Of course the answer is that there isn't an answer to this question. Some of you came to a talk I gave a few weeks ago, which was largely to promote my new book about infinity, the infinite book. The differences are small. As it does, these pairs of particles move away from one another, and dramatically, the whole system goes to infinite size in finite time, undergoing an infinite number of oscillations as it does so. How does this work? He wants to prove that if you write down all the never ending decimals, things like pie and so forth, there are an infinite number of them, but is it an uncountable or a countable infinity? The word is chucked about a lot by some people trying to express how huge something is ~ and although in physics and math it is understood what it means ~ most people just think ot it as meaning SO bloody many that it would take way too long to count. The world would be full of unfinished projects because there would be no end to the amount of advice that would need to be taken before they could be completed. How long will it take to cook a 12 pound turkey? This is much closer to home in a way, easier to understand. But if you now look at the series, you’ll see that your infinite switchings creates a very odd, ambiguous situation. Infinity sign never gets old because it owns great eternal love significance. equation can go beyond the critical space as infinity includes all points. What is the birthday of carmelita divinagracia? But curiously, they’re not ruled out by relativity or by conservation of energy or other laws of physics. We tend automatically to think of infinity as being big, but you have to remember that it can also be very small. It seems reasonable. There’s a wonderful graphic example that builds on this paradox, which was created by David Hilbert, who we mentioned earlier, who was a great enthusiast for infinities, and it’s the idea of having an infinite hotel. There’s a little story about Hilbert that I told when I talked the other week; I can’t resist telling it again. The whole idea of taking infinity and putting it in mathematics, in a quantity that you can manipulate, and prove theorems about was very controversial in Germany when these ideas were first presented. It doesn’t behave like any number, no matter how big it is. So just to carry on talking about the mathematical type of infinity, the first thing to appreciate about mathematical infinities is that infinity is not a big number. What is the conflict of the story of sinigang? There is no largest infinity. This might be something like numbering the stars in a universe that goes on for ever; it’s something where you never get to the infinite number in the count, it’s a so-called potential infinity. How many zeros are in a gazillion? This story becomes more interesting if we focus on this type of universe which starts expanding, reaches a maximum and then contracts to a big crunch in the future. But let's put it another way. Join Abigail Bollenbach in this new video series, where she’ll take you on a different cosmic adventure each week. Beyond the infinity known as ℵ 0 (the cardinality of the natural numbers) there is ℵ 1 (which is larger) … ℵ 2 (which is larger still) … and, in fact, an infinite variety of different infinities. You might indeed find that people in the end were clamouring for a finite life if they were given eternal life under the same conditions that we know and appreciate today. What would life imprisonment mean? I want to not live on in the hearts of my countrymen; I want to live on in my apartment.” Very sound thinking. If you asked how many sevens are in the number 21, I’d say three. This is called the lemniscate - it’s a graph, in effect, in polar co-ordinates that was first written down by Jakob Bernoulli, one of the famous Bernoulli family of mathematicians. Suppose we try and do some arithmetic on Nietzsche’s idea. You can have a space time where you can send your computer off on a path and it will do an infinite number of steps, but that possibility means that any radiation that latches on to the same path, as it was incoming, would have its frequency driven to infinity as it followed the computer around, so these types of universe are unstable. Infinity, rather like buses, come in threes; there are three types of infinity which we might attempt to distinguish, and I’ll have a fair bit to say about the first two in this talk. There is another way to look at this question. You shouldn’t think of it as being rather like an extremely large number, only just a little bit bigger. * We ask whether it is possible for physical infinities to arise in the universe and whether a machine could ever complete an infinite number of tasks in a finite time. On the one hand, the potentially infinite universe of stars and galaxies, as we would now call them, but on the other hand, what Pascal regarded as much more subversive potentially, the infinitely small, because if the world was infinitely divisible, then within your hand in front of you, there was a manifestation of something which was physically infinite. To infinity and beyond - the quest for SOAP interoperability By Sam Ruby, February 1, 2002. My way of looking at this is like this. If you were to line up all the natural numbers and all the real numbers side by side in two columns, the real numbers would stretch beyond the infinity of the natural numbers. So what does that mean? What’s more than infinity? In Newtonian physics, it turns out that super-tasks are possible. But the infinities were rather controlled, in that you could imagine that your answer had two pieces in the calculation, one bit was infinite and the other bit was finite. Well, infinity, or lazy eight as it seems to be called in America, as a piece of iconography has a relatively short history. Interesting question, if I’m reading it correctly. ... which should be read as a one followed by sixty zeros -- and is a number so large it might as well be infinite. Some people regard this as so unsatisfactory that they think it’s a powerful argument for the universe being finite, but in a modern picture of the astronomical universe, it’s not such an alarming idea. If you’re Abraham Robinson, a mathematician of the 20th century, a so-called finitist, you don’t believe in any of these things. Suppose you have a desk lamp and you have a switch programmed on it such that for the first half minute, it is on, for the next quarter minute, it’s off, for the next eighth minute, it’s on, off, on, and so on forever, or not quite forever, but an infinite number of switchings, and the question is, after one minute, is the lamp on or off? * We look at the different conceptions of 'infinity' that exist in mathematics, science and philosophy. All that’s a signal of is that you haven’t included in your description the friction of air as completely as you could have, and if you do, you’ll get a shockwave – a very sudden change, but not an infinitely quick change. ... all basically comparing a pair of zeros and ones and passing on the results. The two ideas were closely linked, because he argued that if you had a region that was a perfect vacuum, then motion would have no resistance when it moved through it, and it would move to infinite velocity. To infinity and beyond. The lesson from this is that infinite series that diverge or alternate; they don’t have uniquely defined sums that you have to define the process by which you’re producing the sum as well. The great area where infinity has been paramount in the discussion of what’s going on is the search for a fundamental theory of elementary particles, and until 1980, for nearly 40 years, the working theories of particle physics were bedevilled by the so-called problem of infinities, that you could do calculations to predict what you should see in experiments, but you got infinite answers from those predictions.