Now that I've gotten that out of the way, let me set up the background. Recently, over the last couple weeks, I've been reading one of the most fascinating series of posts ever. I won't tell you what they are about because you would think I was joking. And if you are going to read them, start with the first one because the order does matter.
Now, by the end, it starts to get philopsophical and gets into discussions of truth, being, God and the universe. Or Life, The Universe, and Everything if you will. Eventually the idea of a "First Cause" comes up. There is a long history (remember, this is all very un-informed) of using a "first cause" type argument to prove the existence of God, from St. Anselm to Thomas Aquinas to Des Cartes to Kierkegaard. And that's not even mentioning any non-western philosophizing. [Aside: You can thank Mike for this pretentious/non-sensical post. He never should have let me read Philosophy and Theology.] One of the currently "popular" arguments for the existence of God or some other personal "first cause" is called the Kalam Cosmological Argument, which I just learned of yesterday from the author of that long, weird post series. Now, let me mention here, for lack of a better place, that I'm not sure I believe that anyone could ever come up with a logical proof for the existence of God. I'm just throwing that out there. I mean IN YOUR FACE AQUINAS!!!
Basically, the Kalam argument goes as follows:
1. whatever begins to exist has a cause.
2. the universe began to exist.
3. therefore, the universe has a cause.
You can read a more in depth analysis here that really goes into why it must logically be a personal cause etc. The argument is simple, concise, and a little too neat for me. I tend to be suspicious of simple syllogisms that posit to irrefutably prove an ineffable truth.
Here's my problem. One of the crucial premises to this argument is the impossibility of an actual infinite existing in nature. If it is impossible, then the universe has to have a beginning thus it has to have a cause etc. However, I am not convinced of the argument showing that the universe has a beginning. [As a quick background for those of you who don't know what an "actual infinite is, like me before yesterday: an actual infinite set is one in which part of the set has the same number of members as the whole set does. Think of an actual infinite library with half red books and half black books. If it was actually infinite the number of red books would be equal to the number of black books but also equal to the number of red books plus black books. Weird huh? A potential infinite is an infinite set than can be added to. Like the highest number you can think of, and then add one.] Intuitively, we can understand that the existence of an actual infinite is impossible in the world of plants and trees and rocks and things. However, is it also impossible with time? Does the universe necessarily have had a beginning? Here's the argument (basically) that William Lane Craig, one of the contemporary proponents of this theory, gives:
A beginningless series of events in time is an actual infinite. In other words, if the series of past events had no beginning, it is actually infinite. If premise one (ed. an actual infinite can not exist) is correct, however, it follows that a beginningless series of events in time cannot exist. Consider the following example. The Battle of Hastings took place in 1066. The Declaration of Independence was adopted in 1776, 710 years after the Battle of Hastings. If the series of past events in the universe is actually infinite, we can say that the Battle of Hastings was preceded by an infinite number of events. We can say the same about the Declaration of Independence. In fact we can say that the set of past events before the Battle of Hastings is equal to the set of past events before the Declaration of Independence, because part of an actually infinite set is equal to the whole set, as noted above. But how can that be? 710 years separate these two events, i.e., 710 years were added to the set of past events before the Battle of Hastings to get to the Declaration of Independence. By definition, however, nothing can be added to an actual infinite. Hence the series of past events before the Battle of Hastings cannot be actually infinite. Craig thus draws the conclusion to the first philosophical argument as follows: "[s]o the series of all past events must be finite and have a beginning. But the universe is the series of all events, so the universe must have had a beginning" (Craig, The Existence of God, 47).
So here's my problem. How do we know that the progression of events we see as "time" or "history" is adding to a potentially infinite set? This seems like a perfect place to deploy the anthropic principle. Maybe the only reason we see these events occurring in a series is because that is the only way our consciousness (however you want to classify that ontologically) can perceive the actual infinite set of quantum states of the universe that make up everything. How can we know that all "past" and "future" states of the universe that we interpret through thermodynamics as having a direction don't all exist together and that the progression of "time" is just how we interpret it? How could we exist and see it any other way? We have to make order out it somehow, right? Let's go back to the imaginary actually infinite library. Imagine yourself perusing these shelves. First you see a red book, then a black, then another red and so on. You can see that there is a pattern. You can predict what color will come next, and you can tell the last 5000 colors that you just walked past, even though there are an infinite number of books before the one you are at and there were an infinite number of books before the one you were at 5000 books ago. That doesn't mean that the 5000 books between the beginning of your journey and your current position don't exist, or were added to the set, it just means that you passed 5000 books. Could it be that the universe has just this same kind of order and that our progression through it is analgous to walking by a set number of books that already exist in the set? Does this make any sense?
Of course, there are problems with what I just said. First, time being actually infinite also implies that the universe cannot have an end. In my theology, the only thing with no beginning or end is God, so does that mean that God is the universe? That idea has a name, I just don't know what it is. Second, I'm not entirely sure that I understand Cantorian actual infinite set theory well enough. Third, most cosmological observations DO point to the universe having a beginning. Fourth, if all parts of the infinite set of the universe, that is, the quantum state of the universe at each individual planck time (approximately 10^-43 seconds), are all coexistent in some overarching reality, where does that leave cause and effect, which is the basis for all of human existence and understanding? If the whole set exists, then our paths are all predetermined and we are just cogs in an arbitrarily directed set of unrelated events. Which in turn means that everything we interpret as "time" and life and death and even existence is misguided and we only see it that way because we have no other choice but to observe it as such. There's that anthropic principle again.
