Hi everyone, Tai-Danae here. It's nice to e-meet you all! Feel free to drop me your questions below! You can also find me on Twitter at @math3ma.
@zamalin2
6 жыл бұрын
in my opinion you are going too fast, I can imagine how difficult it will be for someone who didnt ever see how a basic group is formed or how parametrization works to follow the main idea.
@35571113
6 жыл бұрын
Hi Tai-Danae, nice to meet you!
@JoeSusco
6 жыл бұрын
zamalin2 you can always change the speed!
@earfolds
6 жыл бұрын
I think pausing just a little longer after sentences such as at 1:20 might help, as well as slowing down a little. Other than that, I'm really looking forward to more episodes with you!
@agatasoda
6 жыл бұрын
Random Q for you: What kinds of infinities are there in music? I know that one could make musical fractals which(doesn't have to but) leads to at least one infinity are there others? o.O
@pbsinfiniteseries
6 жыл бұрын
Hey y’all! Many of you have asked a great question: Why are we calling loop concatenation a “multiplication”?? Technically, loop concatenation is a “binary operation,” i.e. a way to combine two inputs and get one output. Addition and multiplication of numbers are probably the most familiar examples. In practice, mathematicians often use the word “addition” to describe binary operations that are commutative. And although I don’t mention it in the video, loop concatenation is not commutative! (Do you see why?) So we just call it “multiplication” instead. And thanks for all the feedback! I’ve got another idea to help us get used to this notion of multiplying things that *aren’t* numbers, and it won't involve fancy algebra language. I’ll share it on my blog (www.math3ma.com) hopefully next week. Stay tuned! - Tai-Danae
@nicholasjenkins7163
6 жыл бұрын
Hey Tai-Danae, great first video! I have a question, is there a specific reason topologists define loops in terms of their parameterisation instead of saying that loop functions that have the same image are equivalent? it looks to me like they are instead defining a loop in the space M as a path in the space IxM such that the ends of the paths are the same in a projection of the curve onto M
@shalberus
6 жыл бұрын
Thank you! Great video! Very interesting.
@zapazap
6 жыл бұрын
In furtherance: Often there is often one 'natural' binary operation which is simply (sometimes trivially) defined, and a diversity of 'natural' binary operations which are less trivial and which distribute over the trivial one. The term addition is often used to distinguish the simple operation from the others. E.g. operations on polynomials where addition is termwise (simple) but where multiplication is a convolution. en.wikipedia.org/wiki/Convolution
@mgominasian9206
6 жыл бұрын
Amazing episode, can you guys do more videos on Topology.
@Kowzorz
6 жыл бұрын
My intuition tells me that loop addition, whatever that may be, would not be constrained within the [0,1] interval (though part of me not knowing about this field says it'll never not be [0,1]).
@sofia.eris.bauhaus
6 жыл бұрын
my favorite commutative non-associative operation is winning in rock-paper-scizzors. B) (✊ vs ✋) vs ✌ ≠ ✊ vs (✋ vs ✌)
@Cohnan13
6 жыл бұрын
sofias. orange Awesome! The operation might be better called "winner"
@sujitmohanty1
5 жыл бұрын
That's awesome!!!
@shubhamshinde3593
6 жыл бұрын
Infinite series is still is good hands!
@B3Band
6 жыл бұрын
Shout out to the green screen guy for somehow getting her hair keyed correctly. I know that wasn't easy! You can see the insane amount of motion blur they used every time her head even slightly moves!
@Kram1032
6 жыл бұрын
2:55, 5th line, I assume that's a (-1) rather than a (=1)?
@cappucino7908
6 жыл бұрын
yep
@philp4684
6 жыл бұрын
Also, 4th line: "Anti-communatitivity".
@Sooyush
6 жыл бұрын
Ha ha nailed it
@ShroomLab
6 жыл бұрын
Putting some loops together sounds intuitively like addition. On the other hand concatination is often represented as multiplication (at least they share operator symbols)
@unvergebeneid
6 жыл бұрын
"The cool thing is that this forms what we call a Lie algebra...... ok, moving on."
@Enboc
6 жыл бұрын
Man, Tai-Danae goes light speed compared to Kelsey. Love this channel, though.
