Holly is no longer the sharpest knife in the drawer, having lost his I.Q. of 6,000. Which of the remaining artificial intelligence units on board the Red Dwarf has the highest I.Q, Kryten, or the Talkie Toaster?
I'm not sure there is a certain answer for this, within canon.. But here goes my shot:
I'd have to say that first would be Over-clocked Holly, then Over-clocked Talkie Toaster. (Even with Talkie's limited IQ, the boost was sufficient to overcome any natural IQ.) Their existence is in an aborted timeline, though, so it's questionable if they count. But Holly's in that timeline appears to have been vastly superior to any other in the show.
Holly's intelligence isn't consistent. There's Holly, the 68 IQ machine that confuses black grit on a lens for Black Holes, and there's Holly, the inventor of the Holly Hop drive; I'd give him the prize, normally, except that his IQ is identified as 68 several times. (This seems contrary to what we see, based on his speech, but perhaps there is a sub-processor for that.)
Kryten appears to exhibit the most intelligence, based on his ability to calculate long odds on a number of episodes, as well as his ability to adapt to various systems he encounters (such as learning how to operate a foreign computer system.)
But this isn't consistent.
It's identified (I believe in the book 'Better Than Life') that when Kryten was 'Smarter' he knew that Silicon Heaven was an invention, but as his IQ has dropped over the years, he had become firmly convinced of it's reality. In 'The Last Day' he firmly believes in it, yet by the time of the Episode 'The Inquisitor', he's back to not believing in it. This suggests an intermittent fault in his AI. Look at how he was when they found him; David's tinkering seems to have actually UNDONE some of the damage time had done.
But I have to give the prize to Talkie Toaster. Talkie is the most stable IQ through the series; he was not originally very smart, but he spent most of the series in the trash heap. (His intelligence does seem to vary from his original incarnation to his re-built one; in the new form he's far more Toast obsessed.) As a result, he didn't suffer from the damages to his IQ that the more active AIs (Holly and Kryten) did. He's not the brightest.. but he's consistent.
Why Talkie? Lacking a sufficient statistical sample to determine a mean IQ, we have to fall back to the older method of calculating it - Mental Age divided by Physical Age. (This isn't as odd as it seemed; the statistical model calculation was used as a fudge factor; how do we know what someone of a specific mental age should know? Using a statistically determined point lets us define an arbitrary level.) Since machines can be turned off, we'll ignore that time, for our calculations. Talkie has the least operational run-time of any of them, yet appears to be able to at least speak in coherent sentences; even though he's not that bright, in terms of calculation, the others haven't continued to gain intelligence over their long existences, so, technically, he's basically a child-prodigy among doddering, senile old systems.
Then again, if you hold the novels to be canon, Talkie ends up thinking he's a moose, so YMMV. :)
- Talkie has the highest 'IQ' (but only because of the definition)
- Kryten appears to be the Smartest (in terms of adaptability, ability to learn, etc.)
- Holly has the greatest sum of knowledge (courtesy of the Ship's data banks.)
The problem is how do you define smart, with an AI. :)