The Mathematics of our Universe

[@anehakansson7771]

As a professor of physics I always love to see good accounts on subjects students often find difficult. This is not only good, it's excellent.

[@gregoryn7258]

check this one too, Mr Professor kzbin.info/www/bejne/eJm2eaWOaLyildk

[@anthonymcguinness1789]

I don't like with videos like this people dislike what they don't understand so frustrating.

[@yohanalaiser2667]

Ane Håkansson sorry I need an answer to the question at my comment if u can. If gravity is not a force (rather a geodesic as explained in the video), why do things accelerate when falling.

[@anehakansson7771]

@@yohanalaiser2667 I'm not sure I follow you here but let me give you my interpretation of your question. Let's stick to massive particles since massless particles, although they follow geodesics, do not accelerate. Massive particles, not influenced by forces, allways follow geodesics. In Newtonian geometry, this necessitates the introduction of a gravitational force in order to curve a particle's straight trajectory around a massive object, i.e. forcing the particle to accelerate. The idea of general relativity, on the other hand, is that these geodesics are curved in the spacetime near massive objects and, as a consequence, the notion of a gravitational force has no longer an explanatory function. In summary, the acceleration is still there but has its origin not from a force but from the interaction between the massive body, the particle and spacetime, alltogether creating a curved geometry embedding the particle's trajectory.

[@budaiestanaruemanuel836]

@@gregoryn7258 Great piece of flattard comedy you post there

[@jeunjetta]

Congrats on having a talent for explaining things in a systematic "chain of thoughts" to get us to the complicated point without breaking a sweat. Nice work. Thanks :) I wish text books could be more like you ;)

[@jeunjetta]

@Malek Abbasi it's ok. We're connected on LinkedIn now. Best not to put email addresses on public websites ;)

[@doronq1847]

I am making an Whatsaap group for people who want to share and elaborate their ideas, about specific topics, latest information about ( Science : Space, biology, Chemistry, and etc ) most likely about the how the universe was made. DM me on instagram @Miobetta_ and i will invite you to the group, and please be active... :))

[@AurelienCarnoy]

Yes. That chain of thought was my life saver. So good of a video.

[@AurelienCarnoy]

@@doronq1847 hello i'm trying to show people that gravity is the same as the dark emergy wich is also the force of the vacuum. Am I on to something ?

[@AmitKumar-qz2us]

"All this- whatever exists in this changing universe, is pervaded by consciousness" --Isa Upanishad .5000-BCE. Consciousness is the intelligence, the organising principle behind the arising of form. The quantum field or pure consciousness is influenced by intention and desire. There is a deep connection between consciousness and matter. The quantum double slit experiment has shown that a measured electron can appear either as a particle or a wave, but NOT both at the same time. Consciousness shapes our material world. DNA is a transceiver of information, some from the space time dimension and the other form the quantum world. The cosmos is made of events of the mind. The act of observation bonds the observer and the observed. Anything you observe becomes part of your reality. All things are connected and act as a single organism. This connection is undiminished by time and space. An action at one end of the universe is this felt at the other. Quantum rules does not care for Newton’s third law, which states that every action has an equal and opposite reaction. Quantum rules dictate that every action has a multitude of reaction possibilities. The brain receives info about its surroundings in space. After comparing new information with old memory, the brain sends it on via quantum connection to the dimensions that await its information. The brain needs REM sleep. The brains job is to maintain the physical portion of the link, between the body and consciousness. All matter is electrical in nature. In quantum physics an electron is a point particle, because it occupies no space, and is thus a imaginary mathematical point. If all the atoms in the world stopped moving, the world would disappear. .. Every human is a quantum matrix-a myriad of interlacing processes in constant flux. In nature there is nothing like a circle, it can only be a vortex spiral with ever changing evolution-nothing can remain same for ever and till ad-infinitum. The quantum world thus transcends time and space. Virtual particles have free access anywhere , everywhere , everywhen. Since our wolrd is 4 dimensional, the quantum points can arrange themselves in anyway. They get instructions from the transceiver called DNA. A male and female contributes ½ of the DNA to produce a new born. Consciousness creates our space time. Since quantum stuff reacts to consciousness, the universe is constructed by consciousness. By adding the dimension of time to 3D space, our consciousness is given the ability to evolve. In quantum physics it is meaningless to think of a particle having a trajectory through space. For in the quantum world all things are possible. It is the same in this space time world till choices are made. Most of these choices are automatic, as they are made necessary by the past. Matter is not condensed substance but a diffused form of energy. Newton’s classical law of Inertia states that F=MA ( the basis of the first world war ) M=mass A= acceleration. In the quantum ZPF Inertia is just the resistance, or the drag that objects experience, when accelerated . Gravity is a push, NOT a pull. The virtual photon flux between a dipole and the vacuum ZPF is what the scalar waves are. Scalar waves are faster than light with no loss of energy. All thoughts- attitudes, decisions, concepts, alignments, agreements, polarized struggles etc are constructed holographically in the brain. Identities that create experience are created holographically as personas, sub personalities, and archetypes, and as polarised constructs in the deeper mind. "All material and spiritual phenomena of the universe are present in the individual. Similarly, all those present in the individual are also contained in the universe. This is how the wise desire to perceive." Every atom within us depends on the rest of the cosmos. We are NOT independent from this cosmos. We are part of it. This is the reason we must live in harmony with the laws of the universe by exercising our free will. ...

