I am sorry that you had such an experience! Understanding dedekind cuts is not that easy... I don't think that you are supposed to know the concept in your first analysis class... I hope you find the video informative! maybe you can go back to your professor and tell him that now you know what a dedekind cut is!

I am glad you enjoyed it! As I rewatched the video, I felt like I am speaking a little too fast sometimes; and that i should pause more to give time for people to think more about the ideas there. Some of those ideas are very deep and they need some reflection. So, hearing that you find the video interesting is reassuring!

@@academyofuselessideas yeah it's a bit fast but that's not a problem AT all , of course there some beautiful and deep insights in , no worries about the speed sir , and thank you soo much for this authentic content 🤗

Dr. Slim , super thanks for this! There is a book I consider it as a two copy book, just in case someone loses one - The dictionary of symbols of mathematical logic edited by Robert Feys and Frederick Fitch

@@barneyross8083 Oh, i don't know that book, i must check it out! thanks for the recommendation!

@@philosophieoverdose9332 Thank you! I am glad you find it amusing! the next video in the series is about deduction systems... but i might want to change it so i am not sure when i'll publish it... as usual, share your thoughts or ideas either here or on our discord server!

🤔😕🤔

Thank you! this is part of a live stream on number theory that we do on tuesdays and thursdays. The material is not as polished as it would be in a video, but I hope to make videos on these ideas for quick review at some point. Have fun prepping for the Olympiad! If you'd like to ask any questions, feel free to send them here, or to join our discord server and ask personally!

Definitely! we also have a series of streams called "tackling proofs" that was dedicated to showing proofs (if you have a particular theorem you'd like to see a proof of, please suggest it!) As the streams get a little bit more technical, we will do more proofs. For example, in our next number theory stream (Learning number theory), we plan to prove some basic number theory results (the plan is to do fermat's little theorem, wilson's theorem, and lagrange's theorem but i am not sure if we'll have time to do all of them). Similarly, in our next "let's talk analysis" we plan to prove the archimedean property, and some other basic analysis results! If you'd like to learn more about proofs, or some specific proof, please ask!

Sure will do , thanks a lot! TBH a single stream of yours has so much quality content it takes time for me to go through, BTW I do not have mathematics background but trying to learn, thanks for all your help, apologies for asking for content which you have already covered.

@@barneyross8083 Not at all! Enjoy your math journey, and ask as many questions as you'd like to! I am curious of what you're learning now!

@@academyofuselessideasCurrently started studying Mathematics for AI, started with linear algebra, thanks for asking.

nice, linear algebra is a great place to start learning math! it has many applications and yet it can lead to some very abstract concepts!

Thank you! I made the episode when the channel was even smaller, and i took the episode down because it didn't have many views... but i was talking about this in a stream last friday, so I decided to reupload it... I actually have a couple of follow up videos to this one! maybe i should reupload them as well!

@@academyofuselessideas Please do that, the way you are offering 'useless' ideas , won't take much time to picked up by more useless people like me 🙂. This channel is the best reco given to me by YT reco system! Thanks for everything!

@@barneyross8083 i am glad you're enjoying it! shamelessly promoting the channel, I'll point out that we have a discord server in which we talk more about math and other stuff! if you stop by there, say hello!

It is a real life story!

@@academyofuselessideas i cant believe it...

@@kakerix5936 sometimes reality is stranger than fiction. I did show her this video when i made it, and she found it funny

I like the idea of tying number theory to programming more! I'll try to include more coding, and I'll check on some references for including more programming problems. One way I enjoyed learning math was solving project euler problems. Many of them are number theory related... if you have any competitive programming questions, join or discord and ask personally! your message gave me the idea of doing some competitive programming streams! Thank you!

