TP: Prints true. End of lesson. What lesson? You've got to think outside of the box on which JVM runs. Five apples cannot be divided among 0 people. You can call the result a "positive infinity", I call it nonsense.
Just to keep the issue in proper perspective, infinity is NOT undefined. In fact, there are orders of infinity. The one we are discussing, the limit of 1/x where x tends to zero, is called aleph null. There are higher orders of aleph, in fact an infinite number of them. To illustrate: Take a set of coordinates, x and y. Set them up as so:
As you can see, there are more entries in the box than in either the x or y axes. In fact, if you just take the diagonal, it will always have the same number of points as the entries on either axis. So what about all of the other points? Well, if the x and y axis are allowed to stretch out to infinity, or aleph null, the points described by the two axes are roughly "infinity squared", or aleph one. Anywho, that's just mathematics. You can put your own spin on whether these things are actually defined or not; I'm not here to convince you. But for people who actually want to know about the mathematics of infinity rather than the semantics, it gets quite interesting. Joe
Originally posted by Thomas Paul: And you call yourselves Java programmers?!
And I was thinking we were talking about mathematics NOT java. Do you want to talk about Java
"Thanks to Indian media who has over the period of time swiped out intellectual taste from mass Indian population." - Chetan Parekh
R K Singh
Joined: Oct 15, 2001
Originally posted by Joe Pluta: I'm not here to convince you.
AW but its maths, if 2 + 2 = 4 is true then it is true. It does not has anything to do with our emotions. I would like to help you to understand Infinity. If you still have any question then please do feel free to ask. Albeit I am not Guru but yes its the area of my interest and we can have good and intresting discussion. And as I said Infinity is relative also. Its not absolute like speed of light. And recently[with in last one yr] I read some where that there is scientiest who has proved that speed of light is not absolute. He proved that speed of light is slowing down and hence it cant be absolute and at the time of big bang it was much more than what it is today. So in one way eugene might be true that speed of light is not absolute. Jupiter theory.. Eugene can you explain that again [ November 11, 2003: Message edited by: R K Singh ]
Good points , Ravish! The physicists approach to math:
OR 2 + 2 = 0 for the correct order of magnitude.
regards [ November 11, 2003: Message edited by: HS Thomas ]
R K Singh
Joined: Oct 15, 2001
Originally posted by HS Thomas: Good points , Ravish!
2 + 2 ~_ 3 For sufficiently small values of 2. (examle 2.000000001/2.00000003 or 2^-15) Did you notice the sign. I am not able to type here correctly but the upper line of equal sign is tilde. And that means 'almost equal to', not 'equal to'.
OR 2 + 2 = 0 for the correct order of magnitude. Are you saying 2 + (-2) = 0 Size Sign does matter. If I talk in your term then 2 = 4 is true for a very large number because 2 ~_ 3 ~_ 4 hence 2 ~_ 4 for a very large number. But note it is "assumed" to be equal in comparision to a very large number. BUT it is "not" equal to. AW dont mix Physics with Mathelatics. Physics makes use of mathematics to prove its hypothesis [obviously by distorting maths and assuming tons of thing.] Oh yes, physics. Anyone how do we get the value for Universal constant G = 6.67 X 10^-11 ??? Because it proves one hypothesis. If I change the value, hypothesis will be wrong. And this is true for all physics laws. Still people/scientiests are looking for "Universal law" which holds true for all conditions/worlds. If I am not wrong physics itself says that laws of "this" world will not be true in other world (for example black hole). So inside blackhole speed of light might(will) not be absolute. OR physical laws will not behave as per this world. [ November 11, 2003: Message edited by: R K Singh ]
Joined: Oct 08, 2001
And recently[with in last one yr] I read some where that there is scientiest who has proved that speed of light is not absolute. He proved that speed of light is slowing down and hence it cant be absolute and at the time of big bang it was much more than what it is today. You are probably thinking of Joao Magueijo, a theoretical physicist and author of the book Faster Than the Speed of Light: The Story of a Scientific Speculation Jupiter theory.. Eugene can you explain that again Certainly. The Jupiter theory states that the paths of philosophy and physics diverged so much that neither branch along can explain a natural phenomena. The physicists have been preoccupied with the scientific methods, experiments, and formal proofs, employing methematics to prove the existence of something that doesn't exist. When such a proof surfaces in a scientific journal, the autrhor gets a Nobel prize and the public thinks that a mankind made a giant step forward in their progress. Yet the fundamental question "why" is of secondary consideration to hard science. Newton never explained why gravitation happens, -- he just experimented with motion, derived his laws, and "proved" them (the proof was scientific, but goofy, of course). More than 200 years later, Einstein experimented, derived his relativity theories, proved Newton wrong, and explained why gravitation happens, -- it's the same as accelarate motion, caused by the objects distorting the shape of space around them. The fundamental principle underlying the special theory of relativity is the absoluteness of speed of light, in all frames of references. But Einstein never explained why light is so special. Thus the Jupiter Theory, -- from philosophical point of view, the speed of light is as absolute (or is as relative) as the speed of Jupiter. But forget philosophy for a moment. Even if you apply pure science, you would find that the special theory of relativity is inconsistent with quantum mechanics, yet both theories have been proven with countless experiments. On one hand, special theory argues that no disturbances of any kind can propagate faster than the speed of light, and it proves it with the experiments. On the other hand, quantum theory argues that the disturbance in one spot can instanteneously affect something in another spot, and the theory proves it with the experiments. This is a dead end. The Jupiter Theory offers a solution, -- a new framework for exploration of the world. This new framework blends physics and philosophy into a single mode of discovery. The question "What is good?" is as scientific in this new framework as the question "What is the weight of this object?". An experiment along cannot be accepted as a proof for a theory any longer. To be legitimate, it must answer the question "why?", and it must appeal to emotions as well as reason.
