It's scripted and staged...

@@dark_sunset "if there's unlimited pieces of glitter we need unlimited pieces of jar" lol what part of that sounds scripted to you?

she already could handle more than me… you can have more infinities than infinity? is that like when i told my mom i loved her infinity plus 1 and thought i had her beat? lmao you mean she could’ve said i love you times infinity plus another infinity…? jeez maybe i did love her more lmao

@@ChunderThunder1 he’s just disappointed that a child is already thinking at a higher level than he is.

@@dark_sunset I love how people say that, when it is clearly easier to just have an expert tell something to a kid and have them react to it, than writing dialogue that sounds authentically kidlike and getting a childactor to remember it. Also if it were scripted wouldn't you write a kid character who is intuitively wrong more rather than less often?

Lmao 😂

Well said.

Glitter is forever.

😂😂 soo true.

The herpes of the craft world

Her phd in mathematics is another way to tell she understands the subject lol.

This is how circular reasoning works. If you explain how your lies is the truth you have to do it that way otherwise people will laugh at you.

@@mauricemenard2243why are you copy pasting this comment

Ask the god Hazard .@@pinto_8261

If the god of atheist HAZARD is able to create life that no one is able to reproduce he should be able to respond to this simple question.@@pinto_8261

Infinity is a sandwich

@@ATIARImusica tasty sandwich

Probably tastes like chicken

Brain development.

This is how circular reasoning works. If you explain how your lies is the truth you have to do it that way otherwise people will laugh at you.

Heck yeah, it's a super endearing quality you see a lot in mathematicians. I figure you only become a professional math doer if you really, really like doing math.

Being an expert is one thing, being a communicator is unrelated. Being both is really unusual. Brilliant.

She once got into an argument with a triangle and honorably conceded when she determined it was right.

Every mathematician is like this, almost down to a t in personality. It's just the effect really understanding math has on people, no matter who they might be

she's on molly

I thought it would take FOREVER to explain. ;)

Yeah, she's sharp.

Absolutely. There is a kind of magic that happens when you hear a person talk about something they are passionate about. You could be totally uninterested in the topic before, but suddenly something sparks when you hear them talk, and you want to know more. It's fascinating and beautiful.

@@AracneMusic we kinda are a good passion detector , don't it? you just know that they put their lifetime into the subject before making the every sentence to make us understand. Definitely beyond fascinating ,i would say.

As a fan of maths, she communicates extremely complex concepts very precisely with no filler sounds. The points she made about the axiom of choice blew my mind. People talk about how counterintuitive it is but the examples she chose are so perfect yet not the natural go-tos that I've seen people mention. I've mainly heard the Banach-Tarski Paradox like the student mentions. Doing induction on the reals is so mind-boggling. It's like drawing infinitely many, infinitely small dots on a page to colour it in. And then the circle thing? Chef's kiss.

this was obviously scripted

True .

@@ladderlappen4585 why do you think so ? I'm saying true to the wide variety of students .

repent to God

​@@Baggerz182Or what

No? At the experts state, they were literally stating theorems and ideas previously used in mathematics to explain infinity, just like in the other stages

Once you stop counting you start thinking.

It's the equivalent of asking "can there be something that isn't a part of everything." Infinity isn't a description of a product, it's a description of a process that has no end. To restate: it isn't simply that there are "infinite integers" it is that if you were to try and create the set of integers, that process would not end. And so, any description of infinity needs to include the interval of calculation to make comparisons between the processes (and an injected stopping point). eg, if you were limited to calculating the numbers of "X" category between -10 and 10, 1 per second and had 10 seconds, you might come up with 0-9, or 1.1 1.2 1.3 ... 2.0 or -10, -9.9 ... -9 which we can prove are different % of the infinite sets of integers v. natural numbers v. real numbers. It depends on the process used.

There's the classic infinite hotel thought exercise.