@@academyofuselessideas Thanks sir can you just specify or list down multiple math and physics (yes physics related problem too was asked in ACM icpc finals) Topics like discrete math, number theory, algebra (even in algebra real analysis topics like Lagrange interpolation are used ) , advanced algorithms and simply everything which one needs to study to get on top on CF or win ACM ICPC ? It will be really very helpful if you provide these topics and sub topics concept lists in detail

Unfortunately, I am not an expert on this. I know what is required to solve some problems, but not really enough to wirte a comprehensive list... however, what we could do is to recommend a book... I wonder if people would be interested in doing a series of streams on competitive programming based on one of those books ("competitive programming" by Steven Halim, for example)

I just checked "competitive programming" by Hamlim and it seems pretty interesting... they have a few chapters with the math needed... maybe we can do some streams on that!

That's a great point... yes, in the end, it is best to be me and hope to find the people that enjoy my style!

Thank you so much for your kind comment! I am glad you are enjoying the videos! I am also glad that analysis is being taught at a highschool level. I didn't know about nexttoward... i just looked it up and it is pretty interesting... thanks for sharing that! I might look into it in more detail!

Thanks! I just checked the introduction and preface, and it seems like a great material... I'll check it in more detail later today!

Nice, that's what i had in mind but for some reason I didn't see it during the stream! Thanks so much!

Thanks for sharing! I will keep it up for a while. I am thinking of editing the video and make it shorter. For example, I noticed that most of the time, I can accelerate to 2x and it is still easy to follow (I was speaking very slowly, apparently)... Anyways, I'll keep it until I get the edited version... The thing is that since the streams are long, most people don't watch them so far

Cool insights! thanks for sharing! When I heard the problem for the first time, my solution was to just use hamming code 7,4 to solve the puzzle. However I didn't talk about Hamming codes in the solution I presented in the follow up video (not sure if you watched it but you can find part two either in the description, or as the video suggested at the end of this one). The generalization that I explore in one of the follow up videos might also be of interest! Thanks for engaging with the video, and I hope you had fun thinking about the problem (and I hope that the follow up videos were fun as well!)

Pretty great! i think that your approach is reminiscent from the hamming code (7,4). The answer is slightly different than the one given in the follow up video... and if you keep going in the series, you will find a generalization of the problem (what happens when alice can lie more times and what happens when she can choose arbitrary numbers).... Intuitively, the more numbers Alice has to choose from and the more lies she can tell, then Bob will need more questions to win the game (and if the number of questions is limited, as shown in the last video, Alice can have a winning strategy) In the following video, I insist on the problem of whether it is possible to find a solution with less answers... I have an out of the box solution that uses less answers but that it might be consider cheating. Of course, the solution i have has to "cheat" in some way since you have a proof for the lower bound... If you are curious let me know and I'll share my idea with you! Thanks for your great comment! I hope you enjoyed the video!

@@academyofuselessideas Sure, I am interested in what the "cheat" is? The thing that comes to my mind is to use statement itself in the statement. Like "This statement is false." is neither a true nor a false statement.

​@@NemanjaSo2005 Nice, something like that is what i have in mind! (which is why i didn't put a restriction in the type of questions that Bob can ask. If i wanted to avoid a "cheat" i could've said something like Bob can ask questions of the form, "is the secret number one of the following: ...?" but i thought that the narration would be a little clunkier that way, and also, the questions i use for the solution in the next video are a little more involved (not sure if you checked out the next video and what you thought of the solution!)... I don't want to spoil the "cheat" for people still thinking about it, so I will leave a comment in the last video of the series about it, and why i think it is interesting! Also, I hinted at the cheat on the next video (that's why i have captain Kirk saying that he could beat Alice in less questions). I'll tag you on my comment on the last video... and if you want, we can also talk about it on discord!

​@@academyofuselessideasOh, I didn't see the other videos as they are unlisted and in description. I will look at them now.

