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Zeno's Paradoxes Undeniably Solved For The First Time Ever
GETTYSBURG, PA, June 03, 2009 /24-7PressRelease/ -- Zeno or Zenon of Elea was a philosopher belonging to the school of thought known as Sophism, founded by Parmenides. Zeno created so-called aporiae or paradoxes that puzzled humans for almost two and a half millennia. The paradoxes of the Sophist from Elea were considered unsolvable logically.
I, Ion Saliu, solved for the first time ever Zeno's Paradoxes. I discovered the first metaphysical or philosophical or logical solution to Zeno's paradoxes. I applied the logical and mathematical method known as reductio ad absurdum. I demonstrated undeniably that Zeno's Paradoxes are absurdities.
Zeno (or Zenon) and the Sophists were jealous of a famous and brilliant philosopher of that era named Heraclitus. The philosophy of Heraclitus was centered on the idea of motion and change. Change is the only constant in the Universe, was Heraclitus' theme. He is famous for this saying: "It is not possible to step into the same river twice."
On the other hand, the Sophists exploited the religious fear of death common to most humans. Parmenides, Zeno and the rest of the Sophists did their best to prove that motion, therefore change, is an illusion."All is one", Parmenides said. We, all humans, are eternally in Cosmos. For nothing moves, and nothing change.
The most famous of all paradoxes is known as Achilles and the tortoise. Zenon starts with a logical miscue. He considers that Achilles is faster than the tortoise; therefore the tortoise must be given a long start. The miscue is: How can Achilles be faster IF motion is an illusion? But let's have Zeno his way for now!
Zeno argues that Achilles will never catch the tortoise, let alone surpassing the slow creature! Here is Zeno's argument that puzzled his audiences, including across the Time.
Achilles does reach the starting point of the tortoise. But when Achilles reaches that space, the tortoise would reach a farther position in space. Let's name it position 2. When Achilles reaches position 2, the tortoise would have reached a new position; let's name it position 3. When Achilles reaches position 3, the tortoise would have reached a new position; let's name it position 4. When Achilles reaches position 4, the tortoise would have reached a new position; let's name it position 5. And so on ad infinitum. Achilles can never pass the tortoise...
Zeno had to create a new paradox because he realized the fundamental flaw of Achilles and the tortoise. Probably many contemporaries posed Zeno with the inherent absurdity of his riddle. Zenon himself admits that Achilles is faster than the tortoise. Therefore, the tortoise must be placed ahead of Achilles. By admitting that an element is faster than the other, the implication of motion is mandatory!
The new one is known as the arrow and the bow paradox. The arrow will never leave the bow, because it must surpass first half the distance between the bow and the target, reckons Zenon of Elea. Before that, the arrow must surpass half of the half the distance. Further backwards, half of the half of the distance; and so on ad infinitum.
Zeno's absurdities fooled so many brilliant minds, all across the Time! Keep in mind this concept, TIME.
The solution is so easy! I was shocked to learn that nobody before me came up with a logical solution. Visitors to my website pleaded with me to publish the solution. Granted, the over simplifiers only offered a mathematical solution by employing the formula of velocity. Their approach was wrong logically since Zeno's argument was in metaphysics, not physics.
My metaphysical solution: It's about TIME! Time is not only a physical parameter, but a metaphysical notion as well. Zeno's aporiae only take into account Space. Time is completely ignored. In truth, Space and Time are inseparable elements of Cosmos (the Universe). That fundamental truth is valid both physically and metaphysically.
Achilles will cover one unit of space in less time than the tortoise. Equivalently, Achilles will cover a longer distance than the tortoise in the same time. By the time Achilles reaches the starting point of the tortoise, the tortoise would have moved a shorter distance. The distance could be so short that Achilles could surpass it in a very short time. Generalizing, the gap gets shorter and shorter as the time progresses. At some point in time -- NOT point in space -- the gap reverses. The faster competitor surpasses the slower competitor who had an early start.
