After trying several passes at the first few paragraphs of this article, I’m realizing that this is a pretty hard article for me to read. I think I’m having trouble right from the first sentence:
There are infinitely many quantitative differences between analog factors.
I think my difficulty is understanding what “analog factors” means. I looked up the definition of analog and found this from google:
relating to or using signals or information represented by a continuously variable physical quantity such as spatial position, voltage, etc.
Using this definition, I guess analog factors are those that could be placed on a number line with all real numbers. You could have infinitely many quantitative differences between analog factors in the same way as there are infinitely many real numbers between any two real numbers.
This sentence also tripped me up:
There are also digital factors that already involve only a few categories or just two categories.
I think that I have mostly been conceptualizing the word “digital” as synonymous with binary. So, I looked up digital and found this definition from google:
(of signals or data) expressed as series of the digits 0 and 1, typically represented by values of a physical quantity such as voltage or magnetic polarization. relating to, using, or storing data or information in the form of digital signals. “digital TV” involving or relating to the use of computer technology. “the digital revolution”
(of a clock or watch) showing the time by means of displayed digits rather than hands or a pointer.
relating to a finger or fingers.
This definition seems to indicate that digital often does mean binary but not entirely. It made me realize that digital is based off the word digit, which apparently means the numerals 0 to 9. So, I guess digital factors are like the integers, which have a finite number between each other.
If there are analog factors, then there are digital factors? Hmm. What are factors?
From dictionary.com, factor - “one of the elements contributing to a particular result or situation”
Ok, that makes sense. That’s in-line with what I thought a factor is. So some of the elements that contribute to a thing can be analog and others digital(?).
It makes sense for analog factors to have infinitely many quantitative differences.
I get the idea at millions (and other large-ish numbers). Why something like 20 (and presumably 15 or 30)? More precisely, why does something like 20 approach analog?
Oh, like just focusing on the bottleneck (the door is the bottleneck, not the truck bed).
Some things I was thinking of/noticed that are possibly breakpoint related (and other stuff):
I recently learned about a breakpoint related(?) thing in my class. It was about breaches in contract law.
The idea is that there are different types of contract breaches depending on if something big(?) happened or not. If something happened that defeats the main purpose of a contract (idk like not paying or not doing the work) then you have a material breach. Contract law allows you to get out of the contract and possibly(?) get money or something. On the other hand, if a breach is about something minor than the contract stands (you can attempt to sue for the minor breach, but you still have to perform the contract).
The classic case is Jacob and Youngs vs. Kent. Apparently Jacob and Youngs used the wrong brand of wire in a project. The court rule that since the wire was just as good in all important respects as the brand Kent wanted, the contract was fine and Kent could not get out of it.
I think it’s relevant that the law differentiates between those breaches that matter to the contract and those that don’t (instead of treating all breaches as defeating the contract).
yes. when buying a house, having a pool or not is digital (and binary). number of bedrooms is digital and non-binary if you’re looking at houses with 1-5 bedrooms, so there are 5 possible values for bedrooms.
It’s generally too many to give individualized attention to every possibility, so you need to use rounding or breakpoints.
This makes sense.
What would be analog factors? Something like size or color (which can be treated digitally I guess?)
Color would be analog if you did light frequency but red/green/blue/purple/etc is digital/categories.
Size and other measurable quantities are analog in general (but if you’re buying a drink, maybe the only sizes are small, medium or large, which is digital). People also commonly try to treat things as analog quantities like quality, comfort or beauty which aren’t measurable in the same way as length, time or temperature. Whether comfort involves a hard to measure analog quantity, or several of them, or is actually something else, is debatable.