The thing about vectors is that they have direction and magnitude, and if you have two vectors in a space and you want to find the space between them, you do not walk in a straight line. You navigate through a high-dimensional space where each dimension is a concept and the position in that dimension is how much of that concept you have, and the shortest path between two points in that space is not a line. It is a curve, and the curve is not linear, and the curve depends on the shape of the space, and the shape of the space depends on the data.

Julian Marsh was a data person. He was thirty-three years old and he had founded a company called Idealistic, which was a data company that collected data about data and then used that data to help other companies collect their own data more efficiently. The company was valued at two hundred million dollars, which was a number that Julian did not understand and did not care about and did not think about, because the number was not a vector and the number had no direction and the number was a magnitude without meaning, and Julian cared about vectors.

He cared about two vectors in particular. The first vector was called Ideal, and the second vector was called Greed. Both vectors existed in the same high-dimensional space, and the space was the space of Julian's life, and the dimensions of the space were things like truth and money and fame and fear and ambition and regret and the desire to be remembered and the desire to be forgotten, and Julian's position in each dimension was a number, and the numbers were changing every day, and the trajectory of his movement through the space was not a line. It was a curve, and the curve was complex, and the curve was what he was trying to understand.

The curve was not linear. Julian had learned this in his twenties, when he had tried to be linear about things and the linearity had not worked. He had tried to be linear about his career, and he had thought: if I learn to code and then I learn to sell and then I learn to manage, I will reach the point where I am a successful founder, and the line would connect those three points. It did not. The space between the points was not empty. The space was high-dimensional and filled with data, and the data was about people and about markets and about Julian himself, and the curve through the space was not what he had planned.

The same thing happened with love. He had tried to be linear about love. He had met a woman named Claire in a coffee shop in Palo Alto, and he had thought: if I am kind to her and I listen to her and I learn about what she wants and I give her what she wants, she will love me, and the line would connect those actions to that outcome. It did not. The curve was not linear. Claire loved him for a while. Then she did not. The space between loved and not loved was not empty. The space was high-dimensional and filled with data, and the data was about Claire and about Julian and about the dimensions of their relationship, and the curve through the space was not what he had planned.

He was standing in the office of Idealistic on a Tuesday in 1999, and the office was full of young people in t-shirts and jeans who were building the future, and Julian was standing at the window looking at the trees and the grass and the California sky, and he was thinking about vectors, and he understood that he was somewhere in the space between Ideal and Greed, and his position in that space was changing every day, and the change was not a movement toward one vector or the other. It was a movement through the dimensions, and the dimensions were the data, and the data was his life.

His company was being valued at two hundred million dollars. This was a number that the investors cared about and the press cared about and the other founders cared about, and Julian did not care about the number but he understood that the number was a vector, and the number had direction and magnitude, and the direction was upward and the magnitude was two hundred million, and the vector was pulling him through the space, and he could feel the pull in the dimensions. His position in the money dimension was changing. His position in the fear dimension was changing. His position in the ambition dimension was changing. His position in the truth dimension was moving in the opposite direction.

He was interpolating between two concepts. Interpolation is the process of finding values between two known values. If you know the value of a function at two points and you want to know the value at a point between them, you interpolate. Julian was interpolating between Ideal and Greed. He was finding his own value in the space between those two concepts, and the value was changing every day, and the change was not linear, and the curve was complex, and the curve was what his life was.

Claire had left him six months before, and he had tried to interpolate between the man she had loved and the man she was leaving, and he had thought: if I can find the vector that points from me to the man she loves, I can move along that vector and become that man, and the interpolation would give me the value of the man she loved at every point between the man he was and the man he could be. It did not work. The space was too high-dimensional. The data was too complex. The curve was not a line.

He went home that evening and he wrote. He did not write code. He wrote on paper, in a notebook, and he wrote about vectors and about the space between Ideal and Greed and about the dimensions of his life, and he wrote about Claire and about the curve through the space between the man she had loved and the man she was leaving, and he wrote until the notebook was full and then he wrote in another notebook and then he wrote on the walls of his study, and the writing on the walls was the only honest thing he had done in a year.

The investors came the next week. They were men in suits who talked about growth and scale and exit strategies, and Julian listened and he thought about vectors and he understood that the investors were vectors, and their direction was away from Ideal and toward Greed, and their magnitude was money, and the vectors were pulling on him, and he could feel the pull in the dimensions, and he could feel his position in the truth dimension moving in the opposite direction.

He signed a term sheet. The term sheet was a vector. It had direction and magnitude and it pulled him through the space. His position in the money dimension rose. His position in the ambition dimension rose. His position in the fear dimension rose. His position in the truth dimension fell. He interpolated between Ideal and Greed and found his new value, and the value was closer to Greed than it had been a week before, and the change was not a decision. It was a curve through a high-dimensional space, and the curve was shaped by the data.

Claire came back. She came back three months later and she stood in his office and she looked at him and she saw that he had moved through the space and his position was different, and she saw the change in the truth dimension and she knew that she could not interpolate back. She knew that the curve between her and the man she had loved was not a line and the data had changed and the space was different and the curve was not reversible. She left again.

Julian kept writing. He wrote every day. He wrote about the vectors and the space and the dimensions and the curve. He wrote about the thing he had learned: that love is not a vector. Love is the curve through the space. Love is the data. Love is not the direction and magnitude. Love is the high-dimensional shape of a life. And the only way to bear witness to that shape is to write it down, to record the position in each dimension, to document the curve, because the curve is what exists and the vector is just an abstraction and the abstraction does not capture the data.

The company grew. The valuation rose to two billion dollars. Julian moved through the space. His position in the money dimension was extreme. His position in the truth dimension was low. He interpolated between Ideal and Greed every day, and the interpolation was a curve, and the curve was his life, and the curve was what he was, and the only record of the curve was in his notebooks, and the notebooks were filling up, and he was writing on walls, and the walls were full, and he was running out of space in the high-dimensional space of his life, and the notebooks were the only documentation he had of the curve, and the curve was the only proof that he had existed in the space at all.

He sat in his study one night and he looked at the notebooks and he looked at the walls and he understood that the curve was the love. The curve was not the vector toward Greed or the vector toward Ideal. The curve was the actual shape of his life through the space, and the curve was the only thing that was real, and the vectors were abstractions, and the abstractions were not love. The love was the data. The love was the curve. The love was the act of writing it down, because the act of writing is the act of bearing witness, and the act of bearing witness is the only defense against the erasure that comes when you move so far through the space that you can no longer remember your starting position.

He wrote one more sentence: Love is not a direction. Love is the curve.