@RobertAdoniasCostaGomes
6 жыл бұрын
I like it, though... and, if you remember Gabe's speed from his SpaceTime episodes, you know Tai-Danae is just the tip of the iceberg haha
@Ensorcle
6 жыл бұрын
Associahedron: Coolest word I'll learn today.
@thstroyur
6 жыл бұрын
Learn another: amplituhedron
@sidhantrastogi6678
6 жыл бұрын
At 0:56, there's also the third way of multiplying (2*5)*3
@nicholasjenkins7163
6 жыл бұрын
Sidhant Rastogi associativity only means that 'moving the parenthesis' doesn't change the output, not changing the order of the the numbers themself.
@flymypg
6 жыл бұрын
While the specific notion of associativity may not resonate with very many viewers, the most important concept here is presented at the very end: The associahedron. This is NOT a special case! Many higher-level properties of simple objects and concepts map into geometric entities, giving simplicity and symmetry to what may appear to be great complexity when dealing with a vast number of what at first may appear to be special cases. Once you find a geometric mapping, then a suite of tools becomes available to analyze and manipulate that mapping, with a significant level of separation from what is being mapped. In particular, such geometric mappings allow "special" properties to be identified and studied in isolation, without needing to work with the full detail of the complete representation. This is the power of geometric abstraction. Once you learn a little about it, then it seems to pop up everywhere, in fields as diverse as particle physics, electronics, software, chemistry and so on. This is also the power of "pure" mathematics, having an arsenal of basic tools that can be applied to an array of situations. Geometry in this case.
@atmunn1
6 жыл бұрын
I like this new host. She does go a bit fast, though.
@recklessroges
6 жыл бұрын
and you can slow the video down in the settings, (the cog-wheel in the bottom right of the video.) And there is no limit on the number of times that you can watch the video.
@placidesulfurik
6 жыл бұрын
"Now, to do this each car must travel at twice their original speed... but that's fine." I did not expect to crack up like that, quality delivery.
@nom654
6 жыл бұрын
"We'll discover that all of the different ways of multiplying 100 different loops in a topological space can be encoded in a 98-dimensional polyhedron called an associahedron." That sounds absolutely mad! I love it. I wonder what you'd consider the identity in loop multiplication.
@leonardo21101996
6 жыл бұрын
First, we need to determine if there is an identity at all. And based on how it is defined, I doubt there is one, but I didn't do the calculations, so I couldn't know.
@NotaWalrus1
6 жыл бұрын
There indeed is no identity for this particular way of defining the operation, but that's okay, it doesn't mean we can't encode it.
@fandangomcgee1821
6 жыл бұрын
7:14 My mind just imploded
@vigneshdesmond
6 жыл бұрын
Literally Brainfucked
@98giordano1
6 жыл бұрын
Before Associahedron - ahh, this is some interesting stuff about the associative property, I don't really get vectors but overall it's understandable and somewhat intuitive. After Associahedron - ahh, this is why I won't study maths in university : brain hemorraging.
@Czeckie
6 жыл бұрын
yaaay, Gerstenhaber algebras mentioned in popsci video :)
@L4wLiP0p
6 жыл бұрын
I wouldn't mind Tai-Danae speaking a bit slower.
@BroChill2K
6 жыл бұрын
This chick is pretty rad... I like her. What I don't like is her dark shirt behind a dark background. Who thought that was a good idea?
@Lyle-xc9pg
5 жыл бұрын
"dark shirt"
@arielsproul8811
6 жыл бұрын
me before watching the video multiplying things that aren't numbers? Illuminati confirmed
@fdelhomme
6 жыл бұрын
Oh, god, please ! x)
@modolief
6 жыл бұрын
Lol! :-)
@mikeyoung9810
6 жыл бұрын
I like the new hosts (still miss Kelsey). Good luck to the new hosts.
@sdmartens22
6 жыл бұрын
Thanks for the video and welcome to the show Tai-Danae! The Jacobi Identity got me thinking how do mathematicians "perceive" a Lie Algebra? For instance I perceive a group as a structure in which one can solve ax=b (implying the algebraic properties); I might perceive a vector space as a structure in which objects can be decomposed (skipping the lengthy properties and focusing on the idea of basis). I'd like to know how mathematicians perceive the other algebras you mentioned for the the sake of understanding them better myself, maybe that could be a topic for infinite series. Thanks for your time.
