How to Science [Part 2: Our Universe = Math?]
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- Опубліковано 24 вер 2017
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This is a very inspiring series. I really love your channel and your way of teaching. Very interactive and from the ground up, fostering real understanding instead of mere knowing. Keep up the great work, and thank you
Thanks for watching!
So happy Welch Labs is back with a new series. So exciting and new topics and AMAZING production quality. Thank you
Those two quotes really end the video of nicely. From my two favourite physicists: Feynman and Casey Neistat.
Although their work may overlap at certain points, I still think they're both briliant.
Since when is Casey Neistat a physicist?
Since when Feynman is a physicist?
Plz google who is Casey Neistat.
Oh my god, the last 3 comments...you guys are being sarcastic right? Is this some higher level of irony you guys are trying to achieve, by being sarcastic about my sarcasm.
If not, Jesus....
The best definition I've ever heard for "mathematics" is: the study of patterns.
Mathematical notation is just our way of describing various patterns.
It's not that the universe is "built" from math, it's just that there are patterns in the universe.
I was about to go sleep but I guess that's not gonna happen.
You deserve a billion subscribers........... your presentation and way of explaining in just so simple.
I would love to see a video about fourier transform
Check out Looking Glass Universe's FT videos, one of the best channels on UA-cam and one that makes Welch Labs look like a bunch of amateurs.
I absolutely LOVE your videos, I somehow totally missed that this new series started but I was actually re-watching your old videos and found it! I'm so glad you're continuing to make content and can't wait for more :)
Awesome, thanks for watching!
I missed you so much, i'm glad that you're back, keep uploading you deserve more sub and views.
You could build a kind of stroboscope with a wheel with regular openings that rotates quickly in front of a light source (say, the sun) in an otherwise dark room. A clockwork mechanism can then measure the speed and total number of rotations of the wheel while the temporal aliasing the stroboscope provides allows you to measure the frequency of the vibrating string.
Pretty sure they didn't even have this kind of zootrope-type technology yet. But this is still the most original frickin idea in this thread, and I kinda wanna build one so I can see a guitar string vibrate...
If you find a way to get a constant rotating speed, the rest is easy. Maybe a big enough flywheel would rotate efficiently enough to keep a constant speed for long enough to get an accurate measurement. I think you could get a very manageable error this way. I'm not sure about the quality of the time keeping of the 1600s though...
But if you measure the frequencies of two strings with the same length which have a ratio of two between them,
won't you see exactly the same motion ?
Pollux, true, you kind of need to know how long a second is to measure how many vibrations per second there are... OTOH, if you manage to get the wheel speed constant enough, you can scale your way up to the time interval that you measure comfortably enough. Either way, the right gear transmission ratio might again help to convert any source of constant rotation into the desired wheel speed.
Geli, well, I don't think they had zoetropes in the 17th century but they sure had all the tools and abilities to make one. I mean a kindergardener could make the wheel itself with cardboard and scissors. And the clockmaking abilities were quite developed already in that time period so I think it would've been well within their means to make a device like that. Now sure, I did use 21th century knowledge to come up with this idea in the first place. It would've been much harder to invent a stroboscope with the intent to investigate continuous motion if you haven't grown up with temporal aliasing effects from cameras and actual stroboscopes in the first place.
I trow away all my works to see this interessting video . Great researches ! I hope you the best !!!
I love your videos, they inspire me to learn mathematics and physics in a deeper way.
Thank you so much for providing the music you used!
You're welcome!
Maybe try to cover a string in chalk or some other colored powder and let it hit a piece of paper that is moved in a constant speed by the side. There will be a colored line everytime the string slaps the paper. You can calculate the frequency by counting the hits on the paper and knowing the speed of paper.
It would get less frequency due to the friction when hitting
Bonus points for Feynman’s brilliant explanation of the scientific method!