@@NemanjaSo2005 I feel like my strategy might be confusing... The follow up videos are the suggested ones at the end of the video...it seems like the video itself is not clear enough but I hope people get to see them. In one of my previous videos, I also did something similar with the cards at the end. It was a choose your own adventure video, where you could pick the next video depending on what you thought (though it was very simple. I would've liked to do a longer choose your own adventure video, but it is hard to come with ideas that would work in that format)

Thanks for the suggestion. I wanted to experiment using AI voices because some people find my accent distracting (you can hear my voice in some other videos). I think that the strength of my videos lies on the script. Of course, if many people dislike the voice, I will get back to recording it myself. Once again, thanks for sharing your opinion!

Thanks for sharing your solution! Unfortunately, 🤔 I don't follow 🤔 i think that you can choose p and q such that n^2 > 2. But i am not sure, i am a little confused by the definition of n, is it n= p/q + pq/4 or is it n=p/q + 1/(4pq) or is it n=p/q+q/(4p) or something else? It might work though! i will need to think about it more! Thanks again!

@@academyofuselessideas Let A = {m in Q such that m^2 < 2} I showed that this set doesnt have maximum. Suppose m = p/q is the maximum. We have m^2 <2 --> p^2 < 2q^2 If n= p/q + 1/(4pq) n^2 = p^2 /q^2 + 1/(2q^2) + 1/(4pq)^2 It is clear that 1/2 + 1/(4p)^2 < 1<= 2q^2 -p^2 Then, p^2 +1/2 +1/(4p)^2 < 2q^2 --> p^2/q^2 +1/(2q^2) +1/(4pq)^2 < 2 --> (p/q+1/(4pq))^2 < 2 Then m<n and n^2 < 2. Therefore, A doesnt have maximum.

@@Miguel14159 thanks for the detailed explanation... cool! i think that in the first message, the parenthesis 1/(4pq) would be helpful! (maybe you can still edit it?) Anyways, the explanation is pretty informative... thanks!

it is! I am trying something different on that video!

Fr 😭

@@mdn1712

Feel free to join our discord server if you'd like to talk more about it but here is my not so long answer. Imagine that there are two worlds: the physical world and the world of ideas (your dog lives in the real world but the idea of "dogness" lives in the world of ideas). Mathematics construct objects in the world of ideas, and in principle, it does not care if such objects have a counterpart in the real world. Of course, this is not how it used to be. Humans create ideas to help them understand the real world. For example, the real line is an abstraction that help us to understand how to measure things in the real world. However, mathematicians realized that linking the mathematical objects to the real world is hard and it comes with some issues for the practice of mathematics. So, we are at a point where the practice of mathematics do not care much about how things correlate with the real world.... So, does that mean that mathematics is not useful in the real world? No, it does not mean that, it only means that many mathematicians don't care about those applications (which is why many mathematical texts are dry and full of theory instead of applications). But, there are other people who do care about applications and find those connections! often, those people find connections that not even the mathematicians imagined! Who are those people? i would say that engineers, physicists, and even some mathematicians are there looking for those connections. But the ability of finding those connections is different than the ability of doing pure math. So there are good mathematicians that have no idea about applications, and some people who know a lot about applications but are not really that great at developing new math (they understand the math but they might not push the existing math). I would say that for most of undergrade math, it shouldn't be too hard to find applications in the real world. Or at the very least, it should be easy to justify why the theorems you learn have repercussions in some applications. However, finding those links gets harder as you do more advanced math (since much of advanced math developed to understand mathematical objects better and not to find applications). As a quick example, calculus finds a lot of applications, and often, when you are calculating some functions, you use tricks like changing limits, or switching integrals, or changes of variable... but you can easily find examples in which those calculations don't seem to work. Many of the theorems that you prove in analysis are aimed to find under what conditions you can do those "tricks". Another, thing that lead to the development of a lot of analysis was the development of fourier series which were a very practical method to find solutions to the heat equation in physics. It turns out that to be sure that the method works, you need to prove a lot of things in analysis first! But if you are an engineer, or a physicist, you can probably just use the methods and trust that someone else already proved that they worked. For a masters in mathematics (or even a phd) you can do a lot of applied stuff, but it will depend on the professor you're working with. If you like applied math, you can definitely find people who're interested on that type of math. And that's more or less the conclusion: if you like applications, you can find a lot of cool applied math... if you prefer more abstract math, you can also find a lot of abstract theoretical math! none of them is better than the other, but one of them might be better for you... So, i'd encourage you to find what you like and go towards it! Hope this helps! let me know if you have any other questions!

