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Regarding answering scientists and those who have blind faith in them about the age of the world, first, just like the flaw in their “vestigial organ” logic, the entire concept of measuring the age of the world the way the scientsts do is based on the assuption that the world was not created by a Creator. But if you say that the world was created the way the Torah tells us it was, that is, a full-blown world, complete with starts visible in the sky, ful-grown trees and animals (and a human), a totally, fully developed and mature world, then their logic falls apart.
Because when the world was created, it already had an age. In other words, when Adam for instance was created, he was an adult, even though he was one day old; there were fully grown trees; the sun’s light already reached the earth; an entire world existed, full-blown and OLD. How old was the world at the moment it was created? I dont know — it doesnt say. But we do know that it didnt start from scratch. And so lets say a “scientist” would chop down a tree 1 week after it was created and find maybe 50 rings insude – would that prove that the tree was 50 years old? To the scientists it would, and the “tree ring” concept is used as one of their “proofs” that the world is over 6,000 years old. But the truth is it prove no such thing, becuase when the tree was created it was created as an adult, 50 year old tree.
So even if dating would be accurate, it still doesnt prove that the world was not created 6,000 years ago – because when it was created, it already could have been thousands or millions of quardrillions of years old.
That is the first thing to understand when dealing with the “true believers” of science. But even if they will come up with somethgin that cannot be explained by the above, there is a Torah principle that you must know that has been used long before any of today’s scientists orbttheir grandparents were born, that tells us that although the world was in fact created 6,000 years ago, we know that it possesses all and every characteristic of a world that is much, much older. The Torah actually expects scientific measurements of the age of the universe to return an age of much, much more than 6,000 years. And we have known this for centuries.
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The Divrei Chaim does not tell us the location of the Yaaros Dvash. But the Divrei Yoel (Simchas Torah p.613) identifies it as being in 2 places: Vol. I, Drush 1 and Drush 15. There, it quotes a Medrash (Rabbah 10:4) that before the Sin of Adam the Mazalos operated much more rapidly. After the Sin, the Mazalos operated much slower and longer. With this Medrash, he explains the fact that we pasken that both the opinion that the world was created in Nisan, and the opinion that the world was created in Tishri, are true. Says the Yaaros Dvash: because the Mazalos operated much more rapidly before the Sin, between the time the Mazalos were created on the 4th day, and the time Adam was created, on the 6th day, the Mazalos had already run their course from Nisan to Tishri.
The mistake in their system is that they are not measuring the amount of time itself that occurred. They are identifying various events that already happened and are saying:
1) We measured the amount of time it would take this event to occur
2) And this event has already occurred
3) Therefore, the amount of time it would take to make it occur has already elapsed.
The flaw on that logic is that they only measured how much time it would take if those events would happen NOW, in the post-chet world. But since those events took place before the Chet, they took much less time, and so the occurrence of those events does not indicate the elapse of nearly as much time as the scientists think.
If they would find a way to measure time itself, meaning the amount of moments that transpired during the course of history, they would come up with 6,000 years.