[@aryamanmishra154]

I am an incoming Physics major with immense love for theoretical Physics. Generally you don't find these kind of videos which explain how GR works. You sir are a Hero for what you have accomplished is stunning, I have been sticking to this channel for a year and all videos are worth it.

[@raghavdodla1376]

Bhai tu theoretical physics kaha se pursue karvraha hai??

[@abyssiaart3042]

Your name sounds indian,do you mind if I ask any good institutions for theoretical physics in India?

[@draconic1922]

​@@abyssiaart3042 iisc's i guess u need to write kvpy exam for it

[@houstoncambodia]

First 40 seconds and you've already made me understand WHY time is the 4th dimension, something I've never understood.

[@anand.suralkar]

Cool

[@martiddy]

@Enter the Bragn’ bro!, did you even watched the video?. Spacetime IS a physical thing because it can bend and stretch. Also, it does interact with mass (that's it how it bends in the first place). I don't know what are you talking about.

[@theultimate2345]

@Enter the Bragn’ who had told you??

[@raymondflores5176]

@@martiddy its a theory not law besides time is a man made tool at the end of the day and predestiny cannot exist if the concept is once again invented by man

[@mfp5431]

ikr

[@georgepaul6240]

I'm more confused than a homeless man on house arrest,I need to go revisit how equations are derived

[@christopherdunn5645]

Did you reference that from somewhere? I'm sure I've heard it before.

[@georgepaul6240]

@@christopherdunn5645 I don't know about references but one of my friends wrote the homeless man thing in his English essay

[@anand.suralkar]

What

[@r_se]

@Enter the Bragn’ kek

[@r_se]

@Enter the Bragn’ honestly can't tell whether your comment was a parody or you're just braindead. poe's law comes into effect once again.

[@factjuniorroll]

"I'm not like those other dimensions." -Time

[@wonderfullife5665]

Baby, believe me...

[@thereisnonegoodbutgodjohn363]

kzbin.info/www/bejne/hKSVaaKPrayIiKNh I’d love to know your thoughts on this

[@thereisnonegoodbutgodjohn363]

@Linh Nguyen So is this kzbin.info/www/bejne/hKSVaaKPrayIiKNh I’d love to know your thoughts on this

[@pooodonklooopdoop5672]

What a pick me

[@thereisnonegoodbutgodjohn363]

@@pooodonklooopdoop5672 We all have sinned lied, lusted, disrespected parents, stolen etc Therefore none of us are good and able to get into Heaven. But God out of His love sent his son Jesus (also God in Human flesh) to die on the cross for our sins and rise again from the dead (nobody can do that only God). Jesus said if you Repent of your sins and put your complete trust in Him for your salvation, you’ll have eternal life, given to you as a free gift.. John 14: 6 Jesus said to him, “I am the way, the truth, and the life. No one comes to the Father except through Me.

[@shrikant8446]

This channel should grow fast Love from INDIA💐🙏

[@canriecrystol]

Man, when math generalize it's just beautiful. The feeling of just knowing nothing but specific cases is what makes me keep pushing myself forward. Can't wait to see more!