@justanotherman1114
2 жыл бұрын
I know this might be late but anyways. There are things called lie groups, which are basically higher dimensional surfaces( manifolds) with a group operation. You can think of Lie groups as symmetries of some other surface (or manifold) where the symmetries are continuous e.g. think of symmetries of a circle. You can rotate the the circle which is a symmetry of the circle. Moreover, you rotate the circle continuously by any angle. So symmetries of circle form a lie group. Since Lie group itself is a manifold, we can see what happens at the tangent space of the identity element. The group structure gives the tangent space a lie algebra structure. TL;DR, You can think of lie algebra as an differentiation ( or differential/. Infinitesimal) version of group multiplication ( technically conjugation).
@fyermind
6 жыл бұрын
The intro of vector cross products and matrix multiplication didn't feel like it added to the video. Without any description of what they were or why thy worked that way, and without any hint that they wouldn't be important later to understand what followed, they shut out people who could have followed and enjoyed the second half of the video. One of the things I've loved about the past year of Infinite Series is that it is a series I can direct students to who think math is kind of easy, but aren't convinced that it's fun. The show has always been rather technical, more so than Numberphile, less so than 3Blue1Brown, but has generally maintained the same level of accessibility that makes all three shows great. I look forward to new content, but this is a lesson I will have to rebuild rather than share for less experienced students.
@NAMEhzj
6 жыл бұрын
Hmm so you say this leads to rich mathematics? What my Professor did in his lecture was just define two curves x:[a,b] -> T an y:[c,d] -> T to be equal when you have a continuous function f:[a,b] -> [c,d] with x = y°f, so speed does not matter. But we also did it in the context of integrals over curves in R^N and not in a general topological space. The integral over such two loops are then the same.
@jamiecoombes828
6 жыл бұрын
Congrats on your first infinite series video! It was really informative and the fast pace is totally fine. I'm studying undergrad physics so this video was really helpful with understanding the non-associativity of the cross product. In Python, string and array concatenation is defined with the + operator. In Base 1, concatenation and addition are the same thing. Why do we define loop concatenation as multiplication here, rather than addition? Thanks :)
@pbsinfiniteseries
6 жыл бұрын
Great question! Technically, loop concatenation is a “binary operation,” i.e. a way to combine two inputs to get one output. Two familiar examples are addition and multiplication of numbers. And in practice, we often use “addition” to describe binary operations that are commutative. Although I don’t mention it in the video, loop concatenation isn’t commutative! So we call it “multiplication” instead. - Tai-Danae
@sofia.eris.bauhaus
6 жыл бұрын
in theoretical computer science they tend to use a ring operator (∘) for string concatenations. for me concateations feel more like additions too.. also languages like Perl and PHP use a period (.) as a concatenation operator, which is deeply unsettling.
@hindigente
5 жыл бұрын
Wearing black against black CGI background makes you look like a floating head with floating hands and it's just too funny. Great video otherwise. This used to be the best KZitem channel, I wish so much there were more of these...
@NikolajLepka
6 жыл бұрын
I'm liking the new host. She's going a bit too fast though
@ulteriormotif
6 жыл бұрын
Nice topic, well presented. I was all ready for the video to dwell overly long in the familiar territory of Matrix multiplication but then it took an interesting turn to loop concatenation. I didn't have any issues with the pacing except for the massive cliff-hanger it ended on... wait we can encode instructions in shapes? Tell me more.... *video ends*
@Omnifarious0
3 жыл бұрын
I miss this series. And I think Tai-Danae Bradley was one of my favorite hosts for it.
@austinnguyen9107
6 жыл бұрын
Kelsey, u look different...
@nomanmcshmoo8640
6 жыл бұрын
You rocked this!!! Good job!!!! Excellent presentation!!!! You are a worthy successor to Kelsey!!!!!
@rafaelmarques1773
6 жыл бұрын
The pace is fine. People who complain are not used to Gabe's original pace for sure. That being said, you should know that if something isn't familiar for you already, you probably want to give some pauses and review some points. It's fine really.
@firebrain2991
6 жыл бұрын
I'm surprised, if i remember correctly, sci show gets a lot more push back when it comes to new hosts than this. Well, keep up the good work-- I'm excited to see the rest of this (infinite) series!
