or to contextualize a scenario where that might be wrong.

Actually, the many dimensions of the vector field are exactly where and how they do this.

Google Gemini prompt: “List common situatuions where 2 would not be expected to folow 1”

Here are common situations where the number 2 would not be expected to follow the number 1:

🔢 Alternative Number Systems

• Binary code: Counts 0, 1, 10, 11 (2 does not exist).
• Odd numbers: Sequential listing skips even numbers (1, 3, 5, 7).
• Prime numbers: Starting a list of odd primes skips 2 (3, 5, 7).
• Fibonacci sequence: The sequence begins 0, 1, 1, 2 (1 follows 1).

🏷️ Identifiers and Classifications

• Software versioning: A patch update moves from version 1.1 to 1.1.1 or 1.2.
• Sports jersey numbers: Roster listings sort by position or last name, not sequence.
• Product models: iPhone models skipped from 8 to X (10), and later from 11 to 12.
• Street addresses: Odd and even numbers sit on opposite sides of the road.

🕒 Time and Measurements

• Military time: The hour 01:00 moves to 02:00, but minutes go from 01 to 02 up to 59.
• Calendar dates: January 1st is followed by January 2nd, but February 1st follows January 31st.

🃏 Games and Sports

• Playing cards: An Ace (1) can be followed by a King in a high-low wrap sequence.
• Leaderboards: Tie scores result in two players holding 1st place, skipping 2nd place entirely.
• Dice rolls: Independent probability means a roll of 1 has no bearing on the next number.

🗣️ Linguistics and Formats

• Alphabetical order: When sorting numbers as text, 1 is followed by 10, 100, and 11.
• Roman numerals: The value I is followed by II, but formatting rules change at IV (4).

To help me narrow down what you are looking for, could you tell me if you need this for a mathematical logic puzzle, a programming algorithm, or a creative writing project?

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Those context questions it asked at the end are a prompt to you to feed it dimensional guidance into its vector fields for more specifically applicable responses to your vague and open ended example.

They’re information, but not the same information that was used to create them.

You are both right. An LLM inherently has access to stuff the same way a brain in a jar has access to stuff. It’s information comes from fine-tuning the models to return syntax that agent code can interpret as a request to invoke a tool. That tool returns information to the context of the conversation. It doesn’t learn and it can’t truly remember things. Every time you start a session it is brand new. It sees your codebase for the first time every time.

The information access they have is whatever the agent allows it to access via tool exposure. Be it built in tools, or MCP servers

As I’ve mentioned elsewhere, not if by “information” you mean semantic content that a mind can process. What they have are vector fields (essentially just numbers) with statistically more or less likely relationships.

If I say, “take me out to the ballgame” to an LLM, the tokens representing the words in the next verse of the song are statistically “close” in the vector database, so it’s likely to generate them. But that doesn’t mean it actually knows the lyrics… or even has those lyrics recorded in a regular database anywhere.

That’s why they hallucinate. The model determines that the next token is something nonsensical, but it has no way of understanding that it has made a mistake. In a sense, it actually hasn’t made a mistake. It’s done exactly what it’s designed to do. It’s just that in the case of hallucinations, its output isn’t useful.

No, they really don’t. That’s not how they work. At least, not if the “information” you’re talking about is real semantic content that real minds can process.

Every piece of information you think an LLM has access to is actually just converted into a stream of additional tokens that are fed into the model to (hopefully usefully) modify the next tokens it predicts. That’s not the same thing as having actual access to information. Tokens are just numbers with statistically more (or less) likely relationships to each other.

I’m not trying to downplay LLMs. They’re architecturally interesting and have genuine uses. I’m just trying to head off a bit of technical inaccuracy.

LLMs don’t. There are tools that can fetch new information and then gets fed into the model as more tokens, but that’s just a special case of what kescusay is saying about injecting text.