So, now that you are hopefully as confused as I am, can anyone explain where I might be wrong? Does anybody know Cantorian set theory really well? Can anyone prove the existence of God? Does anybody want to punch me in the eye for making you read this? Is anybody still there? Is anybody ever there? Is anything even real? Am I getting purposefully and obnoxiously philosophical and trite? Okay, yes is the answer to the last question.
But if you stuck around til now, guess what? You get to look at this cool picture! I guess you get to look at it if you just scrolled down and didn't read any of the post, too.
Actually, this picture makes all the arguments moot. If the existence of guitars like this don't prove that God exists, nothing can.
10 comments:
The universe and our existence are infinate. I think of it like a three part play that is infinately long. the first act was before we came to earth and were born. the second act is right now on earth. and the third act is the after life. we will exist infinately. try to wrap your head around that. If you don't believe in existing infinately, then try thinking about you not existing at all. Thats even weirder. But good thing we don't have to worry about it because we will live for an infinate amount of time.
See, but I can't agree that it's like a three part play. If the universe and our existence are indeed actual infinites, then our existence before being born is equal to the total of our existence. And if, as is traditional when thinking about the afterlife, our time here on earth determines our eternal fate how can that be possible since our time here on earth is not just mathematically insignificant in comparison to an actual infinite timeline, it is actually exactly ZERO.
Another problem I see with beings such as us being actual infinite ontologically is that it would put us on the same level as God who is the "Alpha and Omega." The Causeless cause, if you will. I am not willing to say that I am of the same essence of God. His image? Yes. His essence? No.
By the way, I use He for no better reason than that it is the longstanding pronoun used to refer to God.
who's to say we can't become like God is? and what if God was like us, and He had a God, etc...
I agree that what happens here on earth will determine how we spend the rest of eternity. but i believe that everyone will live eternally, but in different circumstances depending on how they spent their life here on earth.
I feel very philosophical, but its probably just the time of day.
If we had a big bang right now, then time would restart, but all of the "features" of this universe would be cast into the next, since there would be no absolute cosmic singularity.
If there actually is an identifiable mechanism that indicates that this will happen in the future, then the problem of causality is resolved, since we know that it happened in the past.
You're welcome... ;)
Hm. I'm not sure what you mean, Mr. or Ms. island, when you say "if we had a big bang right now..." Do you mean if we had another singularity expansion within our current universe? How would that happen? Another universe expanding within our own? Seems kind of strange. Is that the next universe you speak of? And why would the "features" of the current universe transer to the next? Is there something fundamental about the properties of our universe that indicates they would be the same in any other universe?
Maybe I missed your point. But also, maybe you're not there any more, so it doesn't really matter.
Well, there is no "within" when a BB occurs, as there is a total annihilation of space and time, but the features of this universe would only be "convolved" into the next one if there is no absolute cosmic singularity.
HOW... would it happen?
;)... I can explain it, if you're game to follow some very intuitive physics?
Although, you might also look at these theories, which essentially accomplish what you're talking about in different ways.
http://arxiv.org/abs/hep-th/0407213
http://www.nature.com/news/2006/060501/full/060501-8.html
http://www.kurzweilai.net/articles/art0592.html?printable=1
... and I'm a guy... sorry.
Okay, I misunderstood your first comment a little. I get the idea of a cyclic universe, that is, one in which the universe repeatedly exapnds and then contracts "through" a big bang type event every so often (i.e. not very often at all, like a trillion years or something) thus eliminating the need for an abolute "Big Bang Singularity"
However, I'm a little unclear on the ramifications of a universe like this. So, sure, if you're still there, I'm game to follow some physics. I'm in the middle of reading those links you provided, and unfortunately I'll be away from my computer most of the week, but go ahead. I'm all ears. Or eyes as the case may be.
There are different ramifications with each model, but any cyclic model has the potential to justify causality if the process is perpetual.
The model that I'm going to describe isn't an expansion/recollapse model, but you should be able to follow along and clearly understand how this mechanism will work if I do a good job of explaining it. The idea is to show you one way that it is proven to work.
Imagine that you could get into a sealed jar and then use a vacuum pump to suck everything except yourself out of it, so that you were surrounded by a zero pressure vacuum.
Okay, now we know from quantum theory that the vacuum has real and virtual particle potential, but you'd have to compress or condense the energy out of your zero pressure vacuum to isolate enough energy in one spot to achieve the energy density of a matter particle.
Simple enough if you have a pump that can do that, but notice that the surrounding ambient pressure is now negative, because you have further rarefied the vacuum.
If there were no walls containing the vacuum, then matter generation from vacuum energy would cause the vacuum to expand as negative pressure increases.
Now, the thing to remember here is that you also increase positive gravitational curvature when you create a real, massive particle, from vacuum energy, so the increasing antigravitational effect of increasing negative pressure gets offset and counterbalanced by this increase in positive gravitational curvature.
That causes tension between the vacuum and ordinary matter to increase as the vacuum expands, so eventually the integrity of the forces that bind this structure will be compromised... and it'll blow.
So, in this model, matter generation from vacuum energy causes the universe to expand until growing tension causes a big bang.
The second law of thermodynamics is never violated in this model.
My Pet... ;)
Very best site. Keep working. Will return in the near future.
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