# Breakpoints, Categories and Margins of Error
**URL:** https://discuss.criticalfallibilism.com/t/breakpoints-categories-and-margins-of-error/365
**Category:** Elliot Temple
**Tags:** cf-article
**Created:** [October 17, 2021, 12:42pm UTC](https://discuss.criticalfallibilism.com/t/breakpoints-categories-and-margins-of-error/365 "2021-10-17T12:42:01Z")
**Posts on this page:** 8
**Page:** 1
### Author:  [@Elliot](https://discuss.criticalfallibilism.com/u/Elliot)
#### Post date: [October 17, 2021, 12:42pm UTC](https://discuss.criticalfallibilism.com/t/breakpoints-categories-and-margins-of-error/365/1 "2021-10-17T12:42:02Z")
> **[Breakpoints, Categories and Margins of Error](https://criticalfallibilism.com/breakpoints-categories-and-margins-of-error/)**
>
> There are infinitely many quantitative differences between analog factors. But
> there are only a small number of relevant qualitative differences for a
> particular context with a few goals. Qualitative, notable, important, meaningful
> differences –...
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### Author:  [@Fire](https://discuss.criticalfallibilism.com/u/Fire)
#### Post date: [October 8, 2022, 6:22pm UTC](https://discuss.criticalfallibilism.com/t/breakpoints-categories-and-margins-of-error/365/2 "2022-10-08T18:22:53Z")
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:
> 1. (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”
>
> 2. (of a clock or watch) showing the time by means of displayed digits rather than hands or a pointer.
>
> 3. 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.
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### Author:  [@Elliot](https://discuss.criticalfallibilism.com/u/Elliot)
#### Post date: [October 8, 2022, 6:31pm UTC](https://discuss.criticalfallibilism.com/t/breakpoints-categories-and-margins-of-error/365/3 "2022-10-08T18:31:59Z")
> **[Digital vs. Analog Thinking](https://criticalfallibilism.com/digital-vs-analog-thinking/)**
>
> David Deutsch wrote in The Beginning of Infinity:
>
> \> Another thing that they \[computers\] have in common is that they are all digital:
> they operate on information in the form of discrete values of physical
> variables, such as electronic switches...
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### Author:  [@Eternity](https://discuss.criticalfallibilism.com/u/Eternity)
#### Post date: [October 9, 2026, 4:22am UTC](https://discuss.criticalfallibilism.com/t/breakpoints-categories-and-margins-of-error/365/4 "2026-10-09T04:22:35Z")
> [@Elliot](#):
>
> There are infinitely many quantitative differences between analog factors. But there are only a small number of relevant qualitative differences for a particular context with a few goals. Qualitative, notable, important, meaningful differences – differences that connect to some kinda relevant intellectual concept – are sparse and rare.
If there are analog factors, then there are digital factors? Hmm. What are factors?
From [dictionary.com](http://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.
> [@Elliot](#):
>
> If a digital factor involves millions of categories (or even just twenty), then it should be treated like an analog factor and breakpointed. It approximates analog.
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?
> [@Elliot](#):
>
> And if it does fit through your door, then it will generally also fit in your truck, so you don’t really have to worry about both issues, just the smaller size constraint.
Oh, like just focusing on the bottleneck (the door is the bottleneck, not the truck bed).
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### Author:  [@Eternity](https://discuss.criticalfallibilism.com/u/Eternity)
#### Post date: [October 9, 2026, 4:31am UTC](https://discuss.criticalfallibilism.com/t/breakpoints-categories-and-margins-of-error/365/5 "2026-10-09T04:31:41Z")
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).
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### Author:  [@Elliot](https://discuss.criticalfallibilism.com/u/Elliot)
#### Post date: [October 9, 2026, 3:54pm UTC](https://discuss.criticalfallibilism.com/t/breakpoints-categories-and-margins-of-error/365/6 "2026-10-09T15:54:52Z")
> [@Eternity](#):
>
> 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(?).
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.
> [@Eternity](#):
>
> 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?
It’s generally too many to give individualized attention to every possibility, so you need to use rounding or breakpoints.
> [@Eternity](#):
>
> 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).
This makes sense.
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### Author:  [@Eternity](https://discuss.criticalfallibilism.com/u/Eternity)
#### Post date: [October 10, 2026, 5:07am UTC](https://discuss.criticalfallibilism.com/t/breakpoints-categories-and-margins-of-error/365/7 "2026-10-10T05:07:31Z")
> [@Elliot](#):
>
> 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.
What would be analog factors? Something like size or color (which can be treated digitally I guess?)
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### Author:  [@Elliot](https://discuss.criticalfallibilism.com/u/Elliot)
#### Post date: [October 11, 2026, 2:29am UTC](https://discuss.criticalfallibilism.com/t/breakpoints-categories-and-margins-of-error/365/8 "2026-10-11T02:29:07Z")
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.