http://plus.maths.org/content/do-infinit...t-nature-0
EXCERPT: What would you see if you came to the edge of the Universe? It's hard to imagine so it's tempting to conclude that the Universe doesn't have an edge and therefore that it must be infinite. That's not a necessary conclusion however. There are things that are finite in extent but still don't have an edge, the prime example being the surface of a sphere. It's got a finite area but when you walk around on it you'll never fall over an edge. The question of whether the Universe is finite or infinite is one that still hasn't been answered, and there are mathematical models that allow for both possibilities. More generally, the question of whether any infinite quantities can arise in the Universe is a deep one.
[...] "What people understood early on was that the inflationary theory gives a whole bunch of suggestive predictions, many of which have come true and many of which will be tested in upcoming experiments. That gives us a lot of confidence in inflation, but it also has very interesting side effects." [...] One of these side effects is that inflation might have gone on at different rates in different regions of the Universe. In some region, the rapid doubling in size will have stopped after a while, resulting in a region of observable Universe like ours. In other regions though, because of spatial variations in the make up of the universe, inflation might go on forever. "You have an infinite spacetime not because you've postulated spacetime is infinite, but because you thought of a process that naturally leads to an infinite spacetime," says Aguirre. "I think that's a very interesting difference, because you can test that process in other ways." If your tests make you believe that this is what actually happened, then the infinity of spacetime pops out as a result of a consistent theory.
Intriguingly, theory also suggests that the extent of space and time depend on your view point. With his general theory of relativity Einstein told us that time and space are inextricably linked, hence the term spacetime. If you want to say something about space or time separately, you need to chop that spacetime up mathematically. "It turns out that even questions like 'Is space finite or infinite?' can depend on how you define space and time separately," explains Aguirre. "There is spacetime, that's what Einstein teaches us; we can choose to cut it into space and time separately in many different ways. They're all fundamentally valid, they'll all give the same results to any particular experiment we think of, but they have different intellectual implications and some are much more convenient for certain purposes than others."
"If you've got an infinite spacetime, there will often be certain ways that you can cut it up so that it looks like the Universe is, say, finite and expanding. [It may be expanding] forever and getting infinitely big, but at any time it's finite. At the same time, the very same spacetime can be chopped up in such a way that at any time it's spatially infinite, so it's an infinite, expanding Universe." In an inflationary Universe it turns out that once the inflation stops there is a most natural way of chopping it up; a way in which the Universe is close to homogeneous. And this gives a Universe that is spatially infinite. "Inflation very naturally gives rise to homogeneous infinite universes that would evolve into something like what we see. I think it's really neat that we can get suggestive evidence for such a rich, and multifaceted, and interesting picture [in which] the Universe is infinite." [...]
http://plus.maths.org/content/coincidenc...and-chance
EXCERPT: Football fans pay attention! How would you like to make hundreds, maybe even thousands, of pounds each week by betting on your favourite team, guaranteed to get the result right every time? Well, now you can. I have devised a computer program, based on complex statistical algorithms, which is 100% accurate every time ... and I am willing to sell one of a limited number of copies to you for the modest sum of £1,000.
It may seem like a lot of money, but just think, you could make it all back in a single bet. I know you'll need convincing — after all, who wants to part with a thousand pounds without some sort of guarantee — so I'll give you the first prediction for free. In fact, I'll send you one free prediction every week for the next five weeks, and when you see I'm 100% accurate I can guarantee you'll be praying there is still a copy of the program left.
Imagine you received this email from me just before the start of the football season. Would you have taken up my offer and sent me £1,000? Of course not. But what if my first prediction had been correct? Luck, you'd have thought. But what when the second and third predictions were also correct? What about when all five turned out to be correct?
At some point, surely even you would have been convinced. After all, no one's luck is that good. Is it?
So, do you take me up on my offer: yes or no?
Well, if you said yes, I'm afraid you've just thrown away £1,000. Because there is no software, no statistical method. In fact, there isn't even luck. Just quantity....
http://www.theepochtimes.com/n3/1037968-...-the-past/
EXCERPT: ...If one day a time machine is built based on Dr. Mallett’s design, what may happen when the switch is flipped? A message from the future could instantly appear.
The time machine would only be able to send information along the timeline from when the machine is first turned on until when it is turned off. So, if it stays on for 100 years, binary messages could be sent to any time within those 100 years. Someone from the future may know that the machine will be activated on a given date and send a message through to that time.
In a BBC-Discovery Channel documentary featuring Dr. Mallett’s work, the narrator said that with time travel, “At stake is nothing less than what it means to be a human being.”
If we could go back in time and fix all the suffering of the world, if we could go back and prevent the bad things that happen in our lives, what would that do for personal growth and wisdom? How would our society change?...
