my point regarding the set framework was not that it is the correct answer (although within its assumptions it is correct). my point was that because it answers a more general question, that generalized question is reasonably well connected to the original paradox, which counters the original comment to OP stating:

This is very much not the Ship of Theseus

so im basically saying it kind of is in the sense that its a general form of the Ship of Theseus. i was questioning the "very much not" and then it somehow turned into a divisive discussion lol

and no, as i explained in my previous response, i think the Ship of Theseus is an ill-posed question. i said it would be more accurate to define something in four dimensional space. but i guess it kinda just passes the buck. maybe its even more accurate to define something in the dimensions it exists (3 space, 1 time) and compare things based on a spectrum of similarity, instead of using binary -- the same or not the same.

how do you go about answering the question?

the question can be answered from a more generalized perspective. essentially, the question is a special instance of the more general question of when a ship is no longer the same after one or more parts is replaced -- which logically includes the replacement of all parts.

this is a common strategy in logic, especially rigorous logic such as mathematical proofs. recent example being the proof of the Poincare conjecture:

https://en.m.wikipedia.org/wiki/Millennium_Prize_Problems

A proof of this conjecture, together with the more powerful geometrization conjecture, was given by Grigori Perelman in 2002 and 2003. 

another example being, Fermat's Last Theorem was proven by a more generalized problem:

https://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_Last_Theorem

Wiles's path to proving Fermat's Last Theorem, by way of proving the modularity theorem for the special case of semistable elliptic curves, established powerful modularity lifting techniques and opened up entire new approaches to numerous other problems.

btw, in my view the literal question is fundamentally flawed -- regarding replacement of parts, not a literal ship. is a tree still the same tree after its grown? its assuming that the definition of an object is a fixed moment of time in three dimensional space. as soon as you include a fourth dimension, the question and answer becomes more clear. also the levels of four dimensional similarity can be used to describe to what degree a ship is the same, or any two objects for that matter.

but i think i dont understand what youre claiming. what do you believe people think the question is asking?

yeah i wonder if desantis has connections in the real estate industry that is looking to sell off coastal properties to right wing poor people before they get washed away

if youre in engineering and youre looking to make a meaningful contribution to civilization (climate change is a huge problem, we could use your help), i recommend applied mathematics (Stats, DiffEqs and LinAlg) and computational theory. a lot of engineering ideas are modeled and simulated before they ever become real. being able to demonstrate a proof of concept is going to give you way more options than not. but in general as far as math topics go after the calculus courses:

• algorithmic analysis
• complexity classes and orders (big Oh, little oh, theta, little omega, big omega... but almost always big Oh tbh)
• optimization (discrete, continuous, machine learning)
• decidability

• ordinary: things like rabbit population modeling (single variable stuff)
• partial: quantum mechanics, heat, wave equations, navier stokes, general relativity

• lots of eigen (or singular) value decomposition
• special matrices (blocks, sparse, graphs, etc)
• its in everything but we only require students to take one course focused on number crunching by hand -- silly

• linear regression
• experimental design
• categorical analysis

• proofs from basic arithmetic axioms
  • building up from naturals to integers, rationals, reals, complex
  • algebra, delta (and epsilon) limits, fundamental theorem of calculus, and beyond (Lebesgue integrals)

• systems with different axioms
• rings, groups, sets, topology, and on and on, endless topics, all pretty interesting honestly

for a long time i didnt think i would understand these topics in a meaningful way. obviously im not saying i know all of them at an expert, off-the-cuff level, but there arent many problems that are so intimidating or seemingly impossible to understand that i feel i cant solve given enough time -- assuming theyre solvable. to be able to look at problems in quantum mechanics or general relativity or whatever, and understand it enough to ask interesting questions, and even make insights that giants in the field happen to have made in the past (perhaps that havent ever been made), its quite a feeling.

it makes feel awful that people are taught to hate it. its so beautiful.

oh dang, lin alg in college algebra. i can see how that could be more difficult than stats.

really? wow, im genuinely surprised. i found stats to be far more challenging than college algebra, even calc i, but maybe it was the stats prof i had.

im not sure what colleges accept statistics over algebra.

forestry sounds like a brilliant career field to get into. applying algebra and textbook algebra are of course two different things as well as for statistics, but i would really recommend taking a step back, slowing down, and figuring a path to perfecting those subjects. having a strong foundation could significantly increase their career ceiling.

also im a little surprised that one could be proficient in stats without a demonstrated proficiency in algebra. stats is generally regarded as far more difficult. something is up. it might be worth taking algebra at a different school (online is probably easiest).

additionally, as a student that moved around and had to attend 13 different schools, the transferability varies greatly. i had to take multiple courses multiple times because of it. some schools would accept CLEP (exam tests for course credits) and others wouldnt.

i see. i apologize if it came across as promoting Buddhism (im not any religion). although i suppose im not opposed to it - at the very least the secular aspects - i was referring to their definition of the word because i think it captures the concept of compassion best. sometimes people refer to compassion as just meaning that you feel bad for people or something to that effect.

anyway. i would consider that we do have a moral obligation to act for a number of reasons: (1) we live a symbiotic existence; and (2) when i look into peoples eyes i see myself living a different set of circumstances.

