1. Information density is subjective, lexical complexity is how you measure it. The OP is talking “weight”, I’m talking “mass and gravity.” One of them will get you the other in most situations, so for the causal physicist it doesn’t matter, but if you’re getting into tweaking the universe then your mental model and approach matters significantly. My comment right now could be seen by some as being information dense, since I’m staying roughly on topic and tossing many concepts out, but “lexical complexity” might be the most lexical complexity in the whole thing and taken word-for-word I’m sure less than 1% of it is domain specific. “The program must use parallel processing on the CPU.” That seems decently information dense, but “the” is found in nearly every block of text ever written, “program” - are we talking television? Theater?, “must” is no better than “the”, and so on. Compare it to “#include <immintrin.h>“
2. Most people don’t realize how far that goes with LLMs. The vocabulary it has is dictated by the words in the conversation. If I ask you “what time is it?” you don’t respond “shoelace” because you’d sound crazy, although you could say it if you wanted, but the model absolutely won’t say it because that word literally does not exist yet. The end result feels the same, but the difference matters and it’s why it’s suggested not to use negating instructions. For example: “Do not mention elephants.” Well that mathematically wasn’t possible until you said it. Not having the word in the list of possibilities is a lot better than hoping it adheres to the “do not mention” part. My example prompt took that same idea from the opposite direction. The model must respond, it will be grammatically complete and coherent, and as much as possible the only words it has are the ones tightly associated with making my point for me. It didn’t ramble about baking a chocolate cake because it can’t, and making that the case is the goal with prompting, not specifically density. Word density > language density; feels similar, very different.
Perhaps this comment itself is the irony you were seeking. I spent several meandering paragraphs and included analogies to drive home the point that you should focus on the words that matter most.
What you might not have fully realized is that it’s exactly what enabling “thinking” does as well. That’s why that exists and it literally does what you’re doing as well: it primes the system. You say “light sensor and amplifier” and at some point it outputs “photodiode and transimpedance amplifier” - now you’re off into advanced responses. The thing is, if you knew it you could have just used those words in your question and received much the same response. “Thinking” exists to turn “So, I was wondering..” into academic prose that raises the probability of academic tokens in the response.
You can kind of cheat the system by doing the same thing for a fraction of the token cost by using something like Haiku to provide a comma separated list of advanced topics and jargon associated with {Your question}, then tack that onto your prompt to Opus with thinking disabled. Obviously easier if you’re using the API, but I’ve run hundreds of millions of tokens though that process and it’s consistently and measurably better than their default thinking. I believe that’s because Anthropic and OpenAI drank their own kool-aid and are treating it like a sentient being that needs to add “hmm…good question” so it feels more thinky about things ‘cause that’s how we do it. The fact that it isn’t, and doesn’t, is why I developed the example prompt I showed earlier; it’s an extreme play on the offloaded “thinking” I also use.