lovely perspective. Yes, i used functions to post the problem but i could've presented a similar argument with many other mathematical objects. One of the points I wanted to make is that we take for granted that, for example, the real numbers exist. But even that is not that trivial. You have to believe a lot of things about sets before you can accept the existence of real numbers (whether one accepts those believes or not, it is ultimately a matter of faith).... If you believe the ZFC axioms, then everything follows and "standard" mathematics seems consistent (we should add the believe of consistency to our list of believes but i have not much problem accepting that). So, we know that any world in which the axioms are satisfied will be a model for standard mathematics (it will be a world in which whatever we proof is actually true). But, is that the physical world? does the physical world satisfy those axioms? I need to work more on verbalizing why I find these questions interesting and important... but i hope that the video had sparked some curiosity. Thank you so much for letting us know your stand!

imagine a computer with registers where you can store an arbitrary natural number, for each number in a register you can find the successor of that number, you can also access all the registers, and you can code recursions as well... Roughly speaking, a function is computable if you can program it in such computer (there are many definitions of computability but this one is very concrete for those who have coded). It seems like the basic operations in that computer are very simple but it turns out that you can code a lot of things using those simple operations... however, you can prove that you cannot code every function from the naturals to the naturals! (the argument for why this is not possible is similar to cantor diagonal argument for the uncountability of the real numbers). Roughly speaking and handwaving a lot, this is what saying that the Busy Beaver function is not computable... Computable functions are probably better explaining real-world functions than general functions but it is also hard to work out with computable functions. Anyways, I am glad you brought that this up because i wanted to talk about computable functions in the video but i didn't want to make it too complicated. I am more interested in posing the philosophical question.

I love it.... this might be similar to @balpedro3602 point of view (from what i gather from his comment)... I feel like more mathematicians should be aware of the ontology of mathematics and of the main positions that one can take... thanks for sharing your perspective! maybe one day I'll talk more about anti-realism (though i am not an expert). I feel like this topics are underrepresented in youtube!

I am glad you enjoyed it!

great and valid perspective... if you have the believe that the formal system that you chose is consistent, then all your math is correct in any world satisfying the axioms (and deductions) of your system. But, here is why i think the philosophical question is important. If you do math with the intention of modeling the physical world, what if the physical world do not satisfy the axioms of your system? or more in general, how do you know to which worlds you can apply the deductions you get? Of course, it is perfectly valid to say that you just apply it to the model given by your formal language (you can create a model just from your language rules). Though, in such case, you must be comfortable with that in a similar way in which a chess player is comfortable saying that all his knowledge of the game might just apply to the game itself and not necessarily to model a real battlefield. This is one of the reasons why I find the philosophical questions interesting! they help us realize what we believe! In any case, thank you for sharing your perspective! it is a pretty cool one!

@@academyofuselessideas That's a good question to think about. On one level close to math, there's Q1 "what if the physical world does not satisfy, or people reject, those low level axioms (including the case of the axioms not being consistent)?" My answer to that is that there are many ways to build up to the properties we actually use (e.g. many ways to construct the real numbers, alternative axioms found when Russell's Paradox was an issue). There's Q2 "what if the real world doesn't match those higher-level concepts like the real numbers?" to which I'd say that then we switch to a different concept as the need for a more accurate model arises. I think there's a third, more interesting question about the philosophy of science embedded in your comment that I'm having trouble seeing/articulating, though.

