Wednesday, October 8, 2014

The Search for Worthy ... Humans

In the end of פרק ו, Koheles is in search of the worthy man, free of sin. פסוק כ"ח says: "אדם אחד מאלף מצאתי ואשה בכל אלה לא מצאתי." I have found one man in a thousand. And a women in all of these I have not found. I'm not quite sure how to understand this and right now, I'm not going to try. But R' Chaim Kanievsky has a startling ha'ara on this pasuk which vastly changes how we approach it mathematically.

If we were to look at this pasuk statistically, one would say that the ratio of worthy men is 1:1000 and of worthy women is 0. Not so, says R' Chaim. In no place do we ever find the word "אדם" referring only to males. It refers to Man as a species. Therefore, we must view the 1000 as being a mixture of men and women, presumably an even mixture of 500 and 500. Koheles therefore tells us that one in a thousand human beings are worthy. And within this thousandth, he found none to be women. Although this doesn't change the state of the women, it does change the ratio of worthiness for the men. Instead of a 1:1000 worthiness ratio, according to R' Chaim Kanievsky's interpretation of the pasuk, it is 1:500.

Thursday, February 20, 2014

Pi in the Torah

This week, the הפטרה is read from מלכים א פרק ז. There is a difference of opinion as to which part of the פרק is read. The ספרדים and some אשכנזי shuls will read the part that contains a reference to the figure of π. פסוק כג states that the pool was 10 אמות in diameter and 30 אמות in circumference. The obvious difficulty is that π is more than 3. Even if the פסוק were to round to the nearest whole number, it would be 31.

There is a famous approach to this problem which is said over in the name of the גר"א although I am not sure there is any written evidence of it. The word used for the circumference is וקוה. However, it is read וקו. If you drop the leading ו which is simply a וי"ו החיבור, you are left with קו and קוה. The respective גמטריות of those words are 111 and 106. If you divide 111/106 and multiply that by the apparent figure of π used - 3 - then the result is 3.1415094! That is correct to 3 decimal places!

I once heard an interesting addendum to this. There needs to be some meaning behind the figure of 30 אמות. The thickness of the walls was 1/4 אמה (I'm not sure where we know that from.) Therefore, the inner diameter was 9 1/2 אמות. If you multiply that by π you come awfully close to 30. I thought heard this in the name of the מלבי"ם but I looked it up and he definitely did not say that.