6:30 "What do you think?" My guess is, I would have used the same technic that was used for measuring the speed of light, it's very simple and clever at the same time: a rotating device with open and closed slots, and you look at the vibrating string through the device, so that when you match the vibration speed, you see the string still (like when a camera is filming an helicopter and the rotor looks weirdly still)
man u got this mate, wow , 2pimnd, wow, same like eoe eoe wow
I perused the comments to see if anyone else guessed this as well. Yup, this is my guess too. Like a black circle pinwheel with 1/4 cut out, or a thin slice as Thomas suggests. Then spin it and look through, keeping track of how fast you spin it (use gears etc so say you turn 1 turn and the pinwheel turns 100 or something like that.) and you can pretty accurately guess the frequency. According to Google middle C is 261 Hz - you'd have to spin the wheel pretty fast, but it's not out of the question.
Wooo! Welch Labs rocks!
As always, amazing work!
man, you're a legend. thank you for putting your time into this.
Fill up a tube with water, listen for the nodes of the standing wave as you slowly empty it. 1st node distance=wavelength ( might hear other harmonics, loud one is the fundamental tone). (doesnt have to be water, but its easy to have a air tight seal that way, but any adjustable length chamber would work. IE how wind instruments basically work).
so glad that Welch Labs is back
great series
0:58 - As far as I'm aware a simple fraction is a fraction with integer (whole number) numerator and denominator. How do you make the distinction that 5/6 is worse than 3/4 or 2/3?
Not only are they all simple fractions but they all follow the simple formula n / (n+1)
I think it is more like "the fractions have small denominator" and small being
Because your ear does math but it doesn't like counting by 6ths. Like having a measuring tape that has notches for thirds and fourths but not fifths and sixths.
My doubt exactly
@@antopolskiy I think you may be right
I would fill my tub with water and place the strings on its surface. When a string is struck, it vibrates and generates waves on the surface of the water. I would measure the number of vibrations generated, the distance between two consecutive waves, and the time it takes for a wave to hit the walls of the tub, thus determining the speed of the wave.
nice! would be quite difficult to measure the distance between moving waves though. and the speed of the wave has nothing to do with the vibration frequency, as far as I understand.
You should do a video on complicated (or at least odd) math concepts and how they can relate to the universe, such as how irrational numbers can be used in the universe and complex numbers can be used to predict aspects of the universe, similar to your imaginary numbers series from a while ago. Maybe even teach people new things in the process
I was thinking about tying a piece of graphite to the string, and put a piece of paper rotating or moving a fixed rate underneath the string, so that when the string moves, you can see it on the paper. Kind of like a seismograph.
You make such quality videos that they seem made from a +1M subribers channel... nice video and keep it up!
Flavio Ryu He totally deserves the 1M though
yea definitely
So great to see someone else is a fan of Max Tegmark
Welch labs restored my faith in humanity and UA-cam XD Keep up the quadra awesome work
Thanks for watching!
Idea for measuring string frequency :
Get large heavy pendulum (with about 1kg weight) like the ones used to make clocks, but heavier, because we're going to need to have it drive a mechanic system
Get a bunch of gear wheels and a large piece of paper you roll into a cylinder 5 cm in diameter, stick it to a set of gears
Calibrate pendulum so the cylinder spins once every 2 seconds
Dip the middle of the string in ink or smear it with charcoal (I think you know where I'm getting at )
Place paper cylinder parallel to string
Start cylinder spinning
Poke string and then quickly place cylinder next to the string
Take measurement
Count how many string marks are on the cylinder , and there you have it
I need the next episode in my life NOW! :)
Great stuff man🙂
This video is excellent, as always. Are you going to go into what we can predict with maths? Such as quantum states?
These videos are so high quality, do you have a day job or something or is this channel full time for you?
What do you mean by simple in "simple fractions"?
This is really amazing
Sir, it is what I was searching for,visual lab.I want you to make video on shortest distance between two lines.
