Extent of space (APOD 23 Mar 2006)

[Chris Peterson]

I'm fully aware of the definition of infinity, infinity is simply no limit.

That isn't any definition of infinity I've ever encountered.

What happens if any of these values are assigned infinity?

Values can't be "assigned infinity"; infinity itself isn't a value.

If the "Whole" cannot be measured, how can a "Part" be measured based on the same measuring criteria?

It doesn't seem to stop people from measuring the distance between "1" and "3" despite the fact that the range of integers is infinitely large. An infinite Universe can be understood perfectly on a theoretical basis even if parts of it are not measurable (and it seems likely that parts outside the observable Universe will remain eternally unmeasurable).

[Dr. Skeptic]

I'm fully aware of the definition of infinity, infinity is simply no limit.

That isn't any definition of infinity I've ever encountered.

What happens if any of these values are assigned infinity?

Values can't be "assigned infinity"; infinity itself isn't a value.

If the "Whole" cannot be measured, how can a "Part" be measured based on the same measuring criteria?

It doesn't seem to stop people from measuring the distance between "1" and "3" despite the fact that the range of integers is infinitely large. An infinite Universe can be understood perfectly on a theoretical basis even if parts of it are not measurable (and it seems likely that parts outside the observable Universe will remain eternally unmeasurable).

Let's hear your definition of infinity if you don't like mine.

infinity

In general, infinity is the quality or state of endlessness or having no limits in terms of time, space, or other quantity. In mathematics, infinity is the conceptual expression of such a "numberless" number. It is often symbolized by the lemniscate (also known as the lemniscate of Bernoulli), which looks something like the numeral 8 written sideways (). This symbol for infinity was first used in the 1600s by the mathematician John Wallis.
Infinity can be defined as the limit of 1/x as x approaches zero. Sometimes people say that 1/0 is equal to infinity, but technically, division by zero is not defined. Another notion is that infinity is a quantity x such that x + 1 = x. The idea is that the quantity is so large (either positive or negative) that increasing its value by 1 does not change it.

http://en.wikipedia.org/wiki/Infinity

[Dr. Skeptic]

It doesn't seem to stop people from measuring the distance between "1" and "3" despite the fact that the range of integers is infinitely large.

That is exactly why quantum mechanics states there are a finite number of units between 1 and 3, in both time and space. The imagination can perceive an infinite amount of units, the science of quantum cannot.

A very short history of the universe:

An event happened 13.5 billion years ago that created space/time and mass/gravity that existed as something else (not of our 4 dimensions) before time. It has been expanding and cooling ever since, and now we are here.

I like this story, it contains the entire universe in an empirical forum where empirical and conceptual numbers need not mix.

[Chris Peterson]

That is exactly why quantum mechanics states there are a finite number of units between 1 and 3, in both time and space. The imagination can perceive an infinite amount of units, the science of quantum cannot.

I can't speak to the limitations of your imagination, but I assure you that quantum mechanics has no problems at all with infinites. And to be clear, quantum mechanics implies the concept of the Planck length, and while mathematically elegant, it has not been observed, and even saying that it is the smallest unit of length is an oversimplification. In any case, even if that is what it is, there is no reason that there can't be an infinite number of those units on a ruler that is infinitely long. An integer number line is similarly quantized, and there remains an infinite number of integers.

An event happened 13.5 billion years ago that created space/time and mass/gravity that existed as something else (not of our 4 dimensions) before time. It has been expanding and cooling ever since, and now we are here.

That's pretty close to my own view as well. I don't happen to think that the Universe is of infinite extent. But I recognize that this is a philosophical position, not a scientific one. It stems from my perception of the Universe and my own sense of what is and is not elegant. I accept that there is no reason that the Universe can't be infinite; there are unfalsified theories that require it to be so. I'll keep my opinions, but I'll also maintain sufficient skepticism to be prepared to change those opinions in the face of changing evidence.

[Phil G]

One: I'm fully aware of the definition of infinity, infinity is simply no limit.
Two: That isn't any definition of infinity I've ever encountered.
One: Let's hear your definition of infinity if you don't like mine.