@@nathanberrigan9839 my thoughts went to the diagonal argument and countable vs uncountable infinity

As a mathematician I often tell people that the (countable) infinity is not the biggest you can think of and sometimes they even get angry with me and tell me that if something never ends, there can't be anything bigger. Especially people on social networks quickly get aggressive. I think people should learn the concept of infinity as soon as possible. Maybe at the age of that first girl. I think at that age students would already understand the Cantor trick. At the same time the would learn the concept of proof by contradiction, which may be the most essential tool in maths.

​@@skyscraperfan I still don't get how some invites are bigger than others. Is it more so that you can get to a bigger number faster? But the "size" of each set is the same? I saw someone draw a circle centred on a point x, and someone else drew a bugger circle centred on the same point. Then someone claimed that for every point in the small circle, there would be the same point on the big circle (injective). But then they tried to say that the bigger circle had more points and was therefore a bigger infinity. That's just false to me. For every point in the big circle, there is also a point in the small circle. If you couldnt always find another point, it wouldn't be infinity. Both of those circles have the same "amount" of points to me. Is a countable infinity perhaps something that is more tangibly infinite. Whereas uncountable infinite has so many "linking" points that you count it far enough. But each set is the same size

because there's no longer any huge gap in their knowledge (expert) so i'm guessing that the only thing they can discuss is about their overall understanding about infinity and it's significance in the world

What you just laid out is the overall problem with the field of science in general. When you close off the circle and only invite experts to talk to experts no one teaches anything, nothing new is actually invented of real value and all dialog devolves into mental gymnastics and thought exercises.

Because you can't trick another expert about the existence of infinite out of the world of ideas.

Mathematics is philosophy.

​@@vandel_mathematics truly is the universal language of this world 🫡

So true, I still regret not having a good professor my whole grad life, in high school, I was so much addicted to Maths and all the wonders it had in it, but later on I started hating Maths just because the professors sucked out all my interests....All I had to do was learn and mug up the questions and their solutions delivered by the professors because that was only what used to show up in exams, no creativity, nothing...

@@bumblebeeflies20 that's interesting, I'm curious what the highest courses you took were. I've found that my upper level math courses were all solely proof-based and required lots of creativity and critical thinking rather than just computation

she's simply a superb communicator

She? Watch your language.... 😂

@@arisgreek8697 keep yourself safe 😁😁

Who struggles with knowing what infinity is and where it's used?

​@@marrycinati2604 wait until you meet an average adult.

@@marrycinati2604 Bro i know adults who cant do division. Trust me people are dumb

Such as ? What concepts did she understand that some Adults didn't ? Give examples .

​@@philharmer198that more than what you can count doesn't necessarily mean it is infinity lol..

What's that white thing on the college student's head? At 6:40 ?

@@ishakHafiz12I would assume it’s a Yamakah.

@@masneomlock5344 wow Though somebody already told me that it's something called kippah and then i googled and found out that yamakah and kippah both are kinda the same thing. Thanks though

"she's" trans you know? "she" has balls.

How do you know it’s a woman? What is a woman?

Well, we can imagine infinity just fine. We make bad conclusions with it, but that is different than not being able to imagine it. Most people reach erroneous conclusions about most things they imagine.

There is no use in knowing what infinity means to real life. I think it's much better for retiring individuals to study aspects of medicine, so that they could understand their doctor appointments, and what they're conditions means. It is much more interesting to study what is already there to what is theoretically possible

Do it now! Like in the video most concepts are intuitive and you don't have to do the math. Then in most cases it is much more useful to know that a concept exists rather than knowing how to do it exactly.

