Poll tax

In his column today in the NY Times, Nicholas Kristof calculated that our war in Iran is costing about $1.3M per day. He points out that this is a conservative estimate, since it does not take into account the higher cost of gasoline and other items, or costs that will continue beyond the war itself, like long term healthcare for maimed and injured soldiers.

If you multiply this out, the total comes to about $683 billion per year. Considering that about 154 million Americans voted for president in 2024, that is essentially an average poll tax for the year of about $4,300 per voter.

This war doesn’t look like it’s going to end anytime soon, so the total poll tax you are paying if you voted for this president, on average, will come out to about $13,000 over the next 3 years. That is, of course before you take into consideration the increased costs for groceries, gasoline, healthcare and tariffed imports like furniture and other items needed by you and your family.

But there is a silver lining. You can take comfort in the fact that those other people, the approximately 50% of voters who didn’t vote for him, also need to pay an average of $13,000 more over the next 3 years.

If the entire cost of this war had been paid only by the people who actually voted for him, you would have needed to pay an average of upwards of $26,000 for the privilege of voting for this president.

Isn’t democracy great?

Holy crap!

The phrase “holy crap!” is part of American idiomatic speech. It dates from around 1935, and was first used in a popular comic strip.

Today the U.S. Secretary of Defense explained that the United States needs to continue its mission of blowing up entire buildings filled with little schoolgirls, as well as committing whatever other military atrocities he deems necessary. His justification is that this is a holy war, and that Jesus would approve.

Or maybe he just wants to make sure everybody understands that he is a drooling, grossly amoral, shockingly incompetent idiot, who likes to cosplay as a Christian. I don’t think, until today, I ever truly understood the term “holy crap.”

Uncanny

Even the most realistic AI movies are immediately recognizable as AI. There’s something about their eerily too perfect slickness which registers in our brains as fake, should we care to let ourselves look objectively.

I wonder what will happen, after the technology gets to the point where that telltale difference goes away. What will be the impact when AI videos are able to robustly pass the Turing test?

Once we have fully crossed the Uncanny Valley, and have made it to the other side, will we come to regret the journey?

It’s what’s left out that leaves us in

Great comments on yesterday’s post!

In response to Manu’s comment, it doesn’t really make a difference. The base 96 encoding is equivalent to the same problem posed in binary encoding, except that one base 96 digit represents between 6 and 7 binary digits, since log2 of 96 is about 6.58496. So it’s really just a gloss on a problem that has already been extensively studied: The probability of finding any particular binary string within a random infinite binary sequence. You just apply that 6.58… constant afterward.

In response to Andy’s comment, you will indeed find every valid mathematical proof. But you won’t find a valid proof that Pi is rational, because it can be proven that such a proof cannot exist in any Universe.

In response to the third comment, I totally agree!!! To quote an old TV ad for Seven Up soda:

It’s the nothing that makes us something
It’s what we miss that hits the mark
It’s what’s left out that leaves us in
It’s the light shining over the dark

Those words are also written somewhere in the digital expansion of every transcendental number. And so is every other TV ad jingle that could ever be written, God help us all.

Transcendence

Thinking about Pi Day has got me thinking about transcendental numbers in general. Nearly all numbers on the number line are transcendental.

Roughly speaking, the transcendental numbers are the ones with no repeating pattern in their decimal expansion. Which means that somewhere in their infinite sequence of digits they contain every possible pattern.

Instead of expressing a number in base 10, we could instead express it in base 96. That would allow us to use every printable character as a digit:

␤ !”#$%&'()*+,-./0…9:;<=>?@A…Z[\]^_`a…z{|}~

If we do that, then every transcendental number (that is, nearly every number) will contain somewhere in its sequence of digits every literary work that has ever been written or that ever will or could be written.

Which leads to some interesting questions. For example, how many digits do we need to go out in the base 96 representation of Pi before there is a 50% chance that we would come across the complete works of Shakespeare?

I don’t know the answer, but you can be sure it’s a really really big number. I wonder how we would go about calculating that.

The Pi moment

Today is Pi Day, all across the world, and many celebrate. Some celebrate with a slice of pie, and others just try to think well-rounded thoughts.

Yet there was a moment today that was the actual Pi moment. That moment deserves to be recognized in its own right.

The Pi moment occurred today a little before 2:00 a.m. this morning. Specifically, it occurred about 26 1/2 seconds after 1:59 a.m.

The precise Pi moment happens every year on March 14th at 1:59:26.53589793… in the wee hours of the morning.

Of course that is just an approximation. I would write down the exact time, but then this blog post would become too long.