And explain the projection it uses in its derivation
I guess I would use some light source which is flickering at a specific frequency... I imagine a wheel with small, evenly spaced holes near the edge and some clockwork mechanism which could turn the wheel at specific speeds, so you can easily calculate the frequency. Then I would use some bright light source e. g. sun in a very dark room to shine on the string throught the rotating disc. By adjusting the speed of rotation via some mechanical gears with a known ratio I could change the frequency to a known value and see where I get a stroboscopic effect... I can imagine building such an apparatus with the technology available at that time.
whoa, this is ingenuous and I think it might work. you would have to find the smallest rotational frequency such that when you roll at this speed, you always see the string in the same deflected position. difficult to realize, but certainly feasible, IMO.
my idea was much simpler -- cover a string with a dye and let it make marks on a moving paper as it vibrates.
Agreed Erik - I wrote something similar above (more recent).
A stroboscope? You could do one with an oscillating pendulum (like a piano metronome) and, sunlight, and a dark room.
I'm waiting for a part 3
I’m finally a patron!
Hey, big fan from the beginning, good work ! This time the sound was a bit broken (voice cuts sharply and it is quite upsetting) you should fix it for the next
Thanks for watching! At what time (s) does this happen?
for the whole video, at moments like 00:39 when you stop speaking and there is no music, I can "hear" the absence of noise.
Hi
Only recently came in touch with your channel, thorough 3b1b, and am bingewatching your channel. Thank you for the great work. Especially the imaginary numbers and multiple planes. Eyeopener of the most important eye we have, the mind's eye.
I would like to put this idea into your mind: 'Building A Universe Competition', #BAUniC, openminded research into the formula of the universe, fractal base of reality mainly, but anything that can be rendered in a computer from emulation (yuk) to addressing the fractal and maybe displaying individual atoms in various parts of our cosmos.
Commenting here while there are a few videos left to watch in your channel (oldest first method of binge watching) because of the universe made of maths expressed here.
Cheers!
I think that the frequency was measured using sand. If a plane is vibrating, sand will move away from nodes and towards antinodes, forming a measurable pattern.
Just wow. For every single video here
How we can model the universe using 4 fundamental operations. What is its meaning, philosophically? If those 4 operations (addition, subs ...) are models themselves to describe a phenomena, can there be more accurate models that could shift our interoperation of the world? Who answers such questions? Who should I read? What should I study? Help
Please! Make Something About the importance of Net Neutrality!!
The final question: I am thinking about putting a dye on a string which frequency of vibration I want measure, and having a strip of parchment running perpendicularly to the string around the middle of the string (the point of largest deflection during vibration). I would put the parchment at a distance from the string such that the string only touches the parchment lightly when it vibrates. Now as the string vibrates and I move the parchment as a constant speed (which I think is quite easy, because I can measure time and distance), the string will make marks on the parchment. Knowing the parchment movement speed and the distance between the marks I can calculate the frequency of vibration.
You would want the parchment running parallel with the string not perp no? Then roll it past the middle of the vibrating string would be like one of those earthquake recorders (It could be parchment on a big cylindrical drum. The touching would dampen the vibration pretty fast, but it might be enough to see what's-what - also how to put an ink source on the string? Tricky - but I'll bet there's a way. I think the pinwheel (described elsewhere) makes a little more sense practically, but this is cool and I bet you could make it work.
This Channel is Lit. It's on another level, iqabele!
Can we vibrate a string in water? If so then the ripples that form can be measured pretty easily by counting the number of wavefronts that pass a certain point I suppose.
Very smart!
@@ScienceCommunicator2001 I am honestly surprised you found my comment from 4 years ago
@@omarf4210 your love of science has been rewarded! From your original comment, am able to tell that you'd make a great experimental scientist. May your love of science grow to eternity!
So you are making videos and writing documents in pdf...
Impressive.
I saw your pdf hint.
Can you vibrate a string using a pendulum?
How often do you get new markers, and replace the ink in your printer?
haha - alot.
Guy give thumbs up to the video to support him!
I watch your video: Imaginary number. You got another subscriber.
Woohoo!
mate i hope ur busy, cause i've been checking ur channel like all the while, now i've turned on the notification, thanks to that, but u see, i am waiting and its a hell long of wait
ugh I know - working on it, I promise!
No worries! The end results are worth the wait. Love your work - thanks for doing it.