You say "videos like this" so I assume you've seen other maths stuff on youtube, but Numberphile is a cool channel for anyone that hasn't seen it

@@josephdahdouh2725 Not everything you do has to be useful, and things that don't have real world applications can still be interesting. If you have the time and you find it interesting, why not learn about anything you want to?

i see the pun in here and i hate it but yeah agreed shes great

She riehly is

having studied math myself and partially crossed over courses with soon to be teachers, and i gotta say that's kind of unsurprising to me. Math teachers aren't mathematicians. They are teachers. They stop in their pursuit of mathematical knowledge to be able to put time into getting better as an educator. But at some point, you reach a level of mathematics, where the level that the teacher is familiar with is no longer sufficient such that the teacher has enough excess knowledge to be able to explain things very well. Basically the higher level you go, the more important math will be and the lower (younger) you go, the more you need to be an educator and well versed in pedagogics. High school is somewhere in the middle of that. Yes, being a good educator is important, but if the teacher doesn't know their Taylor Series for example, then it gets a lot harder to explain what a derivative is, no matter how well he could explain it if he DID know their Taylor Series. SO yeah ... not easy being a teacher if you wanna be a good one.

You must have never had me as a teacher.

@@tanmaygarg3885 I've lost it

I’m actually surprised it wasn’t another “been trying to find patterns in the primes” kind of conversations because generally speaking if you study mathematics and physics for long enough you reach similar conclusions about the nature of mathematics itself and how…arbitrary it is. Usually mathematicians are oblivious to this fact and just focus on the particular interesting pattern they are looking into (like finding Waldo in the digits of pi), rather than identifying the nature of patterns themselves and why they exist.

I've been reading her book 'Category Theory in Context', it's amazing.

@@saminthanicnur1873 good to know, thanks!

Interesting. I wasn’t aware of this field when I studied but that was early 2000s and I suppose this wasn’t as advanced as it is today. I would have confused ‘category theory’ with taxonomisation! 😂

@@icarusflying1814 😂

Instant infinite amount of respect for that ;D

This kind of happens in businesses as well I guess. Interesting thought.

Beautifully articulated!

My favorite part was the technical discussion with the grad student, but then, I'm also a graduated grad student that imbibes all math and science I can on UKposts, so I'm quite biased here lol

I guess this is what Terry Tao describes as “post-rigorous”. They both have such deep knowledge that they get each other without using rigorous language.

lol, the "expert" should have been right after the child.

My first instinct was that she has autism. The eye contact, the incredible depth into a single subject, and even her hands on her knees seemed like she wanted to stim, but couldn't. Whenever I explain something deeply (I wish to be on her level someday), I also avoid eye contact. When listening intently as well

yeah they lost me at the "real" numbers. i have no idea what that means

I lost at level 4 and came back at level 5 lol

@@williamzinedineh Real numbers are numbers that aren't imaginary, like the square root of -1. For any x, x^2 cannot be negative. Thus, the square root of any negative number is imaginary.

@@knayvik6482 yeah... that does NOT answer my unstated question

@@williamzinedineh real numbers are any number that isnt the square root of a negative number

And it's looking at maths a different why compared to how it's usually taught.

So you say your dumber students are not afraid of infinity, cause they dont get the greater picture of it and what it means? Nice

@@CharlsDiggens I don't think that's what they were saying

Learn what a strawman argument is and you will understand what you just did there @@CharlsDiggens

@@CharlsDiggens​​⁠​⁠ Yes - dumb, lazy students are better at dealing with infinity. Infinity + 1 … Infinity! 👋🏼😀 Infinity + 2 … Infinity! 👏🏼😀 Meanwhile, brainiac over there is thinking … This is BS. Something has to change; otherwise, what’s the frickin’ point … ?! Pretty sure the expert had a ‘What’s the frickin’ point?!’ moment, as seen on her face at 1:57, when for a moment she realised she was spending her life talking about how infinite jars full of infinite glitter wouldn’t fit into the room she’s in … as if that might help anyone do anything …

Exactlyyyy

You dumb?

Tough

literally 🤣🤣

It's not a WOMAN. He is a biological male who identifies as a female mathematician.

@@emmapasqule2432 does it matter tho ?

@@midchib9236 Pronouns are important and HE should be afforded the correct pronoun based on what is in his pants. You may not care about science, but it's important. He is a mathematician with a johnson.

