The real world applications of the dot product
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- Опубликовано: 15 июн 2020
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When people go into video game design, I hope they know it's nothing like playing video games. It's a lot of arithmetic and logic like this.
Videogame design requires logical skills, definitely. But arithmetic, not really; you might think of videogame programming instead.
A game designer has to carefully specify events in a simulation and their contexts, for instance what unique conditions must be met for a character to grab a ledge (including character states, user inputs, timings, distances and angles), but they shouldn't have to worry how the angle between the character's shoulders and the ledge is computed; this is programmer's role.
@@EcoAku Totally agree! I kind of paired them both together in my example.
you mean they won't let me sit and play video games all day? WTF!
That makes me all the more interested
Blox117 that’s the job for testers, and the majority of the time is to play prototypes instead of finished products
Vectors really need a better introduction in classes.
It's made to seem like it's a really boring thing with too much visualization and math.
They are some really cool stuff that is awesome, that deserve more love and respect
probably a computer class, not math class. Or add computers to math class.
It's much more intuitive in graphics that with formulas on chalkboard.
everything is more intuitive with computers tbh.
I actually never learnt vectors in math (yet) i do them next year
However, i learnt them in physics class and engineering class (yes my school has an engineering subject) so i found vectors to be fun as ik where to apply them
Such as adding forces on a structure
vectors should be introduced in geometry
check out my lectures on engineering maths and units to get A's
ruclips.net/video/IcDEwupQ7Rs/видео.html
If I were a math instructor, I would pride myself on showing a practical application for every concept I taught.
It would make sense if you were a physics professor. Many concepts from pure mathematics don't necessarily have a lot of practical applications, but that doesn't make them any less interesting.
@@helloimnisha what? Of course that makes them less interesting. Much, much less interesting in fact. It might still be interesting for people that inherently enjoy math. But for the rest of us, we simply learn and use math for it's usefulness.
@franciscodanconia45 any link about similar resoruces?
When teaching Math at School, with every topic, there should be an Introduction that explains the practical purpose or examples of some real world applications. This will encourage students to pay attention.
I've no idea why on earth should i learn complex numbers in high school and to make it worse, it was given a name "imaginary number" and letter "i" was used to represent it. They should change it to letter "j" and use "complex" instead of "imaginary".
@Dr Deuteron I know that now, what i meant is, it would have been nice if i had known when i saw complex numbers at high school
Math is not Physics or Engineering. Many applications of particular areas of Mathematics weren't known/discovered until years/decades/centuries after their inception. Pure Math isn't a field about applications of formulae or specific processes, but rather, it is system of logic and reasoning. The applications of mathematics come in the form of other fields entirely; the aforementioned physics, engineering, etc, and trying to pigeonhole mathematics education by forcing applications for topics is an easy way to cripple expansion and exploration in the field and the skills it is used to develop.
@@EpicAsshole : Introducing mathematical topics with some sense of practical use will help students to build their intuition about the subject. Not only will they solve mathematical problems with intuition, it will be much easier to abstract mathematical ideas when there is a strong foundation to do so. In essence, intuition for foundation, abstraction for advanced use. A high school does not need much proof of a formula, rather they need understanding it. An engineer does not need the same mathematical proof background level in comparison to a mathematician, therefore learning should be more need basis.
@@comprehendnature2404 Beyond basic arithmetic, it is quite difficult for most people to really generate any sense of practical use without a fairly strong foundation in the topic; you have the direction of abstraction reversed. Beyond the basics of mathematics, you generally have to be familiar with the abstract concepts before you can apply them to concrete topics and novel problems, as for more advanced topics, the typical person cannot derive the abstract understanding from concrete phenomena.
@@EpicAsshole nailed it. You should understand the idea first and then apply it when necessary. Not the other way around
Always was interested in Dot Products, yeah Vectors are easily applicable to pretty much everything in the foreseeable world, but something as really specific as the dot product is quite intriguing for its uses. Maths always has its place in the universe.
Turns out we’ll have to reinvent math to fit quantum mechanics.... Or maybe is dark matter changing the laws of universe when stuff arises to the ‘macro’ scale?
Would you do on Cross product as well??? I think that needs more of
"Zachary explanation ""
Yeah that would be awesome
Remember how often he used the word "normal?" In 3 dimensions, the normal vector is a vector that points "out" of a 2D plane that cuts through the 3D space. Such a 2D plane can be fully described by two (non-colinear) vectors, such as you'd get by picking one corner of a triangle and "pointing" toward the other two points.
