Critique of a Large Number Contest

Why can’t people submit serious large number entries instead of this nonsense.

Here’s a blog post about large numbers, written in the style of the content in my large numbers website. I couldn’t fit it in any section of that website, so I decided to post it in this blog instead.

Introduction: Hamkins’ Large Number Contest

One day, when I was doing some online research about large numbers on the Internet, I came across this large number contest. It is a large number contest held by Joel David Hamkins and Ruizhi Yang at a top-three Chinese university, where you submit the largest number you can write down on an index card—quite a typical large number prompt. The entries were submitted by 150 undergraduate students at the beginning of a talk held at the university.

The rules for the contest were as follows:

  1. A submission entry consists of the description of a positive integer written on an ordinary index card, using common mathematical operations and notation or English words and phrases.
  2. Write legibly, and use at most 100 symbols from the ordinary ASCII character set. Bring your submission to the talk.
  3. Descriptions that fail to describe a number are disqualified.
  4. The submission with the largest number wins.
  5. The prize will be $1 million USD, divided by the winning number itself, rounded to the nearest cent, plus another small token prize.

with 99999, 10*(10*99)+5, and “the population of Shanghai at the moment” listed as examples of valid submissions.

The first two of these are indisputably valid submissions in any large number contest. The third, however, is a little iffy. Undoubtedly there is a number that denotes the current population of Shanghai, but it isn’t easy to precisely determine what number you’re talking about. It’s kind of a physical quantity in that it counts a value in the physical world (technically human world, but it’s about the same thing), and since it’s hard to precisely determine the exact values of physical quantities, you should stray from giving those as examples of huge numbers. Besides, they aren’t that great; almost all physical quantities would be easily topped by a googolplex, which isn’t that big in the scope of large numbers, and every one of them, under any stretch of the term “physical quantity”, would fall well under a decker (10 tetrated to 10 = 10^10^10^10^10^10^10^10^10^10), which isn’t that hard of a number to think up if you’re reasonably clever.

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