try calculating anything to infinite precision and you'll see what I mean when I say that math isn't really the answer to "everything".

Did you see the questions I asked in a previous post? Try to answer them. Apply any math or accepted theories you want...or even *gasp* some imagination. I'm really interested to see what other people come up with...so far, only StopSign stepped up to the plate.

 

[MrDudeMan]

Originally posted by: EricMartello

Originally posted by: sao123
It is neither paradoxal nor incorrect. Set theory would indicate that your thinking is incorrect. Research the difference between the "small" infinite set called Aleph 0, and the "large" infinite set Aleph 1.

http://mathworld.wolfram.com/CountablyInfinite.html

Both sets are infinite in size, yet one is clearly larger than the other.

Citing another theory and claiming it invalidates another is pretty much bunk. A theory is essentially a guess, and while one may have a higher probability of being "correct", in this case, it really doesn't sway things one way or another.

Here's what I understand you to be saying:

Between 0 and 1 there is an infinite number of fractional numbers.
Between 0 and infinity are also an infinite number of numbers.
0 to infinity, including fractional numbers between the integers is also infinite.

Once you create a SET, you impose limits. You are grouping all numbers, including decimals, between 0 and 1...0 and 1 are the boundaries there...while the potential values WITHIN the set are infinite, there are clearly defined start and endpoint values, which limit the numerical value of the set to <= 1 and >= 0.

The second two sets imply an infinite ray, with 0 as the starting point...this works fine conceptually, and can be used in certain calculations, but has no basis in this discussion...because the starting point is essentially a limit, and true "infinity" has no starting point. There is a difference between infinite precision, and infinity as a numerical concept...just try calculating anything to infinite precision and you'll see what I mean when I say that math isn't really the answer to "everything".

Did you see the questions I asked in a previous post? Try to answer them. Apply any math or accepted theories you want...or even *gasp* some imagination. I'm really interested to see what other people come up with...so far, only StopSign stepped up to the plate.

I've entertained the thought that this thread was legitimate and actually had a purpose, but at this point you are simply being ignorant. Basically what you've established is that you know more about "theory" and "understanding the universe" than the rest of humanity, including some of the best mathematicians and scientists to have ever lived. If anyone disagrees with your so-called profound ideas, you instantly put them down and claim they can't see what you can see. It really puts that thing about you calling other people arrogant and narrow minded into perspective. I'll end with this: you are obviously not open to discussing ideas outside of your realm of understanding, which seems to be the majority, but you will readily ask ambiguous questions to again be given the chance to assert your opinion.

 

[imported_Seer]

++ to above poster.

You're not listening to us at all. You're just spewing nonsense. I fail to see how the entire existence of everything we know or dont know about is invalidated by the idea that we can scale infinitely. For example:

Originally posted by: EricMartello
Citing another theory and claiming it invalidates another is pretty much bunk. A theory is essentially a guess, and while one may have a higher probability of being "correct", in this case, it really doesn't sway things one way or another.

And the concept, much less theory, of infinity is supposed to invalidate the all of existence by making "everything nothing"? Tell me exactly how THAT isn't bunk.

Your example, but changed.
If I move from A to B on your infinite number line, I am now in a different position. That is a fact, plain and simple. I am now A-B units from my starting point. What a surprise. A != B. Fact, indisputable. The existence of an infinite number of numbers to the left and right of either A or B does not change that simple undeniable fact that A != B. Relative to the end of the numberline (+ and - infinity), my position has not changed. But relative to any other single point, my position has.

So, lets say the universe is infinite, or that there are infinite universes, or whatever. If I move my fist from the side of my body to your face, will you still say my fist hasn't moved and is in fact in the same position as it always was?

This is what you have been saying (paraphrased):

Duuuude, everything is nothing. Because, infinity, yeaaaaah. How do you know you actually exist? Whoah.

Time for an actual quote:

just try calculating anything to infinite precision and you'll see what I mean when I say that math isn't really the answer to "everything".

WTF???? No one in their right mind would claim math is the answer to everything!!!! PLEASE PLEASE PLEASE show me where we have said this!!!

 

[Blouge]

> Set theory would indicate that your thinking is incorrect.

What is this "set theory"? I know only of multiple set theories, each supported by various axioms. Whether the axioms are true or not depends which on which mathematician you talk to. There are also the sets that are not well-founded (i.e. the sets contain themselves and need to be drawn as a graph). Does the "set theory" include those kinds of sets, or not?

