Monday, May 19, 2008

Mathematics and Jewish Mathematics

I am purposefully going to be a bit oblique in this posting. I'm avoiding "naming names" as people tend to react to labels without really thinking, and thinking is what I'm after.

To my knowledge there have been no recent halachic problems with the principles of mathematics and mathematical related concepts, some of which fall into the area of science as well. Frum Jews accept that 2+2=4. The accept that 32 ounces=one quart. They accept that there are 60 minutes in an hour (more or less). They accept that 100 pennies=one dollar.

Along with the aforementioned "laws" are two others: 1) the whole is equal to the sum of its parts and 2) no part can be greater than the whole. This is where things get a little sticky in the frum world. There are those who act as if these principles are false when it comes to religion.

If the whole is equal to the sum of its parts, then there is no "whole" without all the parts. We have Klal Yisroel--let's call that our whole. There are any number of parts that make up that whole. They are not all identical but they are all parts. Because there can be no whole without ALL the parts, every part has value. Try paying for something that costs $1.00 with only 81 cents. There are some parts of Klal that are clearly not happy with this state of things. Not only do they feel that other parts of Klal have no value, but they don't seem to consider them parts of the whole at all. Some parts seem to feel that if the other parts disappeared altogether the whole would be strengthened, not diminished. Some parts seem to feel that unless all the other parts are exactly like them then those different parts cannot belong to the whole.

Some parts believe that they are "the" part of the whole, that the whole consists solely of them. They believe that they are not only "greater" than any other parts, but that they are "greater" then the whole they are considered a part of.

It is also an established principle that polar opposites only exist because of that opposition: there can be no left if there is no right. They are defined only in relationship to each other. But there is another corollary to that principle: there are an infinite number of points along a line. A line exists only as a collection of these points. Where there is left and right there must be a mid point that separates them.

For any part of Klal Yisroel to wish that something would happen to "disappear" the other parts is outrageous; I don't care if you are on the left or the right of the Klal line. Sinas chinam has no place in Klal; neither does supreme indifference.

Our government frequently talks about getting rid of pennies as a form of payment; too much trouble for such little value. The talk has never come to any real action. The general population isn't fired up about the penny problem. They may be small but they play their role, and who knows that if you get rid of the pennies now, nickels won't be next, and then dimes and then quarters and half dollars. "Let's just go to paper money and have dollar bills" is heard. There is a cost to that. Put in a dollar bill into a vending machine now and you get change coming out. Make a dollar the smallest amount of money and nothing will be able to cost less than that dollar. There will be a real price to pay for getting rid of small change.

Some people won't stop to pick up a penny lying on the ground; others will. They recognize that if you have enough pennies they can become a nickel or maybe a dime or maybe more. There are lots of pennies in Klal that get lost every year, and lots of people who don't seem to care. "Their choice" is one comment. "Not really a loss because they weren't worth much anyway" is another. Don't want to carry around that huge pocketful of change? Then make change and turn your pennies into nickels. But remember you can't do that if you don't have 5 pennies to begin with; 3 won't do. And while we are at it, let's also remember that a half dollar may be bigger in size physically but it isn't worth more than the dollar it is a part of. To make up that dollar you would need two half dollars, not one. And those half dollars may come from different mints, have been minted in different years, have different pictures on them and different wording. Yet, they, too, are both half dollars.

The change I keep in my purse may not be the same combination that others have. I'm a combination of differing coins. That should be no problem. The problem arises only when we don't remember that no matter how we divide things, it still takes 100 pennies to make a dollar. We really can't afford to lose those pennies. A whole is the sum of its parts.


Anonymous said...

This really has nothing to do with your point, but actually, the mathematics of wholes and parts isn't a simple as commonly thought, at least with infinite sets. For instance, there are the same number of whole numbers, even numbers and odd numbers, despite the fact that the whole numbers are the even ones plus the odd ones. Also, according to the Banach-Tarski theorem, a sphere can be cut up into pieces that can be reassembled into a larger (or smaller) sphere.

Anonymous said...

I think I'd even pay to hear a rav get up in public and say that the reason we don't have to be inclusive of all members of Klal is due to the Banach-Tarski theorem.

You make a good point that there doesn't seem to be any coherence among all Jews and that some members of Klal don't care about others. With the numbers showing us how many Jews we lose who go off the derech, who intermarry and whose children are not Jewish, how are we just letting them go? There is some kiruv work but hardly what is really needed to counter this awful trend.

Anonymous said...

It's not mathematics that bothers some Jews but arithmetic. They know how to do division really well,separating everybody and everything into little categories, and they are also really good at multiplication if you judge by the number of children being born. They've even got subtraction down pat, because they keep removing more and more people from the whole. It's addition they have trouble with. They only think of addition as multiplication, but there are lots of numbers out there who need to be added back to the whole.

Lion of Zion said...


completely off-topic, but in reference to your comment a few posts back: i inquired and there is no boy scout camp this year because of a lack of interest. that actually pretty much describes scouting all together today (in bklyn at least)

(profk: sorry to use the comments as a bulletin board)

Anonymous said...

We pick and choose which people or groups we worry about losing. When Russia suddenly opened its doors we had lots of groups forming to to help the Jews who came out from Russia. Years before it was the same with the Jews who got airlifted to Israel from places like Yemen.

I guess we care more about those Jews who we see as oppressed. If they were someplace where they couldn't be Jewish we run to help them once they are free to come here or Israel. It's the ones who are already free to practice being Jewish and who don't that we seem to write off.