@hellfirelordofevil
6 жыл бұрын
Really good video guys! It seems a little fast though it would be easier to follow at about 80% to 90% the speed
@AbuSayed-er9vs
6 жыл бұрын
Good job.What about Grossman or Clifford algebra(which plays a rigourous way to visualise geometry in terms of anti commutative algebra),please make some video on it if you like.
@rkpetry
6 жыл бұрын
...associative but not commutative-you could put the sock inside the shoe and then your foot inside that, or, put your foot inside the sock and then that inside the shoe...
@pcrig
6 жыл бұрын
I have my issues with this host, mainly pacing and mentioning complicated concepts (such as vectors) with no context or introduction. I'm digging the new look of the art and animation though, that grid background was by far the worst part of the channel. I hope this host surprises me in the future! Cheers
@Cohnan13
6 жыл бұрын
I guess the pace is an issue, but with respect to the new concepts, just ignore them if you aren't interested, but they are useful to those whose curiosities are picked to know what to look for. This kind of disclaimer would be useful though, because I know how unsettling it can be to hear things you don't understand to be randomly thrown at you.
@3_up_moon
6 жыл бұрын
Face and hands. Very creative idea for a host!
@dbartholemewfox
6 жыл бұрын
I really like abstract algebra--at least I like what little I've learned. But you are going a bit to fast on this episode. Please more algebra, though!
@AgglomeratiProduzioni
6 жыл бұрын
"Imagine multiplying three numbers: what if what you multiply are not numbers?" Ok, stop it, this is becoming VSauce.
@d0themath284
6 жыл бұрын
+
@crazyfire100
6 жыл бұрын
why?
@tennison-chan
6 жыл бұрын
Nice topic and nice voice!
@lobachevscki
6 жыл бұрын
Hi! great video in general. Mathematician here, so this video was just a refreshener, i would like to point out 2 things: As many people said: you could probably slow down a bit. It will be less info but maybe you will deliver even better. (This applies to Gabe as well, it was my general complaint with his performance in Space Time). I think this was an step up on the bare minimun level needed to understand the subject. I think you are delivering complex concepts in a more abstrack way than the former host. You might use more concrete examples (not only to known basic math, but examples from real life; reviewing what you just said and stuff like that) I don't mind, i enjoying this videos, you are doing great in general, keep the good work!
@3ckitani
6 жыл бұрын
98 dimensional polyhedra. Seems interesting...
@marcushendriksen8415
5 жыл бұрын
But what sort of algebra does this loop concatenation belong to?
@pratixadesai6950
6 жыл бұрын
Amazing video! I really like the fast pace.
@damirradoncic7390
6 жыл бұрын
Hey Tai-Danae, great first episode! Im a swedish 27 yo that has got a masters in engineering and your presentation pushed the boundry of what I know - thanks! Since I've taken quite a lot of math classes in uni, following your presentation wasnt that hard - but for somebody that still is in uni or in high school, the speed of which you introduce and jump between concepts and terms might be hard to understand. I've followed the PBS series on youtube since the first episodes, and all presenters did this in the beginning - so im confident you'll do a great job!
@letsgokrzy9564
6 жыл бұрын
is it just me or is the brightness of the camera used to record this to high? put the iso down a bit.
@HallucigeniaIV
6 жыл бұрын
I find it hilarious that there is Lie Algebra and Poisson Algebra, Together they form the Algebra of Poisonous Lies
@timkarl4099
6 жыл бұрын
Do they do those hand movements in their interviews?
@eddielloyd1947
6 жыл бұрын
I always thought you could put your shoes on before your socks...
@michalchik
6 жыл бұрын
Good new host for pbs infinite. Needs to expand on a couple of things. I found the details of the loop multiplication seem a bit undermotivated. Why this way?
@SlipHailz
6 жыл бұрын
Hi. I just have one question. What is the relationship between loop multiplication and closed integrals? They seem to obey the same path rules; however, closed integrals are associative.
@pmcgee003
6 жыл бұрын
These curves were geometrically the same, but their parameterisations were different. The path integral is, I think, going to be independent of the parameterisation.
@stuartdover2775
6 жыл бұрын
Just a guess. With the concatenation, it's the parameterization that causes conflicts with associativity (the speed of the car), whereas with closed integrals, there is no such parameterization so the conflict disappears.
