Old Papers (and maths!) (by alaric)

This weekend, I've been going through old papers and dealing with them. This involves sorting them into three categories:

1. To be shredded and turned into logs with our log maker
2. To be filed in the cabinet (with many subcategories corresponding to the files therein), and sorted by date where applicable
3. Demanding some action (which, for now, means putting them into my in-tray, rather than disrupting the activity in progress)

The magnitude and importance of this task is not to be underestimated - when we moved here I had a new baby, a very sick wife, and two jobs to deal with; unpacking and properly setting up my office never really happened, as opposed to setting up a desk and digging through boxes to find the things I needed to get started. So my once-pristine filing system was never quite established, and my "to file" tray grew fat with paperwork I needed to put somewhere. There was slow progress, of course; but then two years later the house flooded, so we had to rush a lot of furniture and stuff from downstairs up into the office, then pack a lot of stuff up and send it into storage while the house was repaired... and we weren't living in the house for nearly a full year, so more often than not I was working on my laptop from wherever I could get an Internet connection. Once again, my paperwork was in disarray.

But, three years on, we're finally catching up. I've gone through my filing cabinet and re-filed the mish-mash therein, then gone through my to-file tray and the various piles of papers dotted around the place, and dealt with them all. "To shred" has been by far the biggest category; as I write, Sarah is sitting feeding sheet after sheet into the shredder. And I've found a bunch of interestings that need further action.

For one of them in particular, the action is to write it up. Many years ago, I bought and read a book on statistics in order to refresh my memory, as I was working on a system for analysing the actions of large numbers of people. Now, I didn't enjoy statistics much when I was doing A-level maths, and reading the book reminded me why: I find the random-variable notation unnecessarily vague and confusing, and the various other notations used in statistics seem inconsistent to me.

I recall reading this book on a long bus journey (the bus from Tottenham Court Road to Gallows Corner in Romford, to be precise), and deciding to take matters into my own hand, and designing m own notation for statistics based on set theory. I like set theory and find it sensible and logical, so this was an obvious choice. I wrote my notation down on a sheet of paper, tucked it into the book, and took it home.

Many years later, I found the sheet of paper inside the book, and put it in my TODO pile, as I needed to take a second look at it and do something with it. This never happened. Until now.

So without further ado, here's the content of the sheet. It still needs more thinking about, but if I write it up into the computer now, this is more likely to happen than waiting for me to encounter this bit of paper again.

---

Let L be a multiset of real numbers.

• SUM(L) = sum of x, where x is an element of L.
• |L| = the number of elements in L.
• L(n) where 1 <= n <= |L| = nth largest element of L
• MIN(L) = L(1)
• MAX(L) = L(|L|)
• MEDIAN(L) = L(|L| / 2) if |L| is odd, (L(floor(|L| / 2)) + L(ceil(|L| / 2)))/2 otherwise
• SUM^2(L) = sum of x^2, where x is an element of L
• VAR(L) = SUM^2(L) - (SUM(L))^2 etc.
• L ~ D iff L is distributed as per D (D is a distribution as per normal stats notation)
• SRn(L) is a multiset of all possible sets of n random samples from L with replacement
• SWn(L) is a multiset of all possible sets of n random samples from L without replacement

Let L be a multiset of records (named tuples) of real numbers (a,b,c,...)

• La is a multiset of just the as
• Lab is a multiset of the products, a*b
• sigma(L) f(a,b,c) is the sum of f(a,b,c) across all the elements in L
• pi(L) f(a,b,c) is the product
• L ~ (D1, D2, ...) iff. La ~ D1 and Lb ~ D2 and so on
• cov(a,b)(L) = sigma(L) ab - M(La)*M(Lb)

...and there it ends!

2 Comments

• 

  By sarah, Mon 11th Oct 2010 @ 11:27 am

  After two days of shredding I am going on strike love! I want to get the living room good again :/

  Statistics if a weird one - when I was doing the MRes and we had the Stats lecture I had the whole thing of I didn't know their names for things but when asked to guess what to do I came up with the same process as such.

  (I think I remember telling you about lecture following me to coffee to inform me I knew far more about Maths than I thought I did!)

• 

  By sarah, Mon 11th Oct 2010 @ 11:27 am

  I have also seen Maths lectures wrap themselves in knotts with it 😉

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