The phantom of Zenon. |
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This was written in Japanese to the homepage of Justnet in 1999 year, was translated to English in November 2000.
And, this time, it, revised, was issued from Nifty December, 2003. This was rewritten in May 9, 2005. | |||||||||||
That strange happening occurred in the night of the midsummer I can't get in good sleep.
When it happened to fall into a doze, it is that one ghost appeared on my dream suddenly.
He was staring at me in the sharp eyes. It must be Zenon ! Once I saw through his contradiction. So, he has appeared, trying to make revenge to me ! At that time, I thought like that at once, stared at him conversely with the unyielding spirit. Just then, Zenon, while holding a cloud on his face gloomily, says "You know what surely, too, and you are not here". And, his eyes, glimmering mysteriously, stared again at me. "Why! Does he intend to pick a fight at me ? It's Silly!". I despised Zenon from the bottom of mind, sneered at him secretly. However, the opponent is the ghost anyway. If I anger him, he would give me the harm of something or other. It is terrifying terribly. "Oh! Zenon ! You are great. Please tell me why my thinking doesn't reach to the truth.". Not to anger him, I asked him like that with the modest behavior. | |||||||||||
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Just then, Zenon says "Listen! My real intention is into my contradiction". But, it is uncanny logic. "Why! Isn't it strange ?" Carelessly I asked him like that. It is because my mind was being shaken by his abrupt words terribly. Of course, Zenon gives a sharp glance at me. I trembled in the fear in spite of oneself. But, it is awkward probably if he notices my trembling. I may be killed by him at a moment in his advantage like that. I looked at Zenon with feigned calm. But, Zenon's attitude is strange. He only regards me sadly. But, what a noble looks it is ! And, what a plaintive looks it is ! His eyes are being filled with the sorrow and mysterious affection tinged with pity. I, holding my breath, regarded him in spite of oneself. He is giving off the blue aura from the whole body. And, I felt it pours into my heart quietly though it doesn't know why. |
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However, when I blinks my eyes a moment, it can't find out Zenon anywhere any more. "I shouldn't have come here.".
His regretful voice, echoing slightly, only joggled the darkness strangely. Since then, Zenon doesn't appear at all.
"I have won to Zenon at last !". Insolently, my heart was filled by the delusion like that. However, why would his eyes have been giving off the nobility and sorrow ? Somehow, his eyes make me feel the profound spirit. I couldn't but think about Zenon. |
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It is said Zenon left many paradoxes for us. The race of Achilles and the tortoise is known as one of the paradox like that as well. However, this race is different from the usual race a little. That is, since the quickness of the tortoise is slower than the quickness of Achilles considerably, the starting line for Achilles is situated behind considerably far from the starting line of the tortoise. Achilles chases the running tortoise, under the condition like that. Instead, there isn't the given goal. Therefore, it has to judge the winner or loser, confirming whether Achilles can pass the tortoise. In other words, if Achilles can pass the tortoise, the winner is Achilles. And, if he can't do like that, the tortoise wins the victory over Achilles. But, it seems Achilles necessarily can pass the tortoise sometime if it thinks of this race with common sense. In other words, it seems Achilles wins the victory. However, Zenon says "It is impossible Achilles passes the tortoise". It states the outline of that reason next. | |||||||||||
First, Achilles and the tortoise start to run at the same time with the signal of the start. When Achilles reaches to the starting line of the tortoise, it can suppose that the tortoise, going a little along from one's starting line, reaches to some point, that is, the S point. Moreover, when Achilles reaches to the S point, even if the tortoise runs slower than Achilles, it seems the tortoise is a little along from the S point. In other words, it seems that the tortoise reaches to some point, that is, Y point, going a little along from the S point. If at that time, the tortoise, getting off guard, does a nap and so on in the Y point, Achilles may catch up with the tortoise. However, the very honest tortoise is keeping concentrating to the race in full power. |
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Therefore, it seems there is the tortoise a little along from the Y point when there is Achilles in the Y point. In other words, at that time, the tortoise reaches to some point, going a little along from the Y point. Of course, the interval between Achilles and the tortoise becomes shorter as they run. Needless to say, it is because Achilles is quicker than the tortoise. However, the above mentioned relationship of them doesn't change if the above logic is proper. In other words, Achilles always is situated behind the tortoise. Of course, the tortoise and Achilles have no size in this case, though it may be superfluous comment. Therefore, it is impossible that Achilles strides over the tortoise in his last one step. Now, would it be possible that it finds out the contradiction of this logic with using only this logic ? I made one snail participate in this race, to solve this problem, though it may be doubtful method. Of course, the quickness of the snail is slower than the tortoise considerably. Therefore, the starting line for the snail is set a little along than the starting line of the tortoise. In other words, the starting line for the tortoise is situated between the starting line of the snail and the starting line of Achilles. | |||||||||||
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Now, they are running actually in the world Zenon's logic rules. They left from each starting line all together, hearing the sound of the starting gun. In front of eyes, the snail is running desperately. And, the tortoise is chasing the snail patiently too. Then, from the most far distance, Achilles approaches them in the speed like an arrow. However, that sight is a little strange. If you observe Achilles and the tortoise and snail at the same time, you may fall into the confusion. So, please make your consciousness concentrate to Achilles and snail for the moment. By the way, it is better to decide the ratio of the quickness as follows, if it tries to make the reasoning easy. * Achilles : tortoise : snail = 4 : 2 : 1. Then, their starting line and arrival points are supposed as follows. |
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* Starting line for Achilles -- 400m -- starting line for tortoise -- 300m -- starting line for snail -- 100m -- F point -- 100m -- B point -- 25m -- C point. | |||||||||||