[@atulraj2668]

Wow, you always choose great topics and explain them so brilliantly. Hats off

[@bikashthapa7316]

you just literally summarize whole differential geometry under 22 min

[@MK-13337]

Technically he gave a basic summary of metric spaces and a slight intro to the concept of curvature. Basically the first lecture of an introduction class to said subjects. Still very very entertaining :)

[@MK-13337]

@Astute Cingulus Did you reply to the wrong comment my dude?

[@doronq1847]

hey, I am making an Whatsaap group for LONELY people who want to share their ideas, about ( Science, Space, Time portal, Wormholes, Curvature in time, and many more ) DM me on instagram @Miobetta_ and i will invite you to the Whatsaap group, and please be active... :))

[@das_it_mane]

@@doronq1847 we gonna be calculating the Gaussian curvature of ass & titties?

[@chimetimepaprika]

Dude, this series is so badass. I have been slowly getting into tensor analysis lately and it's straightup blowing my goddamn mind.

[@Daisy_Darkly]

I'm seriously bad at math and have never taken a class above algebra but man, this stuff is so cool.

[@Momgoose80]

This is random, but I'm a painter and watching this video it dawned on me what I'm missing in my attempts to paint the curvature of water. Just learning things for fun, and it turned out very applicable. Thanks!

[@anemonekm7117]

This is so well explained, I found myself figuring out the answers, before you even said them. You make very advanced things seem so simple! Thank you for these videos :)

[@HarshRajAlwaysfree]

This was the best video i saw this month Thanks :) Now im overflowing with ideas and motivation to continue pursuing the path of science

[@kianatehrani]

Please make more of these kinds of videos! You explain everything so clearly! I’ve never been good at math but I always found it beautiful and wished I could understand it better. You’re helping me (and others like me) greatly!! Thank you!!

[@RaviSharma-dh3en]

Seeing this was magical. A difficult concept explained so simply. I just enjoyed it . And thank you for it.

[@bronjo9343]

Man you just nailed it!!! It was really interesting . Waiting for your next vid. 🔥

[@stephenbarnard2856]

I'm a second year engineering student and I love this content! It gives me the background (which the university often neglects) to a bunch of the complicated maths we do. Keep it up bro!

[@gwyn.]

12:20 Maybe I forgot this in high school but it blew my mind

[@bmw123ck]

So Snell's Law can apply to a person that needs to cross a river...??

[@zachstar]

@bmw123ck exactly

[@obviouslymatt6452]

MajorPrep how does light know which way is fastest, and how does it know where b is?

[@stassoad2546]

@@obviouslymatt6452 because we are living in the simulation

[@brandonhughes645]

@@obviouslymatt6452 it's the least energy path. Search the principle of least action by Richard feynman. It's a brilliant read. www.feynmanlectures.caltech.edu/II_19.html

[@vishalchavda8938]

Wow, it's like learning math without math !!! Incredible explanation. I have never thought I would learn about geodesic in just about 20 min.

[@timothyrosenvall1496]

I love watching both your channels because on one you’re a funny goofball and on the other you’re a well educated and professional educator. Too often I think people forget that people can be more than one thing, but all the content you produce has been fantastic!

[@homelessbulletballinventor3074]

Bet those dislikes are from the flat earth people need who are probably measuring the circumference of a circle right now to prove their point.

[@afuckingchineseweeb7058]

@Joseph Cocchiola You are saying that you are "way more advanced", but it seems that even in such a short comment, you made several spelling and grammar mistakes. Even your language skill isn't on par with your skill in maths, being such a rude person while talking to others, claiming to be way more superior to others while not pointing out why doesn't seems to be a personality that a well educated person often have.

[@death_parade]

@Joseph Cocchiola If you are as "advanced" in calculus as you say you are, kindly explain to me about any one real world application of Frobenius method.

[@markgearing]

Nope, they’re from people who cringed when he stated that “time is the fourth dimension”, then stopped watching at 40 seconds when he failed to correctly pronounce “temporal”.

[@death_parade]

@@markgearing You mean the oversensitive kind.....

[@markgearing]

Death Parade - Perhaps, but more likely the kind who like to be educated, but know how to tell when they’re about to have their time wasted.

[@lluviadai96]

Finding this channel is the best thing that has happened to me this year. It satisfied all of my questions without me having to read through a bunch of math papers. Thank you!

[@AviatorAS777]

You are absolutely amazing in your lucid explanations! You have a knack for explaining complex topics in a very understandable manner. Do hone this skill!!!

