Ps3 – use classic PS2 gamepads on the PS3

Unless Sony made the controllers send the same signals and have the same connectors there's no way that a PS2 can talk to a device created in the future without some intermediate hardware (as you suggest). However, it's not really in Sony's interest to do this themselves.

Wiki Answers and Answer Bag would appear to agree with me.

Though you're not the only one suggesting this. Though I don't see any answers that suggest how it might be done. Some sort of device like the USB to PS/2 converter you can get for PC mice and keyboards is what you need.

Short Answer

PS2 games were made for an older CPU. They cannot run on the CPU designed for the PS3.

Long Answer

PS2 games were created to work on Sony's Emotion Engine CPU and their Graphics Synthesizer GPU. This CPU/GPU combo was put in all PS2 units and in the first variants of the PS3 (the NTSC 20GB and 60GB models) to make them backward-compatible. These models can play almost all PS2 games.

The 80GB Metal Gear Solid IV bundle had the GPU as well, but replaced the Emotion Engine chip with software emulation of the chip. It can still play most PS2 games, but support isn't as good as the earlier models with the actual EE CPU.

Models since the MSG:IV bundle had neither the CPU nor the software emulation of the CPU required to play older games.

Sony has a knowledgebase article that explains which three versions can play PS2 games. They also have a compatibility tool that you can use to see if specific games can play on those specific models.

PS1, being a system simpler and older than the PS2, is easier to emulate using only software. In 2000, Sony bought a Playstation emulator called Virtual Game Station. While the first PS2 models incorporated hardware of the PS1 (like its CPU), later PS2 models completely emulated the PS1 via software (and were thinner).