@@emmapasqule2432 lady, she has a female skull shape which is congruent to female ratios of shoulders to hips. its a biological woman wearing ugly clothing with a bad haircut. are you stupid?

Yeah I got surprised when they give a solid answer to that (afaik) on-going debate about Mathematics whether it's a discovery or an invention.

@@RT-ol4hh Take your meds and breathe :)

@@RT-ol4hh Maths as a human construct does not mean it's a social construct... It's a human construct because it relies on chosen axioms. It does have a connection to "reality" (a concept not that easy to define) as it is the main tool of physics and we see its practical consequences every day. So, we can build some very tangible objects relying on an massively incomplete human construct. And that's awesome!

@@RT-ol4hhPeace and happiness upon you too. No need to be so harsh with yourself and the noodle; ramen can be delicious.

IS an art and ISNT an art, as a language has a lot of fails(really big fails to be honest, incomplete, undecidable, sometimes inconsistant) and something like that shouldnt be art but at the same time chaos(and all non-chaos thing inside it) is often a type of art too ❤️😂 ok too much math logic

Right?? She’s a dream to listen to, even for someone who knows nothing about maths! She is the type of teacher who can gift learning itself, not just knowledge

Stop lying

@@ohnah6261 Infinity yourself

@@Alic4444 ?

I have definitely met people who chose their field of math because she and her circles are so welcoming!

I read “meeting her in prison” 👯‍♀️👯‍♀️

Downloading it now because of this recommendation ❤

I am 1st year undergrad and will save it now too for later, thanks for the recommendation.

He also didn't believe in infinities. Many think that when you do stomp on one, the theory is wrong. Also they thought the same about imaginary numbers.

Bro why is everyone praising her so much. I mean she seems like a nice kid so thats good but i just refuse to believe there are people so mentally limited that they couldnt come up with what she came up with at her age, or better AT ADULT AGE

Then you haven't seen some adults.

This is true.

99% of illiterate adults maybe

@@marcioamaral7511 fr

You gotta be one of them if you don’t understand how much 99% is

99% is an outrageous statement

If you are given the answers it helps

She is Indian after all

@@supu8599 It's also scripted and staged, like all videos in this series...

@@dark_sunset is it ? 🤨

@@supu8599 the talk with the graduate student definetly a little bit I think, they both try to explain it in a way a normal person could understand. They both definetly know what the axiom of choice is in depht, but they explain it in a very general way.

Is the book readable for people who don't study mathematics? Do you need a lot of formal knowledge to understand it?

​@@Ms19754 You could do it if you have an undergraduate degree in Math or extensive experience reading proofs but probably not otherwise, unfortunately. Lot of great resources on UKposts, though!

Maybe one day she'll invent the Riehl numbers...

@@Ms19754 not really, you need pretty much an undergrad in maths to follow it

@@UsernameXOXO well done 👍🏻

I feel you. If only maths were as easy to manipulate and practice for me as they are to conceptualize. Conceptually I get it. I get lost in all the notation and coding though.

free bj for you when we next meet

@@danielcohn6884same. The concepts make sense but applying the concepts and remembering formulas, steps and all the components are were I’m lost. Feels like a whole world of knowledge exists behind mathematical knowledge.

Maybe you've also matured in your reasoning ability...I wouldn't necessarily put ALL of the blame on your professor nor give all of the credit to this woman!

That's why it's necessary to get admitted to a good university!

I think it's infinitesimally better!

​@@magiquemarker idk if you're having a dig at the video or not, but just in case you aren't: infinitesimally means to an extremely small degree, not to an infinite degree :)

@@tophmyster The smallest number thats after 0, which has infinite decimals at that

@@tophmyster But I do believe the 'infinite' in that word is the very same infinite we are speaking about in this video (as in infinitely centisimal or something like that).

@@JesseTate The correct terminology is "infinitely better," not "infinitesimally better," and the infinitesimal quantities that you encounter in several disciplines of mathematics are not defined with the same "infinite" sense as the infinity concept discussed in this video.

