Q. Also, how will quantum mechanics change our philosophical conceptions of what can be known for certain, if anything? All answers are open and thank you in advance for your replies!
A. Logic? No effect. Logic is what it is... a purely human invention... A branch of mathematics... A useful tool for thinking about how the world works (the quantum world included) and, for separating truth from fantasy.
Truth? Well that would depend on what you think "truth" means. If, by "truth," you mean the true nature of reality, then I would have to say that quantum physics has somewhat muddied the water. Back before Gallileo's day, all the experts were pretty confident that they knew everything there was to know about the universe, and how it worked, and our place in it. Ever since though, the more we learn, the less we seem to know. For every question that we answer, there is an immediate follow up, "But Why?" Plus, we discover three or four new questions in the process.
There must be something true about quantum physics, because it gives us predictions that are as accurate as they are surprising, but the things that it DOESN'T tell us, are maddening. QM has opened a whole new world of "But Why?"
Truth? Well that would depend on what you think "truth" means. If, by "truth," you mean the true nature of reality, then I would have to say that quantum physics has somewhat muddied the water. Back before Gallileo's day, all the experts were pretty confident that they knew everything there was to know about the universe, and how it worked, and our place in it. Ever since though, the more we learn, the less we seem to know. For every question that we answer, there is an immediate follow up, "But Why?" Plus, we discover three or four new questions in the process.
There must be something true about quantum physics, because it gives us predictions that are as accurate as they are surprising, but the things that it DOESN'T tell us, are maddening. QM has opened a whole new world of "But Why?"
Can we really say that anything can extend infinitely?
Q. In mathematics, we are taught that many functions, relations, and concepts can extend infinitely? But isn't the distance of such objects limited by the current size of the universe?
I'm going to ask this in both the Mathematics section and the Astronomy section to see if I get different answers.
I'm going to ask this in both the Mathematics section and the Astronomy section to see if I get different answers.
A. The distance of anything is limited by the size of the universe.
However, the size of the universe could be... infinite.
There is no evidence, yet, that imposes an upper limit to the size of the universe. At best, what we found so far is evidence for a lower bound (a minimum size) of at least three times the portion we can see.
The attempts by WMAP to find "curvature" to the universe ends up with showing a "flat" universe. By itself, this result does not prove that the universe is infinite (there exists finite but edgeless spaces that are geometrically flat), however it does leave the possibility open.
There is still a possibility that the universe is both flat and infinite; it could be flat and finite (but without an edge); it could be made of finite sections, each section connecting to the next one by a "fold" -- the soccer ball analogy of 2008; it could even be curved (and finite) -- but our measurements are simply not accurate enough to show the curvature.
Right now, you can use whichever one suits your idea, but you cannot prove the other ones are wrong. At least, no yet.
There are many scientists who are working on what could have existed before the Planck Time (the earliest moment we can explore with our present knowledge). For most of their ideas to make sense, the universe has to be finite in spatial extent (and it must be embedded in higher-dimension spaces).
But, so far, that is only wishful thinking. And that is not sufficient (yet) to discard the possibility that the universe could be infinite in spatial extent.
Of course, if the universe is infinite now, then it was already infinite at the Planck Time and, although not impossible, that does raise more questions.
To paraphrase a beer commercial (beer and astrophysics are compatible):
Stay curious my friend!
However, the size of the universe could be... infinite.
There is no evidence, yet, that imposes an upper limit to the size of the universe. At best, what we found so far is evidence for a lower bound (a minimum size) of at least three times the portion we can see.
The attempts by WMAP to find "curvature" to the universe ends up with showing a "flat" universe. By itself, this result does not prove that the universe is infinite (there exists finite but edgeless spaces that are geometrically flat), however it does leave the possibility open.
There is still a possibility that the universe is both flat and infinite; it could be flat and finite (but without an edge); it could be made of finite sections, each section connecting to the next one by a "fold" -- the soccer ball analogy of 2008; it could even be curved (and finite) -- but our measurements are simply not accurate enough to show the curvature.
Right now, you can use whichever one suits your idea, but you cannot prove the other ones are wrong. At least, no yet.
There are many scientists who are working on what could have existed before the Planck Time (the earliest moment we can explore with our present knowledge). For most of their ideas to make sense, the universe has to be finite in spatial extent (and it must be embedded in higher-dimension spaces).
But, so far, that is only wishful thinking. And that is not sufficient (yet) to discard the possibility that the universe could be infinite in spatial extent.
Of course, if the universe is infinite now, then it was already infinite at the Planck Time and, although not impossible, that does raise more questions.
To paraphrase a beer commercial (beer and astrophysics are compatible):
Stay curious my friend!
Is it true that in mathematics, there are more solutions than questions?
Q. I have come across this statement elsewhere but I'm not so sure if I have just misunderstood it.
But is it possible that mathematical solutions can be more than mathematical questions?
Please support you answer. Thanks!
Unique and correct solutions for each particular problem is meant here - not incorrect solutions...
But is it possible that mathematical solutions can be more than mathematical questions?
Please support you answer. Thanks!
Unique and correct solutions for each particular problem is meant here - not incorrect solutions...
A. well thats a good question
but to be honest, u can never tell which are most and least! evey day there are new generaations of solutions to open questions the same like here in YA
at the same time there r questions opened witout answers! really there r mathematical question still remain without any answer! each time a question in resolved, other questions accure..
its like that.
but to be honest, u can never tell which are most and least! evey day there are new generaations of solutions to open questions the same like here in YA
at the same time there r questions opened witout answers! really there r mathematical question still remain without any answer! each time a question in resolved, other questions accure..
its like that.
I want to know more about engineering mathematics ?
Q. I'm studying at Open University.My senior told me that engineering math are very difficult. Is it true?
A. Yes and no. In any engineering discipline math is critical, and you need a good number of courses, but if you pay attention in class, ask questions when you're confused, and do your homework, it isn't that much harder than any other technical class.
Sometimes new concepts can throw you. When you first start learning algebra, having letters stand in for numbers was a new concept. Once you "got it", the course became no harder than learning addition and subtraction. The same is true for calculus, matrix algebra, differential equations, and the other fun things they teach in an engineering curriculum.
Sometimes new concepts can throw you. When you first start learning algebra, having letters stand in for numbers was a new concept. Once you "got it", the course became no harder than learning addition and subtraction. The same is true for calculus, matrix algebra, differential equations, and the other fun things they teach in an engineering curriculum.
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