@@diribigal 🤔🤔 Great questions! They are a lot of fun to think about!

nice! yes, i forgot that advantage and disadvantage is a matter of perspective! thanks for sharing! In any case, i hope that the video helped you to reflect on your own philosophical position!

great insights! yes, originally I had a fuzzier version and a more precise version but I realized that the video was longer without improving the point i wanted to make. I gather that you believe that if a sentient being can imagine something, then that thing exists, even if perhaps just in the mind of the person that imagined it (so unicorns exist because we can imagine them but whether unicorns exists outside the mind of sentient beings is a different question). That's a valid stand! And yes, the definition of function is limited to having one output per input. And if you want to represent something like a circle, you could use a "relationship" instead. (using the language of sets, a relationship between A and B is a subset of the cartesian product A times B (set of pairs (a,b) where a is in A and b is in B)). In that setting a function is a special type of relationship in which for every a in A, there exists b in B such that (a, b) is in the relationship (This guarantees the existence of f(a)); and moreover if (a,b1) and (a,b2) are part of the relationship, then we must have b1=b2 (thig guarantees the uniqueness of f(a)... and the two conditions together justify defining f(a)=b). This definition is a little convoluted so please ignore it if it is confusing you... what i am saying is actually something very simple in a convoluted way. Anyways, thanks for the insight!

​@@academyofuselessideas I've studied set theory on my own online because I really dislike how mathematicians get very snobby intellectually after they've studied set theory and talk down to others who may not fully grasp or fully agree with everything in set theory but due to lack of practice in mathematics may not be able to fully express one's ideas in the lingo used by mathematicians. So, anyway, while I definitely won't pretend to fully remember or grasp all of the concepts in set theory, I do have a general understanding of it and so I mostly understood your points. And, yes, unicorns exist. God (or gods) exist. Dragons exist. The question is not *if* these things exist but who or what are they, how, where, when are they, and which versions are we talking about? This is why I reject materialism and its polar opposite and I reject atheism since I find the views that all is (or isn't) tangible or that God doesn't exist (at all in any sense) to be contrary to our experience. Now, maybe our experience is all an illusion, or maybe it is real, but either way -- who am I to assume I understand God or the metaphysical when I only minimally understand myself, others, and the physical?

nice! i hope you enjoyed your set theory course! i didn't mean to sound too technical because what i was trying to say was really simple... but maybe i should've found a simpler way of saying it. Indeed, that philosophical perspective is pretty interesting. Thanks for sharing it. It is nice to see that people really spend time thinking about these topics!

What an interesting question! Here are my (first thoughts). If you have a real function f:R -> R, and the function is bijective (this is the same as invertible), tne you can always change the scale of the axis to make it look like a line. Indeed, if f is a bijection, then it is invertible, meaning that you can find g, such that for every x, g(f(x))=x. So, if you change the y axis from linear to be scaled by g, you will get a line. However, this is not saying much. The cool thing about exponentials and logarithm is that you have a whole family of functions that become lines. Indeed, the functions of the form k exp(a x), all become lines when you use the logarithmic y axis (they become the functions a x + log k). This is cool because we have known for a long time how to do linear regression (like if we observe data, we know how to find the line that better fits the data), so if the relationship happens to be exponential, we could do linear regression in the logarithmic scale and maybe find a good fit. I think that you can use the same trick for any family of functions of the form f(x)=ax+b, where f is invertible (the exponential case is an example of this where f(x)=exp(a x +b)=exp(b)exp(ax)=k exp(ax))... I hope this makes sense, but if not, please ignore it!