[@reubenphilip_712]

This is actually so easy to understand. The examples you used were great

[@rajatsharma2496]

20:00 gives me goosebumps, now i know everything is moving in straight line in curved spacetime

[@tom.odonnell]

This is seriously one of the coolest videos I've ever seen. I've never understood WHY we believe space curves around heavy objects. So the conclusion made at 13:00 legitimately blew my mind. It makes so much sense to me now, and it's based on nothing more than simple physics.

[@neuroxik]

5:58 Wow, about the 0 Gaussian curvature, I had never seen it that way. I had also never asked myself the question but that's beside the point

[@brownavatar8]

Fascinating. 👏👏👏Bravo to this explanation.

[@MrRObot-bin]

Your work is awesome! It is so interesting and it helped me choose my career path! Greetings from Mexico!

[@ralflopez864]

What path did you chose?

[@navierstokes2356]

Have you chosed physics?

[@TheMimoJimi]

I understand it not, but wish to understand it, so I keep watching it. It does entertain.

[@destoria2]

20:33 just gave me fooking goosebumps. You changed my view on the world. Holy sh*t.

[@physis6356]

great video! It's well adapted for both experienced people in maths and beginners!

[@winterbelle03]

this video is proof that math is really fun when youre not in class

[@zachstar]

Hope you guys enjoy! Here's the follow up video: kzbin.info/www/bejne/o57XfZqPi6qogNU Oh and as someone pointed out, small typo at 16:40, the second term in parentheses should also be (1/2e1 + 2e2) (accidentally put a dot product instead of an addition sign).

[@karanraina1431]

Hurray...! 🤔🙄

[@karanraina1431]

Put some video on vectors.. What cross product and dot product mean.. Where its useful.. Just need a good explanation for a middle schooler...

[@LeoHsieh]

I saw your books at 6:19 "What is Mathematics? " is a masterpiece classic by Courant and Robbins! I love that book a lot

[@Karnex1]

It's so weird seeing someone with that profile picture talking about Math... Altho you are probably thinking ''it's cartoon so she's not underage''

[@DarkMatterr]

@@Karnex1 it's very common and admirable

[@freshmagnettv]

@@Karnex1 nice generalization. Are you woke supermacist (racist - If Right Winger/intellectual - If left Winger) American?

[@Karnex1]

@@freshmagnettv Does my name sound American to you? Your name sounds like some nice dish I would eat at Indian Restaurant! P.s. he changed his profile pic it was some loli hentai shit if I remember correctly

[@freshmagnettv]

@@Karnex1 stop with the whataboutism. It's his account, as long as he's not literally spreading some CP via his 'pfp', who are you to judge him? And yes I said American as an insult, not as literally refering to you as American. I respect Russians and eastern Europeans too much to have slandered you as such.

[@cooldude4376]

I was just wondering if I should finally read my newest book, A Mind for Numbers. Instead, I decided to watch this video so I can lay down in the warmth of my bed. I looked behind you and noticed you have a copy of it on your desk! I'm not one to agree on signs and synchronicity but I definitely need to read this book now.

[@noob0wns]

You are really good at explaining things. Thanks for the video

[@abuzar.a5307]

you sir, is amazing

[@michaelibrahim9275]

6:53 That’s why you curve a big slice of pizza when you hold it; it can’t droop down because it has 0 Gaussian curvature

[@ok-mr3on]

woooah

[@jjc6530]

Excellent explanations

[@higherdimensions1459]

Gauss: Theorema Egregium Möbius: *Hold my strip*

[@jona3684]

Wow! Great job giving the background to all of this. I knew about curvatures and all that but not how it relates to light, refraction, geometry etc. Very well done!

[@maths-pro-by-khan-sir]

*Sir being a mathematician I always love to have enhance my knowledge by watching your videos* *💕 Love from India 💕*

[@tigranmeliks]

I'll have to watch this at least one more time. Fascinating

[@MykolaDolgalov]

This video is great! I'm glad I've become your patron on Patreon. You deserve much more support for your work!

[@zachstar]

Thanks so much! Really appreciate the support and glad you enjoy the videos :)

[@MykolaDolgalov]

@@zachstar I edited the comment to correct grammar (I had swyped quickly on the phone), and the heart has gone. I'm 43, by the way, and I find your videos very valuable. I'm a lifetime learner, and I hope to teach my children to value education. Thanks again for your wonderful deliverables.

