Fermat's Last Theorem on an + bn = cn never works for any integers greater than two. Pierre de Fermat wrote that he had a proof for this theorem but no one has ever discovered it. No one has ever been able to reproduce the proof since, until mathematician, Andrew Wiles, developed a proof in 1994, fulfilling a dream he had since childhood.
Wiles achieved this great feat using the Taniyama-Shimura conjecture proposed in 1955. Sadly, Taniyama committed suicide in 1958. However, Shimura did live to witness Wiles's use of their conjecture in his proof of Fermat's Last Theorem.
Anyway, it is remarkable that Wiles was able to develop this proof, but Wiles used a 20th Century conjecture to develop his proof, so we know that this is not the same proof that Fermat had worked out since he worked it out in the 17th Century. So what was his Fermat's proof? Will we ever know if it truly existed, and/or what it was?
Tuesday, May 14, 2013
Is infinity squared larger than infinity?
I am right!
No I am right!
I am right times infinity!
No, I am right infinity times infinity!
When I was a child, my late brother, Sam, and I had many arguments. One that stood out was the largest known animal. I was big supporter of marine animals and he was a die-hard dinosaur fan. He said Seismosaurus. I said the Blue Whale. We got into an argument, and infinity times infinity came up.
This is puzzling, because infinity is supposed to be "infinite" after all, but can infinity be manipulated in quantity, say only all odds, or evens, or multiplying infinity by itself? I was reading about a mathematician that came up with some interesting ideas about the different quantities of infinity. He considered adding a decimal to every number and then having infinite decimal places for each number. I read that he ended his life in an insane asylum. Some say that it was due to his deep ponderings of infinity and some say it was more because of how many of his ideas were poorly received in his time.
Some mathematicians refused to accept infinity. They say it does not exist. The universe is finite and infinity is just something dreamed up in our heads, but is it really?
Most cosmologists accept the idea of inflation, that the universe blew up much like a balloon after the Big Bang. This inflation occurs faster than light speed. So space-time is expanding faster than we could ever travel to find its edge. This would mean to me that like Schrodinger's cat, infinity would both exist and not exist at the same time. Since no matter how far you traveled there would always be more space in "front" of you, but at the same time the expansion is just occurring faster than the cosmic speed limit, so it is finite? Right? I don't know, just a thought. I have considered that the physical "reality" that we perceive actually has the same properties of quantum mechanics, and the infinity idea is one example.
Many theorists think that if you reached the "edge" of the universe that it would just loop back on itself. This would mean that if you were able to take a wormhole across the universe, you could end up standing behind yourself watching yourself enter the wormhole. Very interesting.
Another big theory being thrown around of the multiverses: one is that there are infinite universes, meaning that also that there would be infinite versions of yourself in these other multiverses. I was thinking of developing a way to escape our little version of reality to see what else is out there. Then I realized that if the math was right about the infinite copies of me, as I am travelling to the other multiverses, I would then run into infinite Mes making their own little escapes from their realities. What would this mean? What would be the consequences, if any, to this sort of infinite encounter? Would our little universe be destroyed due to the overload of matter caused by the infinite Mes? And would all of their universes also suffer a similar fate? Well if the universe we experience is finite, then surely infinite copies of me would be too much for it, but if it is expanding faster than it is filling up, perhaps our universe would be ok, and maybe we would all just switch places in each universe/multiverse ensuring each ones sustainment. I could continue on with this rambling, but I will leave that for a later blog. There is much to be said about infinity, apparently.
No I am right!
I am right times infinity!
No, I am right infinity times infinity!
When I was a child, my late brother, Sam, and I had many arguments. One that stood out was the largest known animal. I was big supporter of marine animals and he was a die-hard dinosaur fan. He said Seismosaurus. I said the Blue Whale. We got into an argument, and infinity times infinity came up.
This is puzzling, because infinity is supposed to be "infinite" after all, but can infinity be manipulated in quantity, say only all odds, or evens, or multiplying infinity by itself? I was reading about a mathematician that came up with some interesting ideas about the different quantities of infinity. He considered adding a decimal to every number and then having infinite decimal places for each number. I read that he ended his life in an insane asylum. Some say that it was due to his deep ponderings of infinity and some say it was more because of how many of his ideas were poorly received in his time.
Some mathematicians refused to accept infinity. They say it does not exist. The universe is finite and infinity is just something dreamed up in our heads, but is it really?
Most cosmologists accept the idea of inflation, that the universe blew up much like a balloon after the Big Bang. This inflation occurs faster than light speed. So space-time is expanding faster than we could ever travel to find its edge. This would mean to me that like Schrodinger's cat, infinity would both exist and not exist at the same time. Since no matter how far you traveled there would always be more space in "front" of you, but at the same time the expansion is just occurring faster than the cosmic speed limit, so it is finite? Right? I don't know, just a thought. I have considered that the physical "reality" that we perceive actually has the same properties of quantum mechanics, and the infinity idea is one example.
Many theorists think that if you reached the "edge" of the universe that it would just loop back on itself. This would mean that if you were able to take a wormhole across the universe, you could end up standing behind yourself watching yourself enter the wormhole. Very interesting.
Another big theory being thrown around of the multiverses: one is that there are infinite universes, meaning that also that there would be infinite versions of yourself in these other multiverses. I was thinking of developing a way to escape our little version of reality to see what else is out there. Then I realized that if the math was right about the infinite copies of me, as I am travelling to the other multiverses, I would then run into infinite Mes making their own little escapes from their realities. What would this mean? What would be the consequences, if any, to this sort of infinite encounter? Would our little universe be destroyed due to the overload of matter caused by the infinite Mes? And would all of their universes also suffer a similar fate? Well if the universe we experience is finite, then surely infinite copies of me would be too much for it, but if it is expanding faster than it is filling up, perhaps our universe would be ok, and maybe we would all just switch places in each universe/multiverse ensuring each ones sustainment. I could continue on with this rambling, but I will leave that for a later blog. There is much to be said about infinity, apparently.
