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Since I have been thinking about infinity and cosmology recently, let me jot down a few more thoughts I had in the last 2 days.
“I also favor the idea that nothing does not exist and has never existed.”
What do I mean? I mean that I favor the idea that it is impossible for things to pop up into existence as if by magic, like, for example, the idea that the entire universe could just come out of nothing.
Since the universe exists now, either it has always existed or it came out of nothing. I believe there is no way a universe can magically pop out of nothing, for the very reason that absolute nothing can never produce anything from it. Why is this? Well, because of the very concept of nothing.
Therefore that rules out the “universe bursting out of a magical big bang” idea. What do we have left out of the two alternatives? The universe has always existed. Why has it always existed? Why does it exist?
I don’t know.
But since we exist, that means that “absolute nothing” in the sense of nothing having ever existed has already been proven false. Something (like, for example, the universe) clearly has existed and continues to exist. Which then leads me to think it will always exist. Thus the idea that time is infinite seems quite plausible.
Can I grasp the concept of infinite time? No. But it just seems that’s what it is.
The fundamental element.
During this very interesting exchange in the comments section of this post about infinity (The question remains: how could the universe be infinite), for a second, my world entirely disintegrated.
I wrote, as a comment:
I just thought of something – like in a “Zeno paradox” kind of way. Shouldn’t the definition of a point be impossible? Because the minute you say a point, a dot, you can think, well, it could be smaller, and if it could be smaller, then it could be even smaller, and so it goes, infinitely so, to the smallest of the smallest right before it’s nothing. But that is so small that it’s impossible for us to ever “reach” because we, humans, are limited. So this means a point could never be a definite or stable thing. It just keeps going smaller and smaller and smaller – see what I mean?
I’ve just realized I’ve been lied to – ever since primary school when they told me a point is a dot. LOL
Maffblogger (intheshadowofsacredtopology.wordpress.com) replied:
…It’s useful to imagine a point as a dot, but it certainly isn’t one, as you’ve pointed out (pun intended) it possesses no properties such as length, area, etc., but its does have one thing: position! And that’s really all it is, a position. But you’ve made a good point, since we’ve come this far, what do you think about lines? They seem to have length, but no width. You could always imagine a line being narrower and narrower, until perhaps it disappears altogether. …
And I went through years of school thinking it was a dot!!!! They lied to me! LOL My world is disintegrating 😉
“But you’ve made a good point, since we’ve come this far, what do you think about lines? They seem to have length, but no width. You could always imagine a line being narrower and narrower, until perhaps it disappears altogether.”
Yes, it’s the same problem as above. I had never thought of any of this through all my years in school. A new stage begins. You must know of the Zeno paradoxes, right? Actually, when I thought of the “dot problem” above, I also immediately associated it with Zeno’s racetrack paradox. http://www.iep.utm.edu/zeno-par/#H3
And you know what I just thought? There are infinite ways of tracing a path around a sphere (I mean, on the surface of the sphere).
I was picturing your sphere and a path going around the sphere. Actually I pictured a red party balloon (it’s just prettier). So then I went around the balloon, like in a perfect circle, looping back to the beginning. And then I thought, well, we could wiggle around the perfect circular path, like zig-zag and stuff, so you are covering a much longer path to loop back to the point where you started. Now you could do this, i.e., trace paths, in infinite ways. And then I thought: maybe you can’t. But you should be able to.
I can’t decide. Because we’re back to the dot/position problem. If you think that a point is just a position, you can’t trace it, because it has no width or length. But we can trace a path. So I guess you could trace infinite paths. But then you think, but what is a path? It’s a line. And what is a line, it’s a bunch of points. And what is a point? It’s nothing – or is it one of those weird things in math that “tends to nothing”? And what is a position? It’s math, it’s abstract, it’s not real. Everything just disintegrates.
Anything that has to do with infinity is mind-boggling to me. I’ll have to think about this path/line problem a bit more.
