## There’s a big difference between nothing and almost nothing

Monday, September 18th, 2017

The most valuable insights are both general and surprising, Paul Graham says:

F = ma for example. But general and surprising is a hard combination to achieve. That territory tends to be picked clean, precisely because those insights are so valuable.

Ordinarily, the best that people can do is one without the other: either surprising without being general (e.g. gossip), or general without being surprising (e.g. platitudes).

Where things get interesting is the moderately valuable insights. You get those from small additions of whichever quality was missing. The more common case is a small addition of generality: a piece of gossip that’s more than just gossip, because it teaches something interesting about the world. But another less common approach is to focus on the most general ideas and see if you can find something new to say about them. Because these start out so general, you only need a small delta of novelty to produce a useful insight.

A small delta of novelty is all you’ll be able to get most of the time. Which means if you take this route your ideas will seem a lot like ones that already exist. Sometimes you’ll find you’ve merely rediscovered an idea that did already exist. But don’t be discouraged. Remember the huge multiplier that kicks in when you do manage to think of something even a little new.

[...]

And of course, ideas beget ideas. (That sounds familiar.) An idea with a small amount of novelty could lead to one with more. But only if you keep going. So it’s doubly important not to let yourself be discouraged by people who say there’s not much new about something you’ve discovered. “Not much new” is a real achievement when you’re talking about the most general ideas. Maybe if you keep going, you’ll discover more.

It’s not true that there’s nothing new under the sun. There are some domains where there’s almost nothing new. But there’s a big difference between nothing and almost nothing, when it’s multiplied by the area under the sun.

1. Jim says:

“F=ma” actually tells you virtually nothing. It’s just a tautological definition. The important thing about motion in Newtonian mechanics for say a system of particles is that the “force” in the above equation is always a function of the position and velocity of a moving body and does not involve for example higher derivatives. So F is always given by a function of the position and velocity of the particles involved and the equation “F=ma” reduces to expressing the acceleration of each particle as a function of the positions and velocities of all the particles.

If the “force” F were given as a function involving the second or higher derivatives of the particles involved then formally we could still write “F=ma” but the resulting differential equations would in general be of a totally different type from those actually arising in Newtonian mechanics.

The crucial point of Newtonian mechanics is that the equations of motion are a certain type of second order differential equations. The expression “F=ma” is a formal tautology.

In developing say classical celestial mechanics of point particles one doesn’t even need the concept of “force”. The concept of “force” then adds nothing to the differential equations which determine the motion.

2. Wang Weilin says:

“It’s not true that there’s nothing new under the sun.”

This statement is false.

The laws of physics, chemistry, quantum mechanics, thermodynamics, etc., for all purposes here, have been constant for billions of years. The fact the we observe them with human understanding or have learned to use them in the last few centuries doesn’t make them new…just new to us.