The Trouble with Gravity
Gravity is one of the four forces in physics. I have read a lot about this force and how it has shaped the universe. I first became interested in gravity when reading about Einstein and Newton. These two gentlemen's ideas intrigued me. One thing stood out to me in Einstein's theories of space-time. Basically space-time is warped by the bodies placed in it, such as planets and even Newton's apple.
I have also done research into quantum mechanics, and I have read that physicists are searching for "gravitons" little particles of gravity. My trouble is that I had come to think of gravity as sort of a displacement of space-time. It does not make sense to me that a particle should be expected. If you are mixing cookie batter, and you place chocolate chips in the batter, the rest of the batter must move to accommodate the chips. A new particle is not introduced to cause the displacement besides the chocolate chips, themselves.
I emailed one of my favorite theoretical physicists about this, Brian Greene, but I have not heard back. I figure he is either too busy, or he thinks my question is too ridiculously simple to waste his time. Oh well. I hope to get answers from some of my physics professors, because I must be missing something if all of these well-educated individuals all believe gravitons are waiting to be discovered.
If, and its a big if, the gravitons do not exist and gravity is simple space-time displacement, would that fix the issue we have been having on the search for the theory of everything? If gravity is mere "displacement" does it belong in the major forces category at all? I am sure that my ignorance is probably why I am not understanding this, but I need more information to resolve my trouble with gravitons.
My ex-boyfriend from many years ago said to me, "There is no such thing as gravity. The Earth just sucks." Maybe he was right. LOL
I have also done research into quantum mechanics, and I have read that physicists are searching for "gravitons" little particles of gravity. My trouble is that I had come to think of gravity as sort of a displacement of space-time. It does not make sense to me that a particle should be expected. If you are mixing cookie batter, and you place chocolate chips in the batter, the rest of the batter must move to accommodate the chips. A new particle is not introduced to cause the displacement besides the chocolate chips, themselves.
I emailed one of my favorite theoretical physicists about this, Brian Greene, but I have not heard back. I figure he is either too busy, or he thinks my question is too ridiculously simple to waste his time. Oh well. I hope to get answers from some of my physics professors, because I must be missing something if all of these well-educated individuals all believe gravitons are waiting to be discovered.
If, and its a big if, the gravitons do not exist and gravity is simple space-time displacement, would that fix the issue we have been having on the search for the theory of everything? If gravity is mere "displacement" does it belong in the major forces category at all? I am sure that my ignorance is probably why I am not understanding this, but I need more information to resolve my trouble with gravitons.
My ex-boyfriend from many years ago said to me, "There is no such thing as gravity. The Earth just sucks." Maybe he was right. LOL
Friday, May 10, 2013
Will Reversal of Entropy Lead to a World Power Fight over the Remote?
Recently, I read some findings from a lab in Germany where an experiment had been conducted to surpass absolute zero. In theory this state really did not exist, but when this feat had been accomplished, the scientists observed the strange behavior of the particles in this extreme state. It was expected that there would be no energy at absolute zero, but these particles were in super-high energy states. The paper I read explained that this could mean properties such as entropy reversal.
Now this is very important to me, because I imagine what wonders we could do, if such a tool was developed. I imagined tissue damaged or lost in a bad accident being completely restored to its original condition. I imagined accident clean-ups, or s crime fighting tool. Perhaps regeneration from reverse entropy could keep people from aging and maybe even defend us from death.
Now, of course, all of these ideas do not exist, yet, but these are the sorts of things I ponder over, frequently. Now, as I thought of all the wonders we could do, I then imagined some of the evils that could also occur. Two warring nations may use such a devise to reverse outcomes or to have more than one chance at a successful attack.
I imagined two world leaders with remote controls in their hands fighting over what outcome would be the final one, much like two sibling might fight over which program or what part of a show or movie was to be watched. So then I thought, maybe if I am ever involved in such research that I should not tell anyone, but that just didn't seem right either, and it does seem to me that eventually all secrets will be made known, and if one withholds information from peace seeking nations, the hostile ones may steal the technology and develop a counter device. Then we would really be in for a fight.
Just some speculations on the positive developments that could come from such research, and then on the other hand the nightmare that could also happen if such powerful technology is used for destructive purposes.
Now this is very important to me, because I imagine what wonders we could do, if such a tool was developed. I imagined tissue damaged or lost in a bad accident being completely restored to its original condition. I imagined accident clean-ups, or s crime fighting tool. Perhaps regeneration from reverse entropy could keep people from aging and maybe even defend us from death.
Now, of course, all of these ideas do not exist, yet, but these are the sorts of things I ponder over, frequently. Now, as I thought of all the wonders we could do, I then imagined some of the evils that could also occur. Two warring nations may use such a devise to reverse outcomes or to have more than one chance at a successful attack.
I imagined two world leaders with remote controls in their hands fighting over what outcome would be the final one, much like two sibling might fight over which program or what part of a show or movie was to be watched. So then I thought, maybe if I am ever involved in such research that I should not tell anyone, but that just didn't seem right either, and it does seem to me that eventually all secrets will be made known, and if one withholds information from peace seeking nations, the hostile ones may steal the technology and develop a counter device. Then we would really be in for a fight.
Just some speculations on the positive developments that could come from such research, and then on the other hand the nightmare that could also happen if such powerful technology is used for destructive purposes.
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