So in re-reading the above, I don’t know if I’m on firmer ground, but the answer must involve the “tends to nothing yet is not nothing.”
How did I get there? By thinking about this question:
Does 0.999… = 1 ?
No, it does not. It can never equal 1 because that contradicts the “…” at the end there – that is, the “…” involves infinity, and infinity as we have seen, is something that is often beyond the scope of math. The infinity here means there will always be a 9 at the end, and therefore, that is not sufficient to equal 1. That is the point!
So… this provides us with the beginning of an answer to our dot problem (and how many lines could you trace on a sphere).
A dot exists, but we can never “catch hold of it” because it’s too small, it is truly infinitely small. However it will never be nothing, that is the beauty of it. It is obviously the inverse of the above 0.999… issue. A dot is what exists just before we get to nothing – and we, as humans, can never “catch” that. It is the magic moment when you go from nothing to something, the very beginning, like the conception of light and life, if you will, in mathematics.
Very well – so now onto “how many lines could you trace on a sphere” question. This just might be unsolvable like the question “what is infinity + 1” or “what is infinity + 1 minus infinity + 1”. You can see an answer to the last question that makes sense to me here:
There’s generally no answer. In the typical number systems, there is no such thing as infinity.
In the extended real or complex numbers, infinity minus infinity is undefined (or indeterminate, if you prefer that way of thinking about it).
For cardinal numbers, there’s no well-defined subtraction between infinite cardinals either.
For ordinal numbers, let me substitute ω for infinity (the smallest infinite number), and assuming left-associativity of your operations, we get:
ω + 1 = ω + 1
(ω + 1) – ω = 1
(Only left subtraction works for ordinals, that is to say given x ≤ y there is a unique z such that x + z = y, but in general you can’t find a unique z such that z + x = y.)
((ω + 1) – ω) + 1 = 1 + 1 = 2
If you paranthesize your operations differently you obtain zero in the same manner, although that has nothing to do with infinity but more to do with how the problem is ambiguously stated. You will have the same ambiguity if you substitute 4 for infinity.
I can’t opine on all the comments about the different types of numbers, but what makes sense to me is that our regular math system often breaks down when you meander into infinity, that is, the answer is that there is no answer. “Break down” may not be the best term – math is simply ill-equipped to deal with infinity, it’s limited in that respect.
So if lines are a bunch of dots, and dots are infinitely small, how many lines can you trace on a sphere? You need to define the problem further to play with the concepts. If the line in question can be of infinite length, then I would guess the answer is an infinite number of lines. But what if you say that the lines can only go up to the circumference of the sphere X 2? What if the length of each line must be equal to the circumference? Maybe better start with that. And a sphere is already too complicated an object.
Take a square. How many lines can you trace parallel to one of the sides inside the square, without redrawing one line on top of the other? Is it an infinite number or is it less than infinite?
And my brain feels like a pretzel!
Very important question. Curiously the MSM is not focusing on it – which is not a good sign. The interviewee, HARVEY WASSERMAN, also talks about stripping voter rolls – something I hadn’t even heard of.
I think it would be as easy as apple to pie to rig these machines. How many, how vastly, I don’t know.
But with the stakes being so high, Hillary and the Republicans have certainly done everything to look into how to make it happen. I don’t think Sanders would do it.
From the interview:
HARVEY WASSERMAN: …And this year, about 80 percent of the vote nationally will be cast on electronic voting machines. There is no verifiability. In six key swing states—Florida, North Carolina, Ohio, Michigan, Iowa and Arizona—you have Republican governors and Republican secretaries of state, and no method of verifying the electronic vote count. At midnight or whenever it is on election night, those two guys can go in there with an IT person and flip the outcome of an electronically counted vote within about 60 seconds. So all this millions and millions of dollars, people out campaigning and so on, can be negated by an electronic vote flip late at night on election night, and there is no way to verify what’s happened.
