Boltzmannbrain

I think I am just missing the point of the partial sums part. I don't really know the point of it. Why is it part of the process?

I am still confused. I would understand if the definition was something like an arbitrary symbol like they did with an imaginary number i. That would make sense to me with what your saying because it wouldn't be a value that already has a definite meaning. You are calling it meaningless, but 1 has meaning. This is why I am still stuck with the problem in my OP.

Ok, I agree, but isn't it also saying that the infinite sum of 1/2^n equals 1? Then getting back to my original issue, if the definition is correct, doesn't this mean that there is an end? This end would seem to be at 1. Is it wrong? Other sources that I am reading have the equal sign with only two bars too.

Isn't the notation on the bottom saying that the limit is the total sum? If it doesn't actually equal 1 like the notation suggests, then why is it even used in the first place?

I could not find the part that you quoted in the link that you gave me. But I did read in the same Wiki link (under the heading "Convergent Series") that the infinite sum of 1 + 1/2^n = 2. They don't seem to be saying it is just a definition either. What is going on here?

This is just the limit, right? I want to know if the sum of all n fractions actually equals 1, but I see on your next response that you answered what I wanted to know. Thanks. The only thing is that I was told on a different forum that there is a solution, being 1. They seemed quite knowledgeable too. Hmm, it's not letting me put the link to the other forum. If you go to mathforums dot com and go to real analysis, scroll down about 21 threads to my thread (from mathmath) called "How close to 1 does this infinite sum get". They seem to be agreeing that the sum does actually equal 1.

My new issue in my journey to try to understand infinity concerns the "ends" of infinity. I was told on here that the infinite sum of 1/2^n = 1, and not just gets close but actually equals 1. I can't help but notice that we are giving infinity a definite beginning point at 1/2 and a definite end point at 1. What could n possible equal to get to this point? If this last point really is a solution to the equation, then wouldn't it have to be 1/infinity, or in other words, the "infinity-ith" point? If so, how can it be said that the natural numbers can numerate all points of a set of size aleph-null?

Very interesting, thanks for this. It is a little clearer. However, I wouldn't be honest if I said that infinity makes sense to me now.

I understand that there only needs to be some bijection. But doesn't this seem a bit strange to you that we can exhaust all elements of I and we also can't exhaust all elements of I (using N)? It is a yes and no answer. I never see that in math. Is it allowed?

The two sets N (naturals) and I (integers) have a one-to-one correspondence and are said to have equal size/cardinality. But if we put them one-to-one in a specific way, such as the naturals to the naturals from I, we see that the naturals of I get used up leaving 0 and the negative integers. This seems to show that a correspondence from N to I can also not be one-to-one. The curiosity I get from this is just too much. It almost seems like this is an example of something that can be proved to be true and can be proved to be false. I would have to think that my problem is that I am not allowed to correspond the naturals to only the naturals of the integers, but why not?

I think since there are so many dust storms, and thus probably a lot of charged particles, this video makes the most sense. Start watching at 1:20 And here is just an example of what lightning does in dirt/sand

Yeah, I definitely do not take the BB to be realistic. Though I did think it was quite interesting when I first heard of it. Ok

Yes I watched the lecture. I am getting frustrated that you are understanding what I am saying. If your brain only lasts for a few seconds, or even a millisecond, you only have memories of the structures. They won't actually be out there because your memories may not be of the actual structures. And what you see maybe illusions, a dream, a picture, i.e. a facade I don't know why Susskind went in the direction he did. This is a type of solipsism. It is quite difficult to rationalize your way out of it. But let me guess, you are going to keep arguing anyways?

I take it you did not read what I said carefully enough. What if your Boltzmann Brain only lasted for a few seconds? How would you know that the universe/structure actually exists, and are not just false memories? I am not actually asking this question to get a response. I am just saying that your argument against a BB was not convincing.

I get the feeling that you think I am arguing for a Boltzmann Brain. I'm absolutely not. Moreover, you did not give a very convincing reason why a Boltzmann Brain is not the answer. The BB would explain everything that you mentioned. The structure out there, would actually be just your BB. Everything including your memories, conclusions, arguments, etc. would only exist for as long as the brain exists. It is like proving solipsism false; it is very hard to do so. When we are this far down the rabbit hole trying to explain away constants, laws etc. and how they came to be, a Boltzmann Brain may be a lot less crazy than the actual answer.

I felt we were in fringe-theory territory to explain away fine-tuning mysteries. No matter how distasteful, everything should be considered.

You may also be interested in reading about the Boltzmann Brain. Matt O'Dowd does a good summary of it.

I think we can all agree on this. I don't understand what the problem is.

Thanks for this +1 I definitely see what you are saying. I was not specific enough in the OP. But I think you answered my questions for the other "types" of infinity.

+1 Thanks for this, but it is very unsettling for me. What I am interpreting this to mean is that infinity can have a final element (or end) but it also cannot have a final element. It is also hard to grasp that something that is defined as having no end, can end. I suppose that infinity ends in one respect and does not end in another. I am struggling to find the difference between the two "ends".

Interesting +1 But I have to ask, how can 0 come after numbers > 0 in an ordered set? Yeah, thinking about how these strange mathematical concepts may cross over into the real world is almost scary. My math professor told me something that was absolutely mind-blowing to me. I asked him what he researches as a faculty member with a doctorate in mathematics. He said that they look at physical phenomena (exotic phenomena I presume) to understand more about math. So in some limited sense, or maybe not even limited, it seems to me that there is almost no difference between math and physics. Maybe eventually we will find that they are both the same thing. +1 I find that very interesting and important to remember.

Forget that analogy. I was thinking that maybe it matters in what perspective the infinite objects are being considered. But we probably don't have to get into that.

Good point (+1 ), but there is still something unsettling about an infinite "row" or "list", in particular. The whole row somehow exists, but also doesn't exist from a certain perspective. Does perception play into mathematics sort of how observation plays into physics? +1 Yeah, I am trying to keep all of this in mind. When I said that there may be a gap in our understanding (or at least in my understanding) of infinity, I was sort of referring to your points in your post. There might just be a property of infinity that allows it to somehow exist in and out of the ether. I will look at those properties that you mentioned. Thanks.

I was afraid of that answer. I don't understand how something can exist but not end. This is why I am so interested in this topic. It doesn't make clear sense. Something seems wrong, or at least there is a gap of knowledge to be filled.

Do all the objects exist that are in an infinite set?