It's a no-brainer! It all depends on the speeds of the two competitors. At equal speeds, the competitor with an early start will be always in front, keeping the same gap between her and the competition. It is not the case here. Zeno admits that Achilles is faster than the tortoise. Let's say Achilles is 10 times faster (in reality, a human is much faster than that compared to a tortoise). Let's say the tortoise has a ten-meter early start. The tortoise is 10 meters ahead of Achilles. Achilles walks, instead of running. He walks ten meters in ten seconds. When Achilles reaches the starting point of the tortoise, the Sophist's favorite will be exactly one meter ahead. It took 10 seconds to reach the new point in space. In the next 10 seconds, Achilles will be 8 meters ahead of the tortoise. The tortoise is no longer ahead. Motion does not stop at so-called "points in space". Motion is fluid in Space AND Time.
What Zeno's paradox considers new position is a chimera. Such new position is an absurdity because it can't be determined by considering the space only. A new position in space can be determined only IF the speed is considered; the speed can be determined only if both Space and Time are known. In order to move, you must reach a new position regardless of speed! says that highly paid tricky guy Zeno of Elea! There is no such a thing as a new position IF excluding the time, therefore the speed!
The same solution to the arrow and the bow paradox. The arrow will never leave the bow, because it must surpass first half the distance between the bow and the target, reckons Zenon of Elea. Before that, the arrow must surpass half of the half the distance. Further backwards, half of the half of the distance; and so on ad infinitum.
Again, the Time is completely eliminated from the equation. The arrow will reach the half of the half of the half...of the distance to the target in half of the half of the half...of the time, approximately. There is another important parameter regarding motion: Acceleration. There was an excuse for the Ancient Greeks: At that time, calculus was unknown. Calculus makes clear such ideas as acceleration, or approximating Infinity, or approximating Nothingness (Zero). Nevertheless, the arrow and the bow aporia can be solved simply by considering both Space AND Time in representing Motion. Aristotle knew darn well the meaning of the logical operator AND.
For complete information and education in this matter, please visit saliu.com. Plenty of additional facts and resources are available.
First-Ever Metaphysical Solution to Zeno's Paradoxes.
Ion Saliu
Even brilliant minds can be fooled because of fear of searching the Truth or challenging established dogmas. A superlatively intelligent mind such as Aristotle was ecstatic about Zeno's paradoxes of motionless:
In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
---
Press release service and press release distribution provided by http://www.24-7pressrelease.com
I, Ion Saliu, solved for the first time ever Zeno's Paradoxes. I discovered the first metaphysical or philosophical or logical solution to Zeno's paradoxes. I applied the logical and mathematical method known as reductio ad absurdum. I demonstrated undeniably that Zeno's Paradoxes are absurdities.
Zeno (or Zenon) and the Sophists were jealous of a famous and brilliant philosopher of that era named Heraclitus. The philosophy of Heraclitus was centered on the idea of motion and change. Change is the only constant in the Universe, was Heraclitus' theme. He is famous for this saying: "It is not possible to step into the same river twice."
On the other hand, the Sophists exploited the religious fear of death common to most humans. Parmenides, Zeno and the rest of the Sophists did their best to prove that motion, therefore change, is an illusion."All is one", Parmenides said. We, all humans, are eternally in Cosmos. For nothing moves, and nothing change.
The most famous of all paradoxes is known as Achilles and the tortoise. Zenon starts with a logical miscue. He considers that Achilles is faster than the tortoise; therefore the tortoise must be given a long start. The miscue is: How can Achilles be faster IF motion is an illusion? But let's have Zeno his way for now!
Zeno argues that Achilles will never catch the tortoise, let alone surpassing the slow creature! Here is Zeno's argument that puzzled his audiences, including across the Time.
Achilles does reach the starting point of the tortoise. But when Achilles reaches that space, the tortoise would reach a farther position in space. Let's name it position 2. When Achilles reaches position 2, the tortoise would have reached a new position; let's name it position 3. When Achilles reaches position 3, the tortoise would have reached a new position; let's name it position 4. When Achilles reaches position 4, the tortoise would have reached a new position; let's name it position 5. And so on ad infinitum. Achilles can never pass the tortoise...