AMY GOODMAN: They didn’t do this with President Obama in 2008.
HARVEY WASSERMAN: They did. He had too many votes; he was too far out. They couldn’t—it would have taken them too many, to flip too many states. [inaudible] believe Obama won by well over 10 million votes. The last—the final vote count was in—official, was in 7 or 8 million.
AMY GOODMAN: But what gives you this idea?
HARVEY WASSERMAN: Because we’ve seen it happen. When you compare exit polls, which are generally accurate to within 1 percent, with the electronic outcome, there are huge variations. And we have documented many dozens of different things that they have done over the years to flip electronic votes.
Too easy, too much at stake, and with a hugely stupid public to add to the equation. Not good. The only thing that would impede one side to rig the machines on a vast scale is the fight from the other side to ensure that it isn’t done.
Now, given that Sanders is an outsider, Hillary could do this to him in the primaries, with the support of the DNC, which is outright resounding for Hillary, and he may not have the means to fight it, in the sense of not having the means to discover it in the first place, as in not having the means to audit a huge nation-wide voting operation.
There are relatives.
I just wanted to note this wonderful little joke here, before I forget it, because I liked it so much. Had never heard it before until recently.
More than 10 years later, and I have not progressed in clarifying anything regarding the concepts of infinity, and consequently, of the universe/cosmology.
I just took a look at this post that I had written back in 2005:
For me, the question remains, just as I had stated it then: “So how can the universe expand? This doesn’t seem logical to me.”
The idea of an infinite universe makes no sense to me, and neither does the idea of a finite one. In short, nothing makes sense. What’s even worse, nothing seems like it can make sense.
As I explained to Jack, if the universe is finite, where does it end? How can it have a boundary? And if it has a boundary, there must be something on the other side of the boundary, thus contradicting the very definition of “finite”. If it is infinite, how can infinity exist for physical things? It makes no sense to me. If the universe somehow loops onto itself, I’m lost as to how that could be.
“I was thinking along the lines of the problem that infinity is outside the scope of rational thought, or logical thought.”
That was another idea I had. But how could there not be a way to understand the universe rationally or logically? That doesn’t make sense either. In short, nothing makes sense. The more I think about it – not that this is a priority for me – the less anything makes sense, and I find no claim that lets me stand on firm ground.
Therefore, by exclusion of the two patently impossible explanations, that the universe is finite, and that the universe loops onto itself, I, for the moment, shall rest with the thought that the universe is infinite, even though my mind cannot comprehend or apprehend infinity applied to anything physical.
Who knows what the future shall bring!! 🙂
update Feb. 22 2016
A reader left a comment mentioning the idea that the universe would be like the surface of a ball. Right there it already doesn’t make sense to me. A 2-D surface cannot be 3-D space, so it makes no sense to me how you could logically talk about a surface being something that, by definition, is not and cannot be space.
However, as I mentioned in my reply to this reader, his comment made me realize something more accurately: the concept of infinity, by definition, requires that there be no boundaries ever in any direction or sense. I had thought of this before, but now it simply stands out so bright and clear, in the most fundamental way. This has a very important consequence: any concept, image, or framework that contains any boundary automatically contradicts the concept of infinity as applied to anything physical when related to space. That’s why I can’t imagine a ball or any surface as a model for infinity. It’s boundaries and more boundaries. Why do other people claim this is a logical way of thinking about space regarding it’s infinite aspect, that is, the very aspect they claim has no boundaries? I don’t know – it makes no sense to me.
It’s hard to be shocked anymore, given the sleaze that oozes out of every pore of both the Republican and Democrat parties, but here I am, shocked.
It’s due to this article:
The Jeffrey Epstein Affair Imperils Hillary Clinton’s Presidential Prospects
The case of the high-flying (alleged) pedophile reveals a broken American political process
You can go to the wikipedia page on Epstein to read a much more detailed account of all his criminal pedophile activities, including having settled up to now no less than 17 accusations, which are in addition to the time he served in jail for soliciting prostitution from a child.