[@frankdimeglio8216]

@@zachstar THE ULTIMATE (AND CLEAR) MATHEMATICAL UNIFICATION (AND PROOF) REGARDING PHYSICS/PHYSICAL EXPERIENCE IS NOW DEMONSTRATED, AS E=MC2 IS F=MA: TIME DILATION ultimately proves (ON BALANCE) that E=mc2 IS F=ma, as ELECTROMAGNETISM/energy is gravity. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. (Importantly, balance and completeness go hand in hand.) The stars AND PLANETS are POINTS in the night sky. NOW, A PHOTON may be placed at the center of WHAT IS THE SUN (as A POINT, of course); AS the reduction of SPACE is offset by (or BALANCED with) the speed of light (c); AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Indeed, ultimately and truly, TIME is NECESSARILY possible/potential AND actual IN BALANCE; AS E=MC2 IS F=MA; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. GREAT. Accordingly, INSTANTANEITY is thus FUNDAMENTAL to what is the FULL and proper UNDERSTANDING of physics/PHYSICAL EXPERIENCE; AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. It ALL CLEARLY makes perfect sense. Gravity IS ELECTROMAGNETISM/energy. E=mc2 IS F=ma. ELECTROMAGNETISM/ENERGY IS GRAVITY. E=MC2 IS F=MA. GREAT !!! Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=mc2 is F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Consider THE MAN who is standing on what is THE EARTH/GROUND. Touch AND feeling BLEND, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. The stars AND PLANETS are POINTS in the night sky. GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Accordingly, the rotation of WHAT IS THE MOON matches it's revolution. Great. MOREOVER, a given PLANET (including what is THE EARTH) then sweeps out equal areas in equal times consistent WITH/AS F=ma, E=mc2, AND what is perpetual motion; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. INSTANTANEITY is thus FUNDAMENTAL to what is the FULL and proper UNDERSTANDING of physics/physical experience, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. Stellar clustering ALSO proves ON BALANCE that E=mc2 IS F=ma, AS ELECTROMAGNETISM/energy is gravity. Objects (including WHAT IS the falling MAN) fall at the SAME RATE (neglecting air resistance, of course), as E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. "Mass"/energy is gravity. ELECTROMAGNETISM/ENERGY IS GRAVITY. E=mc2 IS F=ma. THE DOME of a PERSON'S EYE is ALSO VISIBLE. (Notice the flat AND black space of what is THE EYE.) The stars AND PLANETS are POINTS in the night sky. The sky is blue, AND the Earth is blue. THE EARTH/ground AND THE SUN are E=mc2 AND F=ma IN BALANCE, AS ELECTROMAGNETISM/ENERGY IS UNIVERSALLY PROVEN TO BE GRAVITY in what is a mathematically unified fashion. E=mc2 IS F=ma. The middle distance in/of/AS SPACE AND the full distance in/of/AS SPACE are NECESSARILY linked AND balanced. MAGNIFICENT !!!!!!!!!! INSTANTANEITY IS thus FUNDAMENTAL to what is the FULL and proper UNDERSTANDING of physics/physical experience, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. It is ALL CLEARLY proven. Again, the stars AND PLANETS are POINTS in the night sky. GREAT. Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE. GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. It is all CLEARLY proven !!!!!!!! TIME is NECESSARILY possible/potential AND actual IN BALANCE, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. GREAT !!!!!!!! BALANCE and completeness go hand in hand. By Frank DiMeglio

[@ambiven10]

This channel is so awesome.

[@reddy.shreya2616]

That's brilliant 😎🤘and very professional

[@utkarshbasu252]

Hey man, I mostly watched you for funny content but today I was struggling about a part in my research paper and this video helped a lot. You explained the concepts very nicely. Loads of love and gratitude from me ❤️

[@WestOfEarth]

I've taken some rather advanced mathematics courses, and your explanations are far superior. You definitely have a gift for taking complex maths in physics and making them relatable to the general public.

[@tariqhurrah4850]

Its really awesome. I never have seen such an informative video

[@namaoui]

this was a brilliant elaboration. thank you for sharing and all the efforts. you have a new subscriber !!!

