Posted on 02/20/2015 6:01:20 PM PST by LibWhacker
I’m almost 62 now and I have yet to have an answer to my question. It is something that Mankind will never really know, unless the next Star Trek Movie explains it of course.
How anyone can look up at the Night Sky and think all of this is just some sort of coincidence baffles me to this day.
The odds are beyond staggering, but it doesn’t matter to some people. They think the Science is settled, LOL.
The question is a contradiction in terms. "Where" assumes the existence of space. That's what she ought to have said while you were sitting on the front stoop.
Cordially,
However, the set of all real numbers is uncountably infinite.
His whole point is that he expects us to discover there is a finitely smallest unit of space. In finding that we will resolve a number of the conundrums that result from quantum mechanics, and especially trying to combine quantum mechanics with relativity.
I just finished reading David Foster Wallace's book "Everything and More". When dealing with infinite quantities mathematicians have to be very careful how they state things. Having an infinity and an equal sign in the same equation is almost always a bad idea.
It's the expression "ten times smaller" that makes me bang my head against the desk. Are they being deliberately ambiguous or really that ignorant?
Good science is good. But ya have great points. Coincidence, Creator or whatever, man want’s to know. It’s the nature of the beast. Answering the infinite question.
Very clever.
“My own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose.”
J. B. S. Haldane (5 November 1892 – 1 December 1964) was a British geneticist and evolutionary biologist.
Similar remarks that seem derived from this have in recent years been attributed to Arthur Stanley Eddington, as well as to Haldane, but without citations of an original source.
I like the queer version.
Yeah, I caught that after my post. See #34.
“Inside the museums, infinity goes up on trial”
B.Dylan
If you know L'Hospital's Rule, you can easily construct limits which superficially appear to be indeterminate forms like ±∞/±∞, 0/0, 1∞, ∞0 which can be constructed from actual limits which are +∞, -∞, 0, 1, or any real number.
For example:
limx→∞ (1+x)α/x. Superficially, this looks like 1∞. But, for every N, no matter how large it may be 1N = 1. This is pretty much a textbook definition that the idea of 1∞ = 1. However [you can verify this very quickly with a calculator or by plugging numbers into the google web page search] You can make the above limit any positive real number by choosing α correctly. For example, if α = 1, then limx→∞ (1+x)1/x = e. If α = 0, that limit = 1, If α = -1, it's 1/e. If α = ln(π) limx→∞ (1+x)α/x = π.
You can do the same thing with any indeterminate form that looks like ∞/∞. Just tune the limit properly and it can be 0, ∞, or any other number you like, including the OP's "1." That's why indeterminate forms are symbols, which have no meaning.
The number of reals is infinite. The number of integers is infinite. The statement [number of reals]/[number of integers] has no meaning. The cardinality of the reals is greater than that of the integers. There is no bijective function [1-1 and onto] that maps the integers to the reals. There is a "sense" in which there are more reals than integers, but that "sense" is not translatable in terms of "the number of objects in the sets," because both are infinite.
Infinities are to mathematicians as high current live wires are to electricians: There are tools for handling them, and they won't harm you as long as you're careful. Rigor is the key.
This physicist may want to get rid of the concept of infinity in physics, but he can't. The reason he can't is that he cannot get away from the concept of zero. And as long as you are talking about zero, infinity is always on the other side of that coin.
Because, to be "infinitely small" means EXACTLY this: no matter how small it is, there is something smaller. We have a name for that: it is zero. A thing which is smaller than all other things has no existence.
It's been half a lifetime since Calculus; could you remind me what is L'Hopital's Rule?
If you try to find the limit of liberals’ stupidity, you’ll see that infinity does indeed exist.
Hasn’t quantum mechanics abolished the concept of infinitely small already? Isn’t the planck length the point at which the universe “pixilates” — that is, at which no smaller thing could exist? Or does the theory of inflation suggest that the size of the planck length itself has grown?
Also: How weird would it be if there isn’t enough matter in the universe to cause a Big Crunch, but there is something else altogether which would limit the universe’s size before Heat Death? Some force or property of space which limits expansion, the way you can only stretch a waistband so far before it resists further stretching?
Hi-di-ho ho-di-hi
modern kids:
https://www.youtube.com/watch?v=gcq4Tq68KJk
old school:
https://www.youtube.com/watch?v=z7at9X_ympQ
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.