## Number of galaxies

Hukyl - You are fine on all points except one.

Infinite is NOT a number.

There is no such thing as an infinite amount of anything. It does not exist in reality.

 Recognitions: Gold Member Science Advisor Staff Emeritus http://mathworld.wolfram.com/CardinalNumber.html The cardinal numbers are a superset of the natural numbers, and are the proper number system in which to express the size of a set. (a.k.a. how many of something there is) The cardinal numbers can be divided into two classes; the natural numbers (a.k.a. finite) and the rest (a.k.a. infinite). I'll admit to being a little harsh and nitpicky, but that decision was directly influenced by the attitude of the one to whom I was responding! You may well be right that reality is discrete (otherwise, at the very least, there would be an infinite number of points in the universe), but we certainly don't know for sure.
 Infinite can be used in math just fine. But it doesn't exist in reality. Reality math is perfection - and stands above science (which adheres to linguistics). However all of math is not reality. For instance the old trickery of continuously steping 1/2 the distance towards an object, mathematically you will never reach it. That expression stands outside the math of reality. I reject the claim that infinite as a value of anything exists in reality.

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 For instance the old trickery of continuously steping 1/2 the distance towards an object, mathematically you will never reach it.
If stepping half of the way took one unit of time each time, you would be correct. However, I tend to cover 1 meter in half the time it takes me to cover 2 meters!

If I'm running at 1 meter per second and I want to cover a distance of 16 meters, the "old trickery" only tells me that I can't make it all the way to 16 meters in less than 16 seconds!

 Originally posted by Hurkyl If stepping half of the way took one unit of time each time, you would be correct. However, I tend to cover 1 meter in half the time it takes me to cover 2 meters! If I'm running at 1 meter per second and I want to cover a distance of 16 meters, the "old trickery" only tells me that I can't make it all the way to 16 meters in less than 16 seconds!

Apparently you have no clue what I said.

THe mathematics I used have nothing to do with time at all whatsoever.

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 THe mathematics I used have nothing to do with time at all whatsoever.
I think they do; it just was not explicit!

In any case, tell me how you would go about mathematically proving:

 For instance the old trickery of continuously steping 1/2 the distance towards an object, mathematically you will never reach it.

 X is the distance you are from the point you are trying to reach, in the beginning. The function shows your distance as you take steps such that each step cuts your distance from the point before the step, in half. Here is the function that proves it: X(Y) = (.5 to the power of Y) times (X) So, if one was to reach the point you are originally a distance of X from - then one would need to find a value for Y in the function that results in: X(Y) = 0 And there is none. Thus if you continuously take steps that "half" your distance to a certain point, you can never reach it. Furthermore - The function is conjoured just now - so if I am mistaken it is a fault of my function. The logic still stands.

 Okay. What about gravitational redshift? And you do realize that expanding space would redshift waves passing through it, right?
Wrong. The expansion of space would be imperceptible because we are embedded in space. The whole premise is ludicrous.

 It certainly isn't well known to me. I'm not inclined to accept that link as a reputable source due to its absurd treatment on Olber's paradox. If you opt to defend their article, consider also a more serious paradox related to Olber's paradox; we should be observing an infinite amount of EM energy if the universe was infinite and homogenous.
So, in other words you have no argument against it? It gives a simple explanation of the MBR and you cannot dispute it so you find something that you don't agree with and simply call it absurd.

Olber's Paradox does not take into account the fact that there is much intersteller gas and dust to absorb and re-emit the radiation as 3K heat. Quite simple really.

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 Wrong. The expansion of space would be imperceptible because we are embedded in space. The whole premise is ludicrous.
It would manifest itself as a tendancy for things to expand. Things like solar systems or atoms are self-correcting so their actual sizes would not increase as the universe expands (in a classical picture, it would manifest as a slight force), but something like an intergalactic light wave or cosmic microwave background radiation is not self-correcting, and the expansion of the wave causes redshifting.

 So, in other words you have no argument against it? It gives a simple explanation of the MBR and you cannot dispute it so you find something that you don't agree with and simply call it absurd.
Correct, at that moment I had no argument against it. I had not yet attempted to formulate one. I brought up Olber's paradox because it was so blatant.

 Olber's Paradox does not take into account the fact that there is much intersteller gas and dust to absord and re-emit the radiation as 3K heat. Quite simple really.
Yes; which is why it's astonishing that the link you gave didn't bring that up.

It is curious why it's 3K nearly everywhere, instead of having a temperature gradient where gas steadily cools as it gets further and further away from galaxies. It's curious enough that in my mind it's a serious flaw in the model.

But as I mentioned, there's a more serious version of Olber's paradox which this explanation does not solve. The energy received from a star drops off as the square of the distance from the star... but the number of stars at a particular distance increases as the square of distance. Add up all of the energy received from all of the stars, and you predict that we should be observing an infinite amount of energy, if the unvierse was eternal, infinite, and homogeneous.

