I just spent the past hour listening to Leonard Peikoff's lecture on The One In the Many. He described the process in which he formulated his DIM hypthesis, and ended with a timeline his book on it. He said he was caught up with the formulating the problem of induction. Induction is defined as:

The act or process of reasoning from a part to a
whole, from particulars to generals, or from the
individual to the universal; also, the result or inference
so reached. (Open Aether's Dictionary Bot)

I'm going to make a prediction about his conclusion on induction. He's going to conclude with an objective definition of intuitive leaps. Eintstein said that it takes an intuitive leap to formulate a theory or to solve a problem. What is that intuitive leap? Peikoff defined intuition as abitrary in his lecture. The intuitive leap is the arbitrary leap from particulars into a greater whole. That leap alone is not the end. It results in a hypothesis that must be tested and verified against reality to produce a theory or solution.

Let's use Newton as an example:

Newton has been teaching Calculus all day, drawing parabolas on the blackboard for second order equations. He draws one that goes up and comes back down. He goes to eat lunch and gets an apple. He still has parabolas running through his mind and decides to take a walk tossing his apple hand to hand. As he does that he notices something. "Hey, that looks like a parabola!"

That's Newton's intuitive, or arbitrary, leap. Continuing:

Newton goes back to his classroom with his apple, and tosses it in front of him as he stands at the chalkboard. He draws out it's path. He grids it out, figures out its equation, and sure enough it is a parabola! Hypothesis proven, and he applies it to another object. That results in the constant g that is around 10 meters/sec. He comes up with an experiment with cannon balls, and he's predicting where they'll land dead on.

He begins teaching his class about parametric equations. That results in another intuitive leap, and he considers the moon. The Earth is round and the moon must go around it. He does some work to come up with a parametric equation based on his parabolic equations. What do you know, the equation's path goes around the Earth and he's predicting the phases of the moon with it.

Hypothesis proven! So he calls this action gravity, and publishes a book on the theory of gravity.

And that is how the great ideas come about. Through intuitive, or arbitrary, leaps.