Vector arithmetic treats meaning as a manipulable object. You do not just say what you want; you shape the semantic position that represents what you want. This turns search into a language of operations, where addition, subtraction, and blending act like grammar rules.
Start with a Base Vector
You begin with a query that represents your core intent. This might be a sentence, a paragraph, or even a whole document. The system embeds it into a vector. That vector is your base position in the semantic landscape.Now you can move it.
Addition: Emphasize a Dimension
When you add a vector, you reinforce a trait. Think of adding "historical context" to a technical explanation. You are not just adding a word; you are adding a direction in semantic space that pulls the query toward historical discussions.You can use addition to:
- Shift tone: add "plain language" to reduce jargon.
- Shift focus: add "economic impact" to explore financial framing.
- Shift audience: add "beginner" or "expert" to adjust depth.
Addition is a way of nudging your query toward a subspace of meaning without losing the base idea.
Subtraction: Remove an Unwanted Theme
Subtraction removes a semantic influence. This is crucial because real topics overlap. If you search for "information compression," you may get a flood of file compression results. Subtract "file compression" and the query drifts toward the abstract concept rather than the technical niche.Subtraction is not simple negation of a word. It removes a cluster of related meaning. You can use it to:
- Remove format: subtract "bullet points" to favor narrative.
- Remove domain: subtract "legal" to move away from law-focused results.
- Remove framing: subtract "marketing" if you want raw research.
You do not have to manually filter each result. The subtraction reshapes the query itself.
Blending: Composite Intent
Blending combines multiple inputs into a single vector. You can do this by averaging vectors or by weighted sums. The result is a composite intent that contains multiple influences.Example:
- You want a product strategy analysis with a design lens.
- You blend "product strategy" with "industrial design" and add "user behavior."
- The results are not just about one domain but the intersection of several.
This is particularly powerful when you have multiple short texts that each represent part of what you want. You build a query that is closer to how you think: not a single phrase, but a cluster of influences.
Partial Addition and Subtraction
You do not need to fully add or subtract. You can apply weights. A partial subtraction says, "move away from this theme, but do not abandon it entirely." This gives you a fine control that matches real-world intent.Example:
- You want a technical explanation, but not too technical.
- You add a technical vector at 100 percent, then subtract a deeper technical vector at 40 percent.
- The result stays technical but becomes more approachable.
Query as a Journey
Vector arithmetic turns search into a journey. Each operation is a step. You see the results shift, and you decide whether to keep going or adjust. Over time, you can develop a sense of semantic direction, like navigating a map.This makes search iterative but not repetitive. You are not rewriting queries from scratch; you are moving within the same conceptual space.
Practical Patterns
Pattern: Find the Core Idea
If results are noisy, subtract the dominant but irrelevant cluster.- Query: "compression of information"
- Subtract: "file compression"
- Outcome: more philosophical and theoretical results
Pattern: Change Register
If results are too formal, add a conversational vector.- Query: "supply chain resilience"
- Add: "plain language"
- Outcome: clearer explanations and fewer academic papers
Pattern: Explore Intersections
Blend two domains to find overlap.- Query: "urban planning" + "public health"
- Outcome: material on walkable cities, air quality, and social wellbeing
Risks and Limits
Vector arithmetic is powerful, but it can mislead if embeddings are biased or poorly trained. A subtraction might remove more than you intend if the vector represents a broader theme than expected. That is why feedback loops and visualization matter.Why It Matters
You are no longer limited to phrasing. You can operate directly on meaning. This makes search more expressive, more precise, and more aligned with how you think. You shape the query as a concept rather than a sentence.Vector arithmetic becomes a language. You learn to speak it, and the system learns to respond.