From Merriam-Webster's 10th Collegiate [not a scientific] dictionary:

infinity noun (14c)
1 a : the quality of being infinite
.. b : unlimited extent of time, space, or quantity : boundlessness
2 : an indefinitely great number or amount <an infinity of stars>
3 a : the limit of the value of a function or variable when it tends to become numerically larger than any preassigned finite number
.. b : a part of a geometric magnitude that lies beyond any part whose distance from a given reference position is finite <do parallel lines ever meet if they extend to infinity>
c : a transfinite number (as aleph-null)
4 : a distance so great that the rays of light from a point source at that distance may be regarded as parallel

(C)1996 Zane Publishing, Inc. and Merriam-Webster, Incorporated. All rights reserved.

02/Jan/08 is the first time I've read this thread, and I've found it interesting, if somewhat repetitive. Except for a couple minor incidents, this has been a civil argument, so a round of applause to all participants.

Apparently, according to M-W, infinity did not exist before the 14th century. Or do they only mean as a noun, or human concept?

Back in the 40s-50s when I was in school, I was told that infinity [as a mathematical concept] includes everything. Therefore 1 or 73 [e.g.] can not be added to it, since they already exist within it.
Peace, Phil G

[Phil G]

Empirical measurements of the universe are meaningless if the universe is infinite.

May this non-scientist ask, Why?

If the "Whole" cannot be measured, how can a "Part" be measured based on the same measuring criteria?

I don't understand this. It sounds like: We can't measure the distance to the moon because we can't measure the distance to a galaxy so far away it can barely be seen.

Peace, Phil G

[Phil G]

Infinity means without boundaries. It is said there is no edge of the universe (no boundary). So, by definition, isn't it infinite?

Not necessarily. The universe can be 'boundless, but finite'. A decent two-dimensional analogy is the surface of a sphere. It has no boundary (you can never encounter an edge while your motion is confined to the two-dimensional surface), and yet it has a finite surface area.

First of all, since when is a sphere, or its surface, two-dimensional? Or was that just a typo?

Then, isn't the surface of a sphere its boundary?

Peace, Phil G

[Phil G]

To over simplify the point, A Planck's Length is the smallest measure of distance, 1/2 of a Planck's Length does not exist.

My non-scientifically-trained mind is having trouble with this.
I presume that Planck's Lengths are mathematical units. Correct? [It's not in my dictionary.]
If that is so, then they would be integers or rational numbers, right?
How can an integer or rational number not be divisible yet again?
At least not until it has become infinitely small.
So, then, is a Planck's Length infinitely small?

Or am I just way too far in over my head?
Peace, Phil G

[Chris Peterson]

My non-scientifically-trained mind is having trouble with this.
I presume that Planck's Lengths are mathematical units. Correct?

No, a Planck length is a unit of absolute distance, 1.6 e -35 meters. It's not a simple concept, but you can read about it in this Wikipedia article.

[Qev]

Infinity means without boundaries. It is said there is no edge of the universe (no boundary). So, by definition, isn't it infinite?

Not necessarily. The universe can be 'boundless, but finite'. A decent two-dimensional analogy is the surface of a sphere. It has no boundary (you can never encounter an edge while your motion is confined to the two-dimensional surface), and yet it has a finite surface area.

First of all, since when is a sphere, or its surface, two-dimensional? Or was that just a typo?

Then, isn't the surface of a sphere its boundary?

Peace, Phil G

A sphere is a three-dimensional shape, most certainly. The surface of a sphere, ignoring the volume it encloses, is two-dimensional. If you were a two-dimensional being living on the surface of a sphere, the directions 'up' off the surface of the sphere, and 'down' towards its center wouldn't exist for you. This is basically an (imperfect) analogy of possible ways that space can be curved.

[Dr. Skeptic]

Try reading Steven Hawking, as he also states the the universe is granular with the Planck's Length being the absolute smallest possible size of the granules. If you have another theory that accounts for quantum mechanics (or disproves it), I'd love to hear it.

There needs to be a quantum limit to the number of Planck's length, it maybe static or it maybe fluid, but it is finite. Without a assigning a finite value to the universe, it takes on the equivalents as an undefinable religion where empirical data is irrelevant.

To state that the universe is ∞ and is expanding is nonsensical to both physics and mathematics - a non-limit cannot increase, cannot be defined (other than no limit), cannot belong to a ratio ...