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 Thus if you continuously take steps that "half" your distance to a certain point, you can never reach it.
But it wasn't a complete depiction of my motion anyways. Your reasoning is only valid when my distance from my goal is in the interval (0, X]; not when it's in the interval [0, X]. Your argument only tells me that over the period of my motion where my distance is (0, X], I cannot have reached my goal.

 Originally posted by Hurkyl [B]It would manifest itself as a tendancy for things to expand. Things like solar systems or atoms are self-correcting so their actual sizes would not increase as the universe expands (in a classical picture, it would manifest as a slight force), but something like an intergalactic light wave or cosmic microwave background radiation is not self-correcting, and the expansion of the wave causes redshifting.
On one hand BBT says to ignore the relative motions of galaxies at the edges of the visible Universe moving through space near light speed according to the doppler interpretation of red-shift. It says that these speeds do not violate relativity because it is only space itself that is expanding. On the other hand it can say that the expansion of space can cause physical relativistic effects within space seen in the red-shift. So which is it? Is the expansion of space exempt from the laws of physics within it or is it not?

 Yes; which is why it's astonishing that the link you gave didn't bring that up.
Did you read the article? What I said about the paradox is pretty much what it says as well.

 It is curious why it's 3K nearly everywhere, instead of having a temperature gradient where gas steadily cools as it gets further and further away from galaxies. It's curious enough that in my mind it's a serious flaw in the model.
The gas is EVERYWHERE and there are galaxies in every line of sight.

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 Did you read the article? What I said about the paradox is pretty much what it says as well.
Yes I did, and I just re-read it. The article does not say that interstellar gas is blotting out the light from the infinite number of stars.

 On one hand BBT says to ignore the relative motions of galaxies at the edges of the visible Universe moving through space near light speed according to the doppler interpretation of red-shift. It says that these speeds do not violate relativity because it is only space itself that is expanding. On the other hand it can say that the expansion of space can cause physical relativistic effects within space seen in the red-shift. So which is it? Is the expansion of space exempt from the laws of physics within it or is it not?
This is fairly confusing...

General Relativity says that variations in space-time can change the frequency of a photon passing through it.

Inflationary models predict that the majority of space has a quality that will result in the redshifting of light.

Why would near light speeds violate relativity anyways?

According to General Relativity, the expansion of space (and all of the other dynamics of space-time) is governed by Einstein's field equations.

 The gas is EVERYWHERE and there are galaxies in every line of sight.
So? That's no reason why there shouldn't be temperature differentials.

 Originally posted by Hurkyl [B]Yes I did, and I just re-read it. The article does not say that interstellar gas is blotting out the light from the infinite number of stars.
No it says that the radiation is absorbed and re-emited as 3K heat.

 This is fairly confusing...
The confusion is inherent in the absurdity of BBT.

 So? That's no reason why there shouldn't be temperature differentials.
The reason is that the matter emits planck radiation at a specific frequency. Read the article. It tells you that.

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 The confusion is inherent in the absurdity of BBT.
I suspect the more likely explanation is that your confusion about BBT and GR is carrying through to your posts.

 The reason is that the matter emits planck radiation at a specific frequency. Read the article. It tells you that.
It says:

 From astronomical observations we observe that most matter in the universe is in the gas phase at 3 K. Stars of course are much hotter.
It does not explain why most of the matter in the universe should be 3 K.

Also, you still have not explained why we observe only a finite amount of radiation and not infinite.

 Originally posted by meteor There's contantly discussion about if the universe is infinite in size or not. I want to pose the question in another way: Is the number of galaxies infinite? My answer: No
Wouldent that really relay on if matter is infinite or finite

 Originally posted by CrystalStudios For instance the old trickery of continuously steping 1/2 the distance towards an object, mathematically you will never reach it. That expression stands outside the math of reality. I reject the claim that infinite as a value of anything exists in reality.
yea if you think about it you will never reach that area if you take perfect steps. A quark has an infinte amount of points on i just becuase it is one of the smallest units dosent mean you cant move half of it

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 Originally posted by Hurkyl It does not explain why most of the matter in the universe should be 3 K.
It certainly does just that right in the first paragraph.

" It is recalled that one of the most fundamental laws of physics leads to the prediction that all matter emits electromagnetic radiation. That radiation, called Planck's radiation, covers an electromagnetic spectrum that is characterized by the absolute temperature of the emitting matter. From astronomical observations we observe that most matter in the universe is in the gas phase at 3 K. Stars of course are much hotter. The characteristic Planck's spectrum, corresponding to 3 K, is actually observed in the universe exactly as required. "

So the basic laws of physics state that the interstellar matter should emit em radiation "characterized by the absolute temperature of the emitting matter". Now if this matter is in constant bombardment by electromagnetic radiation it is obvious that it is bound to absorb some of this radiation which will raise the absolute temp above absolute zero. So we have slightly thermalized matter emitting planck radiation characterized by its temp.

How much simpler can you get for an explanation of the 3K CBR?

 Also, you still have not explained why we observe only a finite amount of radiation and not infinite.
Ok first you tell me why on earth you would expect it to be infinite?