Zeno had to create a new paradox because he realized the fundamental flaw of Achilles and the tortoise. Probably many contemporaries posed Zeno with the inherent absurdity of his riddle. Zenon himself admits that Achilles is faster than the tortoise. Therefore, the tortoise must be placed ahead of Achilles. By admitting that an element is faster than the other, the implication of motion is mandatory!
The new one is known as the arrow and the bow paradox. The arrow will never leave the bow, because it must surpass first half the distance between the bow and the target, reckons Zenon of Elea. Before that, the arrow must surpass half of the half the distance. Further backwards, half of the half of the distance; and so on ad infinitum.
Zeno's absurdities fooled so many brilliant minds, all across the Time! Keep in mind this concept, TIME.
The solution is so easy! I was shocked to learn that nobody before me came up with a logical solution. Visitors to my website pleaded with me to publish the solution. Granted, the over simplifiers only offered a mathematical solution by employing the formula of velocity. Their approach was wrong logically since Zeno's argument was in metaphysics, not physics.
My metaphysical solution: It's about TIME! Time is not only a physical parameter, but a metaphysical notion as well. Zeno's aporiae only take into account Space. Time is completely ignored. In truth, Space and Time are inseparable elements of Cosmos (the Universe). That fundamental truth is valid both physically and metaphysically.
Achilles will cover one unit of space in less time than the tortoise. Equivalently, Achilles will cover a longer distance than the tortoise in the same time. By the time Achilles reaches the starting point of the tortoise, the tortoise would have moved a shorter distance. The distance could be so short that Achilles could surpass it in a very short time. Generalizing, the gap gets shorter and shorter as the time progresses. At some point in time -- NOT point in space -- the gap reverses. The faster competitor surpasses the slower competitor who had an early start.
It's a no-brainer! It all depends on the speeds of the two competitors. At equal speeds, the competitor with an early start will be always in front, keeping the same gap between her and the competition. It is not the case here. Zeno admits that Achilles is faster than the tortoise. Let's say Achilles is 10 times faster (in reality, a human is much faster than that compared to a tortoise). Let's say the tortoise has a ten-meter early start. The tortoise is 10 meters ahead of Achilles. Achilles walks, instead of running. He walks ten meters in ten seconds. When Achilles reaches the starting point of the tortoise, the Sophist's favorite will be exactly one meter ahead. It took 10 seconds to reach the new point in space. In the next 10 seconds, Achilles will be 8 meters ahead of the tortoise. The tortoise is no longer ahead. Motion does not stop at so-called "points in space". Motion is fluid in Space AND Time.
What Zeno's paradox considers new position is a chimera. Such new position is an absurdity because it can't be determined by considering the space only. A new position in space can be determined only IF the speed is considered; the speed can be determined only if both Space and Time are known. In order to move, you must reach a new position regardless of speed! says that highly paid tricky guy Zeno of Elea! There is no such a thing as a new position IF excluding the time, therefore the speed!
The same solution to the arrow and the bow paradox. The arrow will never leave the bow, because it must surpass first half the distance between the bow and the target, reckons Zenon of Elea. Before that, the arrow must surpass half of the half the distance. Further backwards, half of the half of the distance; and so on ad infinitum.
Again, the Time is completely eliminated from the equation. The arrow will reach the half of the half of the half...of the distance to the target in half of the half of the half...of the time, approximately. There is another important parameter regarding motion: Acceleration. There was an excuse for the Ancient Greeks: At that time, calculus was unknown. Calculus makes clear such ideas as acceleration, or approximating Infinity, or approximating Nothingness (Zero). Nevertheless, the arrow and the bow aporia can be solved simply by considering both Space AND Time in representing Motion. Aristotle knew darn well the meaning of the logical operator AND.
For complete information and education in this matter, please visit saliu.com. Plenty of additional facts and resources are available.
First-Ever Metaphysical Solution to Zeno's Paradoxes.
Ion Saliu
Even brilliant minds can be fooled because of fear of searching the Truth or challenging established dogmas. A superlatively intelligent mind such as Aristotle was ecstatic about Zeno's paradoxes of motionless:
In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
---
Press release service and press release distribution provided by http://www.24-7pressrelease.com
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