@tracyh5751
6 жыл бұрын
Tai-Danae does a great job here. I think the writing has too little detail though, and assumes that people are familiar with linear algebra. You could use division and subtraction as examples of non associative/non commutative multiplications as warm up mulltiplications and then go into the linear algebra for the more advanced viewer.
@magne14527
6 жыл бұрын
Do not slow down. This is a video. We people can go back and listen, pause. Cant wait for the next one!
@ocircles738
6 жыл бұрын
Gj Tai, relieved that you turned out to be a good host :) looking forwards to that 98d polyhedron !
@Antheloras
6 жыл бұрын
I love this show an though I'm not an mathematician in any way, Kelsey always had a talent to make me understand and appreciate those often difficult topics. I think Infinitite series is still in good hands, you made a great first impression. Still i would really appreciate it, if you speak more slowly and keep in mind that not all have a mathematical background. An 10 or 11 min video at a slower pace and with maybe with a few more examples or explanations (eg why or how vector multiplication is different) would help me a great deal :-) I'm looking forward to next weeks episode.
@zexion47
6 жыл бұрын
at 0:38 the face shifting is really jarring.
@Shockszzbyyous
6 жыл бұрын
a loop is what you think it is it's just a loop *thinks about loops in programming*
@matissetec
6 жыл бұрын
If I understand what was getting said here this is a completely correct place to go! You are, in a sense physically looping the hardware to get the 'loop' to occur. So the start point and end points are the same. You can 'speed up' or 'slow down' by imagining you can do more operations at once or less. Which also makes sense if you look at how computers work nowadays and imagine scaling the number of threads allocated to a program, and the amount of prefetch or on the fly calculations you do.
@bentoomey15
6 жыл бұрын
I love where you're taking the channel. And I like how you're showing the notation while you're saying the statement to low-key introduce people to the language of mathematics. Also, dropping the definition of a Lie algebra in for funsies - dig it. I'd love a short series on the importance of Lie algebras in modern math and physics, with some explanation of their properties (it might be tough to hit the right level for this channel, granted).
@filippozar8424
6 жыл бұрын
What makes an operation a multiplication other than using the same sign? Couldn't I define loop "multiplication" in the same way but use some other sign and call it for example "ding dong"?
@yq0706
6 жыл бұрын
Filip Pozar basically just think of "multiplication" as a function that takes two inputs and gives one output back in the same set. For instance you "multiply" two loops to get back the same loop. "Addition" is also "multiplication"
@cappucino7908
6 жыл бұрын
Yes you could call it anything you like.
@NotaWalrus1
6 жыл бұрын
usually mathematicians call any operation that takes two things from a set and gives you another thing in that set a multiplication or an addition. You can define it in other ways and explore their consequences.
@ralphinoful
6 жыл бұрын
Great video. As a host, you're content is more dense, and you move through the video faster. I personally can follow it, and enjoy the faster pace. I don't know what kind of demographic watches this content, but you might alienate some people who don't have formal training, or a degree in mathematics.
@KHUSHISINGH-fy1je
6 жыл бұрын
Ralph Strocchia please see this also kzitem.info/news/bejne/uKGLt6CPgJGol34
@Hextator
6 жыл бұрын
The faster pace made me feel like my (and possibly "our", of KZitemrs as a whole) intelligence was being respected more, like I could be trusted to either keep up or handle slowing down/pausing/replaying the video as necessary otherwise. From an aesthetic perspective, though, the speed seems out of place. replacing the cute host with another cute host was an ace move either way
@pelerflyp5398
6 жыл бұрын
The thumbnail misled me.. :(
@RalphDratman
6 жыл бұрын
Good video, well done, very clear. Thank you. Unfortunately I could not quite grasp multiplication in the form of loop concatenation (am I saying that correctly?) -- that is, not on the first viewing. But for this series, given the choice between a presentation that is too slow and one that is too fast, I'd put up with the too-fast one rather than plodding along, which can be more frustrating.