1 is a bit obvious. unfortunately not so obvious for some. being good to others and holding the line can break races to the bottom. such as cutting corners on safety to out compete a company can force other companies to do the same.

2 is a bit cosmic and mystical to some i think but i would argue it isnt at all. each consciousness is unique but we all share this remarkable experience of being alive and observing whatever this reality thing is.

id say doing nothing can definitely be immoral. the nazis in Germany were far out numbered, within the country and of course around the world. had people stepped in early, the Holocaust wouldnt have ever happened. climate change is another one. doing nothing is roughly equivalent or indistinguishable from being complicit.

however, if the idea is to act in a way that one believes in moral but violates the consent of others, that is also immoral. examples such as death cults where parents will kill their kids because they believe theyre trying to save their souls before a coming rapture and its the only way to get into heaven.

this is a reason why i argue for the philosophy of consent and compassion being recognized as universal morals because theyre actually able to provide insights into questions that are typically just argued as arbitrary or flexible (ie but its my morality so its the right thing to do regardless of the consequence to others). its not a religious stance. its a logical stance.

at the same time though, it says nothing about the internal morality including struggles with supposed thought crimes (sins of thought). something i most certainly dont subscribe to but honestly probably "sin" less than those concerned with it because its difficult to improve upon yourself if youre constantly beating yourself up. self reflection is good, but it can go too far.

from my recollection (ive done my best to internalize the wisdom but dont remember verbatim), according the Buddhist meaning of compassion, it is the witnessing/experience the suffering of others and being compelled to reduce their suffering (with their consent of course).

i would say compassion is among the least questioned morals and is typically used as a hallmark of a "good" person (a person who does all they can to be as good as they can be). im not sure what these bad things are that you do and how bad they are; however you seem open to the idea of being good or being better, but maybe youre also uncertain/lost/depressed?

lol i was being facetious. i honestly wasnt aware of the specific donation criteria for organ transplants. makes sense that the standards would be high.

although i wonder how scientific it is. i would assume that weve progressed enough scientifically that organs can independently be kept alive and verified for proper function to expand availability.

however, i just wondered if it would create a circumstance that is conducive to unethical/immoral behavior such as shmurder for the sake of getting a kid an organ on a waitlist. but then again, if anything, it would make it less conducive because of the higher availability.

Slight bit of nuance to clarify your slight bit of nuance to clarify here. The original comment said "consented while alive before their organs can go to anyone else". Technically "anyone" else could be an entity in medical science. :)

ive been up in here trynna getta mafuckin scholaship

lol its wild that OP would consider themselves the AH

most people in the US are ignorant. and in my experience, any Americans ive interacted with who are ignorant/naive on certain topics, they at worst the same as what ive experienced with people from other countries who are also ignorant/naive. the majority of the time, honestly, people from other countries are exceptionally xenophobic but look down their noses at us "stupid Americans".

if someone says something xenophobic about a Chinese person, most of them are rightfully offended. but if its xenophobic about a US person, some can even cheer it on and state things are brazen as "i hate Americans".

and even further, some can even talk shit about MAGA - again usually rightfully so in their critique - but are they really ones to talk? some of the generally accepted mainstream culture can be openly racist and have a severe lack of diversity. the US at least tries to bring other cultures into the country instead of maintaining some kind of tribal/ethno-state.

obviously this is all beside the point of the criticisms we all share regarding the US system. we are all subjected to the corrupted crony capitalist rule. and no, we didnt choose this system. it was forced upon us. we live in an oligarchy. to that point, maybe we should stop falling for their trick to divide the people of this world.

lol no such thing as too many Wirtual streams

and entitled

im a bit agnostic to the title of mathematician being gatekeeped because i no longer consider myself mathematician anymore (unless out of convenience when asked about my abilities) because of the nonsensical, arbitrary elitism.

(1) we have so few mathematicians, and the topic itself is so unpopular already. we need so much help in climate change, i really dont think we should be pushing people away who have a love for it, especially those who have good hearts. which leads me to my other point.

(2) when is someone no longer a "mathematician"? we shun people if they dont have a degree, been published, do research, or work in industry/university level. but what about mathematicians working for amoral finance companies, the fossil fuel industry, and whatever other place destroying the world. where is our shunning of the mathematicians who are traitors to humanity? what happened to using our powers for good?

i was gatekeeped my entire 12 year long journey to earn my bachelors degree. my entirety of 18 years of post secondary is filled with unnecessary suffering, just to be too burnt out to put up an effective fight. no, im not a mathematician. im a computational theorist. EVERYONE is welcome to be one. beware, i am a tenth degree black belt in it, so if you challenge me, you might find out :p

agreed, it makes no sense and proves the point of choosing a bear. does the screenshot have to include their self promotion though? i feel like this might be encouraging rage bait/gorilla marketing.

yeah never seen this either but it feels like stolen valor

do you mean the mathematical structures underlying the laws of thermodynamics or how the laws of thermodynamics apply to mathematical structures?

hmmm a professional mathematician. what about an amateur or hobbyist?

when does a person become a martial artist? perhaps its a matter of degree (abstract degree, rather than academic degree)? a black belt mathematician lol sounds kinda cool