Silverstein continues by saying how Bill Clinton’s entanglement in this sordid affair could affect the upcoming elections:
What all this means is that Hillary Clinton’s husband has already been implicated in the Epstein scandal and that his dubious private behavior, which has already once distracted the entire nation from more important business, could do so again if Ms. Clinton does indeed run for president.
But, wait, would that derail him from voting for Hillary Clinton? Probably not, he says:
What’s worse, at least from my personal standpoint, is that if Ms. Clinton were to become the Democratic nominee I still might vote for her because the likely Republican candidates have retrograde and vile public views about race, class, gender and gay rights, and those are important to me, and especially because the two main parties are virtually indistinguishable when it comes to fundamental economic policy. Because both are bought and paid for by Wall Street and financiers like Jeffrey Epstein, as well as other powerful interests who overwhelmingly fund our political campaigns.
And, hear this, neither would a pedophile scandal that is being largely ignored by the left-wing media along with Bill Clinton’s involvement in it, affect his college-age daughter’s choice to vote for Hillary. Silverstein says he probably will not vote for Hillary, but would if his daughter asked him to. Just why would the little garbage he has for a daughter vote for Hillary?
she [his daughter] is appalled and outraged by the GOP’s stone age social politics and because she would like to see a woman become president. And that’s a good enough reason for me. Maybe.
“It’s also true, in my view, that Ken Starr, who sought to impeach Bill Clinton in the mid-1990s, is a twisted zealot and that it’s probably a bad idea to impeach a president for sexual misconduct, because that has nothing to do with his or her ability to govern effectively,….”
Mr Silverstein’s credibility takes a serious hit with the above statement. The chief law enforcement officer of the land lied, under oath, in an attempt to deny another American citizen her right to due process under the law. He carried on a major coverup, also regularly lying to the American people for over 8 long months, attacking Lewinski’s character, only giving up when the irrefutable evidence of the semen stained dress became public. Mr. Silverstein’s “version” is the persistent urban myth perpetuated by the Democratic Party and Clinton sycophants.
Observer.com: How the DNC Helps Clinton Buy Off Superdelegates
As floodgates open to donations from special interests, the future of the party is auctioned to the highest bidder
I was just going to note another of my comments that got censored on the Internet, on the blog that I created for this purpose, but then it turned into a whole post, so I’m posting it here as well.
The Spectator has an article depicting the ignorant-on-psychology approach that some conservatives spouse:
It’s not church doctrine on marriage that needs to change. It’s almost everything else
This explains why my comment to the above article was censored:
When you are completely ignorant about treating psychological problems, like the Church often is, and so is the Spectator crowd, you are going spout this non-sense that homosexuals have nothing to treat and should go about their lives with their minds deformed. This creates the problem that every kind of homosexual perversion is normalized in their minds and many will effectively insult and sexually harass others because of their homosexuality, along with worse crimes. The dominant discourse will always be “what a cross LGBTs have to bear”, not “let’s inquire about why they experience all kinds of perverted sexual feelings towards people of the same sex”. People who are ignorant about human psychology simply cannot answer or investigate the question. Hence the idiotic stance that results from these conservatives.
Last but not least, I know I’m not the only one, but sometimes, when I read such aberrant articles, I feel like the only person who realizes that these so-called Christian/Catholics interpret the Bible any way they want, and then say the Bible is the word of God – and so it must be true. It would be nice to tap on their shoulder and ask, ‘Haven’t you noticed that every century you have changed the discourse and every time you still proclaim your version is the “word of God”? Cute game, isn’t it?’