With a pendulum you could calculate the time that the string vibrate, and see how it varies according to it's lenght... Knowing this I believe you could relate the time with the frequency
do you mean to measure the time it takes for the string to stop vibrating?
1: add a pin with a tip of ink at the mid of the str
2: put the str on a roll of paper
3: rotate the roll with high speed
4: vibrate the str
5: count the dots(d) within known interval (i)
6: freq=d/i
just wrote down the same type of idea in the comments. high five!
The one huge problem with this video is it's too short. Now I have to wait for a part 3....
~2:00 "when they sound good together the square root is a simple fraction. If not it us complex"
Wait. Where did the imaginary number came from?
/S
A complex fraction doesn't need to be a fraction with a complex number in it...
2025UA-cam
Congratulations, you're a humorless Einstein.
In other words, whoosh.
My guess would be to take a circular paper and cut slits at a regular intervals towards the center of the paper. Then attach to gears and a lever, if you look through the slits while turning the paper you would see the string at certain points in its vibration. If you counted the number of times you had to turn the lever in a set amount of time to “freeze” the strings vibration, you could calculate the frequency
How is 4/6 a simple fraction, but 5/6 not?
Well 4/6 = 2/3 which is arguably simpler than 5/6
toyodathon08 4/6 is 2/3
5/6 is also a simple fraction. It's a minor 3rd. Pretty popular sound in pop music.
There are books like "Tuning, Timbre, Spectrum, Scale" that explain not only how music works, but also why. Welch didn't say why some ratios sound good.
Simple = good is not the real answer.
azraksash Simple = good is what could be said in hindsight.
Simple = not good when you use timbres or scales that clash with that ratio. So, string instruments can work well with simple ratios, but bells and metallophones can sound bad depending on the constructions. To have a "string" sound that sounds good with a complex ratio you need to modify the spectrum of the sound.
but weren't all of your ratios simple fractions, even the ones that "don't sound good together"?
i think you miss-spoke. what you seem to show is that the ratios that "sound good together" can be reduced, while those which don't sound good together cannot be simplified further.
It doesn't have to do with whether the fractions can be reduced, but rather, how small the numbers are when the fraction is reduced.
Dylan Parker, I think you might be thinking of a different definition of "simple fraction" than he is. He just means a ratio of two smallish integers.
ah, that might explain it - i thought a simple fraction was just one that used 2 integers only, i.e. a/b (for a, b in Z)
Shouldn't position of 2 strings and ear also affect result?
I don't think that's how sound works. Although, if you had asked about the relative motion of the ear you may have had a point because of the Doppler effect.
I haven't looked at the pdf, but here is how I would do it with that day's technology. I would have a belt which I could rotate a known speed, say 1 revolution per second. That would drive a pully of known size, so I easily calculate how fast the wheel was spinning. On that wheel I could mount a disc which had N equally spaced holes on the outside circumference that I could peer through. I would then watch a vibrating string through those holes and find a gear size and a given N which could make the string appear to be standing still when viewed through the holes. This is getting too long, but there is a problem of getting a submultiple of N (or the rotational speed, or a combination), but that is easily solved.
awesome! I saw another very similar solution above.
Good video! But I have a doubt! What do you mean by simple fractions... I know about simplest form of a fraction. Simplest form of a fraction is when the numerator and denominator have the HCF as 1 right.. Then what are simple fractions.. in the video at 0:59 you show the graphic and it says 3/4 is a simple fraction where as 5/6 is not a simple fraction. But 5/6 is a fraction in its simplest form, as both 5 and 6 are co-prime. So....What are simple fractions.. And what do you mean when you say ratios of their lengths is simple. I am confused! Can someone help me here.
I noticed this too and I'm quite confused as to why he picked 3/4 and 2/3 over stuff like 7/12 and 5/6.
lenghts 25 and 35 reduce to 5/7 yet they do not sound good together, anyone care to explain?
What are simple fractions ???????????
Is math related to science?
Daniel Mathews no exactly, but as a tool
Daniel Mathews
Insert relevant xkcd here
Math is the language we use to understand our observations and form scientific theories.