@@academyofuselessideas This is the first time I hear about bijection. I just had a look at injective and surjective functions and bijection sounds like the solution! I guess if you just want linearity anywhere in the graph, so that f(x)=x^2 can be displayed as f(x)=|x|, then you would need to take the symmetry of a function into consideration but would be able to drop the injective part. I get why we need the surjective property but it's also so tempting to imagine f(x)=1/X as just two diagonal parallel lines 😄 Thanks for the really helpful reply! Something less to ponder about 😄

@@academyofuselessideas it's also very good that you mentioned how logs can help us run linear regressions better. It made me realise that if we transform the data with log, then minimise the (mean) squared error, we technically take the log (mean) squared error. Maybe it is possible to use the linearity scaling technique I mentioned to run regressions more effectively? I know machine learning can have the problem of local minima. It might be possible to optimise the process this way, even if the result is a minimised function of a (mean) squared error

it's pretty cool when you find people to discuss ideas! let me know if you find something interesting in that exploration!

cool, i hope you explore this log transformation more. One thing is that if you apply any increasing function to another function, then the location of the minima don't change. Sometimes you can do tricks like that to make the regression problem simpler (which is kind of what one do with applying the log to things that have exponential behavior). Indeed, optimization is full of cool tricks!

awww... those two are my most favorite adjectives to describe almost anything!

@@academyofuselessideas Wise words!

Thank you for your thoughtful comment. I am glad that the video kindled such insightful thoughts! We hope that asking these questions will help us understand the world better, and to develop also interesting mathematics (and applications)

I never thought about it but that's a little funny. It reminds me of a Bertrand Russel observation. He notices that studying math is similar to seeing things. Humans have a natural range of vision for which they don't need much effort seeing things, but if they want to see very large things far away they need telescopes, and if they want to see very small things they need microscopes. So Russel says that math is alike, there is a level of math that people can naturally address (in this example calculus), but if you want to see far you need to develop more and more tools (like differential equations, functional analysis, etc), and if you want to see smaller things you need also to develop tools (like real analysis). I guess that's why it is called advanced calculus, because it is harder to see than calculus even though it lays its foundations, but that's just my 2 cents. Your observation is very funny and insightful!

Thanks for your comment! I like the emoji thingy!

Definitely! The motivations for linear algebra tend to be "easier" in a way... if you want an answer soon, feel free to join our discord and ask there, I'll give you my answer... or join one of our streams and ask... it might not be as polished as a video but I should be able to give you my perspective on the spot!

@@academyofuselessideas Thanks! I just like the way you present the topic in the video. By the way, I'm self-studying linear algebra, and I'm just curious about any intuition or history or how it evolved that kind of stuff other then the proofs in textbooks.

@@徐聖旂 It's nice that you are selfstudying linear algebra. What materials are you using for that? If you are on discord, we can discuss this more... many books don't give enough motivation and you can easily get lost on the abstractions. Linear algebra is a great topic because it is formal but you have tons of examples and applications, so with good materials, you shouldn't have troubles staying in track... I can't think of any textbook based on a historical perspective, but if I come up with one I'll let you know... I'll also ask over discord to see if someone else in the community has a suggestion... I might also ask it in the community tab of the channel!

🤣 Hopefully the podcast is a nice surprise and you enjoy it! Maybe the smarter thing would be indeed not to get drunk... good point!

😅 I blame your professor! Rudin is a decent good if you have someone explaining the motivations and ideas behind the topics... Luckily now you can get a lot of great insights from people online! (A few years ago, professors were the only source of information which made learning a bit harder!) I like Real analysis by Jay Cummings because he gives a lot of motivations and the writing is very friendly for self study (just in case you still want to learn the topic). Also feel free to ask if you have any question, I may not know the answer but sharing your pain sometimes helps!

@@academyofuselessideas i did like rudins book, my prof just didn’t go into motivations just straight into proofs. I hate saying it but he was not a good teacher. Otherwise it was so cool to learn about infimum,supremum, Archimedes principle. One day I will do the textbook on my own 🤞😁

@@erythsea I am looking forward to read your book! or at least your writting on those subjects (or any other subject you decide to write about!)