I found the Last explanation easier to understand than the fourth.

@@codesuzakugeass Yeah round four lost me a bit. I knew the college stuff (took those classes in college myself). Then they went crazy for a bit(as in beyond my comprehension at the moment). Had me feeling like I do when people start talking about topology beyond 3 dimensions(well I'm not great at 3d either, but still). Then back to sense at the end lol.

why is she dressed like a dude tho?

No.

more math and please do at least one on chemistry! How can you do bio and physics but not do the central science of chemistry

@@saimaurice3652 maybe on organic chemistry

She once got into an argument with a triangle and honorably conceded when she determined it was right.

🙏🙏

It's because as you become more educated in a subject, you will naturally become more and more familiar with the foundation behind the subject. Philosophy is the foundation of pure mathematics.

@@downsonjerome7905 I think we have an escaped philosopher in the room. No, pure maths is its own foundation -- that's kinda the entire point.

@@AlaiMacErc As the expert said in the video, mathematics aren't foreign to philosophy. It was obvious during the Ancient Greeks era and it's still the case. Especially when you choose your assumptions, axioms, to explore further.

PhD stands for doctorate of philosophy - in any field getting to that level is no longer about basic facts and mechanics and more about various ways to think about the field.

@@AlaiMacErc Pure math is built upon its axioms. But those axioms aren't some magical universal truth. The axioms are literally only "true" because a bunch of scholars decided they wanted them to be true. The reasons behind why we would accept some axioms or reject some others is based on philosphy

She did mention it.

@@divinepraiseeric yep that's what I meant. I was hoping she would and was happy she did. poor wording on my part

ok

I love infinite dimensional spaces. The only problem is most people think they are imaginary. It is extremely difficult for people to visualise a duocylinder in 4D. There is an object in 164,438 dimensions, which the 164,437-headed Brahma cannot visualise. The 10,000,000- headed Brahma cannot be imagined by anyone. You need to understand what I am talking about. It need not be gross physical spatial dimensions.

What I don't understand is that infinity must be destroying information. If you add a infinity to a random number, it's infinity. And if you subtract that same number again, then it's still infinity. But if you add Infinity to a number and then subtract Infinity right away, it's still gonna be Infinity. You can never return to that number, or any number again. So Infinity is like the event horizon of a black hole? I dont understand what to do with this information.

@@maduude8809 you are still thinking of infinity as finite you can not add a number to infinity because it is already a part of infinity

@@ralphwiggum1203 but that's what they did in the hotel experiment? But to be honest I couldn't really follow the last examples because I have no idea what the mathematical terms mean. Cardinal Principe, transfinite numbers, ordinal etc. And also I don't understand why it is important that there is a difference to be made between countable infinity and uncountable. Cool and all, but since it's infinite anyways, what use does that distinction have? I only studied chemistry which had two math classes, so my mathematical knowledge is pretty limited ^^

That’s such a great question! This is how I think about it: When we say that the rationals are dense in the reals, we’re saying that if we choose some sort of epsilon (a certain tolerance where we say “close enough”) and then pick a random irrational number, then we can build a rational number that gets within “close enough” to the irrational number we got. So say we pick pi. If we care about being at least 0.1 close to pi, we can just choose 31/10. If we want to be at least 0.01 close, you can choose 314/100. And so on But! No matter what epsilon you choose, there are infinitely smaller epsilons that you COULD choose. What ever digit you stop matching at, there are infinitely MORE digits you could be matching. You can’t ever build a rational number that matches digits to pi far out enough to not have infinitely more digits to go. That’s why the reals are just SO BIG. In this infinite pool of real numbers, each irrational number is, itself, also infinite Not the most rigorous explanation out there, but I hope it helps! Sincerely, an applied math masters student

@@the_piano_nerd4960 Thank you, my question is more about how that doesn't imply the rationals should have the same cardinality as the reals, although this is probably just me not knowing very much about cardinality. Sincerely, a high schooler who does maths olympiad.

