About the Higgs boson in ars technica article 'Narrowing in on the Higgs boson'
"Since the LHC is anticipated to produce its first collisions later this year, it may not be long before we obtain clear evidence of the existence of the Higgs boson. I tend to think that this would be one of the least exciting answers possible, though. The real scientific treat would be if the LHC and other colliders can't find any Higgs particles. This would mean that the standard model, one of the shining examples of the power of particle physics and a theory on which a lot of physics rests, might be wrong; we would have to go back to the drawing board and invent something new."
Attributed as 'real scientific treat' if the colliders do not find any proof of the Higgs boson existence? Why would my mind stop at that particular sentence?
It is not its existence that is doubted, ... but its existence in a ... free form in the universe? ... that the universe is inhabited by a vast number of Higgs bosons, hiding obscuring their presence? ... it is what part of the universe they inhabit, it's what matters.
While this is unlikely, seeing as how the experimentalists have found 60 of the 61 particles that appear within the standard model, it sure would make the next few years interesting, both for scientists in the field and interested third parties like science journalists."
Sunday, 29 March 2009
Monday, 23 March 2009
Archimedes actual infinities, as revealed in his lost manuscript.
Archimedes actual infinities, as revealed in his lost manuscript.
I read in the article 'A Prayer for Archimedes', about the long-lost text by the ancient Greek mathematician which shows that he had begun to discover the principles of calculus.
In the claim put forward by Reviel Netz, an historian of mathematics at Stanford University who transcribed the newly found text, says that the recent discoveries show that Archimedes indeed used the notion of actual infinity.
Infinities, as defined by Aristotle, mentioned here
"The Greek philosopher Aristotle built defenses against infinity's vexing qualities by distinguishing between the "potential infinite" and the "actual infinite." An infinitely long line would be actually infinite, whereas a line that could always be extended would be potentially infinite. Aristotle argued that the actual infinite didn't exist."
An infinitely long line would be actually infinite, hence actual infinity, whereas a line that could always be extended would be potentially infinite, hence potential infinity. Aristotle argued that the actual infinity didn't exist.
I read further
"Archimedes found a relationship between the full area of that slice, which was a section through the plane-sided volume, and the smaller area within it, which was a section through the curved shape. Then he argued that he could use that relationship to calculate the entire volume of the curved shape, because both the curved figure and the straight one contained the same number of slices."
and
"That number just happened to be infinity—actual infinity."
and
"The interesting breakthrough is that he is completely willing to operate with actual infinity," Netz says, but he adds that "the argument is definitely not completely valid. He just had a strong intuition that it should work." In this case, it did work, but it remained for Newton and Leibniz to figure out how to make the argument mathematically rigorous."
Archimedes being willing to operate with actual infinity, an infinitely long line, instead of a line that could always be extended. A potentially infinite line, what Aristotle argued that exists, whereas the actual infinity did not exist.
So, there is not infinity as such, whatever name it can be given, actual or potential, since an infinite line can always be extended. There are no boundaries.
But the infinity of decimal numbers, lying between two integer numbers, it has boundaries. The two integer numbers that lies within. Does having boundaries determine the kind of infinity it is? The infinity of decimal numbers between two integers, can not be extended beyond the integer boundaries.
It cannot be potentially infinite, it can only be actual infinity, what the calculus uses. What has driven Archimedes "strong intuition that it should work", and why "In this case, it did work". And it works when dealing with infinities that the boundaries are known or postulated beforehand.
What "it remained for Newton and Leibniz to figure out, how to make the argument mathematically rigorous.
Confusing the issues amidst vague statements, if "the argument is definitely not completely valid." What is valid, what is completely valid, what is not completely valid, and what is definitely not completely valid. How is validity defined, what is required to make an argument valid.
I read further in the same article
"Newton and Leibniz also worked with actual infinity. Leibniz went so far as to say in a letter, "I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author."
Since Newton and Leibniz also worked with actual infinity and produced calculus, would that not validate Archimedes intuition and his willingness to operate with actual infinity?
And what is meant by Leibniz' statement that nature makes frequent use of it, everywhere. Does that not imply the fractality inherent in all nature's objects, chaos driven processes surpassing, traversing fractal dimensions, from the microscales to the macroscales weaving the perfections of its author, chaos. Actual infinities trapped within the delimiting boundaries of any nature's object, all objects.
