Can infinity exist?

sin_is_fun · Post by **sin_is_fun** » Thu Aug 25, 2005 8:56 pm

What is infinity?Infinity is defined by www.dictionary.com as 'Having no boundaries or limits'.

If anything is infinite it shouldnt be limited.We cannot say 'limited infinity' or 'infinity within borders'.If something is infinite then it means it doesnt have any borders.If it doesnt have any borders then it includes everything else into it.So there is only one thing which has no borders,beginning or end.

The concept of infinity drags us closer to pantheism,doesnt it?

McCulloch · Post by **McCulloch** » Fri Aug 26, 2005 9:28 am

My background and training is in mathematics. In mathematics, infinities (yes there are different infinities) are a very useful concept. But like imaginary numbers (√-1), they cannot be shown to really exist. For instance, calculus generates very useful results based on the idea of infinitesimal (the reciprocal of infinite) gaps. Yet, in physics Planck seemed to show that there really is a lower limit of size.

I think that sloppy logic and unwarranted mixing of concepts brings us closer to pantheism.

Sender · Post by **Sender** » Fri Aug 26, 2005 9:51 am

Many have said this, and if it isn't true please say so. Isn't every snowflake and grain of sand diferent and unique? Everyone's DNA is diferent isn't it" I have heard two teaspoons of DNA can reach to the sun and back five millions times. Is this true? I will respond once this a accepted as true or false. So which is it?

McCulloch · Post by **McCulloch** » Fri Aug 26, 2005 10:17 am

upnorthfan wrote:Many have said this, and if it isn't true please say so. Isn't every snowflake and grain of sand diferent and unique?

I have heard this claim and I have not seen the proof. If someone calculated the number of different ways water molecules could be arranged into snowflakes and then estimated the number of snowflakes that have ever existed, then one could, in theory, estimate the probability that no two snowflakes have ever been identical. But that would still not prove that the improbable has not actually happened. Extremely improbable is not equivalent to impossible. It is improbable that any specific person will win the lottery but is is very probable that someone will.
Maybe I am particularly dense, but I don't quite see how this gets us closer to the concept of infinity or of pantheism or the alleged link between the two concepts.

upnorthfan wrote:Everyone's DNA is diferent isn't it" I have heard two teaspoons of DNA can reach to the sun and back five millions times. Is this true?

Sorry, I miss the relevance of these facts.

Sender · Post by **Sender** » Fri Aug 26, 2005 10:40 am

McCulloch wrote:
upnorthfan wrote:Many have said this, and if it isn't true please say so. Isn't every snowflake and grain of sand diferent and unique?
I have heard this claim and I have not seen the proof. If someone calculated the number of different ways water molecules could be arranged into snowflakes and then estimated the number of snowflakes that have ever existed, then one could, in theory, estimate the probability that no two snowflakes have ever been identical. But that would still not prove that the improbable has not actually happened. Extremely improbable is not equivalent to impossible. It is improbable that any specific person will win the lottery but is is very probable that someone will.
Maybe I am particularly dense, but I don't quite see how this gets us closer to the concept of infinity or of pantheism or the alleged link between the two concepts.
upnorthfan wrote:Everyone's DNA is diferent isn't it" I have heard two teaspoons of DNA can reach to the sun and back five millions times. Is this true?
Sorry, I miss the relevance of these facts.

If all the snow that has ever fallen is unique, and to me that means 8,000 years worth, to you quite a bit more because you think the world is older, and all the future snowflakes will also be unique, how is that not infinity? I mention DNA because of all the billions of people both living and dead have diferent DNA, how is that not infinity? If God created the snowflake as I believe, it shows that the great designer is unlimited is my point. No great revealation, just adding discussion to the thread.

McCulloch · Post by **McCulloch** » Fri Aug 26, 2005 11:22 am

upnorthfan wrote:If all the snow that has ever fallen is unique, and to me that means 8,000 years worth, to you quite a bit more because you think the world is older, and all the future snowflakes will also be unique, how is that not infinity?

That is not infinity. That is just a very large number. There is a very important difference. Even if snow has fallen on the earth for 8 billion years and each year 12 trillion flakes fall and each flake is unique (an unproven assumption) then the number of unique snowflakes would be less than infinite.

upnorthfan wrote:I mention DNA because of all the billions of people both living and dead have diferent DNA, how is that not infinity?

The number of people living and dead is still less than infinite. It is limited by the capacity of the earth for human population and the number of years humans have populated the earth. Both of those quantities may be small or large, depending on your viewpoint but they are both finite. Infinite does not mean immeasurably large or even unimaginably large. Infinite means not limited; beyond any possible limits. These examples do not illustrate infinite.

upnorthfan wrote:If God created the snowflake as I believe, it shows that the great designer is unlimited is my point. No great revealation, just adding discussion to the thread.

If a conscious supernatural being individually created every snowflake, then one might expect greater uniformity. When humans (allegedly made in god's image) create things, we tend to make them the same. Especially when we make great quantities of them. No one makes one single unique watch. We make many watches of each model, as similar as we can make them. The apparent uniqueness of the snowflakes, would be evidence of the random nature of their origin rather than evidence of deliberate intelligent design.

Sender · Post by **Sender** » Fri Aug 26, 2005 12:02 pm

I would think 12 trillion would just be a dusting in my backyard from one snow storm one time. And if it is to continue snowing until the end of the earth, well...if that isn't infinite, then I am jumping off this discussion from failure on agreeing before we start to disagree on what infinity is. Nothing to do with you, I am just not smart enough to grasp that is not infinity.. The evolution theory starts off with unproven assumptions and moves forward from there.

McCulloch · Post by **McCulloch** » Fri Aug 26, 2005 1:21 pm

upnorthfan wrote:I would think 12 trillion would just be a dusting in my backyard from one snow storm one time. And if it is to continue snowing until the end of the earth, well...if that isn't infinite, then I am jumping off this discussion from failure on agreeing before we start to disagree on what infinity is. Nothing to do with you, I am just not smart enough to grasp that is not infinity.

My mistake, I thought that we had already established what infinity is.

sin_is_fun wrote:What is infinity? Infinity is defined by www.dictionary.com as 'Having no boundaries or limits'.

We both agree that there was a time when there was no earth. I think that we both agree there there will be a time where there is no earth. Therefore the length of time that the earth has existed and will exist is finite. For purposes of the debate, it really does not matter how long that is, just that it is a finite length of time. We also both agree that the capacity of the earth to contain snowflakes is also finite. If all of the water on the earth were converted into snowflakes then there would still be room in the universe for more snowflakes. Therefore, the number of snowflakes that have been, are and will be on earth, is finite. Unimaginably large perhaps, but finite. By definition it is finite. Infinite, by definition, is 'having no boundaries or limits.' The number of snowflakes on earth is limited by the size and duration of the earth. Therefore, it is not infinite. You really do not have to grasp how large a number this is in order to see that logically it is not infinite. All you have to do is recognize that there are limits. If there are limits, then it is not infinite, by definition.

upnorthfan wrote:The evolution theory starts off with unproven assumptions and moves forward from there.

Sorry, you lost me. How does is this statement relevant to the discussion?

McCulloch reconstructing upnorthfan wrote:The evolution theory starts off with unproven assumptions and moves forward from there. Therefore, there are an infinite number of snowflakes. Therefore, god created snowflakes. Therefore, pantheism is true.

Sender · Post by **Sender** » Fri Aug 26, 2005 2:32 pm

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Are numbers finite?

McCulloch · Post by **McCulloch** » Fri Aug 26, 2005 2:55 pm

upnorthfan wrote:Are numbers finite?

Do numbers exist in reality? Numbers are an abstraction used to count and measure things in reality (or things not in reality, the numbers themselves don't really care). The whole numbers exhibit one kind of infinity. Here is why. The definition of infinite is without limit. There is no whole number, N, where N+1 does not exist in the set of whole numbers. (This is not a rigorous mathematical proof of the infinite nature of whole numbers, for that review any first year pure math textbook.) Therefore, there is no limit to the size of the set of whole numbers. Therefore, the abstraction we call whole numbers is infinite. Curiously, if you look at the set of real numbers (whole numbers, rational numbers and irrational numbers), it can be shown that this set is infinitely larger than the set of whole numbers. But do not worry about that if you think that the number of snowflakes is infinite.

But this does not show that any thing in existence is infinite. Numbers are an abstraction.