Off-topic: How much do we know what we don't know?

At the risk of alienating all four of my faithful readers, I'll discuss something off-topic that I happened to have thought about randomly and found intriguing enough to write down. Please bear with me while I get philosophical.

How much do we know what we don't know? And how has this changed over time?

I mean, as human beings, we discover new things all the time, through science, experiments and by accident. And we also often discover things that we can't explain. For example, we know we don't know if P=NP. We know that we don't know if the universe is infinite. Or if string theory is true. Or if there's life on another planet.

So, how much do we know now we don't know, say, in relation to what we do know? Is it a 2-to-1 ratio of known unknown to known? Or is it more like 1.5-to-1? Or 1-to-1? And how has this changed over time?

Imagine that, in the beginning of times, we didn't know anything. But we also didn't know we didn't know anything either -- we were totally ignorant of what we didn't know. So this situation might look like point A in the graph below: a little knowledge of something and no knowledge of anything else.

With time, we discovered fire, but we didn't know how to make it. Then we did. And we knew there was day and night, and phases of the moon. But we didn't know why. Maybe that was at point B in the graph. That one took a long time to solve, I suppose.

Throughout history, we learned a lot of stuff and a lot more that we knew we couldn't (yet) explain. With science and technology, we discovered so much new stuff, I believe our knowledge has grown exponentially in the last 100 years.

Why did it take us so long to achieve such growth rate? I don't know for sure, but I believe it has to do with science, technology, prosperity and the nature of discoveries. Each breakthrough led to a new baseline that benefited everyone, exponentially.

For example, by learning how to grow our own food, not only everyone benefited from having more and better quality food, but we also benefited from not having to worry so much about getting the food, which in turn freed us up to discover new things -- say, how to build better houses, or treat a disease.

But, going back to the point, how much new stuff have we discovered that we can't explain?

My guess is that what we know we don't know has grown at least twice as fast as what we do know. For each new DNA sequence we studied we probably found at least another two that we can't yet explain. And for each new molecule, another two have been found by accident. And for every theory explaining something, two conjectures arose trying to explain something else.

My guess is that the graph of human knowledge about the known and the unknown has grown like this, with exponential recent growth, and at least double that rate for the known unknown.

What do you think?

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