This is particularly true of this “we can’t turn away the gays because I love them so much and they’re so nice to me” crowd like Hitchens. “I must have them so near to me in my heart, because I’m such a good little Catholic. And tell me once again how beautiful homosexuality is, Shaw, how utterly nice homosexuals are. It makes me drool. I really want to know how another man would worship me, how he struggles with it, how he’d like to be best friends with me forever. It’s not an abomination at all – who could ever think that, Shaw? I’m just doing my Catholic duty to be good here.”
Really, with “Catholics” like this, who needs GLAAD?
“Two percent of the people think; three percent of the people think they think; and ninety-five percent of the people would rather die than think.”
How three liberals – one heterosexual woman and two homosexual pigs – created a disaster for a child.
One fine day, Kristine, a woman full of typical liberal beliefs, decided to concoct a baby with two of her male homosexual friends, like if they all wanted to shop for a puppy.
Excerpt from her blog:
At 38 years old, I’ve been lucky in my life. I run Red’s, a successful lobster restaurant on the Jersey Shore, with my family and spend winters surfing and teaching yoga in Costa Rica, where I have a great group of friends. By the time I was 33, I’d pretty much done everything on my to-do list — traveled, carved out a career, bought two homes, and had a lot of fun. I’d also married a controlling and demeaning man. After eight years, it became unbearable, and when I kicked him out of my house and filed for divorce four years ago, I felt empowered and free. But I wanted a family. I knew I had too much love in my heart not to have a baby, and I believed it was important that the child have a great dad. About a year after my marriage ended, I was dating a prince of a guy who wasn’t ready for a family — and the pressure he felt from me to have a baby ultimately broke us up. It was around then that I started joking with my best friend, Darren, about what great parents we’d make together.
I met Darren Greenblatt 20 years ago as a freshman in college, and it was love at first sight. We had identical, self-deprecating senses of humor and a mutual love of mischief. We scammed our way onto the lists of New York City nightclubs and went on wild shopping escapades all over town. We also shared strong notions of right and wrong and a drive to be successful in life. Darren — now a fashion industry consultant in New York City — is loyal, kind, fun, generous, talented, and smart. After all this time, he knows me better than I know myself, and he’d be the perfect boyfriend, except that he already has the perfect boyfriend. For six years he’s been with Sam, a sexy, brainy guy who teaches French and African history at a prep school.
One day in the fall of 2006, we were in a lingerie shop where Darren and Sam were helping me find some sexy underwear for a date. In a total I-love-you-guys moment, I blurted out, “You two would be the best dads! When are we going to have a baby together?” We all laughed. And then we stopped laughing. It was too crazy to consider — can you imagine us all raising a child together? But as the months went on, the idea kept coming up, and our conversations about it got serious.
We spent a good year discussing it — whether we could afford it, what would happen if I moved to Costa Rica full time, or if their jobs took them away, or if, God forbid, Sam and Darren were to break up. I’m convinced we talked about having a baby more than any regular couple ever did. Ultimately, we decided that life is unpredictable, so we’d just have to roll with whatever came up, like all parents do.
By Easter of 2007, we’d made our decision. The baby would have my egg, Darren’s sperm, and Sam’s last name. We wrote up a custody strategy with the help of some lawyer friends: I’d have the child with me in Costa Rica and the guys would visit us there, then when I was back we’d all split time between New York (where they live) and New Jersey (where I live).
Because I was past the prime baby-making years, I saw a fertility specialist, who told me everything was in order. It would cost more than 10 grand to be artificially inseminated, so we figured we’d first try to do it ourselves. Sex was out of the question (it would be like sleeping with your brother), so we tried the next best thing: the turkey baster. I bought a digital ovulation monitor, and during my first fertility window, we nailed the sequence in Sam and Darren’s apartment: Darren did his thing in their bedroom, Sam ran it into the guest room where I was waiting. After he left, I sucked up the goods into the baster, did my thing, called out “OK!”, and the guys came in and we gossiped for 20 minutes. The second month we tried it, I got pregnant.