Any mathematical function applied to ∞ leaves ∞ as the product, infinity cannot be altered.

Let my try and explain it this way:
Let's say there are two universes, the empirical universe and the conceptual universe. The empirical universe is where "stuff" resides; Mass/gravity and Space/Time. Then there is the conceptual universe where thought, feelings, and if you want, religion reside.
The two universes cannot be "blended" until either; conceptions are assigned empirical values or empirical values are defined as pure products of conception where the empirical units do not require an empirical definitions. Assigning ∞ as an empirical value not only to the size of the universe but "in" the universe is invalid. (mathematics uses the approach to ∞)

Any questions?

[Qev]

There needs to be a quantum limit to the number of Planck's length, it maybe static or it maybe fluid, but it is finite. Without a assigning a finite value to the universe, it takes on the equivalents as an undefinable religion where empirical data is irrelevant.

No, it just takes on the equivalent of being a very large, unbounded region. The distance between myself and my coffee cup doesn't care how much possible distance exists behind it. The only distances that are meaningful are those between points we choose to measure from.

To state that the universe is ∞ and is expanding is nonsensical to both physics and mathematics - a non-limit cannot increase, cannot be defined (other than no limit), cannot belong to a ratio ...

Neither physics nor mathematics have a problem with an infinite universe. The metric of an infinite space can expand just fine. The infinite space remains infinite, the distance between any two arbitrary points in that space increases. It's not like it's going to run out of room...

Any mathematical function applied to ∞ leaves ∞ as the product, infinity cannot be altered.

You can't apply mathematical functions to ∞ to get a 'product' in the first place; it's not a number.

Let my try and explain it this way:
Let's say there are two universes, the empirical universe and the conceptual universe. The empirical universe is where "stuff" resides; Mass/gravity and Space/Time. Then there is the conceptual universe where thought, feelings, and if you want, religion reside.
The two universes cannot be "blended" until either; conceptions are assigned empirical values or empirical values are defined as pure products of conception where the empirical units do not require an empirical definitions. Assigning ∞ as an empirical value not only to the size of the universe but "in" the universe is invalid. (mathematics uses the approach to ∞)

Any questions?

Infinity is not a value.

I'm not quite sure what this last bit is trying to explain, considering the 'conceptual universe' and the 'empirical universe' are already the same place.

[craterchains]

This is kind of like watching a verble ping pong match, only with typing.

[bystander]

You can't apply mathematical functions to ∞ to get a 'product' in the first place; it's not a number.

-- snip --

Infinity is not a value.

Actually, you can. Mathematics is just a set of rules, and as long as those rules are defined, they can be applied. Arithmetic operations are defined for ±∞ as well as for infinite limits. Infinity may not be a number but it does have value. n/∞ is defined and is equal to 0 as long as -∞ < n < ∞. All arithmetic operations are defined for infinity. (http://en.wikipedia.org/wiki/Extended_real_number_line)

However, I have to agree with your other arguments, just because the universe is infinite doesn't mean that everything within that universe becomes unknowable or unmeasurable. Observations and empirical data still have meaning.

Quantum mechanics is just a theory and it does not explain everything. For instance, it does not explain gravity. General relativity is at odds with quantum mechanics, particularly on the subject of gravity. Even if quantum mechanics was the "one truth", I can not see why there has to be a finite number of plank lengths.

[Dr. Skeptic]

Infinity is not a value.

I'm not quite sure what this last bit is trying to explain, considering the 'conceptual universe' and the 'empirical universe' are already the same place.

Stating the universe is ∞, you are assigning an empirical value to it, if not, you are stating that the universe is non-empirical.

There must be a finite limit both small and large; you have to stop measuring somewhere for empirical measurements of the universe to be valid. It cannot be an arbitrary point, it must be set by empirical laws of nature, if not, it is rendered conceptual - which is non-empirical. When relating or blending a conceptual value to/with an empirical value the product will always be conceptual - not empirical.

Science's cornerstone is empirical data, without a proof set showing that ∞ is assigned an empirical value your arguments remain false.

It is true we "live" in both a conceptual and empirical universe and they are in the same place ... a rock under our feet does not, it is totally passive to the empirical universe and reacts to the universe by strict empirical behavior, properties of life on the other hand are based on non-empirical concepts and cannot be measured using empirical tools.