[@9erik1]

Thanks Zach, this is really awesome -- I had been looking at going back to school for a long time now, but didn't have much of a direction as I was really into math but didn't know where to go. I have been watching similar channels like 3blue1brown for a long time, but I found your channel maybe 2 months ago or something like that, and it has really really helped to solidify my direction and I'm now enrolled and doing a lot of self study. So thank you for that. This was a really good video and very much along the lines of what I'm trying to wrap my head around.

[@brian_xue6972]

I think you've explained it better than PBS, a lot easier to understand.

[@arcanesunku]

I came here 2 years later from your comedy channel and, lovely.

[@samuelthecamel]

You know what they say, time flies when you're in low gravity.

[@igwechi]

This is great stuff! Well done! I’m inspired by your teaching style.

[@AlexTrusk91]

6:57 just realized that even the crumbled parts have zero gaussian curvature :O

[@mike3684]

Wow, that was probably the best primer for General Relativity I have ever watched!

[@jirkakalecky2782]

at 16:41 shouldn't there be + in the second bracket?

[@zachstar]

Yes! That was a typo, thanks for catching that.

[@johnlynch-kv8mz]

3:40 impressive my man , you are resourceful. Earned this video a like.

[@EuanWhitehead]

Wow, this would confuse flat earthers even more so than they already are.

[@devanshsanghavi]

All your videos blow my mind! You explain things so well and give amazing examples. I love the applications videos too.

[@larsn24de]

12:47 How does the light photon know, that it will eventually hit the glass in the future and therefor change it's direction before hand?

[@enderallygolem]

Sounds like quantum mechanics

[@hypercatsinspace7625]

According to Richard P Feynman, it has to do with the way a quantum particle interferes with itself as it moves from one point to another. It takes all possible paths, but the wave functions of paths that describe long travel times cancel each other out, leaving only the function describing the path of shortest time, thus the particle takes this path. This is an 'In a nutshell' description of the phenomenon, and reality is more complex than this.

[@kartikeyedunite]

You are too *creative....* *You rock!* 👏👏👏 Love from India *♡*

[@HarshRajAlwaysfree]

We learn things so easier and faster on youtube :)

[@gregtregoning6917]

Really enjoyed the way you presented the information and I found this video very helpful. I have been trying to relearn the mathematics I've previously taken and move into more advanced numerical endeavors both for career and personal goals...long story short videos like this really help keep the intrigue and interest going for someone like me who has been turned off by math in the past. Thank you .

[@stephenfreel2892]

Use me as an “I’m really interested in theoretical physics and pure mathematics and I’m not here because I’m high” button

[@faizahmad1411]

This topic is complicated for many people, because they don't know anything about geometry. But you gave the example of a piece of paper, which can be easily wrapped around a cylinder, but not around a sphere, because sphere doesn't have zero Gaussian curvature. Your video is super beyond limits. You covered different topics in short time with clarity and logic.Your way of explaining ideas is remarkable. Sir you are very excellent teacher.

[@yann5489]

Tfw when you realize the shit you learnt in high school might actually have been interesting

[@person7614]

It was boring as hell because of how they taught it

[@patriot9455]

A simple and odd example of Gaussian curvature may be the fact that speed as measured by a GPS using satellite tracking will change going up hill or down, even if the speedometer, analog or digital, that measures speed within the vehicle neither shows nor records a change of absolute speed. is that a good real world example of a Gaussian curve. the difference is minute, but with a digital speedometer and GPS with a MPH readout, you can see a few 10ths of a mph difference in speed.

[@DownWithBureaucracy]

"I couldn't find much in my apartment to show negative curvature." *has curved globe stand behind him

[@prasunbagdi6112]

Globe has positive curvature not negative

[@rohank9292]

Superb, superb, superb. Cant like this video enough for giving me the greatest heads up on this aspect of the geometry of the universe that I had heard since almost 2 decades, but never actually understood what it actually is.

[@SeeThat92]

That awkward moment when I look again at my electric shaver, after seeing this video... I know your curves bro

[@hiroakihanyu]

didn't understand much, but i enjoyed your animations: very descriptive and nice to follow when i try to learn or explain sth i try to imagine those kind of animations, it'd be nice to be able to make these :)

[@Juanbaez_]

You should start a series of videos explaining all mathematical functions, its practical uses, history, and how it might be implemented in python. :) Pd: Start from the simplest functions to hardest functions. Only one function per video.

[@debomondal]

Love it my friend. You explained so nicely .

[@lexrogan2207]

Quantum mechanics: nah fam time is just a constant

[@nielsarkalukheilmann2931]

That short illustration of gravity in lighted me. Since I learned about space time I thought I understood it. Until just now. You just got a new sub. Keep going love your channel

[@robertferraro236]

4:11 - what would the curvature of those Quaker oats moving through my large colon be?

[@gigigem5631]

That was really different from the way I've been thinking about the Universe and I was wondering about non-Euclidian geometry, what differences it has with Euclidian, now I got some understanding and that was a lot of interesting information in such a short video and also you've explained and showed it really well, thank you, love your videos on physics and computer science 💜

[@marbleswan6664]

I notice you separate the vowels in the /aʊ/ phoneme. Mind telling what dialect/accent you have? Im taking a survey. It's been a while since english dialect and accent chart surveys have been updated or checked.

[@Guztav1337]

k

[@boukharroubamediane119]

complicated topic but beautifully and excellently explained. bravo and thanks

[@Barnardrab]

One thing that confuses me is what seems to be a contradiction: The assertion that gravitational waves travel at the speed of light, but space can expand faster than light.

[@hanexrazaw471]

Go to a channel called Fermilab..that is explained

[@benwinstanleymusic]

this video blew my mind! Awesome explanations man, I love this stuff

[@zachstar]

Glad you liked it!

[@ISILENTNINJAI]

Nobody: Absolutely nobody: Fat people: I'm not fat I'm just a positive Gaussian curved human.

[@___xyz___]

what?

[@lucao6438]

THIS is the content I was looking for, great job 👍

[@OchiiDinUmbraa]

Just how smart are you? You know math, engineering, physics, computer science and a few more. Do you learn new things while trying to make a new video, or you already know these things?

[@yuvrajsinghraj]

I think both because if he won't know it he won't make such cool vids and to make such cool vids he have to do research on topics

[@Robert-td1xm]

All of those topics you listed are covered through computer science degree course requirements. Engineers have to take classes in most topics. I’m sure he learns some as he’s making videos, but he’s definitely been exposed to these subjects through engineering classes.

[@zachstar]

haha I appreciate the comment! I mean I did well in school and I enjoy learning new things but yeah these videos come with a ton of research. A lot of what I discussed here I didn't know about until 2 weeks ago so I'm learning as I go for sure. I've also gotten some personal help from people way more educated than I (for example in this video I had a physics grad double check my metric tensor example) so it isn't JUST me. But overall I think the video on conic sections and the one on imaginary numbers were the only videos in the last year where I knew most of what I discussed in the video due to school or videos I've watched in the past, everything else starts with me doing a google/youtube search or reading a book and continuing from there.

[@blessingmagagula502]

Had to watch it twice though before I could fully understand everything. Love from South Africa 🙌

[@youngboss5813]

Bro i apperciate this video, one of the only times i've been intrested in math.

[@ethansanders5706]

I found this guy because of his skits, it blew my mind hearing him talking about physics

[@WEAREALLJUSTMEAT]

Time is a spacial dimension, we only perceive it as temporal because we can only see a tiny 3d cross section of the universe at a time. That's why things move, we literally move through time. The particle thst causes Dark energy could exist in the fourth spacial dimension which would explain why we can't see it but can observe it's effect on 3d space.

[@reinaldtorrente202]

dude i love your channel never really understood 4th dimension despite of years of curiosity, thank you

[@jigold22571]

ThankU, You keep things simple and real..

[@cynwraeth1943]

Just found your channel today. Watched a few videos about statistics and this one and subscribed. Quality educational content.

[@OfTheDetermined]

Came across this vid after already having watched a chunk of the Zach Star Himself channel, and I just wanted to say the foundation of those classics are definitely on display here nice gains since btw

[@jinnybeats]

You certainly can point in the direction of time because we're constantly being hit with light and see glimpses into different times. The beginning of time is all around us as well because the universe has been expanding since it started.

[@Noorthia]

Do point in the direction of time, not space. Do keep in mind that pointing into space counts as pointing at direction, not time.

[@anshul8330]

Fantastic explanation! You made it so simple. Bravo!

[@stevelauda5435]

BRILLIANT, I ABSOLUTLEY LOVE THIS THANK YOU ZACH