I was selective about whom I told. Being in the service industry for so many years has made me good at reading people — I knew who could handle the full explanation and who couldn’t. Most of our friends and family are progressive, so the response was pretty positive. Darren’s parents and mine pledged their support and energy. But Sam’s mother and stepfather, devout Evangelical Christians from Little Rock, Arkansas, had a harder time with it. They believe homosexuality is a sin and spend a good deal of time praying for our souls. But they ultimately came to acknowledge our baby as their grandchild, sending gifts and loving notes — which I find admirable. I was less impressed with a few of the guys’ friends in the city, who weren’t as supportive as we thought they’d be; they said it would never work out and told Darren and Sam to “get everything in writing.”
Kristine then goes on to tell how they’re sharing the parenting, tossing the baby girl (Olive) back and forth, if you will, like a football or toy that they share. (See her blog entry for details).
She then goes on to say: “And Olive will also face the challenge of having to explain her family. People ask me presumptuous questions about the custody agreement or whether her daddies play an active role or if I just asked my gay best friend for his sperm. That couldn’t be further from the truth. Darren, Sam, Olive, and I — we’re a family. We’re the real thing. I know we’ll face challenges that a regular family wouldn’t. But while plenty of married couples make great parents, some don’t! I’m just happy that my daughter has a mommy and two daddies who all love each other, and are bananas about her.”
Well, fast-forward a few years, and what do we have? A custody lawsuit from Kristine, which she lost. The idiot says she fell in love with her neighbor in Costa Rica, Alan, where she used to spend half of her time. Alan who is divorced, with kids, wanted to move to California, and Kristine wanted to be with him – without marrying, of course, these are liberals we’re talking about. So she sues to take Olive to form a family with Alan in California. And the two homos say no, the toy is ours.
Along the way, problems develop with their little “arrangement”, as the court decision summarizes:
Though “[Doug and Shawn] have always respected [Kristine] and have cooperated in sharing parenting time with her,” Kristine has sometimes not reciprocated. “[T]he court finds instances of [Kristine]’s unwillingness to allow parenting time of [Doug and Shawn] with the child”, wanting, as her mother, to spend more time with her little girl.
The Court has sided with the homos. Clearly, the court is a bunch of grotesque liberals who thinks two perverted homosexuals are legitimate parents. Not that this case offers a better alternative with the liberal mother. But this is the situation they have created: If Kristine, the mother, wants to move to be with her new boyfriend in California, she loses her daughter – and the daughter loses the only mother she has. Now granted that a woman who decided to have a baby with two homosexual pigs is clearly not fit to be a mother for any child. Nevertheless she is still the child’s mother. If Kristine is forced to stay near the homosexual couple to be with her daughter, it will break up her new relationship with Alan. Just how much resentment and bad blood will that generate between the parties? I suppose liberals are too stupid to ask the question. But the child will surely be affected by it. In the middle of it all is an innocent child, Olive, who starts off her life being in the custody of two homosexual pigs and an equally irresponsible mother, none of which can provide to the child a loving home with a mother and father who love each other. Only a demented liberal would think this is right and, what is more aberrant, that this is progress.
Listen to Kristine’s words: “Darren, Sam, Olive, and I — we’re a family. We’re the real thing.”
No, you’re just three disgusting human beings. And now you have created a complete mess of an environment for an innocent child.
Kristine was right about this: “And Olive will also face the challenge of having to explain her family.”
Indeed, let’s see how that will go when Olive tries that: OK, I have a father who is too perverted to have a healthy relationship with a woman, so he sticks his banana in the behind of this other guy, while my mother took something from him and inserted into her, to make me, but then she wanted to have this other guy stick his banana into her, but the two homos, my father and his pig of a friend didn’t like that. So now my mom is really mad at the two pigs because they took me away to live with them during the week, and they tell my mom she shouldn’t have tried to take me California, and that I should just forget her when she isn’t there, because my dad has a homo for a friend and which little girl needs a mother all the time anyways?
See, Kristine, the “real thing”!