And please, don't go to the argument: does the rock even exist if we don't conceive it first.

[kovil]

The Universe is both/and; it is both empirical and conceptual, at the same time.

Likewise it is both/and; it is both finite and infinite, at the same time.

It is a matter of which way you are looking at it, at the time.

You can see it as Ying or as Yang, it is both/and.

The Universe is not an either/or situation it is a both/and situation.

Infinity is not a quantifiable quantity, so one cannot use it like a number in an equation that is operated. It can stand in an equation that is not operated to give a numerical answer,, but is standing to elucidate a relationship.

[Dr. Skeptic]

The Universe is both/and; it is both empirical and conceptual, at the same time.

Likewise it is both/and; it is both finite and infinite, at the same time.

It is a matter of which way you are looking at it, at the time.

You can see it as Ying or as Yang, it is both/and.

The Universe is not an either/or situation it is a both/and situation.

Infinity is not a quantifiable quantity, so one cannot use it like a number in an equation that is operated. It can stand in an equation that is not operated to give a numerical answer,, but is standing to elucidate a relationship.

You are correct, it is both.

My point is that the units of measurements cannot be interchanged, using empirical based science to "quantify" observations.

From Wikipedia,

Scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. It is based on gathering observable, empirical and measurable evidence subject to specific principles of reasoning.[1] A scientific method consists of the collection of data through observation and experimentation, and the formulation and testing of hypotheses.[2]

Because infinity cannot be assigned a measurable value or tested, it cannot be part of empirical science, thus it is not a scientific solution for quantifying the size of the universe.

[Qev]

There are no measurement problems with an infinite universe. That I measure a distance of 1m between myself and my computer monitor is not dependent on whether the universe is 100 billion light years in scope, or infinite. The only measurements that make any sense are those between chosen points.

Going by the definition of 'empirical', I'm not so sure an infinite universe can be called 'non-empirical'. All that is required is evidence based on observation by our senses. If continued studies of cosmological phenomena lead us to a point where the only valid theoretical shape for the universe is one that is infinite in extent, then it is most certainly empirical. Certain classes of finite universe have already been ruled out by observations of the CMB, and some classes of infinite universe have also been ruled out by other observations.

[Dr. Skeptic]

I'm not so sure an infinite universe can be called 'non-empirical'

If it cannot be measured or assigned a value it is non-empirical.

Empirical
From Wikipedia, the free encyclopedia


A central concept in science and the scientific method is that all evidence must be empirical, or empirically based, that is, dependent on evidence or consequences that are observable by the senses. Empirical data is data that is produced by experiment or observation.[1] It is usually differentiated from the philosophic usage of empiricism by the use of the adjective "empirical" or the adverb "empirically." "Empirical" as an adjective or adverb is used in conjunction with both the natural and social sciences, and refers to the use of working hypotheses that are testable using observation or experiment. In this sense of the word, scientific statements are subject to and derived from our experiences or observations.

The blending of empirical and non-empirical data is a common practice these days by people with a deceptive agenda trying (and many times being successful) to pass non scientific theories as real science, or, by those that don't understand the scientific implications of blending empirical and non-empirical values.

[Publish or perish]

An example of empirical/non-empirical blending distorting science.

http://www.sciam.com/article.cfm?id=whe ... iverse-exp

[Chris Peterson]

This discussion has been going in circles for quite some time now.

The bottom line is simple. From a scientific standpoint, it is currently unknown if the Universe is infinite. Nothing requires it and nothing precludes it. It isn't even known if the extent of the Universe can be determined. There are valid theories (really, variant theories) that propose each possibility; none have been falsified, and in most cases the technology doesn't yet exist to fully test and possibly falsify any theory.

Philosophical discussions about the nature of infinity are rather out of place here.

[NoelC]

Bah, I don't see a ban on philosophy anywhere here. If you think there's a hard distinction between science and philosophy then you need to open your eyes. Imagination and wonder have given birth to science.

And perhaps the extent of the Universe can never be known. The very determination may be non-empirical in itself. That's what's hard to swallow.

Kind of falls along the lines of "how long do you have to fish before you can determine there are no fish to be caught?"

-Noel

[Dr. Skeptic]

Bah, I don't see a ban on philosophy anywhere here. If you think there's a hard distinction between science and philosophy then you need to open your eyes. Imagination and wonder have given birth to science.

