Based on your definition, who should have problems understanding there is a contradiction in this statement: "Turn left and right at the exact same time"?
Based on your definition, who should have problems understanding there is a contradiction in this statement: "Turn left and right at the exact same time"?
Please note that your local-only view prevents your mind to get my answer.Please note that you did not answer my questions.
To illustrate let us consider two “set”s each containing a single object: a line-element. The line-elements are intersecting but non-coincident everywhere. The intersection of these two “set”s is a “set” containing points which are fundamentally different from line elements (we can not say that a point is a line-element with one point as the arguments in this section prove that a line-element is not a collection of points). Similar arguments can be extended to higher dimensions.
In this section we will demonstrate that a line-element is not a collection of points. Line-elements, area elements and volume-elements are as fundamental as points.
I believe this is related to the mystery of how a line, which
is one-dimensional and therefore has spatial extension, can
be constructed from points, each of which is zero-dimensional
and has no spatial extension. You simply can't get a line
from any number, not even a nondenumerably infinite number,
of points, because even a non-denumerably infinite number of
points has no collective extension: you can't put a point "next
to" a point because there is no such thing as "next to" something
having no spatial extension.
A line is not a collection of points. You can, however, always
pick points out of a line. There are always as many as you need,
and therefore always more than you need. If each point is
associated with some ordinal number, then any line segment, no
matter how short, describes ALL possible ordinals (not just the
members of the set of real numbers). But assuming that the
collection of all ordinals is a set leads to a set theoretical
paradox using the usual rules and assumptions, thus it is usually
assumed that this entity is NOT a set. The "points in a line"
constitute some sort of absolute infinity, not a set and therefore
not a transfinite cardinal: whereas the point subsets people pick
out of a line by mapping other sets to them (such as the real
numbers) are sets and therefore are transfinite cardinals.
The mistake people made was in assuming that a continuum (like a
line) could be completely described by any incomplete subset of
ordinal numbers (like the real numbers). If C is the cardinality
of the continuum, then the cardinality of the set of real numbers
is less than C. All of the alephs are less than C.
There are scientists that are getting out of the agreed local boxes.
Take for example K. Ghosh ( http://arxiv.org/PS_cache/gr-qc/pdf/0503/0503003v21.pdf , page 13):
No, we will not get a single point. We will get a collection of spheres whose volume approches zero. Plain and simple.We consider a homogeneous linear array of marbles touching each other. If we now shrink the volume of each marble keeping them in contact (so that the array is always homogeneous) then in the limit that the volume of the marbles is zero we will get a single point.
These discussions lead us to conclude that a line-element is not just a collection of points but is a fundamental
geometric object.
Nut Job said:Any one, who had thept any aspect of this article and/or unduly disturbed the author seriously using e.m radiation in a biological way (telepathy) during the last six years, in particular while the article was getting prepared, or/and encouraged to do so is a descendant of Avatar of Dharmaraj
The belief of Ramanujan (Ramanujan credited his acumen to his family Goddess, Namagiri of Namakkal. ( http://en.wikipedia.org/wiki/Srinivasa_Ramanujan )) do not change the quality of his scientific work.
Ramanujan was a mathematician so great his name transcends jealousies, the one superlatively great mathematician whom India has produced in the last hundred years. "His leaps of intuition confound mathematicians even today, seven decades after his death. ..the brilliant, self-taught Indian mathematician whose work contains some of the most beautiful ideas in the history of science. His legacy has endured. His twenty-one major mathematical papers are still being plumbed for their secrets, and many of his ideas are used today in cosmology and computer science. His theorems are being applied in areas - polymer chemistry, computers, cancer research - scarcely imaginable during his lifetime. His mathematical insights yet leave mathematicians baffled that anyone could divine them in the first place.
The inexhaustible Ramanujan was an observant Hindu, adept at dream interpretation and astrology. His work was marked by bold leaps and gut feelings. Growing up he had learned to worship Namagiri, the consort of the lion god Narasimha. Ramanujan believed that he existed to serve as Namagiri´s champion - Hindu Goddess of creativity. In real life Ramanujan told people that Namagiri visited him in his dreams and wrote equations on his tongue.
Ramanujan could never explain to G H Hardy (an atheist) how he arrived at his deep insights in mathematical terms; but he did say many of his discoveries came to him in dreams, from the goddess Namakkal, and that he had a morning ritual of awakening and writing them down.
He was intensely religious. He often united mathematics and spirituality together. He felt, for example, that zero represented Absolute Reality, and that infinity represented the many manifestations of that Reality. Ramanujan felt that each mathematical discovery was a step closer to understanding the spiritual universe. He once told a friend, "An equation for me has no meaning unless it expresses a thought of God."
Doron, has anyone been disturbing you seriously using electro-magnetic radiation in a biological way (telepathy) during the last, oh, what is it now, twenty five years?
Ramanujan was delusional by today's advanced concept of atheism, whereas K. Ghosh is just a certified pretender. That's why G. H. Hardy, who was the only one at Cambridge to recognized Ramanujan's mathematical brilliance, isn't too often mention as a notable atheist. The modern philosophy of atheism holds that whatever an atheist cannot comprehend is automatically the result of delusion. So that's why you're hanging around here taking your chances.The belief of Ramanujan (Ramanujan credited his acumen to his family Goddess, Namagiri of Namakkal. ( http://en.wikipedia.org/wiki/Srinivasa_Ramanujan )) do not change the quality of his scientific work.
So is the case about K. Ghosh in http://www.internationalskeptics.com/forums/showpost.php?p=7799483&postcount=224 .
Western atheists simply ignore any answer ( as given, for example about belief in http://www.internationalskeptics.com/forums/showpost.php?p=7802875&postcount=228 ) that does not fit to their box.
Goddess Namagiri of Namakkal set up a little test for you. If you pass, your name will be removed from the Center of Phantasmagorical Sphere of the Perpetual Bounce. And so, what is 1729?
Ignorance may hold whether the people are atheists (for example: Nazism, Communism, Piggish Capitalism or any other atheist dictatorship) or religious (Active fundamentalism, which is not really fundamental because it is trapped at the level of thoughts).
A common anecdote about Ramanujan relates to the number 1729. Hardy arrived at Ramanujan's residence in a cab numbered 1729. Hardy commented that the number 1729 seemed to be uninteresting. Ramanujan is said to have stated on the spot that it was actually a very interesting number mathematically, being the smallest natural number representable in two different ways as a sum of two cubes:
1729 = 13 + 123 = 93 + 103
Generalizations of this idea have created the notion of "taxicab numbers". Coincidentally, 1729 is also a Carmichael Number.
I give you a problem to solve - it's similar to the 1729 being a sum of two cubes in two different ways.
Which number satisfies the identity
a^2 + b^2 = c^3 + d^3
where a<b and c<d?
If you answer the right way, you will be released from the Prison of Phantasmagorical Thought on parol.
Ignorant persons are like rigid boxes that are floating upon the wavy surface of the sea, and as a result they get contradiction as an actual realm (the calm state of the sea as the natural base ground for harmony among waves, is beyond their wavy-only awareness).
Ramanujan could never explain to G H Hardy how he arrived at his deep insights in mathematical terms; but he did say many of his discoveries came to him in dreams, from the goddess Namakkal, and that he had a morning ritual of awakening and writing them down.
Cantor believed his theory of transfinite numbers had been communicated to him by God.
Here is Dr. Ghosh answer about the "telepathy" case: