You Don't Know How Mirrors Work
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- Опубліковано 11 лис 2019
- Mirrors are weird. To truly understand them, we'll need not only ray and wave optics, but also photons, wave functions, probability, and quantum mechanics. Brilliant for 20% off: brilliant.org/ScienceAsylum
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VIDEO ANNOTATIONS/CARDS
Quantum Wave Functions:
• Quantum Wave Functions...
Where Does Light Come From?
• Where Does Light Come ...
How do we KNOW light is a wave?
• How do we KNOW light i...
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RELATED UA-cam VIDEOS
Physics Girl on Mirrors:
• Why do mirrors flip ho...
Vsauce on Mirrors:
• What Color Is A Mirror?
• INSIDE a Spherical Mirror
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OTHER SOURCES
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Optics by Hecht
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LINKS TO COMMENTS
It's Okay To Be Smart:
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IMAGE CREDITS
Albert Einstein:
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"Julie Lebrun" by Élisabeth Vigée Lebrun
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Animated Black Hole:
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*Clarification:* In my quantum animations, that is not multiple photons taking different paths. It is a _single photon_ taking multiple paths simultaneously. We're releasing only one photon at a time. Adding those phasor arrows together gives us the _probability_ of receiving a single photon at any given moment.
*Minor Correction:* I show the paths leaving the source at the same time and arriving at the detector at different times, when it should actually be the other way around. Paths that take more time should be leaving the source earlier in order to arrive at the detector at the same time as the others. The reason we can add the phasor arrows together is because the paths arrive at the detector at the same time.
It's a cool video, but I'm surprised with people saying it's a "great explanation" and "coherent" since these phase vectors (as in other video as well) does not seems to cancel out at all, I mean I don't understand, how do they cancel? The Sum vector for them (from the beginning of the first arrow to the end of the last one) is pretty big and I'd assume that IF they cancel THEN it would be close to zero length, this is a huge inconsistency for me... @The Science Asylum please explain this
Nevertheless the part with removing parts of the mirror was super interesting, can this be visualized with a real-world experiment? Is a demonstration even possible?
@@MrSenger00 The only reason they're not perfectly canceling in the video is because there's only 13 arrows in the animation. In reality, there are an infinite number of arrows. There are many arrows for paths _between_ the ones I've shown and many more arrows for paths _off screen._ They would cancel better if I considered 100 paths or 1000 paths instead of 13.
In reality it is the holographic principle taking the whole experiment setup into account. Also the color of the fotons and the gap distances on the mirror have an effect...
Sorry, sorry; I didn't get the Minor Correction. How can the SAME photon leave the source at different times to arrive at the detector at the same time, if it´s the same photon?
@@fberron haha, it's a cool video and some people really pay attention. :-)
The best videos are when you take something you think you understand and apply Quantum Mechanics to it. It's a mind blower every time.
Quantum mechanics is like hot sauce on foods. It enhances the flavor, not many people like it and we can't handle too much of it. It's repulsive and attractive at the same time.
Pizza, but quantum mechanics
To be honest, I don't understand anything until quantum mechanics come in to play.
@@0626love Really until?
After that you can make a video of how last video does not understand QM...
Everyone: Mirrors are simple. Light goes in one way, it comes out another way.
Internet plebs: Mirrors are simple. When light hits the reflective coating on the surface, it bounces at an angle according to the law of reflection.
Nerds: Mirrors are complicated. A usually silver or similarly reflective element that is electroplated onto the surface to serve as the mirror, will absorb incoming light, and vibrate. Those atoms will begin to emit their own light, in all directions, most of which destructively interferes except for in the directions that happen to match up with the predictions of the law of reflection.
Nick: So imagine a micro black hole and a brick wall
edit: guys I'm literally memeing, stop being annoying
Well, we don't need the black hole and the wall really, we just need to understand path integrals. The black hole and the wall are just a tools to do so without calling it "path integral". (I hope "path integral" is the correct translation of the German "Pfadintegral"? If not, please forgive me.)
@@hubertheiser I don't know German, but path integrals (more commonly called line Integrals, though this is a less accurate term) definitely seem like the right term for what Nick was describing.
@@hubertheiser "Path integral" is correct. The path integral formulation of quantum mechanics was the subject of Feynman's doctoral dissertation.
Welp
@@Lucky10279 For example, work would be a line integral of force. (in german: Linienintegral). A pathintegral is a integral of a functional with respect to a function. That's somewhat of a different thing. In the line integral we integrate over one fixed path (i.e. a vectorlike function) that basically serves as an Integration variable. A path integral on the otherhand sums the Integrand, a so called functional, a function of all possible paths, given as all possible vectorlike functions, by all these different paths, i.e. functions.
One could say a path integral is the generalization of the line integral, but they are really just different concepts.
Every video you produce feels like a single piece of an insanely large jigsaw puzzle. This video is definitely an edge piece!
An "insanely large jigsaw puzzle" is the single best description of physics that I've ever seen.
@@ScienceAsylum once I was asked to ELI5 what debugging software was like. My response: Imagine a big jenga tower where you need to replace a block in its center. Now replace each layer of the jenga tower with a 1000 piece puzzle...
@@FjorimDerHuene what sort of software field you're working in? I'm doing software development for a bit over 10 years and can't recall single instance where it would had been as bad as you describe.
@@sk-sm9sh I may have exagerrated a bit to get my point across 😁 and it's only as bad as that if you're debugging legacy code that you didn't write yourself. Nowadays the experience is way better. Some occasions aside...
@@ScienceAsylum I say "why is glass transparent" by Ted-ed And now even after your explanation, idk why mirror reflect 99% photons it receives even though it's 99% empty space and probability wise.. it should reflect like 1 or 2% of original intensity of light.... Can you explain?
What I liked is that the explanation went gradually deeper into it, "layer by layer", from the macroscopic law of reflection to a single photon ... with a few steps in between. It's propably the best way to educate a general audience.
amen
I thought I understood mirrors. I understand mirrors even less now. And that's a compliment.
I never understood mirrors and i understand even less now 👁️👄👁️
I thought I knew I understood mirrors, now I know I don't...
As Feynman said, at some point you have to accept some things just are, and build your intuition and understanding on top of that.
I totally Dunning-Kruger effected myself too with this one.
@@iforgoree if you think you understand quantum mechanics, it means you actually don't, but if you think you don't understand QM, it means you do.
Man, you can't guess how many explanations I've seen in my life why mirrors don't flip - but the example with text on a sheet of paper which you watch from the backside was THE eye-opener. Bravo.
Of course they flip. They flip near to far. The fact that the text looks backwards is just a natural result of the inversion of the cross product of the.. oh no he's gone cross-eyed.
You can do the same with a single cut out letter ~ use F and hold it in front of a mirror to prove it doesent reverse things
@@MrJohnA125 shouldn't that be obvious? If you can do it with a word of text, of course it would also work with a single letter.
0:08 "They seem like they're pretty easy to understand... OR ARE THEY?!" 😂🤣 I sense Michael here
Hey vsauce!!!
H Michael here
"Hey, Science Asylum! Nick here."
This channel is the most underrated in youtube. Such a great content with coherent explanation.
Absolutely
Agree
I like this Chanel too
Ya that was really good I'm glad I watched it. I had legitimately never heard that explanation before and had no idea it was based on probability.
He should become a meme to get known. Thats how it works on itnernet.
“Mirror, mirror on the wall, was is the probability that I can see myself at all?
*Actually, Quantum Physics Forbid This*
DAMN
But... it's "Magic Mirror"
No. Time dilation.
@@navycalvin9337 forbids what? reflection?
This video is brilliant. I have a degree in chemistry and just the other day I had the biggest impostor syndrome attack cause i realized i didn't know how mirror really works. I am now one step further from the perpetual abyss of ignorance.
sus ඞ
@@Legatron17
Ugh...
lol
As a high school student, i feel that every day haha. Whenever i go deep into anything i come to know that i dont know ANYTHING
This video is a great example of quantum mechanics used in everyday lives: as for that last question, I’m in a superposition of yes and no.
Me in high school: why doesn't this guy get millions of views?
Me in college: why doesn't this guy get millions of views?
Me in university: why doesn't this guy get millions of views?
hi brother
@@pizzapizzadesu oh hey joe
Me 6 feet under: why doesn't this guy get millions of views?
Me in High School: "I hate math. Physics has math. I probably hate physics too."
Me in University: avoids any STEM-related subjects and studies [insert useless liberal arts subjects]
Me now: watches physics videos on UA-cam and wonders why high school math & sciences teachers never teach like this
Don't expect anything good from UA-cam anymore. We'll be lucky if they don't ban Nick for not being good enough for advertisement. Their algorithm only favors the famous youtubers, little ones have been disappearing for a while and will vanish even more soon.
Therapist: Symmetrical Einstein isn't real, he can't hurt you
Symmetrical Einstein: 1:00
It is so Super Symmetry.
It is so creepy
"shut up and calculate is a famous motto in quantom mechanic"
thats exactly why i cose mechanical engineering.
"Shut up and calculate" was actually written by N. David Mermin as what the Copenhagen interpretation meant to him. It was a complaint or a derisive remark. Much Like Fred Hoyle deriding the "Big Bang".
In the same vein, Einstein said he would have named his theory the "Theory of invariance" had not Planck already dubbed it the theory of relativity.
Memes are alive.
Shut up and calculate to make sure that bridge won't collapse on the next windy day.
well, shut up and calculate is a great way to describe how finite elements analysis work
Major kudos for not diluting the explanation and still giving a clear answer. I was expecting something to be over-simplified and was pleasantly surprised. Very well done!
people: magnets are complicated. how do they work
Nick: have you ever really thought about mirrors?
Ha ! You have no idea how interesting magnetic fields are.
“Relativistic effect of moving electric charges” Feynman.
Definitely worth a video.
@@guywittig5069 ua-cam.com/video/XczMRsiq9mk/v-deo.html already exists (though I think it was part of a 3 or 4 video series IIRC, so you might have to look up related ones.) Should also look up minutephysics' take on the subject.
@@guywittig5069 How Special Relativity Fixed Electromagnetism: ua-cam.com/video/Ii7rgIQawko/v-deo.html
Also, here's a whole playlist of E&M videos: ua-cam.com/play/PLOVL_fPox2K9MtRv68T_cmWwQUbg9YR4F.html
I definitely understand how mirrors work, thank you!
10 minutes later: okay, maybe I didn't..
Nick, you are an incredible teacher. There aren't many people producing content quite like you can do.
Hey, that was the beginning of chapter 2 of Richard Feynman's book QED, but the animations are much more fun! Great work!
Thanks! 😊
"It's okay to be a little crazy"
Quantum physics takes that phrase and runs with it at the speed of light through all possible paths simultaneously...
When you explained how mirrors don't actually flip images that kinda blew my mind.
That's quite funny because my reaction was: "OMG that is what I have always thought!"
It flipped my mind !
actually mirrors do flip things, just back-front, not left-right as most people think.
@@gawain78 Yeah, me too. I figured it out years ago, as a kid.
Thanks Nick for getting this right! Vsauce got it wrong.
me before watching: how do mirrors work?
me after watching *HOW DO MIRRORS WORK??!?!?!!?!?!*
When you stare into the abyss there's a non-zero probability that the abyss stares back at you.
nice one
When he said that the girl in painting is looking at me, I got real scared
You should be. Those red eyes are freaky.
@@ScienceAsylum hahah i laughed so hard for this one
Same
Were you going to town on yourself?
Me too
came across your channel two days ago and only question is why on earth are people not watching you more and as for your videos they are really great
because most of the people are simpletons.
something we can be sure of even on applying quantum mechanics
Why did you wait until a few days ago to start watching?
@@Soupy_loopy well i needed to think about what he explained.
As a graphics programmer I thought that this video would be mostly what I already know, but you went way more in depth than I expected, and I learned a few things. Goes to show I know a lot about HOW light works, but not too much about WHY it works that way.
An introduction, in 10 minutes! to quantum electrodynamics! Beautiful job!
Nick my favourite the one who teaches everything in the unique way that nobody does and nobody can teach like you phenomenal!!
Imagine he was your teacher in school.
I would dance
@@thingsiplay Then you would have to do the math.
loool i was like what could be interesting about a mirror, boy was i wrong
Lenses are even better ;)
The
“Yes! Kind of. Not really. Ah, maybe”
Part was awesome
You crack me up whenever you get to quantum mechanics. That bit about taking out segments of the mirror yet the photon can still hit the black hole brings a whole new visualization of quantum mechanics. Absolutely amazing.
So when I saw this title, I was a bit disappointed. I mean, mirrors sounded boring to me. But holy cow, this was fascinating. I should have never doubted the Science Asylum
"Or does it?!"
*Hey vsause, welcome to the science asylum*
Vsauce brought me here, in fact
vscience
@ me too
Oh, they should do a collab!
@ wait really? Vsauce recommended thescienceasylum?
Great show! At first I needed to adjust to your way of explaining, but you seem to have the best intentions and are a great teacher.
3:28 YES! YES! EXACTLY!
Warning: Do not try this in your class. You will:
a) Be told to focus on the syllabus
b) Be yelled at and called oversmart
c) Ultimately be confused till you Science Asylum and chill
I did this(a few times), my teatcher always explained it
I missed a warning signal saying "Do not Feed the Black Hole".
Haha I got that
Whenever I feel that I have a reasonable grasp of reality I know I can come here and have those illusions shattered.
I have been questioning myself how mirror actually works for about a decade. I had the feeling it wasn't that obvious all this time... but never went deep enough in the quantum mechanics to understand it. Thanks to you my mind blew... and it was amazing!
Really reminded me of the great New Zealand Feynman lectures. Thank you! I was about to request this video when I saw your video on the types of reflection. So many (even more-or-less reputable) science channels get "flipping" wrong, when it is fairly obvious (and things don't come obvious to me very often). The cutting out parts of the mirror thing toward the end is really fascinating.
Those Feynman lectures are linked in the description 😊
Not only do I feel like I understand mirrors better, the more you dive into the quantum physics of real-world phenomena, the more I start to understand quantum better, too! You are doing an incredible service to your audience, and you absolutely should not stop anytime soon. :D
Among the top 5 science educators for me, both in terms of concise explanation, no unecessary pandering and keeping my interest throughout. Finding this channel in late 2018 was amazing.
This is a terrific video. It's so difficult to come up with a way to show this stuff in easy to understand visual explanation but you've nailed it!
Thanks! 🤓
This is another extremely good video - thank you. I've previously found what TV people would call your "treatment" annoying - seemingly aimed at children, but the sheer quality of the content trumps that. I visit Physics forums peopled by PhDs and I ask the kinds of questions your vidoeos answer, and your answers are clearer and seem more correct. This one gave me the glimmer of insight on an issue I've been asking for years, with no answes emerging - the fundamental reason for diffraction. WONDERFUL. It seems clear to me that your content is up with the very best in the world - Veritasium etc. I still think your treatment is holding you back, but I've come to look forward to "hey crazies" and I wish you all the best for an explosive (in a good way) career on YT.
Me: 7:17
When someone asks me, "Does electrone move by orbiting? "
It pretty much sums up anything in quantum mechanics.
@@ScienceAsylum Hi Nick! I was want to know why the reflection angles of light are equal , and that is the only thing i found about that topic. I want more videos on reflection and reftacting. Thank you for those videos!
@@ekremdincel1505 I want to do one on refraction too.
@@ScienceAsylum oh dear God no.
@@ScienceAsylum Thanks you. You help us to understand physic well.
This is really one of the best science channels on youtube :)
Thank you sir for the heart. I will eagerly look forward to the next video :)
3:14 - nice touch with the terminator eyes!
Dude... I don't know how your views aren't 10x higher... You have some of the best, most fun, and well-explained content of this type on youtube... period... hands down!
Let's all promote this legendary channel. I've never seen such a great channel that explains science and all things and events so well like this channel does. Absolutely amazing!
Such an amazing way to explain hard things without letting details hidden. This is one of the best UA-cam science channels ever... Should have millions of subs!!
Br?
Almost skipped the video because it was about mirrors ...
Amazing! Thanks for introducing quantum into mirrors. I have a new perspective now.
I remember watching your videos a long time ago and then after a while, I forgot the name of your channel. I tried searching and searching for your channel/videos, but I couldn't seem to find it. Until FINALLY, today, UA-cam recommended me one of your videos (finally recommendations that are useful) and I realized that THIS WAS THE CHANNEL I WAS LOOKING FOR!
Welcome back! 😊
I will never look in a mirror the same way again...
Chris Z. Ha! I see what you did there...
I turn my back to the mirror, that way my face doesn't appear to be flipped.
I glad mirrors don''t flip anything. That removes the question why they flip you horizontally, but not vertically.
Thanks for another great video!
This explains it very well: ua-cam.com/video/vBpxhfBlVLU/v-deo.html
Actually mirrors flip in the direction normal to its surface. If you're looking at a mirror, the image is looking at you.
The most loved thing about this channel is that it explains everything not just as law or mathematics, but from the very tiny particles...❤️
Mind blowing!! Another great video Nick! Love your channel!
5:20
"How cool is that!?!"
VERY.
I actually happen to be an engineer and studied detailed laws about reflection like for example how a reflection with an E-field being normal to the plane of incidence differs from another wave having a B-field normal to plane of incidence.
But never the mechanism!
I learned something new here. Thanks!
You're welcome! 🤓
A true scientist tests his hypothesis, and if if fails it's back to the drawing board. Get it wrong, and you've crossed a wrong idea off the list.
I saw the animations and thought "holy crap, it's acting as a phased array", and then realized "no, a phased array is trying to simulate that, stop being so anthropocentric".
WOW, that probabilistic part of the video where the non canceling waves reach the target even if they don´t obey the Huygens principle was a big surprise for me. Now I have a clue how to understand diffraction. Such a simple thing (at first sight) and yet so educative. Thanks a lot for this great vid.
Just wait now for the next leap ... nano structures exhibiting negative index of refraction (will include a to the timeline) and their practical applications like superzoom and invisibility cloacks ...
I know this is an older video of yours, but I just love it, it really made me cheer :)
Thanks! 🤓
Can I just say that I LOVE the fact that you have a picture of a squirrel right there next to ya? My husband and I feed them on our patio (live cat tv), several have become so trusting they eat right from our hand. One even ran up onto my shoulder and leaned in to smell the walnut on my breath. I really do enjoy your enthusiasm, makes this so fun to watch. Hope they show these in our schools, but that would relate to education, so I doubt it. Their loss.
"Why explain the math with symbols when you can explain it visually?"
*Yes! Yes! Yes to the power of Graham's number!*
At work someone said Graham might be able to help so I said they could call Graham's number but it might take a while.
As a physicist, I wasn't expecting that much, I certainly wasn't expecting such a great video inspired by a chapter of Feynman's QED
Not to mention explaining it faster and better than Feynman!
This is really good! Especially Visualizing quantum Mechanic's equation, really helpfull^^
1:35 Holy crap, I threw my phone down and walked away, thats how much my mind was blown
Nick: While I was watching this, my wave function collapsed.
xD
Louis Hansell lol!
I love the way you explain. You make me understand all those difficult notions. Thank you
Great job! Love to see more of the light and quantum interactions
Didn't know your channel, just stumbled upon this in my recommendations...
first 3 min I was like: "okay this is boring, I know that already, if he doesn't bring something up, I'll skip"
Then you bring quantum mechanics...
Subscribed!
I love how you simplified Richard Feynman’s interpretation of this trick called Reflection! Great work body! (Feynman version was simplified, yours is oversimplified).
Awesome Feynman lectures
I remember those lectures too, so much easier to follow with Computer graphics than a Black Board and Chalk.
@@dcsignal5241 yes I am 80s physics grad
I feel so privileged to live in a world with computer graphics, I have no idea how people managed to comprehend these ideas without these tools. Something about imagination and hard work. It really makes non-euclidean 6D differential vector calculus a lot easier to understand.
Yeah exactly what I wanted to comment, it's Feynman lecture with modern graphics!! The best of both worlds :)
That was a simple, of considerable depth, explanation. Loved it!
Possibly....Probably
7:37 "Shut up & calculate!" summarizes my experience with quantum mechanics beautifully XD
Really wonderful explanations in a cool way.
You explained even the reasons behind the basic principals in a simple way,you rock.
Thank you very much
Fantastic graphic on vector addition and the extremes cancelling each other- talk about a picture being worth a thousand words !
4:26 SUPERZOOM!!! Hey Nick, excellent video!! thanks for the mind-blow
Wonderful video, I love the way Quantum mechanic can explain such things and the diffraction explanation killed me;)
"It's just probabilities" is my new favorite quote.
Lmao 7:17 - 7:24 cause when he asked the question I was basically saying the same thing you were. Lmaoooooooooooo
I wish I had a physics teacher like him in my school days ..
Great explanation indeed.
Please please make your next videos on COMPLEX NUMBERS
This one was fabulous BTW... Love your channel
A great video for understanding Path Integral Formulation.
Keep it up bro.
wow, this was so insightful. You make your videos seem like you are in a childrens show, but actually you just teach extremely complex topics in such an easy way, that even a child can understan them.
Right. It's styled like a kids show, but is _distinctly _*_NOT_*_ a kids show._
@@ScienceAsylum Why say it like that? You definitely cover pretty complex topics, but you do so in a way that even kids could understand some of it. Of course, there's only so much someone can get without having the math background though. Math makes physics make so much more sense.
@@Lucky10279 I'm saying it like that because of the new implementation of the COPPA law in the United States. This week, all UA-cam channels are forced to declare if our content is for kids and I'm still a little bitter about it. (Also, if I made a show intended for children, I'd use a lot fewer jargon words.)
Me at 4:46 ... Hey, are those adding up in a line going the "wrong" way?
10 seconds later... 😃😃 I'm learning!
Super video that not only helps explain mirrors, but also shows how counterintuitive QM really is!
I come periodically back to this video. Every time I think I finally got it. Some time later, my brain wave function collapses and I am like "wait, this makes no sense"... back to square one.
Brains are like that, unfortunately. "Use it or lose it." I have to keep reviewing things too so I can keep them in there.
You always manage to add something to my knowledge and imagination, and I am grateful to you for that.😊😊
When he said "or does it?" the quantum probabilities of Vsauce being in the video intensified.
Im glad that PBS Space time sent me here; You deserve many more subs and views.
Now I realize; how did I take the law of reflection for granted? I forgot to question my high school teacher(Even now I am a school student) about how is the law true. But I think I better didn't ask because I wouldn't get to feel the amazement of knowing mirrors in such a depth in the first shot. Great content Nick!
This channel is absolutely amazing, I feel crazy enough to be admitted to the Science Asylum after watching 😂🤪
I'm still trying to wrap my mind around the idea that beams of light are not actually beams of light, but just waves of energy interacting with each other.
3:15 lol, love that touch.
Minutephysics also took up the concept of mirrors but your video is extremely funny.
Keep up the good work.
I finally get the answer I want,bcs my high school teacher don't even know how to explain(or don't even know) why mirror reflect like that
you mean "like that" as in left-to-right (apparently), or "like that" as in at the same angle? :-B
@@irrelevant_noob
"why same angle?"
My teacher :"light behave like light"
mirrors: where if I can't see you, you can't see me actually applies
Indeed!
Unless you're a vampire! Lol
That's only true if you're just seeing eye to eye. In certain angles, as long as I avoid pointing to your eye, I can see your other body parts while you won't see any of my body parts.
@@yvrelna very true. also I wonder if our eyes were in a vertical line instead of horizontal, would the flipping effect follow suit?
Mr. Asylum. The best video on mirrors I've ever seen.
(Ok, yes it was my first and only)😬no really awesome video!!👍🏼👍🏼
I read Feynman's QED twenty years ago, and I remembered many things you illustrated here, but either Feynman didn't discuss, or I just didn't remember, the concept that the photon actually travels all paths at once -- rather than using the probabilities to select a single path. Thanks for improving my understanding!
"Why do math with symbols when you can do it _visuallly_ instead?"
I'm really torn about this statement. I know what you mean and I really like to get a visual understanding of unfamiliar concepts. But at the same time, I can't help but be greatful that we _can_ do math symbolically. It makes things so much more efficient. I'd drive me crazy if I had to actually draw vectors everytime I needed to add vector quantities or do the dot or cross product. I know you weren't saying that all math should be done visually, but I thought I'd share, since a lot of people don't realize how lucky we are to live in a time when so much useful mathematical notation has already been invented.
When my algegra students get frustrated about having to learn the new notation, I tell them to imagine having to write out all the equations and compact expressions as entire paragraphs of text, and they pretty quickly get the picture (pun not intended).
Yeah, I mean, if you want _actual accurate_ numerical answers, you need to use the symbols. But, if all you need is a conceptual understanding, the symbols are overkill.
8. Question everything (EXCEPT THESE RULES) lmaooo.
Touche.
I had this question in my head for years and now, finally, you explain it better than anyone could do it
Thanks
have never seen this channel but this video impressed me! definitely got a new sub
Welcome! Glad you found us! 🤓