And perhaps the extent of the Universe can never be known. The very determination may be non-empirical in itself. That's what's hard to swallow.

Kind of falls along the lines of "how long do you have to fish before you can determine there are no fish to be caught?"

-Noel

I agree! The debate is a chance to teach, to learn, to ponder first time concepts, understand opposing viewpoints... what could be better?

The argument the the universe is infinite "because" it has not been proved to be finite is far to passive of an argument for me.

http://www.newscientist.com/article.ns?id=dn4250

Here's an article that is somewhat speculative but contains good insight to future avenues of studies.


If one finds no interest in this discussion, simply go to one you do find interesting. Or if one finds alternative viewpoints offensive because it is upsetting to a deep-seated prejudges, education is the only cure.

[Chris Peterson]

The argument the the universe is infinite "because" it has not been proved to be finite is far to passive of an argument for me.

I'm not arguing that, and I don't see that anybody else is, either. The point is simply that nobody can say one way or the other whether the Universe is finite or infinite. The tools of science may be able to answer that question, but so far not. To make an absolute statement that the Universe is infinite, or that it cannot be infinite, is unscientific and reflects scientific ignorance.

I'm certainly not offended by philosophical discussion, but science and philosophy are completely different things. While philosophical reasoning may suggest directions of scientific investigation, it is not itself science, and cannot answer any questions about the physical Universe. To pass off philosophical arguments as science, however, is offensive. That is the core of pseudoscience.

[NoelC]

So what we really need to do is to discover (or invent) tunneling on a grand scale (wormholing?), so we can get beyond this pesky speed of light limitation. Imagine being able to see farther than we can imagine.

I'm not arguing for or against this point, but merely bringing it up for possible discussion: What *if* the laws of physics vary depending on where you are. For example, what *if* as you approach the outer "edge" of the universe (assuming there is such a thing) that the speed of light slows, so that it is essentially infinitely far (in distance and time) to the edge. Kind of like the old "go halfway to the finish line, repeat" joke, where the physicist gives up before even starting because he knows he can never get there. Things (e.g., distant galaxies) could SEEM to be an awfully long way off, yet they might not be all that far away in some grand outside-of-space-time sense. Perhaps we're all inside a marble hanging on a cat's collar.

If one considers the universe to be the combination of the laws of physics, i.e., existence of space-time-matter itself (not just the existence of matter), then what *is* the edge (assuming there is one) likely to be like?

-Noel

[Dr. Skeptic]

So what we really need to do is to discover (or invent) tunneling on a grand scale (wormholing?), so we can get beyond this pesky speed of light limitation. Imagine being able to see farther than we can imagine.

I'm not arguing for or against this point, but merely bringing it up for possible discussion: What *if* the laws of physics vary depending on where you are. For example, what *if* as you approach the outer "edge" of the universe (assuming there is such a thing) that the speed of light slows, so that it is essentially infinitely far (in distance and time) to the edge. Kind of like the old "go halfway to the finish line, repeat" joke, where the physicist gives up before even starting because he knows he can never get there. Things (e.g., distant galaxies) could SEEM to be an awfully long way off, yet they might not be all that far away in some grand outside-of-space-time sense. Perhaps we're all inside a marble hanging on a cat's collar.

If one considers the universe to be the combination of the laws of physics, i.e., existence of space-time-matter itself (not just the existence of matter), then what *is* the edge (assuming there is one) likely to be like?

-Noel

You are right, Space/Time and Mass/Gravity are 100% dependent on each other. Space/Time will not exist in the absences of Mass/gravity. The volume of the universe is expanding at the speed of light (+ the rate of acceleration) from the point that matter first came into existence. Outside the volume of Space/Time nothing exists, or at least as the empirical science of today tells us.

Looking for the "End" of the universe from the viewpoint of an observer not tied to the laws of Space/Time, it would appear to be a single Planck's Length that would take a photon 13.5 billion years to cross.

Sorry, I truly believe that using infinity in empirical science is for those who's concept of the universe is overly simplified and haven't weighed the consequences of implying it to the "big" picture.


A static universe is all but proved to be false by observations of this last year (check the Noble Prize), if the universe not static it cannot be infinite.