@@academyofuselessideas haha I’m not smart enough to write math textbook. I meant go through baby rudin on my own 😁

@@erythsea Oh, feel free to ask for any help you may need reading it... I have thought about giving a series of streams on analysis, but I am not sure if i will ever do

I do enjoy Lockhart's "a mathematician's lament", and I agree with his points! you have a good eye... I do have some other ideas about the problems with math education too... Perhaps, you'll see those ideas sprinkled on some of the other videos!

I like to believe that if you show them, they'll appreciate it! but if they don't, it is okay too... It makes me wonder how many types of beauty I miss because I don't understand them

Great point! Your view is similar to the one that I have expressed in other videos... A now classic essay with a similar point of view is "A mathematician's lament" by Paul Lockhart. Paraphrasing Lockhart, if we had set up to make a system to kill the joy of learning, we couldn't have done a much better work than what we do right now.... But this is just the tip of the iceberg. For a while, the education system didn't make any sense to me until I realized that "education system" is a misnomer. It is a system system in which the goal is not to educate free thinkers but to produce future workers. But I am already sounding like an old man shaking my fist to a cloud and probably also wearing a tin foil hat, so I'll leave it at that for now!

@@academyofuselessideas Thanks for the kind words. I'll take them wherever I can get them. I surely haven't gotten any from any sort of education institution I've ever tried to work with. If you ever saw the film _Stand and Deliver_ there's a scene where the admin bureaucrat says to the math teacher "You'll crush what little self-esteem they have left" at his suggestion to teach underprivileged kids calculus. Right. And I'm coming from a CS angle. For incoming freshman CS majors they might have seen programming, and of course the whole math curriculum K-12, but they've never seen discrete math, which is usually a hodge-podge collection of higher, post-calc math topics -- and CS departments suffer very high dropout rates. For example, induction becomes recursion in programming. Where does K-12 deal with induction? Thousands more examples of circus trick style education failing. All in all math is very weak in the USA. If we trained our health professionals like we did our mathematicians there would be 1/1000th the doctors and nurses with sub-50% success rates. Just saying...

@@vonBottorff It is a very deep issue... I think that math shouldn't be mandatory at all... or for that matters, no class should be mandatory... instead teachers should strive to make courses entertaining enough for kids so they want to go without being forced... but all those are just dreams. A more realistic perspective might be to work within the system and help people who want to learn. Luckily, that's becoming more and more possible, there are so much pretty good material online which is accessible to anyone... if only their love for the subject does not get subdued, one can hope that they'll find the resources themselves... In any case, best luck in your journey, we all can make the world we want to see in the world!

Thanks for sharing your opinion and disappointment! Perhaps the conversation itself does not make justice to the smartness of the guests in which case, I blame myself for directing the interview in a way that didn't let their smartness shine, or perhaps we were all too drunk to have a more nuanced conversation, or perhaps the title refers not only to the guests but the audience itself (which i also consider smart) should get drunk while listening! Whatever is the case, I enjoyed the conversation and I found it amusing and thought provoking, and I'd like to thank the guests and listeners again for indulging me. A good reader can elevate a bad book into a great book. It is the same with most things. When we listen to people with the spirit of being amused, sometimes we see that everyone has some sort of wisdom that is shaped by their own experiences, experiences that we cannot have but from which we could learn, when we humbly pay attention. In any case, feel free to check out the other episodes and to express your disappointment (or surprise) in the comments!

@@academyofuselessideas yeah maybe i was a bit harsh in my comment i like most of the stuff on your channel BTW and hope you blow up soon👍

@@realcirno1750No problem! It is good to express your opinions, they give me a new perspective, like in this case, what I can do better for future interviews! Thanks for your lovely wishes!

Hopefully you find it interesting, and you like both paths of the adventure!

I am glad you found it useful! and I also hope you enjoyed this type of "choose your own adventure" video format... both paths are interesting! (in my opinion)

I keep consuming high doeses of hopium... i keep hoping hat the videos will find their audience, and that I'll improve enough to get more people interested! we'll see how things go!