It turns out (and certainly not by fluke) that the cross product takes two vectors as input and produces a third vector that is perpendicular to both. Since we've required our two input vectors to be non-colinear, the only direction that can be perpendicular to both of them is "out" of the plane they define, which (again not by fluke) is exactly what we need for our normal vector.
A couple of fun quirks:
1) There are actually two vectors that point "out" of a plane -- one facing "up" and one facing "down." Getting those backwards in a 3D graphics setting can lead to "interesting" results, as your lighting is effectively turned negative .. assuming the object is drawn at all. There's an optimization called backface culling that (using the dot product!) compares your viewpoint to the normal and if you're "behind" a particular triangle, it won't be shown (its assuming the object is solid and therefore there should be another triangle closer to you that would obscure this one anyway.. If you ever get your camera "inside" and object and it just blinks out of existence, this is probably why.)
2) Because the cross product returns a perpendicular vector, and the dot product returns zero for perpendicular vectors, it implies (AxB).A=(AxB).B=0. This is actually a very useful fact in lots of linear algebra (knowing things whether things are explicitly perpendicular or not is often far more important than knowing how far off of perpendicular they are.)
Finally, I don't really remember the relevance of the cross product in other dimensions. But computing a normal in 3D is pretty darned important on its own!
Yeah,I would love it if you made another video on cross products of vectors
@@altrag Hmm cool, really liked the first fact; was new to me.
Before watching this video, the only real-world application of dot product I knew was to get good grades while majoring in physics. Nice
really?
@@RAGHAVENDRASINGH17 unfortunately, yeah. I'm more of a theoretical physics guy, so I'm less informed about the real world stuff. But as a 1st year physics major, I should know a thing or two about such things. I feel bad, tbh.
@Metric Tensor Nope. I don't regret taking physics as my major. I love it! Something about physics really draws me in, which even I can't properly explain. I even changed my channel niche to spend more time with physics. However, being a freshman, I can't really give you a solid answer, since the euphoria may not last long. But since I don't mind the sufferings as a physics major, things might not change for me that easily. :)
@Metric Tensor first, are you a college major or in highschool?
@Metric Tensor ok so it makes things easier.
Right now, I can only tell you what I'll probably do in the future or what I intend to do.
It's obvious that engineers get paid more than physicists.
So after PhD we generally have three options:
1) Industry job, where most people go for an engineering job. It's quite lucrative, but then you'll probably lose the passion for physics and just getting a job finishing eng major would've been better.
2) Academic, where you get to be a professor and do more research (as a part of post doc and beyond). Funding for research is generally low, due to competition. If you become an experimentalist, generally high fundings. Reverse is true for theoretical physics.
3) Finance, where you get to manipulate the market and predict prices using maths. I'm not sure, as I just got introduced to this topic very recently. But some physicist guy did it in the past or something to make more money. High risk, high reward.
So, as far as I know, these are the options. So whatever you think suits your style. If you have a burning passion for something, do it. Roads will show slowly itself. If you only care about money, then either don't take physics or do extra work for side hustles like me.(I trade options and make RUclips videos.)
As for my future plan, since I'm interested in QM and ML, I plan to create a business related to Quantum computing, but that probably won't be possible anytime soon (I'm also doing a major in CS btw). But in general, I just wanna do research on QM and create business out of whatever I find interesting in the future. But since I'm doing side hustles right now, I'm not worried about getting jobs, as I can just invest whatever I earn today and reap it's benefits later. But it's quite tiresome to do double major and have side hustles. I have to make a lot of sacrifices.
Sooo yeah, that's my plan with physics in nutshell.
I'm not really the most suitable person to give you the information, since I'm just a 1st year student. But I hope this helps. :)
It’s insane how your channel has evolved over the years! You have truly inspired me with every video! Keep it up and stay safe !
Hats off to you Zach for making concepts a hell of a lot easier to understand!
creating animation , learning about these things then explaining intuitively and synchronising sound and video is a lot of work ,,i really appreciate that , i used to think maths is just random equations and has no use and importance but i don't see maths like that any more,. thanks *zach starr*
Your videos are very informative and fun to watch. Thank you so much!
Thanx for answering questions about my favorite subject.
I used to wonder about use of these in real life.
this was really cool. i loved it. u should do more of these kinda video!! REALLY AMAZING
Awesome video, Zach! Your perspectives and insights into the dot product give me a lot to think about. Thank you for sharing. Many blessings.
Thanks a lot! I am a person that can not understand without the logic behind the concept and daily usage of it and these type of videos are helping so much. I subscribed.
Thank you for diving into the most interesting content!!
