From Curiosity to Equation: When to Ask for a Formula

One of the most liberating aspects of this new approach to science is the freedom to begin with a question rather than a formula. In traditional science classrooms, it’s common to be given a formula and asked to use it. But in real-world science—and especially in Sphysix—the process often runs the other way around. You observe something. You become curious. You collect data. Then, at some point, a question arises: What relationship governs what I’m seeing? That’s when the formula becomes meaningful.

But how do you know when it’s time to ask for a formula? Here are some signs:

You notice a pattern in your data.
Maybe a graph of height vs. time curves smoothly upward. You wonder, Is this a parabola? That’s the time to ask, “What kind of function fits this data?”
You want to predict something.
You’ve measured how temperature rises over time, and now you’d like to know how long it will take to reach a certain value. That’s when a formula can turn your data into a forecasting tool.
You want to understand the underlying physics.
Your graph suggests acceleration, but you’re not sure how mass and force relate. That’s the time to ask, “What is the equation that connects force, mass, and acceleration?”
You want to compare theory to experiment.
You measured how fast sound travels through air. You want to know if it matches the textbook prediction. The formula gives you the benchmark.

With an AI assistant like ChatGPT, you don’t need to know the exact wording of the formula. You can ask questions like:

“What’s the relationship between force, mass, and acceleration?”
“What formula predicts the period of a pendulum?”
“How does resistance affect current in a circuit?”
“I see a pattern like exponential growth—what might the equation look like?”

The key idea here is to approach math not as an obligation, but as a tool—one you reach for when it serves your exploration. Formulas are powerful. But they become alive when they answer a question you truly care about.

In Sphysix, we don’t begin with formulas. We let the questions come first. Then, when it’s time, we bring in the math—not to impress, but to illuminate.