Many philosophical, ethical, logical, and legal problems are fundamentally rooted in the continuous-discrete boundary. The world we reside in is continuous, yet we conceptualize them in categories with distinct labels. This served us well; horses and apples are sufficiently distant. If someone confuses between them, we'll ridicule them for their insanity. However, not all examples are as simple as that. Some related philosophical arguments / questions are: - [Zeno's paradox of motion](https://plato.stanford.edu/entries/paradox-zeno/) - [[Ship of Theseus]] - [[Sorites Paradox]] - this is a fascinating example as *a grain of sand* is an atomic quantity, yet this paradox arises. In general, such a "paradox" can always be constructed by the following binary-search esque "algorithm". > [!note] > consider two concepts $P$ and $Q$ with instances $p$ and $q$ that are "sufficiently different". > > Choose an instance $x$ that is "between" $p$ and $q$. > - Where does x belong? If $x$ does belong in a concept, then WLOG $x \in P$. > - Is it "self-evident" that $x$ belongs in P? Or are there questions. > - How divergent is $x$ from a *platonic* instance of $P$? > - Can $x$ (and other known instances of $P$) can be used to articulate a criterion for what $P$ is? > - replace $p := x$ and continue the algorithm. > > If $x$ doesn't belong in neither $P$ nor $Q$; then > - does $x$ form a new category $X$? If so, then it creates multiple subproblems. One can continue this exercise between $P : X$ and $Q : X$. > - is $x$ an amalgamation of $P$ and $Q$? then $P$ and $Q$ are not disjoint categories, but can intersect, with $X = P \cap Q$. # Real-life examples ## Historical Eras There are two types of era-defining going on. - post-hoc eras; defined by future historians to categorize the past. - current eras; defined by the current actors (politicians, marketers) to differentiate the present from the past. ## Difficulties of dating the clear beginning / end - example: when did the [[French Revolution]] begin / end? most point to [[Coup of 18 Brumaire]]. ### The current eras - 4th industrial revolution - anthropocene - 3rd wave, by [[Alvin Toffler]] - [[web3]] ## Specie - [What is a specie, anyway](https://www.nytimes.com/2024/02/19/science/what-is-a-species.html) - https://news.ycombinator.com/item?id=39433339 ## languages vs dialects Language is a different dialect with an army. ## patterns and anti-patterns [[Design Patterns]], [[Anti-pattern]] ## Tax Codes Tax code is full of discretization with severe consequences, as different tax rates are not continuous. - What is a *sandwich* - https://tax.kenaninstitute.unc.edu/news-media/what-is-a-sandwich/ - https://www.tax.ny.gov/pubs_and_bulls/tg_bulletins/st/sandwiches.htm