This is a top class video I found, please do post more
Thanks much for all the hard work :-)
WOW!! so nice explanation and presentation. Thankyou i will share this with everyone
Amazing work man! Learned some real cool stuff!😄💎
Keep it up....always waiting for such stuff..🙏🙏🙏🙏
Hi, great video, I love your work and today I started to support you on Patreon. Hug from Portugal.
Thank you for such wonderful videos! I share them with my matrix algebra class! :)
When I first saw your content, it was harder to follow than the other science RUclipsrs, but as I take more math courses I enjoy your content more and more. Thank you
This video blew my mind.. I've been doing dot products for a long time without knowing any of the actual applications. Thank you!!
This is my first time learning dot product. Thank you.
Awesome! I was just trying to visualize Dot Product, and them I got this cool content. 😮
🙏 🙏 🙏
one of the most amazing explanation for the light equation i have seen!!
Wow, thank you so much for this! I wish I had this explanation in my linear algebra final last week.
i like your real world videos. I dont always check all of it but it its totally fine.
thanks for the free content
Never stop this series
Thanks
for making such video
I googled this topic yesterday, and here it is. Thanks 😃
Today I was studying vector algebra and this video is in my recommendation.
Very useful video 👌
This rendering eqn is so amazing!!
really great video thank you so much! :) please keep it up
I feel thankful. You deserve everything.
Really good stuff, you took your time.
Great work. Awesome video that explain the application of dot product in real world. good engineering concept.
The dot product is also used in transforms. For example, in the discrete Fourier transform.
It's a pleasure to be a subscriber of your channel. Thanks.
awesome explanation of the raytracing equation
A real quality -- Liked and Subscribed!
Amazing. Thank you.
Thank you for the information. I would like to add that Dot products are also used in spectral interpretation in Mass Spectrometry (MS) technology. Briefly speaking, they used dot product to identify a spectra of a sample (in MS, they "transform" samples into ions which will be detected by the MS. these will produce a complex "zigzag lines". These lines are spectra). The spectra of a measured sample were compared to a reference spectra (have been obtained beforehand and validated) via dot product.
Nice topic I understood very clearly
came here from a video about electronics engineering, which is one of my degrees, wanting to understand dot product but was pleasantly surprised when almost half of this video basically explained lighting in game programming (or ray tracing) which is my current field of study :D
funny how the youtube algorithm actually seems to work for real sometimes (while completely broken all other times)
Amazing explaination.
you also described cosine similarity... it is used in Transformer (i.e. GPT for instance) models. Great Video!
Thank you for content
Amazingly superb
Nice work! It’d be helpful if you could distinguish vectors from scalars, say boldface versus normal font. Maybe some (light) music could be nice to make it feel less empty, too.
Thank you so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I finnaly understood the concept and with the application in games it makes way more sense :)
Great video!
Very good video!
Hi Zach Star, I love how you explained dot product in various applications.
Can you do that for Cross Product as well?
Thank youu
great video! 10/10
Nice work buddy 😊
Great didactic explanation !
Huh, interesting.
Hmm..interesting
OOO interesting
Huh. Interesting
Hmmm.. interesting
InTeReStInG
I am happy because I subscribed to this channel.
I was just studying dot product.
I didn't realise how important it was until now.
Thanks
Huh, and here I was thinking of taking Intro to Algorithms this fall. You just made it even more appealing.
Great video
Thank you
hey...ur channel is awesome!....could make a videos on book recommendations in stem fields?
nice animations 💪💯
a little video suggestion:
during a career fair, a representative of a company remarked that most college engineering students consider their dream job as being in design
I would love a video on what other job opportunities might be avaliable after graudation.
thank you
very nice video... would also like to see this for cross product
It was great learning. Thank you so much 😊. Just-had an inquiry , which software you use to show those diagrams illustrations at the beginning while explaining vector composition; work done; etc? Please let me know
hey Zach, you are my star!
In my mechanisms class we had to calculate velocities and acceleration by graphical methods.
It's only until recently I found out we were using dot products (at least for some methods)
Sir please make more videos on how advance maths related to real life
Thanks you currently I am studying vector algebra at high school now I know the applications of vector algebra
Good one
Thank you .Great🌟🌟🌟🌟🌟
Hi, thanks for you videos,
so cool
can you make one about determinant of matrices?
what does the determinant of a matrix represent?
Cool - planning on also making a similar video about the cross product?
Hm... dot product tells me my solar panels produce negative energy at night time.
Better unplug them at night just to be safe.
Well, technically they could. If you apply voltage to a solar cell it lights up just like and LED, but I know that at least on on-grid systems the electronics of the DC-AC inverter prohibits the energy from going the other way. I never worked with off-grid systems, so I don't know how it's done in that case.
Since the sun is out of sight, the irradiance level at nighttime is nowhere near what it is during the day. The fact that the dot product with the line of sight to the sun is negative at night, is irrelevant. The panel can radiate energy to the cosmic background, but it will be a hell of a lot less than the power it would absorb during the day.
Plus, panels have diodes in them that stop reverse current, so they automatically turn off if you attempt to let them "produce negative energy".
This is a real concern for solar thermal panels, unlike solar electric panels, as they would radiate away their heat at nighttime, if not encased in glass. The glass acts as a bandpass filter that lets in 5800K sunlight, and blocks the emission of low frequency infrared that the panel's 300K black surface would emit on its own.
Is it possible to get the name of the music in the background? I've heard it in a couple of his videos, and I think it would be nice to listen to while solving problems. Thanks in advance.
Also, a great video which gives perspective to students.
Somebody give this man an award.
I was clickbaited by the regression line in the thumbnail. It was still a very educational and informative video and I dont regret having watched it.
The dot product was always a really engaging topic imo
Hello Zach, two questions: 1 could the dot product methodology be used for the image recognition? 2 In your plagiarism check example, does the order of the word play important role in the final result?
Learning about the real applications of this positive definite non-degenerate Scalar Product of this Euclidean Space was really interesting :) thanks
Waiting for one on Cross Product too!!!
Hello. Really interesting!
What is the program you use to do that explanation and drawings?
Thanks.
Vector calculus was always my favorite math class haha
Zach star: Shows a lot of wonderful applications of dot product.
Joma tech: *LOOK, A DOUGHNUT!!!*
please make a video about the cross product of vectors as well
Great video as always! I was wondering, what made you want to become a RUclipsr?
So this didn't start off as a youtube channel actually. In the beginning I was interested in starting a business, not being a youtuber necessarily. The first several videos that you see on this channel were instead on a website that I coded where I offered some videos for free and then put others behind a paywall in an attempt to make some side income (at the time I didn't even know about using youtube to earn a living). Since the entire website was video based I decided I should throw some videos on youtube in an attempt to advertise the website. Fast forward a few months and those videos started to get some real views (way way more than the website) and I was getting comments pretty much daily. The comments (mostly positive) made it much more real and I loved the feeling of having people I've never even met tell me these videos actually helped them in their personal life. It didn't take long for me to have more fun posting videos on youtube for free where I got real interaction/views compared to making a little money through a side website which didn't have that kind of interaction. As much as I loved making the videos though I knew I had to make money from it somehow cause they took a lot of time (I was not in the youtube partner program at the time), so I started watching videos on how to make a living with youtube. I began to sign up for affiliate programs, I reached out to advertisers, and I signed up for the youtube partner program. The growth in the beginning was slow and I was making maybe $100 a month. I got my first relatively 'viral' video eventually and that month I got closer to $800 which was an amazing feeling and I started to see the power of youtube. From there I just kept making videos in my spare time, trying to learn new software and just improve the video quality overall. I've always loved teaching math and this was a great way to expand on that. While I was building the channel I was working as a tutor so honestly my entire life was just teaching math/physics lol. In the end I wouldn't say I wanted to be a youtuber, I kind of grew into one after learning more and more about it, realizing I do in fact enjoy making the videos and interacting with the community (and the fact that I can now live off of youtube definitely made it a great investment of my time).
Zach Star Wow, thanks for the response, a great read, and truly inspiring!! I love your videos, and hope to see more content! :)
Quite timely. I took a Computer Graphics course as a breadth elective in completing my CS BS this summer, and it has subverted my expectations of sprites and GUIs by instead being "oops, all linear algebra".
To be honest, a good full computer graphics course should probably a mix of both sprites, GUIs, animation and linear algebra.
all i hear is OMEGALUL in the rendering explanation :)
I love vectors. Can you do one on cross product?
Can you make a video about the most math intensive engineeting paths you could go on?
This Should be on Netflix.
2:13
Hell, it can even be a good tool to scientifically vulgarise the dynamics for higher dimensions without any 2D or 3D gross and inaccurate simplifications : you could use the dot product to show when two position vectors are closing in on each other, to show when they're collinear, and their norms could show if they're pointing in the same or opposite direction, or by how far they're still separate if they're not of the same length, etc...
Dang, i dont know what im going to watch tonight, now that i finished this video upon waking.
Wait.. wait a minute you're Zach Star! Oh wow should've known.. thanks for helpin me out, thanks to you I full understand dot product now
I see them all the time in UE4 shaders, especially metallic, water, fabric cloth, hair and moss.
Not only documents, we can literally compare anything, if we check data based on binary part. We can compare each bit of each data and, for example we can plot 1 on x and 0 on y axis. And then compare angle