@Omnifarious0
6 жыл бұрын
This was a really interesting video, but you asked too much of the people watching. The idea of different rules of 'algebra' or even of algebra as an abstract set of rules you can apply to non-numeric systems is not one that I remember being a part of even a BS level computer science curriculum. Sure, we learned about linear algebra and calculus. But all that stuff was still being presented as sort of one-offs, not as mere instances of an abstract idea. I happen to know about some of this stuff because of studying I've been doing recently. But, it's not commonly known, and while you explained some of it, you left a lot of people with a lot of questions.
@ai_serf
4 жыл бұрын
I feel we need a ladder from pop sci to rigorous math channels. this channel is some what higher than most, and I appreciate it, even if they always leave a lot to be desired, its' still infinitely better than, "some infinities are puny and weak compared to other more mighty infinities who devour their souls, muahaha"
@P44man
6 жыл бұрын
Everyone is saying is you're going too fast. You're going "too fast" for me too, but the truth is, in order for me to actually understand this, you'd need to go so slow it would take you several hours. At least. I dont know why I like watching these video's, when I know I won't really grasp it. But you're not too blame for that, you're an outstanding presenter.
@keithplayzstuff2424
6 жыл бұрын
When you understand something but only because you know math and you know other people will have a hard time keeping up with a fast-paced non-pandering narrator... Yay me, Not yay everyone else
@michaelnovak9412
6 жыл бұрын
first with the new co-host
@knexator_
6 жыл бұрын
How observant
@kandrc
6 жыл бұрын
What happened to Kelsey? And why do all of the PBS Digital Studios hosts--except for Diana--wave their hands around like idiots? Seriously, the (literal) hand waving is distracting enough to keep me from watching videos or to make me stop them early.
6 жыл бұрын
Her voice is so soft and calming
@RobertAdoniasCostaGomes
6 жыл бұрын
ok, I need to stand my ground: please, don't slow down... keep the speed of speech at its current level (it was actually pretty ok, nothing wild like Gabe used to be) I had a problem of not watching Infinite Series so much because I would get asleep in the middle sometimes (I watch these videos before sleeping, normally)... if she keeps the pace up, I can become more of a regular again...
@tj12711
6 жыл бұрын
Many people are asking how the loop example is multiplication rather than addition. Many would say that the difference between Addition and Multiplication is that Addition doesn't obey the Distributive Law and Multiplication does, although this is actually not always the case. The fact is, it's somewhat a matter of notation, and therefore preference. Not exactly a satisfactory answer, I know.
@pierrecurie
6 жыл бұрын
She's talking about homotopy groups (which are associative) - almost. Usually we define equivalence classes where 2 loops are the same if they can be continuously deformed into each other. In her example, it's a simple matter of having the car speeding up/slowing down appropriately; the most important part is the path it travels, and that is the same either way.
@kamoroso94
6 жыл бұрын
I don't know why people are complaining about a fast pace. I had no trouble keeping up, even though the idea of multiplying loops is completely new to me. You're doing great, and welcome to Infinite Series! I loved your first episode and I'm hyped for the next one :D
@Frownlandia
6 жыл бұрын
If I understand correctly, it would be the case that loop products would be associative if there was no metric applied to it? That is, if loops weren't defined as "the interval between 0 and 1" but simply as "a continuous line segment". It's a different mathematical object, but my point is that the non-associativity comes as a result of using part of the number line.
@felixliard8508
6 жыл бұрын
The sock shoe, shoe sock thing is a bad example because if you are looking at it from a "are they both on my feet" standpoint, then it works just fine. It's like saying four times two is eight. Yes, but if you are looking at which number is specifically multiplied first, the two has to come before the four otherwise it's four times two. You aren't looking at the functionality of the numbers in terms of how other numbers might look at them funny throughout the day, it's the fact that it's cumulative, just like socks times shoes equal sock-shoes.
@toamastar
6 жыл бұрын
this was really interesting! i have no idea about this level of maths but the way you explained it made sense! :) also, i googled associohedron as soon as you said it and that looks interesting too! subbed! :)
@drawsgaming7094
6 жыл бұрын
YAY a channel that changed hands without gaining an impenetrable accent Btw You lightly touched on non-commutativity without mentioning (Hamiltonian) Quaternions. HOW?
@peccavo
6 жыл бұрын
Great topic! Love it. Also glad to see you so enthusiastic. For those of us at home, would you mind lowering the tempo a little bit? The video was only 8 minutes - with such rich material (and the same script) you could have paced it out to 10 minutes. I realize you're excited. We're all looking forward to see what part 2 of associativity looks like.