The statement 'modern calculus no longer makes use of the actual infinite; it sticks with Aristotle's distinction', a matter of taste?
I read in the article 'A Prayer for Archimedes', about the long-lost text by the ancient Greek mathematician which shows that he had begun to discover the principles of calculus.
In the claim put forward by Reviel Netz, an historian of mathematics at Stanford University who transcribed the newly found text, says that the recent discoveries show that Archimedes indeed used the notion of actual infinity.
Infinities, as defined by Aristotle, mentioned here
"The Greek philosopher Aristotle built defenses against infinity's vexing qualities by distinguishing between the "potential infinite" and the "actual infinite." An infinitely long line would be actually infinite, whereas a line that could always be extended would be potentially infinite. Aristotle argued that the actual infinite didn't exist."
An infinitely long line would be actually infinite, hence actual infinity, whereas a line that could always be extended would be potentially infinite, hence potential infinity. Aristotle argued that the actual infinity didn't exist.
I read further
"Archimedes found a relationship between the full area of that slice, which was a section through the plane-sided volume, and the smaller area within it, which was a section through the curved shape. Then he argued that he could use that relationship to calculate the entire volume of the curved shape, because both the curved figure and the straight one contained the same number of slices."
and
"That number just happened to be infinity—actual infinity."
and
"The interesting breakthrough is that he is completely willing to operate with actual infinity," Netz says, but he adds that "the argument is definitely not completely valid. He just had a strong intuition that it should work." In this case, it did work, but it remained for Newton and Leibniz to figure out how to make the argument mathematically rigorous."
Archimedes being willing to operate with actual infinity, an infinitely long line, instead of a line that could always be extended. A potentially infinite line, what Aristotle argued that exists, whereas the actual infinity did not exist.
So, there is not infinity as such, whatever name it can be given, actual or potential, since an infinite line can always be extended. There are no boundaries.
But the infinity of decimal numbers, lying between two integer numbers, it has boundaries. The two integer numbers that lies within. Does having boundaries determine the kind of infinity it is? The infinity of decimal numbers between two integers, can not be extended beyond the integer boundaries.
It cannot be potentially infinite, it can only be actual infinity, what the calculus uses. What has driven Archimedes "strong intuition that it should work", and why "In this case, it did work". And it works when dealing with infinities that the boundaries are known or postulated beforehand.
What "it remained for Newton and Leibniz to figure out, how to make the argument mathematically rigorous.
Confusing the issues amidst vague statements, if "the argument is definitely not completely valid." What is valid, what is completely valid, what is not completely valid, and what is definitely not completely valid. How is validity defined, what is required to make an argument valid.
I read further in the same article
"Newton and Leibniz also worked with actual infinity. Leibniz went so far as to say in a letter, "I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author."
Since Newton and Leibniz also worked with actual infinity and produced calculus, would that not validate Archimedes intuition and his willingness to operate with actual infinity?
And what is meant by Leibniz' statement that nature makes frequent use of it, everywhere. Does that not imply the fractality inherent in all nature's objects, chaos driven processes surpassing, traversing fractal dimensions, from the microscales to the macroscales weaving the perfections of its author, chaos. Actual infinities trapped within the delimiting boundaries of any nature's object, all objects.
The statement 'modern calculus no longer makes use of the actual infinite; it sticks with Aristotle's distinction', a matter of taste?
Thursday, 5 March 2009
Suffocating within the narrow, self-imposed boundaries of ideologies
Ideologies, dogmas, doctrines developed, their whole range starting from anarchy and communism on one end to its other end of the spectrum capitalism and fascism, individuals deeply entrenched, they are all, being so absolute, try hard to convince you, that their way of thinking, is the only way of thinking.
Calling it the truth, their very own version of truth.
The concept of truth is non-existent. Its alleged attributes can not be realised outside the mind of the single individual and as such it assumes a variety of contents. This essayist gives its own account on that matter, a clearer perspective avoiding muddling the issue further.
Adhering to the truth or truths individuals resist, deny themselves the exposure to myriads of new concepts and drives them into ignorance and by that stupidity, as less and less stimuli, (how information around us arouse, excites and triggers thoughts in our minds), are taken into consideration, or even information pass unseen, unnoticed, unregistered by our senses and our mind's attention.