FYI, the several commonly-used set theories lead to conflicting answers about infinity. Such as whether certain kinds of infinities are equal. Is the continuum hypothesis, for example, true or false? http://mathworld.wolfram.com/ContinuumHypothesis.html

> Both sets are infinite in size, yet one is clearly larger than the other.

This is quite possible, depending on how you define "size" or "larger". For example, the set of integers is clearly twice as big as the set of even numbers. Yet, the elements can be put into one-to-one correspondence (e.g. each integer and its double), making the infinite sets of comparible size or the same "cardinal" number.

I highly recommend reading the book "Where does Mathematics come from". "Infinity" boils down to the metaphor for the results of repeating some operation indefinitely - results that could never be achieved in practice, but can still be imagined. That's the metaphor called "infinity". Whether the mathematics that you build based on this metaphor is sense or is nonsense, is a matter of opinion.

>true "infinity" has no starting point

I disagree. Maybe your definition of "infinity" differs from the norm. Suppose I write a "0" on the ground (or mark that space in some other way). Then I walk a meter, and write a "1", then another meter and write a "2", and so on. Eventually I'll have travelled an infinity of meters. The "0" position was the starting point. This is infinity with a starting point.

If I look at the set of integers, there is no starting point. FYI 0 is not special, every member of that set is as valid as any other member. No finite set of integers I construct can ever match the set of integers in size, so clearly its an infinite set and it has no clear starting point.

> It is probable that our Universe has physical bounds that limit its size. What might be BEYOND those bounds?

There is a limit to how far north you can travel on Earth - the north pole. But you don't encounter some kind of brick wall when you reach there. Thinking in 3D space it's easy to understand how the Earth is a sphere, but if you knew only of 2D maps then this could be awkward and confusing. Similarly, I think if there is a physical limit to our universe (spatial or temporal), it will be easy to understand if you think in more than 4 dimensions. You can work with a model of the universe in a fewer number of dimensions than 4 to make the problem even easier. It could go on forever, but it could also loop back on itself or there could be a barrier, in the form of a repulsive gravitational field that can't be passed through. The last possibility is similar to an ant trying to crawl out of the bottom of a jar. The glass wall gets too steep.

> Is it possible for there to be absolute nothingness, not even space? What would we call that state?

Sure. "Nothing" suffices.

> Doesn't infinite scaling make more sense if you consider our universe a point on an infinite number line, rather than a container for that number line?

Both views make equal sense to me. You can also have the infinite universe be contained within a point on a second infinite number line, which exists within another point on a third infinite number line. I'm not sure if the concept is useful, but I find it quite sensible.

BTW, the book I mentioned above uses the compactness theorem from mathematics to define a new kind of infinity - a huge integer, called H. It has a precise value, yet it is MUCH larger than any real number, even larger than the infinity of real numbers. Because it's an integer, H + 1, H - 1, and 2H are also all integers. H - 9999999999 is also an integer, and is infinitely bigger than any real number. It's all legitimate mathematics, and even useful - the inverse is 1/H which is an infinitesimal that can be used to do calculus. Using the infinitesimal, you can get EXACT answers such as d/dx x^2 = 2x + 1/H. In order to agree with traditional calculus, you need to apply the real approximation operator and round your precise answer to a less precise, real number. You can also distinguish between 1.0 and 0.999999..... You can even COMPUTE the actual difference! The real numbers can't do this - that's because the real numbers are infinitely sparse on the number line. Real numbers are also limited and can only go up to the real infinity; with this new number system you can go way beyond the regular real infinity and thereby compute limits or sums more accurately.

This is a bit off-topic, but there is another great book "The Five Ages of the Universe" that talks about how, assuming the universe continues to expand, matter will become more and more sparse as the universe ages. Eventually everything will decay and the universe will seem pitch black and totally empty. However, if you view it on larger and larger time and space scales then the universe will always remain an interesting place. I think this is a good example of infinite scaling.

 

[blackllotus]

Originally posted by: EricMartello
- Is it possible for there to be absolute nothingness, not even space? What would we call that state?

You can't have a "state" of nothingness. Ex: you can't point to a particular place and say "there is absolutely nothing there" because if there was nothing there then there wouldn't be a place to point to and call "nothing" because it wouldn't exist. Even a perfect vacuum is not "nothing" because there must be space for a perfect vacuum to exist and space is clearly "something".

 

[sao123]

Originally posted by: EricMartello

Originally posted by: sao123
It is neither paradoxal nor incorrect. Set theory would indicate that your thinking is incorrect. Research the difference between the "small" infinite set called Aleph 0, and the "large" infinite set Aleph 1.

http://mathworld.wolfram.com/CountablyInfinite.html

Both sets are infinite in size, yet one is clearly larger than the other.

Citing another theory and claiming it invalidates another is pretty much bunk. A theory is essentially a guess, and while one may have a higher probability of being "correct", in this case, it really doesn't sway things one way or another.

Here's what I understand you to be saying:

Between 0 and 1 there is an infinite number of fractional numbers.
Between 0 and infinity are also an infinite number of numbers.
0 to infinity, including fractional numbers between the integers is also infinite.

Once you create a SET, you impose limits. You are grouping all numbers, including decimals, between 0 and 1...0 and 1 are the boundaries there...while the potential values WITHIN the set are infinite, there are clearly defined start and endpoint values, which limit the numerical value of the set to <= 1 and >= 0.

The second two sets imply an infinite ray, with 0 as the starting point...this works fine conceptually, and can be used in certain calculations, but has no basis in this discussion...because the starting point is essentially a limit, and true "infinity" has no starting point. There is a difference between infinite precision, and infinity as a numerical concept...just try calculating anything to infinite precision and you'll see what I mean when I say that math isn't really the answer to "everything".

Did you see the questions I asked in a previous post? Try to answer them. Apply any math or accepted theories you want...or even *gasp* some imagination. I'm really interested to see what other people come up with...so far, only StopSign stepped up to the plate.

I purposefully ignored them because they are nonsencial questions without merit or purpose to the question of infinity.

however...
Your theory is flawed and without meaning...
the measurement of time, space, or any property is incapable of being performed if the measuring entity does not have 2 things... a sensory perception capable of quantifying the item to be measured, and a standard to compare it to.

Your infinite number line concept does not conform to the above statement. Zero has been *arbitrarily chosen* as the standard, it could have been any other value, but whatever that value might have been, once a standard has been set, you can measure the distance from that point. I can give you a finite piece of string and a ruler marked 1, 2, 3, 4, 5 and you can measure the string. The string is 4. 4 what? inches? centimeters? seconds? hogaboos? Removing the *arbitrary standard* of the 0 reference point is what makes the numberline meaningless, not the fact that it is infinitely long.

Your time concept exibits the same behavior, there is a point called the present, by which all things can be arbitrarily measured as being past or future, and a quantified means to describe it with.

Infinite scaling - the universe as we know it and measure it have at its very substance & canvas, basic units which are "discrete units", it is not continuous as you would believe. Eventually you will find the smallest particle, even the smallest unit of space, which there is no emptyness between them. Call them packets, pixels, whatever, the canvas of 3 dimentional existence is in discrete units.

To the point of infinite largness, I will defer that answer to laterness because it will be included with one of my other answers.


the videogame analogy is nonsensical. *as a programmer* a video game is a non concious entity which can do nothing more than its defined propertys allow it to. Time will not pass for a videogame, unless it is given a semiphore equivolent, and a reference point to measure it against. This would be no differenct than asking a 2 dimentional drawing how deep are you? **of course the drawing will look at you nonsensically and say, what the hell is deep?**


ah but to your questions:


- It is probable that our Universe has physical bounds that limit its size. What might be BEYOND those bounds?

As in the above example (of the 2 dimentional drawing), in order to exceed the defined limits of 3 dimentional space, one must define a 4th spacial dimention. No matter what you call it, this is the only way to go outside of the defined 3 dimentional existance.
Assuming it is possible at all, Everything which is exclusively in our universe exists with at least 1 or more of the following:
1)A 4th or higher spacial dimention value of 0.
2)The lack of a perception for quantifying the 4th or higher spacial dimention.
3)The lack of a reference in the 4th or higher spacial dimention.


- Is it possible for there to be absolute nothingness, not even space? What would we call that state?
0 Dimentional non-existance, or
4th or higher spacial dimentional existance with at least 1 of the following:
1)zero values for the LWH spacial dimentions
2)The lack of a perception for quantifying the LWH spacial dimentions.
3)The lack of a reference in the LWH spacial dimentions.


- Doesn't infinite scaling make more sense if you consider our universe a point on an infinite number line, rather than a container for that number line?

The universe is the defined boundaries for the existance of LWH dimentional space. Nothing can exist 3 dimentionally without being inside of the LWH defined universe.
Both views of the universe make sense, but neither applies to infinite scaling.

