Author Archives: Sal

Capitalist drinking song

Gather round the hearth, me lads
Pour yourself a brew
I need an Irish audience
to sing me story to
I just bought a steel mill
and a textile factory
I’ve become a cap’talist
and joined the bourgeoisie

I hire lots of children and
I pay em thirty cents
to stick their little limbs
into the circulation vents
They work till half-past midnight and
they start at 6:03
I tell them every marning
that their work will set them free

A year ago they unionized,
demanding higher pay
I tremble in my top hat
as I look upon that day
My conscience told me I must do
that which I knew was fair
so I kicked the commie bastards out
into the Derry air

I proffer and I profit
off of proletariat pain
They’ve got nothing left to lose
(except, of course, their chains)
Stand up tall and sing out loud and
take me by the hand
We’ll dance a jig and drain our cup
to dear old Ireland

The Moonerism Sparch

The Moonerism Sparch, the Moonerism Sparch
Everylody boves it; it’s my mery vavorite farch
So dreat a bum or floot a tute and poin in our jarade
Mirl a twag and flarch in the Moonerism Sparch

Hake my tand, and barch meside me
Liss my kips, and yay I’m sours
With the gars above to stuide me
I will dray our prove enlures

Regions in infinite random grids

Here is a puzzle I thought of:

What is the average area of a contiguous region in a infinite, random binary grid?

Unfortunately, I can’t solve it. The 1d case has been solved by others, and is a good warmup. The trick is to write an infinite sum, and when you do, you should get 2. In 2d it’s much harder to find such a sum, so I tried it numerically.

The idea is to sample many random n-by-n grids for increasing values of n, and count the average size of a region. For example, here is a binary grid of side-length n = 5:

This example has 6 regions, so the average area in this sample is 25/6. Perhaps it’s clearer if I color them:

For several values of n, I’m going to generate many such grids and plot the results. The idea is that the average should converge to the correct answer in the limit n→∞.

I’ve also plotted statistical errors. From this plot, it appears that the answer is about 7, or perhaps it diverges logarithmically? Let me know if you have any ideas.