[fnovd]

There is no contradiction because there is no limit of knowledge.

The limit of y = e^x is infinity. You can keep increasing x and y will increase exponentially. So you plot the function, let's say with the x axis going up to 10 and the y axis going up to e^10. The graph shows very clearly that, while there was progress before, we have even more progress now. Exponentially more, even! What came before is dwarfed by what we have now; if you look at the range of y for x values 9-10 you can see how little of a difference all those others values (1-8) had between one another, compared to the changes we have now. The rate of change is so high that we're basically in an era of semi-complete knowledge. We must be at some kind of inflection point, this is truly a unique era of understanding.

Then you repeat. Set the x axis to 100, and the y axis up to e^100. Oh wait, it's the same graph. That's because it's always the same graph. It's scale-invariant. The slope at every point is always whatever y is.

We're always at right at the limit of explaining the "essential nature" of the universe because the "essential nature" of the universe can only be (to us) what we can understand it to be. We chose e^10 as the limit of the y-axis in our first exercise because that's all the knowledge we knew about. We chose e^100 as the limit of the y-axis in our second exercise because that, too, was all the knowledge we knew about. Choosing these random values as the limits of our function (i.e. the limit of the "essential nature of the universe") leaks information into the visualization that will always paint a picture showing that we're at the most transformative time there ever was.

When we do it that way, we will always come to the same _wrong_ conclusion. We will always dwarf what came before and be dwarfed by what comes after. To think that we're actually living in an inflection point is hubris, it's wishful thinking, it's the sour grapes of mortality.

[ndsipa_pomu]

> There is no contradiction because there is no limit of knowledge.

I don't think we know enough to be able to state that definitively. It's feasible that the universe behaves mathematically (it seems to so far) and thus possible to gain a thorough understanding of the underlying principles, if not the specific facts (c.f. with understanding how to produce integers yet not "knowing" all the integers).

Even if the universe doesn't have underlying rules to be discovered, there's still a limit to number of configurations available to particles etc. within our visible universe. Although that number might appear to be infinite to us, it's actually drastically closer to zero than to infinity.

So, if there is indeed some finite limit, then using y = e^x would be the wrong function as that doesn't approach a finite value.

[fnovd]

This leads to a more fundamental question: What is the universe?

Is the optimal move in an a given chess board considered knowledge? If so, can't we create entirely new sets of knowledge from the emergent properties of an arbitrary set of rules called a "game"? If we can create an infinite set of arbitrary combinations of rules and states (games), then knowledge should be infinite. Maybe not all knowledge is scientifically applicable, but we have learned a great deal about science and engineering from studying chess. In fact, we are starting to learn more about learning as a process and not as some magical thing that human beings can do, just from studying the best way to make decisions in this totally-contrived and scientifically-useless game.

Taking this a step further, let's look at the animal kingdom. If learning about the intricacies of the mating habits of birds can help an arbitrary bird increase its impact on the future gene pool, is that knowledge not worth something to the bird? To bird society? Are the things we learn about ourselves knowledge? They certainly have utility. Is there any limit to what we can learn about ourselves, about the stochastic process of life? Is life not part of the universe?

Is computer science even knowledge? It seems if we're more directly concerned with the physical nature of the universe, we ought not to care about what the system of a computer actually does; we only need to care about what it is, about its physical structure. Except, that's not actually how we pursue knowledge or science at all.

In my view, Asimov's sentiment can be reduced to a complete tautology: we're at the point where we know almost everything there is to know about the things we think we can know.