I return to my roots...
If I have a point, which is defined as a singular discrete unit..
Then compare it to an infinite number line which has infinite points. I can see infinity.

Now compare it to an infinite 2 dimentional plane. I now have infinite number lines of infinite points. This is still clearly more points than the first.

now compare it to an infinite 3 dimentional space. I now have still infinitely more points than I had before.

While infinity is a concept and not a number, it still clearly has both a quantifiable perception, and a reference, therefore it is measureable and comparable. As long as you have those 2 properties, meaning has been established.

 

[Estrella]

Ok, I see a lot of misdirection in this thread hopefully, I can clear up some misconeptions.

Infinity is a EDIT: Concept. When represented as the set of all Real numbers on the number line it extends without ever stopping down the number line.

Infinity is not something you can perform operations on, such as: multiplication, division, subtraction, addition. This is why mathematicians loathe infinities becauase there are no operations unto them. This however does not mean we cannot use infinity in mathematics(i.e. limits, sums).

Secondly, the number zero is not equal to NULL. Null is nothing. Zero is the absence thereof.

A set in mathematics, the simplest mathematical construct which all mathematics comes forth from, with null in it is a set that contains nothing. If the set has zero as the only element in the set, then the set has something in it. In the case of a set, a zero is no different from the set containing one and only one banana.

If I missed anything or mistated something please tell me so I can edit it. Feel free to append anything.

 

[Blouge]

>a zero is no different from the set containing one and only one banana.

So you're saying zero is equal to one? Hmm, I guess I'm not advanced enough for that that branch of mathematics yet.

>A set in mathematics, the simplest mathematical construct which all mathematics comes forth from

Yet more nonsense. You can just as easily frame all of mathematics in terms of operations on an abacus. Mathematics does not come from, and has been around MUCH longer than sets. Sure, you can build things out of sets but there are arbitrary, awkward, and meaningless side effects like the ordered pair (0,1) = {0, {0,1} } = {0, {0, {0, {0}} } = the integer 2. Does the ordered pair (0,1) really equal 2? Whether it's a truth or not depends entirely on how you go about shoehorning things into being described by the sets.

Furthermore, as I explained above, there are many set theories, no "set theory". Please tell me, out of the many conflicting set theories, which one all of mathematics "comes forth from"?

BTW, a point is a much simpler construct than a set. Even a toddler can understand a point. Sets can be quite perplexing: open vs. closed, ininite, uncountable, self-referential, etc. When you are have a set fetish you wind up with awkward definitions of continuity that disagree with geometry (e.g. xsin(1/x) is not geometrically continuous) and elaborate defintions for limits and calculus that confuse people when infinitesimals suffice and are easily understood by everyone (everyone understands what a speck is) including Newton and Leibniz.

>Infinity is not something you can perform operations on, such as: multiplication, division, subtraction, addition

Sure you can, 1 / infinity = 0:
http://mathworld.wolfram.com/Infinity.html

 

[herm0016]

Originally posted by: Blouge
>a zero is no different from the set containing one and only one banana.

So you're saying zero is equal to one? Hmm, I guess I'm not advanced enough for that that branch of mathematics yet.

that is completly wrong. 0 is a number. 1 is a number also. they have the most of the same properties. in a matrix say [0,1,0} there are 3 ellements all clearly defined. if this is a vector they are all clealy defined positions in the x, y and z directions. if the vector was just [0,1] the vector has two ellements in it and has a clearly defined position on 2 of the 3 axis, with out further information this would represent a continous line in 3 space that always has a value of 0 in the x direction and 1 in the y direction with any value in the z direction. a vector with one ellement makes a plane by the same rules. null or "does not exist" (dne) like divideing something by zero is not a number, it does not equate to a single ellement. it is equal to nothing.

 

[Blouge]

>null ... does not equate to a single ellement. it is equal to nothing

Null can be equal to zero, or not be equal to anything, depending on your definition of null. From http://dictionary.reference.com/browse/null:

-being or amounting to nothing; nil; lacking; nonexistent.
3. Mathematics. (of a set)
a. empty.
b. of measure zero.
4. being or amounting to zero.

Apparently you've just chosen to single out a particular definition.

Since you are so interested in comparing null and nothing, please go ahead and do a full comparison involving null, cipher, zero, naught, nil, nada, and nothing and get back to us with the results. Thanks!