Loosing themselves in the complexity, perplexing, ever-expanding, constantly creating and re-creating itself, without realizing that all that enormous complexity suffocates within narrow and limiting boundaries. Bloated to the hilt, squeezing and stretching its rigid boundaries to no avail and certainly unable to offer any viable solutions to problems faced, loosing touch with reality.
A complexity, as such, with an infinite capacity, the same infinite capacity in fitting decimal numbers between the numbers 1 and 2. You have an infinite cohort of numbers from 1,01..... to 2.99998 that lie there but can never pass below number 1 or above number 2.
In the same way all their intellect's productive output, the ideas they carry and develop, it will never pass the narrow boundaries set by their prospective ideologies, dogmas or doctrines or whatever other way it can be called, or the so much revered truth construct. The truths they adhere to.
An educated ignorance, which denies the use of the most valuable of our brain's and mind's processes, that worths a lot. That of the ability to make the strange familiar and the familiar strange.
Calling it the truth, their very own version of truth.
The concept of truth is non-existent. Its alleged attributes can not be realised outside the mind of the single individual and as such it assumes a variety of contents. This essayist gives its own account on that matter, a clearer perspective avoiding muddling the issue further.
Adhering to the truth or truths individuals resist, deny themselves the exposure to myriads of new concepts and drives them into ignorance and by that stupidity, as less and less stimuli, (how information around us arouse, excites and triggers thoughts in our minds), are taken into consideration, or even information pass unseen, unnoticed, unregistered by our senses and our mind's attention.
Loosing themselves in the complexity, perplexing, ever-expanding, constantly creating and re-creating itself, without realizing that all that enormous complexity suffocates within narrow and limiting boundaries. Bloated to the hilt, squeezing and stretching its rigid boundaries to no avail and certainly unable to offer any viable solutions to problems faced, loosing touch with reality.
A complexity, as such, with an infinite capacity, the same infinite capacity in fitting decimal numbers between the numbers 1 and 2. You have an infinite cohort of numbers from 1,01..... to 2.99998 that lie there but can never pass below number 1 or above number 2.
In the same way all their intellect's productive output, the ideas they carry and develop, it will never pass the narrow boundaries set by their prospective ideologies, dogmas or doctrines or whatever other way it can be called, or the so much revered truth construct. The truths they adhere to.
An educated ignorance, which denies the use of the most valuable of our brain's and mind's processes, that worths a lot. That of the ability to make the strange familiar and the familiar strange.
Tuesday, 3 March 2009
Consciousness whole pattern processing regime.
Patterns. You bring along the whole pattern for consciousness to process. In units as it is mentioned in, 'Is consciousness only a property of individual cells?', by Jonathan CW Edwards,
"The second, which I will call the physical substrate, is that of finding a substrate at the fundamental physical level which might support a subjective experience in which many elements are bound into a seamless whole."
Many elements bound into a seamless whole! Each element is, in its turn and for its own accord, a seamless whole made out of or bound from its own specific elements, downscale as far as it is permitted by the granularity (?) of the physical world. Granules, as a general term referring to the size of the physical units possible? Up to quanta or strings?
As a seamless whole is presented to our consciousness as whole patterns and processed as such. All the information elements bound in the pattern, are dragged along, no matter how relevant they appear to be. Even if they are seemingly incompatible or contradict with one another.
Emergence? And its incompatibility pre-requisite for emergent properties to rise? The consciousness whole pattern processing allowing emergence to appear? Working towards achieving that goal?
"The second, which I will call the physical substrate, is that of finding a substrate at the fundamental physical level which might support a subjective experience in which many elements are bound into a seamless whole."
Many elements bound into a seamless whole! Each element is, in its turn and for its own accord, a seamless whole made out of or bound from its own specific elements, downscale as far as it is permitted by the granularity (?) of the physical world. Granules, as a general term referring to the size of the physical units possible? Up to quanta or strings?
As a seamless whole is presented to our consciousness as whole patterns and processed as such. All the information elements bound in the pattern, are dragged along, no matter how relevant they appear to be. Even if they are seemingly incompatible or contradict with one another.
Emergence? And its incompatibility pre-requisite for emergent properties to rise? The consciousness whole pattern processing allowing emergence to appear? Working towards achieving that goal?
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