A good sign you're understanding the concepts. If you're comfortable with your intuitions on infinity, you probably don't really understand the question. Infinity is deeply weird.

I think it was the single most mind blowing thing I have learned in University (2nd to that is the idea of proving something is unprovable using a simple device as a Turing Machine). I am still as confused as you. Now think about how many Rational numbers you can put between every two Reals you pick ;)

@@heyman620 None if you pick the same two numbers 🤔

@@bartholomewhalliburton9854 Wouldn't it make it 1 real?

@@bartholomewhalliburton9854 Refer to it: en.wikipedia.org/wiki/Dense_set

😂

I don't believe in real paradoxes. Every "paradox" is simply revealing a weakness in understanding. Paradoxes don't exist except in the human mind.

@@mouthpiece200 philosopher bachelor here, i want to say that your comment reminded me of Wittgenstein concept of linguistic limitation. I don't think the idea of paradox in itself is a lie or a weakness of understanding because we can understand the implications of both the consequence and the cause of it, but rather a limitation of what we are able to express in symbols to convey a perfect message. If we can identify a problem and we know how to replicate the problem, the only reason that problem has to continue existing as a problem is because we can't get past its blockade on the specific path we take to get to the final location we want or the conclusion we want. It is the same concept of a broken bridge between islands, if we have a boat or we take a plane we can cross between one to the next but if we repeatedly try to get through it by the bridge we will always fail. Such is the language limitations that makes paradoxes real and at the same time not damning us to stagnate understanding because we can take other means, in the case of math, other possible symbols and equations to actually get where we want to get. The paradox remain but our way of thinking develops.

It might interest you that while I was studying math in uni, we almost never used any numbers, and I can't help but wonder if higher level maths would be easier for you than the school stuff :)

@@Nezumior that's very interesting! (even though it sounds oddly suspicious lol) I used to ace the theory portion of my tests, so, probably? i don't want to give myself too much credit since i struggle with the simplest of arithmetics 😅 but i definitely understand more of math when it's in the written form, it's when numbers come in that my brain completely checks out, which is so frustrating because it drove my teachers mad! they couldn't understand why i would get the theory and could not for the life of me put it in practice.

I struggled through Algebra all 4 years of high school. I’d fail a semester, retake it, and barely pass. Rinse and repeat. It wasn’t until the last semester when we focused solely on word problems that it clicked with me and I got a B in the class. Then I failed college Algebra and decided to take a lower level class to meet my degree requirements.

Working with math in simple programming languages (like Python) where you can easily adjust variables and see the outcomes makes it easier to learn. People that think literally and pragmatically can struggle with math in an academic setting.

@@Nezumior it's possible - I am not necessarily great with the calculations etc in the head but by the end of college when we got into the theory something clicked and I went to grad school for it even

The college level shows there are different ways to make collections of numbers. Intuitively, someone would say the natural numbers (0, 1, 2, 3, 4, etc.) are a smaller collection than the collection that is called integers, which contains all the natural numbers AND their negative counterparts (etc., -4, -3, -2, -1, 0, 1, 2, 3, 4, etc.). Then there's another collection called rational numbers. These are all the previous numbers and now they're allowed to have commas (for example 1.25, like dollars and cents). What she explains at the college level, is how you can prove all three collections are infinite, but one infinity isn't bigger than the others, even though someone with no mathematical knowledge would intuitively state that the rational numbers are more infinite than the integers and the integers are a bigger collection than the collection of natural numbers. She proves this by assuming numbers are nothing but symbols we use to order a collection. So the numbers in the natural collection could have a value that is similar to the integers or the rational numbers, but because that's not how most humans think of numbers we don't naturally feel inclined to agree with this. I hope you will understand it better by this explanation. Let's talk money: everyone agrees 500 dollars on your account is more than 2 dollars, -200 dollars would imply you paid for something or have debt. Let's say we would write down all the numbers that appear on your bank account and order them. We can count them as the amount of transactions. We would start with 0, this is when you opened your bank account. Then we say 1, for example, your first paycheck. Then 2, you bought gas for your truck, which probably has a negative value. 3 is a gas bill, another negative value. 4 could be your friend paying back a pizza, so that's a positive value. And so on, and so on. As we progress, you will have a very large collection. If you were to live forever, or pass your bank account down to your children and they pass it on to your grandchildren, given enough time, the amount of transactions will become infinite. You may have noticed the numbers we used to rank the transactions are natural numbers. You probably also noticed the values, ie the amount of dollars that were exchanged during that transaction, are part of the rational numbers. Because the natural collection has become infinite over time, your rational collection has become infinite as well. Because we know there are equal amount of natural numbers as there are rational numbers within this bank account, we can agree the infinity of natural numbers is equal to the infinity of rational numbers.