@Achrononmaster
6 жыл бұрын
I do not get why the parametrization makes any *topological* difference, surely associative to holds for at least that given example.
@rebokfleetfoot
6 жыл бұрын
wonderful explain! thanks! i don't agree that it goes too quickly, but for those who do may i suggest they change the playback-speed to .75 or .50
@wolswinkel
6 жыл бұрын
Small issue, but at 0:55 you said "then multiply by 2", when you meant "then multiply 2 by that". It sounds awkward but could help to get the concept of commutavity across.
@connemignonne
6 жыл бұрын
Sad to see Kelsey go but the new hosts look great. Tai-Danae is awesome and it's wonderful to have the old PBS Space/Time guy back!
@wearealreadydeadfam8214
6 жыл бұрын
This is way over my head. Like I understand but I don’t comprehend. Welp, back to Eons. I like how they talk about dinosaurs.
@readjordan2257
Жыл бұрын
The KZitem chapter titles misspelled "Lie Algebra" as "Lee Algebra", however the subtitles are correct. Strange.
@TheDXPower
6 жыл бұрын
Like the new host, but not a fan of the cliff-hanger right before we actually learned something new... Yeah, nearly every video before this one has had that "warmup material" to make sure that everyone is one the same pace, but it just stopped right after the warmup in this video. Maybe for the next topic record the two hosts and upload them in the same video.
@AndrewYarmola
6 жыл бұрын
Great video! Just one comment, why link to notes on the fundamental group? Up to homotopy (defined on the 2nd page of the notes), concatenation is associative, which may confuse people.
@Shawkster6
6 жыл бұрын
This video is amazing!! I'm like already super interested in topology, but I've never really thought about it much before. This is a PERFECT introduction! I can't wait for the next video :) :) :)
@shadfurman
6 жыл бұрын
Damnit! 20 years and that's what I've been doing wrong! All the weird looks at work now makes sense! I've been putting on my shoes then my socks.
@0-by-1_Publishing_LLC
3 жыл бұрын
(5:00) The irony is that the mathematics you are describing was used in the "Adobe After Effects" animation car-loop sequence seen in your video. 0-by-1.com
@thetexasranger
6 жыл бұрын
I like the length of video, previously was too long sometimes. The new chick is pretty good. And i like the detail and speed here as well
@recklessroges
6 жыл бұрын
Wow you hit the ground running! Tai-Danae makes me feel the channel is in good hands. (I still miss Kelsey, but I hope she is in a better place on that farm for mathematicians upstate. ;-s )
@JWentu
6 жыл бұрын
Thank you Tai-Danae. Nice Episode! Yes, you spoke quite fast but it was also rather clear and articulated, I liked it.
@WernerEdgar
6 жыл бұрын
Love Kelsey, but Tai-Danae is having a stellar debut on the channel. She went deep, but not too much and has a pleasant way of talking and explaining stuff.
@kwinvdv
6 жыл бұрын
Similar to matrices (or second order tensors if you like) quaternions also do not commute, but are associative. Quaternions can be used to represent 3D rotations. I have read that 4D rotations can also be represented by octonions, which also don't commute, but are also not associative.
@harryandruschak2843
6 жыл бұрын
Also ties into complex numbers (loss or orderness), quaternions (loss of commutavity), octonions (loss of associativity), and sedonions (you now have zero divisers.
@MrMetrizable
6 жыл бұрын
Basically homotopy. You can force associativity using homotopy equivalence. i generally think of loop concatenation as addition rather than multiplication though but it really doesn't matter
@MultivectorAnalysis
6 жыл бұрын
Great video! Speaking of multiplication, please consider doing an episode on the Clifford product
@anacaznok872
6 жыл бұрын
This might be a stupid question but why couldn’t the yellow, red and blue cars all complete their courses in 1/3 s ? The sum still would be 1.
@michaelleue7594
6 жыл бұрын
You moved a little fast from about 2:00 to 3:30. The rest of the video was well-paced, but in the future, consider editing for stuff like this: if it isn't important enough to spend time on, then breezing past it with a long list of what amounts to nonsense words isn't going to do anyone any good.
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