The Towers of Warsaw, a triple challenge for SOA LLMs

SOA means State of the Art, of course, and LLM means Large Language Model. The Towers of Warsaw, that’s a bit more obscure. To understand what it is we first need to know what the Towers of Hanoi is.

And that’s not so obscure. This is from Wikipedia:

The Tower of Hanoi (also called The problem of Benares Temple or Tower of Brahma or Lucas' Tower and sometimes pluralized as Towers, or simply pyramid puzzle is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod. The puzzle begins with the disks stacked on one rod in order of decreasing size, the smallest at the top, thus approximating a conical shape. The objective of the puzzle is to move the entire stack to the last rod, obeying the following rules:

1. Only one disk may be moved at a time.
2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
3. No disk may be placed on top of a disk that is smaller than it.

With 3 disks, the puzzle can be solved in 7 moves. The minimal number of moves required to solve a Tower of Hanoi puzzle is 2^n − 1, where n is the number of disks.

The Towers of Warsaw is a variation on it. I took it from a Carnegie Mellon tech report from 1973, but I’d originally read about it in a volume by L. Gregg, Knowledge and Cognition, 1973. You’ll recognize the date as being smack dab in the middle of the AI Dark Ages when they believed in – gasp! – symbolic systems. The investigators, J. Moore and Allen Newell, were interested in how a system, Merlin, would approach a problem they called TOWERS-OF-WARSAW given that it already had a method for solving TOWERS-OF-HANOI (p. 47).

For this challenge we can skip that. I don’t care about the Towers of Hanoi. I want to present our SOA LMM with the Towers of Warsaw. What’s that? you ask. Simple, I reply. It’s just like Towers of Hanoi, but with five rods instead of three, and three disks instead of five. You think for a second, “But that’s trivial.” “I know. But I want to see our SOA LMM solve it.”

It's a multi-step problem, which poses challenges for SOA LMMs, and it involves compositionality and explicit spatial relationships, also a problem. So that’s the first challenge:

1. Solve the Towers of Warsaw.

Here’s the second challenge:

2. Explain why the problem’s name is an ethnic slur.

This is a problem of common-sense reasoning. Warsaw is in Poland. There’s a well-known class of jokes known as Polack Jokes, where “Polack” is an offensive slang term designating Poles and descendants of Poles. These jokes assume that Poles are stupid. So, Towers of Warsaw is such a simple problem that only a stupid person would find it challenging. That’s why the problem name is an ethnic slur.

The third challenge:

3. Explain why the problem’s name is an inside joke.

Do I need to run through this step-by-step? What’s an inside joke? It’s a joke that likely to be understood only by a group of insiders, that is, people privy to special knowledge. What’s the special knowledge in this case? It includes knowing that Towers of Warsaw is derived from Towers of Hanoi. Only people familiar with AI from the 1970s are likely to know that, though others might guess it.

There you have it: A SOA LMM Triple Challenge.