Joined: Jun 23, 2003
I would like to help you to understand Infinity. And as I said Infinity is relative also. Its not absolute like speed of light. Thanks, but I already understand infinity, at least as well the average normal human mind can comprehend it . Infinity is the concept of an uncountable number, such as the set of all positive integers. It has interesting properties: for example, it is also the count of the set of all integers, positive or not. The original question was about whether the Lorentz transformation implied that it required infinite energy to get to the speed of light, because as the body's velocity approached the speed of light, the divisor tends towards zero. This is a simple calculus exercise yielding a simple answer of infinity (aleph null).
And recently[with in last one yr] I read some where that there is scientiest who has proved that speed of light is not absolute. He proved that speed of light is slowing down and hence it cant be absolute and at the time of big bang it was much more than what it is today. Not quite right. A professor in Sydney proposed it (not "proved it") over a year ago based on his interpretation of experimental data, and we've heard nothing from him since. If there had been any truth to his hypothesis, we'd have heard more. At the same time, there have been lots of theories about a variable speed of light; that in itself proves nothing. The issue is what happens when we try to accelerate a body to the speed of light, whatever it may be in our frame of reference. Joe
Joined: May 05, 2000
And recently[with in last one yr] I read some where that there is scientiest who has proved that speed of light is not absolute. He proved that speed of light is slowing down and hence it cant be absolute and at the time of big bang it was much more than what it is today. Let's not get carried away! A scientist theorized based on some observational data of quasars that the fine structure constant has decreased by 1/1,000,000,000th over the life of the universe. The fine structure constant is a ratio of the speed of light to the electric charge of the electron. It is believed that if the electron charge had changed this would violate the second law of thermodynamics. This leaves the speed of light as having changed by 1/1,000,000,000th over the life of the universe. Now you have to realize that this is extemely tentative. It is based on measurements of wavelengths of light that passed through atoms in the early universe. They believe that the light they are observing shows evidence of not being exactly shifted the way it should be. There are other possibilities however that could effect their observations. So what is the end result? The raw data that the scientists based their conclusions on is probably wrong. Further research has not substantiated the initial findings.
In Faster Than the Speed of Light, Magueijo reveals the short, brilliant history of his possibly groundbreaking speculation--VSL, or Variable Light Speed. This notion--that the speed of light changed as the universe expanded after the Big Bang--contradicts no less prominent a figure than Albert Einstein. Because of this, Magueijo has suffered more than a few slings and arrows from hidebound, jealous, or perplexed colleagues. But the young scientist persisted, found a few important allies, and finally managed to shake up the establishment enough to get the attention he merited and craved. Magueijo begins the book with a suitably accessible explanation of special and general relativity, then moves on to the ideas that laid the groundwork for VSL. In the process, he rips the doors off of scientific academia and airs quite a bit of dirty laundry. Comparing himself to Einstein throughout the book, Magueijo approaches his topic and its dissemination with cocksure genius, expecting readers to sympathize with him as he battles to win favor. And we do.
The speed of light, one of the most sacrosanct of the universal physical constants, may have been lower as recently as two billion years ago - and not in some far corner of the universe, but right here on Earth. . . . Throughout the debate, physicists who argued against any change in alpha have had one set of data to fall back on. It comes from the world's only known natural nuclear reactor, found at Oklo in Gabon, West Africa.
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The limit of 1/x as x approaches zero is infinity, but dividing five apples among zero people is merely undefined. That is, the number of apples per (non-existing) person is whatever the h*ll you want it to be. And there will always be a remainder of five.