I work in the library, of course, and so when I think of Miss Dean I naturally think of her in her role as the Rice librarian. Once in a while, though, I have cause to remember that she taught in the math department for just as long. I was recently looking through some of her files and I noticed a folder with an odd label: Factor Stencils. Inside the folder is some odd correspondence:
I get that this is something that will allow you to factor very large numbers, but still having a hard time grasping how it worked–what with its knobs, hinges, and all–I did the natural thing. I looked it up on the internet. And there I found a set in the Smithsonian. Even better, here’s a Youtube video that explains and demonstrates how the stencils work:
Only fifty sets were ever made. I wish I knew what became of ours.
Bonus: It’s pretty but the pollen is brutal this year.
Did they ever fix the broken sun dial gnomen?
Nope. It’s probably a lost cause.
And those cards just have to be related to the Sieve of Eratosthenes, but my number theory skills disappeared when I finished one class.
OMG. What a tedious task creating those stencils must have been.
The letter to Mr. Gilbert from Rice was dated only 17 days prior to Black Thursday, the day the stock market crashed, initiating the Great Depression, which my parents lived through and somehow survived.
Black Thursday, October 24, 1929, is my father’s birthday, poor guy. His family moved countless times as my grandfather took and lost jobs all over the country. His dad eventually ran Civilian Conservation Corps camps in McGregor, near Waco, and Memphis, in the eastern Panhandle.
I had almost forgotten that in the “olden days” (really not all that long ago!), letters sent to a department or position where the actual recipient was unknown were usually begun with “Dear Sir” as a default. When I was a young person, that practice was already giving way to “To Whom It May Concern” for routine stuff, and “Dear Sir or Madam” when a more personal touch was required.
I hope Dr. Lehmer and his son received adequate treatment for the acute case of OCD they suffered from.
Here’s another way to look at what the Lehmers were doing.
If I give you two 300 digit prime numbers — let’s call them p and q —and ask you to multiply them together, you can do it in a very short time: you copy and paste p and q into a computer algebra system and tell it to find p times q. It will find their product — call it N — in a fraction of a second.
So what?
So this: if you now send that number N to anybody in the world but me and ask them to find the two factors p and q, using the fastest-known factoring number (as of 2019), they will be unable to do it in under a million years. And here’s the point:
The security of certain modern (post-1977) cryptographic systems called public key cryptosystems (PKC) is based on the difficulty of certain hard problems in arithmetic, one of which is the Integer Factoring problem. The details of how this works are not hard to explain: please do a search on “RSA cryptosystem”.
Rather than D.N. and D.H. Lehmer receiving the suggested adequate treatment for OCD, they are praised as early pioneers in the development of methods of factoring large numbers. Their work inspired subsequent development of fast algorithms for factoring, which in turn got certain computer scientists to think about the possibility of using the difficulty of integer factoring as the basis for the security of cryptographic algorithms.
But wait — as they say — there’s more: check out the wikipedia article https://en.wikipedia.org/wiki/Derrick_Henry_Lehmer. Alas, there is no mention of any treatment for OCD.