Posted by: C C - Oct 26, 2014 05:37 PM - Forum: Art & Music
- No Replies
http://www.newyorker.com/magazine/2014/1...-ex-musica
EXCERPT: Beethoven transformed music—but has veneration of him stifled his successors? ... For this conundrum—an artist almost too great for the good of his art—Beethoven himself bears little responsibility. There is no sign that he intended to oppress his successors from the grave. Although he expected that posterity would take an interest in him—otherwise he would not have saved so many of his sketches—he did not picture himself in the magniloquent terms employed by Hoffmann and others. “Everything I do apart from music is badly done and stupid,” he once wrote. And the music was the butt of withering self-criticism. On the subject of his late string quartets, which generations of listeners have hailed as a pinnacle of Western civilization, Beethoven once remarked to his publisher, “Thank God, there is less lack of imagination than ever before.” The comment remains staggering after nearly two hundred years, not merely because of the radical understatement—it would be like Shakespeare saying, “ ‘The Tempest’ is not as trite as my earlier plays”—but because of the implicit challenge to contemporary musical life. To perform Beethoven to the exclusion of the living is to display a total lack of imagination....
http://www.prospectmagazine.co.uk/features/are-we-free
EXCERPT: ...The mistakes are so obvious that one sometimes wonders how serious scientists could make them. What has lowered their threshold for careful analysis so catastrophically? Perhaps it is the temptation of glory. What a coup it would be if your neuroscience experiment brought about the collapse of several millennia of inconclusive philosophising about free will! A curious fact about these forays into philosophy is that almost invariably the scientists concentrate on the least scientifically informed, most simplistic conceptions of free will, as if to say they can’t be bothered considering the subtleties of alternative views worked out by mere philosophers. For instance, all the experiments in the Libet tradition take as their test case of a freely willed decision a trivial choice—between flicking or not flicking your wrist, or pushing the button on the left, not the right—with nothing hinging on which decision you make. Mele aptly likens these situations to being confronted with many identical jars of peanuts on the supermarket shelf and deciding which to reach for. You need no reason to choose the one you choose so you let some unconscious bias direct your hand to a jar—any jar—that is handy. Not an impressive model of a freely willed choice for which somebody might be held responsible. Moreover, as Mele points out, you are directed not to make a reasoned choice, so the fact that you have no clue about the source of your urge is hardly evidence that we, in general, are misled or clueless about how we make our choices....
http://www.laphamsquarterly.org/time/grand-illusion
EXCERPT: What science can tell us something about is the psychology of time’s passage. Our conscious now—what William James dubbed the “specious present”—is actually an interval of about three seconds. That is the span over which our brains knit up arriving sense data into a unified experience. It is also pretty clear that the nature of memory has something to do with the feeling that we are moving in time. The past and the future might be equally real, but—for reasons traceable, oddly enough, to the second law of thermodynamics—we cannot “remember” events in the future, only ones in the past. Memories accumulate in one temporal direction and not in the other. This seems to explain the psychological arrow of time. It does not, unfortunately, explain why that arrow seems to fly....
Rebecca Newberger Goldstein’s “Plato at the Googleplex: Why Philosophy Won’t Go Away” is published by Atlantic Books
http://www.prospectmagazine.co.uk/blogs/...n-teach-us
EXCERPT: The philosopher and mathematician AN Whitehead described the history of philosophy as a “series of footnotes to Plato”. Do you agree with him?
If that were the case, what a silly field philosophy would be! A 2,400-year-old man had all the answers? I would like to think that what he meant was that this methodology, this view of maximising coherence, was begun by Plato and that he also formulated questions from a wide range of different areas of inquiry—mathematics, epistemology, metaphysics and political theory—and saw their commonality. In that sense, you can say that all philosophy follows in Plato’s footsteps.
Was Plato a “Platonist” in the modern sense of being committed to a claim about the existence of abstract entities, numbers for example?
The one area of philosophy in which Platonism is constantly referred to is philosophy of mathematics. There was apparently a survey done by the American Mathematical Association and something like 98 per cent of mathematicians described themselves as “Platonists”. There is [in mathematics] very much a sense that you’re discovering rather than inventing. So this is a kind of commitment to the existence of the abstract, but necessarily in insolation from the physical—the structure of physical reality is given by the abstract, but the abstract can’t be reduced to sensory particulars. So it doesn’t have to involve a commitment to a kind of Platonic “heaven” that Russell, for example, makes fun of; it can be the claim that reality can’t be intelligible without referring to abstractions which cannot themselves be reduced to anything other than themselves.
Was Plato a Platonist? Well, there’s the Platonism of the forms which I think he gave up. In the Parmenides, he really criticises the theory of forms. It’s interesting that Socrates is a young man there and he can’t answer Parmenides’ questions. In the Timaeus, which is one of my favourite dialogues, it’s not the forms, it’s mathematics that is the key to intelligibility.
Every theoretical physicist I’ve ever known has believed that not only is reality given to us in the language of mathematics, but that when we have two empirically adequate theories, you go with the one that has the most beautiful mathematics—that’s in the Timaeus too. That’s a Platonism that’s still working. When my scientist friends say that the structure of reality is given in the most beautiful mathematics, I say to them, “That’s a metaphysical argument you’re using right there.” Steven Weinberg said of string theory, “Maybe it’s not true, but we’re going to find some application for it, because never in the history of science has it been the case that such beautiful mathematics didn’t somehow reveal reality.” Whoah! That’s Plato!