So, in this case, if Achilles reaches to the tortoise's starting line, the snail is supposed to reach to the F point. And, in this case, since Achilles ran 400 meters ahead, the distance to the F point from the starting line of the snail is 100m that is 400 meters by 1/4. Then, when Achilles reaches to the F point, since Achilles runs the 400 meters from the starting line of the tortoise, the snail, running 100 meters that is 400 meters by 1/4, reaches to the B point. Moreover, when Achilles reaches to the B point, he ran 100 meters from the F point. And, at that time, the snail run 25 meters that is 100 meters by 1/4. That is, that place is the C point. But, at that time, where would the tortoise be ? Since no one was observing the tortoise, at least, until Achilles passes the F point, nobody can decide the position of the tortoise. If it follows to Zenon's logic, it seems the observer has to observe either of the relation between Achilles and the snail or the relation between the Achilles and the tortoise. In other words, it seems the observer can't see all those relations in the same time. Therefore, it seems it is natural above problem occurs. |
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In this case, we always must try the calculation about the position of the tortoise, imagining the position of Achilles and the position of tortoise if it tries to know the position of the tortoise. If not, no one can know his passed point. However, to tell the truth, it always can't say the above sight is along Zenon's logic if it says it strictly. It is because the relation of position between Achilles and the tortoise shouldn't be stated together with the relation of position between Achilles and the snail. Those relations have to be stated as each independent relation. If not, Zenon's world would collapse at once. However, it dares to think those relations here furthermore. Thereupon, look at the next two charts. |
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1st chart: The sight when Achilles chases the tortoise. * Starting line for Achilles -- 400m -- starting line for tortoise -- 200m -- F2 point -- 100m -- B2 point -- 50m -- C2 point -- 25m -- D2 point -- 12,5m -- E2 point. 2nd chart: The sight when Achilles chases the snail. * Starting line for Achilles -- 700m -- starting line for snail -- 175m -- F3 point -- 43.75m -- B3 point -- 21.875m -- C3 point. | |||||||||||
So, look at the 1st chart. It seems it is impossible Achilles and the tortoise pass the certain point because the distance between Achilles and tortoise becomes shorter as they run. Thereupon, Achilles's last point to reach is expressed in the next equation if it supposes that the distance between the last point like that and the starting line for Achilles is the unknown Z. | |||||||||||
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If it calculates this equation, the value of the Z draws near to 800 meters endlessly. However, as a matter of fact, this means "Z=800m". In other words, Achilles and the tortoise already is parallel at that position mathematically. However, it can't assert that Achilles and the tortoise are completely parallel yet if it follows Zenon's logic. Thereupon, look at the 2nd chart. Achilles and the snail can run more distance than 800m. | |||||||||||
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If so, since the tortoise of the 1st chart almost is in the stopping situation in the position of 800m from the Achilles's starting line, it seems it is possible that Achilles in the 2nd chart pass the tortoise somewhere. But, in this case, the observer isn't looking at the tortoise. It is looking at only the relation of Achilles and the snail persistently. Not until the observer is in the condition like that, Achilles can pass the tortoise. Therefore, at that time, nobody can see the sight of a moment where Achilles passes the tortoise. | ||||||||||
Achilles already is running forward than the tortoise at that time before someone notices the thing. It seems this result, apparently, is proper because it is that the 1st chart and 2nd chart are expressing the same race with the different way for looking. However, when the observer is looking at the Achilles and the snail, if other observer was looking at the Achilles and the tortoise, would what kind of phenomenon occur, on earth ? Probably, it seems at least Achilles possesses two positions at the same time if it follows the Zenon's logic. However, it is impossible the object in motion possesses the two position at the same time at least in this world. If you don't say above mentioned strange phenomenon is the contradiction, what would you call the contradiction ? In other words, it would be that this race can materialize only in Zenon's world. However, Zenon is the philosopher known in the present day. Would this paradox be in the level to be brought up for him ? Or, would there be more profound meaning behind this paradox ? | |||||||||||
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When the phantom of Zenon appeared, he at first said "You know what, too, and you are not here.". Or, Zenon may have intended to say the phenomenon occurs corresponding to the relation between the observer and its object. It is said that the concept of the observer, that is, cognition-person was added into the factors of objective perception by Einstein first. At least, I were thinking like that until now. However, as a matter of fact, the pioneer like that may have been Zenon. Moreover, the phantom of Zenon also stated to me "There is our real intention just in our contradiction.". Then, once Zenon said that the continuously flying arrow isn't moving at all. In other words, the arrow flying the space is flying discontinuously. He must have intended to say like that. If it is really so, it seems his logic also relates to the quantum theory. And, it also seems he imagined the world of possibility at that time. Of course, I also were caught to the image like that when I heard Zenon's logic. In other words, the particles and the undulation isn't in the equal relationship even from the viewpoint of physics. | |||||||||||
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When the perception to one undulation is wished by the cognition-subject,
it seems the undulation like that materializes as the particle.
Therefore, if the undulation is seen from my image, it is the actual existence existing as a possibility, not the reality.
Probably, my image like that will become the obvious truth soon.
By any chance, wouldn't Zenon also have been thinking like that ?
At any rate, it seemed his paradoxes include the deep meaning like that.
However, he must have been restricted of the expression because of the mental level in ancient times.
In other words, it seems the proper method for expression wasn't found. | ||||||||||
His eyes filled in the blue luster make me feel his deep disappointment. Of course it would be because nobody noticed his real intention. It seems that Zenon's eyesight for finding out the truth was exceeding Aristotle and Plato by far. So, it seems it was very difficult all the more that the expression for his real intention is found out. Therefore, it seems it was difficulty other people understand his thought. He must have become the ghost because of the harsh circumstances like that. |
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cotosiro | |||||||||||