@@DarkAngelEU very well explained especially with the bank account thingy props to u

I gather infinity is a made-up concept that doesn't make any sense when analysed... thus going into philosophical.

@@ChillerBaby Thanks mate, makes my day :D

@@DarkAngelEU Thanks for taking the time to write this wonderful explanation! You are awesome :)

That was really cute, she seems to be interested in finding patterns and exploring them to their ultimate consequences, which is pretty much what mathematicians do. I bet she would like fractals

yes, i NMEED THIS

They're*

infinite amount of thanks

@@usernameisamyth Which size of infinity?

@@pooky3672 Uncountable, for sure!

@@sankang9425 which uncountability? Continuum?

Ngl, that black girl and i are the same age but she looks more mature than me. About 17 or 18

I agree, but the more I watch these videos the more I realise I only have the understanding of a small child and that my brain also hurts!

I'm on level .55555555555555555

in general 2*ω = ω for any limit ordinal but ω*2 = ω + ω does have a different order type - this is the classic example to show ordinal multiplication is non commutative

Is the implication of what you are saying is that mathematics is reducible and terminates (in logical terms) with the epistemology of definition ?

@@scotimages Philosophically, I tend to adhere to a constructivist conception of science, which inclines me to think that, past a certain point, all scientific thinking has to reach epistemological thinking: having to question the very principles your scientific thinking is based upon. But I know nearly nothing about mathematics past a high school level, so I wouldn’t be as bold as throwing around wild assertions about what mathematics are reductible to or terminate in.

@@AlexisDayon Yes that is true. Science is like a house where epistemology is the foundation, and if the foundation is true then the peak of the house will be true. I believed that for a long time until i seen with my own eyes, bell's inequality violated by nature. Now im not sure about anything anymore. But im not qualified to speak with any certainty on any of these subjects. I just self study for fun. Do you think reality is deterministic?

@@duckyoutube6318 I like Bertrand Russell’s take on determinism. It goes like this: reality being either deterministic or random "per se" is a metaphysical problem we will never be able to solve scientifically, since it applies to a fundamental principle of reality which is absolutely out of range of any possible empirical knowledge. Nevertheless, determinism is necessary as a methodological assumption for scientific research. Trying to understand phenomenons scientifically is essentially trying to find out by which causes and principles they are determined to happen. (Even thinking that reality is probabilistic like many tend to think in the field of quantum physics is another way to determine phenomenons.) Therefore, if there is a point in reality where determinism ends, all scientific effort ends with it. So, a thorough, sceptic and empirical answer to that question would be: we have no way to assert whether reality is metaphysically deterministic, but we can assert that science needs to be methodologically deterministic.

grad students are usually just REALLY deep in the sauce to be honest

I know the undergrad student and he’s the best!!

@@KBin727 Hello Yoni's alt account 👋

Honestly I thought the undergrad underperformed. He had basically the same conceptual understanding as the high schooler and child with a little more ability to follow proofs. She was still spoon feeding him everything. The biggest jump in this ranking was undergrad to phd.

I would love an explamation of dividing by 0

@@appa609 Almost like he's not a math major...