Interesting post, abstractions are the few stable-ish quantities that weren't eaten by chaotic noise.
Exponentially growing errors are not always chaotic. Suppose you have around 1000 starting cells, with a 1% error in the population size. The number of cells doubles in each hour. The absolute error of the population size can be 10.24 times larger than the initial population 10 hours later; however, the relative error remained 1%. (The billiard ball example is still chaotic, but the tilde character does the heavy lifting: 31.4 with 10% error is an imprecise but usable measurement, sin(31.4 +- 10%) is garbage.)
If the relative error of a quantity remains bounded as the elements of a system interact, then this value could be a useful abstraction.
I do not think that the prototypical scientific method is not valuable in the long term.
In any experiment, there are lots of naturally varying parameters (current phase of the Moon, air pressure, amount of snow on the slope), and there are lots of naturally constant parameters (strength of gravity, room temperature, amount of hydroxyhypotethicol in the solution). There are base and derived parameters. The distances from the sun and the orbital periods vary between the planets, but (distance)^3/(orbital period)^2 is constant.
In the experiment, you measure X and Y. If X vary, but Y is constant, then they probably have no relation. Suppose that we want to find out that is X related to B or C. We control B to vary, and set C to a constant. If X vary, then it is not connected to C, if X is constant, then it is unrelated to B.
In the second scenario, you try to find the minimal set of base parameters that are related to X (growth rate). After some testing, we found that (growth rate) ~~ (initial age). After we found that connection, we can rule out the uncontrolled varying parameters, but there may be a connection between X and an uncontrolled constant parameter. It is possible that (growth rate) ~~ (initial age) times (1 + (amount of hydroxyhypotethicol)), and the first scenario will test these kinds of connections.
It is not enough to find which parameters won't affect the experiment. It is also important to find out which parameters could affect the experiment.
I think a useful concept would be the colour of bits. For example, a digital song can be bought on a CD or downloaded from the internet. The computer does not see a difference between them, because it just sees a number, but in the eye of the law, one of them is legal, the other is not.
The number on the CD is coloured "green", the downloaded number is coloured "red". Green numbers are legal, but red numbers are not. If you upload a song a from CD, it will be red because you can only send red numbers. However, if the studio produces a new CD, it will have green numbers because they have the copyright to the song.
Anyone can copy a digital artwork because it is just a number, but the copied number will be "yellow" coloured. With an NFT you do not buy a number, you buy the right to make this number "blue". This right can worth a lot of money if a blue number has a higher value than a yellow number.
I am a Mathematics university student from Europe. I don't comment often, and English isn't my native language, sorry for any mistakes in my tone or my language. Despite my username, I am not a Colony of ants from Outer Space. I'm reading this site since March, but I heard about this site a long time ago.
I was always interested in computers and AI, so I found LW and Miri in 2015. But I didn't stay at that time. I think my entry point was when someone (around 2018 maybe?) recommended Unsong on reddit because it was weird and fun. I read a lot of stories on the rational fiction subreddit. (Somehow, I did not read HPMoR. Yet.) This March, there was a national lockdown, I got bored, so I looked up again SSC and this site. Since then, I read a lot of quality essays, for which I'm thankful.
During this winter, I try to participate more in online communities. I am interested in any topic, and I know a lot about mathematics and computers, so I might write something adjacent to these subjects.