1. one is profound (but probably false or nonsense)

2. the other meaning is trivial or obvious (but true)

These paired meanings can trick our brains into thinking that the idea is both profound and true: we experience the profoundness of one meaning while experiencing the truth of the other meaning. These are phrases that exploit the odd nature of our minds.

Some examples are (arguably):

• “Love is just a word.”

• “Everything happens for a reason.”

• “There is no ‘I’ in team.”

• “Beauty is only skin deep.”

I’d like to propose a new term: “deepiful.”

A deepiful is a statement that seems trivial or dumb but which has genuinely profound consequences!

A deepiful is the opposite of a deepity (since a deepity is dumb but sounds profound, whereas a deepiful is profound but sounds dumb!).

Here are some examples.

Deepiful 1: if each of a system’s states is equally likely, and we group them into categories (e.g., “mixed up” states vs. “organized” states), then the things that actually happen will (obviously) tend to be from categories containing more states.

This is totally trivial in a sense, yet it’s the basis of entropy!

Deepiful 2: if some organisms are more successful at passing down their genetic material than others, then organisms similar to them will grow in relative numbers.

This is also trivial, yet it’s the basis of natural selection!

Deepiful 3: if you define new words for things and use the shortest words for the most commonly said things, you’ll be able to communicate using fewer letters. Keep going, and you’ll have the shortest way of saying things.

Another trivially true statement, yet it’s the core of information theory!

Deepiful 4: if you have a bunch of dots on a piece of paper, you can draw with a pencil from left to right to connect them together in an endless variety of ways!

This is obvious, and a young child can easily see that this is true, and yet it’s the basis of the concept of overfitting in machine learning!

This piece was first written on September 18, 2020, and first appeared on this site on April 22, 2022.

The space of possible ideas is ABSURDLY, almost UNBELIEVABLY large. If we thought about a different idea every second for our entire lives, we wouldn’t begin to scratch the surface.

As a simple example, let’s consider the number of two-player competitive games played on an 8×8 chessboard, where each player starts with 16 pieces and each piece has a pre-determined fixed rule for how it moves across the board and captures other pieces. There are far more than a quintillion (i.e., 1,000,000,000,000,000,000) such games, and while many of these games are less than entertaining, there will be games in this set that are far better than chess along any dimension of gaming that you should care to consider. In other words, chess is our limited human attempt to mine a tiny corner of game space.

Of course, this type of 8×8 board game is just a tiny subset of all types of games, which is, in itself, a minuscule subset of all types of ideas.

This VASTNESS of idea space is why I find it so valuable when a person or book mentions a powerful, plausible idea that I’ve never heard before, even if no evidence is provided for why I should believe the idea.

The chance that you would independently have thought up an idea that someone tells you about is vanishingly small (even if you feel like you COULD have thought of it). The act of raising a powerful, plausible hypothesis to your awareness can be hugely valuable. Mere identification of a point in idea-space can involve a ton of work, even if it doesn’t seem like it.

Of course, we can then do our own vetting of ideas, even if the people who bring them to our attention don’t give us strong reasons to believe them. For instance, we can check them against facts that we already have strong reasons to believe. And we can ask ourselves, “does this idea contradict the evidence we have, or line up nicely with it? Does it explain things that confused us before and gel with other things we know to be true?” If we’re serious about testing the idea, we can even go out and gather new evidence about whether it’s true.

Some great ideas seem obviously true once you hear them. In fact, I’m a really big fan of trying to state the obvious; but not just any obvious things. The obvious things that people have likely not yet consciously considered. That is, what I like to call the “obvious and unsaid.” It bothers me when people dismiss obvious but rarely encountered ideas on the grounds that they seem obvious once you hear them because obviousness can be an asset rather than a liability.

These obviously true ideas can be especially valuable because they are easy to vet as being correct, yet due to the vastness of idea-space, they very easily could never have occurred to you before. So, stating obvious ideas that are rarely thought about, but which have important implications, can be an extremely efficient way to transmit value to others.

On a related point, when people say “everything’s already been done” or “there are no new ideas left,” the only way these statements could be sensible is if we interpret them as claims about humans rather than claims about ideas. For instance, as a claim that human minds are so similar to each other that, in the VAST space of possible ideas, we’re confined to a sad, well-trodden, little corner of derivative pseudo creativity.

However, I’m much more optimistic than this: while much is derivative, I think there are new ideas all over the place that we can learn to look for. As one person finds a new idea in a corner over there, and they share it over here, human knowledge advances. What’s more, I think that seeing new ideas as “derivative” is kind of missing the point.

Yes, good new ideas are often built from pieces of old ideas, but there’s nothing bad about that. Bricks are the building blocks of houses, and ideas are the building blocks of ideas.