Mathematics *is* a science. Whatsmore, all other scientific disciplines are fundamentally really just some form of applied mathematics.
Daniel Mathews Dude, that's kind of what this video is about. Math is a language to describe patterns, and science is finding patterns in reality, so I'd say yes, they are pretty related.
So music and playing guitar can describe the universe? *Fair Enough.*
:)
Seems legit
-Phytagoras
A simple fraction is a fraction with whole numbers in the numerator and denominator.....but all of those are simple fractions welch, i am confused
Me too, that's where I am stuck
The universe follows a set of rules that apply everywhere. And so does math.
The universe (in my opinion) is not made out of math, but math and the universe are very related...
I love your videos but hate to know that you don't make videos now 🥺
I'd say in a video by someone with a very high mathematical reputation one must use terms very carefully by analysation of mathematical rather than abstract meaning 'cause that word 'complex fraction' really scared the hell outta me.
I wouldn't say that the universe is made from math, but rather that the human invention 'math' was made by observing the universe.
where are you ? why aren't you posting any videos. it has been two months since you last posted. It is sad to see good channels dying.
Still, I am waiting for the part 3...
Working on it!
how about universe is statistics?
HARMONICS! That's how you do measure frequency.
I don't think the concept that our universe is made from math is far-fetched; I believe there are many people who would not consider it unreasonable for math to be the underlying mechanism of how the universe works.
I personally believe that the universe is equivalent to a mathematical infinite precision simulation of the laws of physics.
The idea that the universe is made from math is an empty idea. I rather think about it in the way that the universe is constructed from primitives, and that math is the way in which we humans approximate/describe those primitives.
You use words like simulation and mechanism as if there's some kind of force behind it all, but math isn't a force. Math is just patterns. The extraordinary thing about the universe is the simplicity and consistency of some of the patterns that make it up, but that doesn't say much about the about its ability to be simulated. Elon Musk's theory about the nature of the universe is a compelling approach to resolving the differences between theology and science, but it's hardly a meaningful distinction to draw between a math-generated universe and universe-generated math.
Interesting Michael - do you have a link to describe Musk's ideas? Thx for sharing.
Two English majors disliked this video.
or two gender studies majors.
hw will you decide , good and bad tone.
Our brain is not that capable to get patterns in higher fractions
Tuning forks?
how would you know the frequency of a tuning fork you've built?
Great question! I would measure it using resonance. Perhaps we could set up an experiment with standing waves in a tube, and we would measure the distance between nodes/antinodes to find the wavelength, which can then be used to find the frequency.
What I learnt is that its in our best interest to believe that nothing is impossible.
Also the mathematical proofs are because of our hobby of proving things. Its evident that all mathematical proofs that we may or may not know existed since the existence of the first thing.
This again rises a question that if this world was created with a fine piece of mathematical model? Is there a god?
(Trying to be nice here, so please, if a counter-argument is present, please do it in a polite way)
My interpretation is that God may exist (although I'm not fond of such notion until better evidence is presented), but this isn't the proof that would prove "it" to exist. The connection between mathematics and reality is, based on my limited knowledge at the present times which might change in the future when better evidence is presented, reality has pattern built on the four fundamental forces, and mathematics is able to describe such pattern. This, in my opinion, actually suggests that the universe is governed by a set of natural rules and constants which, although we don't understand why and how are they present, can in some ways make God irrelevant from the picture of creation (in the scientific sense, not the religious sense). The reason why I think of it is as such: when gravity is first discovered by Isaac Newton, it is described as an arbitrary force that serves no purpose other than keeping us on the Earth, pretty suggestive of God. However, centuries later, Einstein proved, with great certainties, that gravity is the result of the curvature of spacetime, which in some ways do makes sense. The constants as we know it now seems arbitrary, but I would rather trust that there are some deeper reasons we haven't discovered yet that makes them in such way then God setting them because for major religion's deities, I just can't, too many problems are present
Just to clarify, the reason I commented is just to have an intellectual discussion, not to criticize anyone's belief, since, being the only one into science in a community is quite boring
You are pretty right actually. There are things that are yet to be proven and in my comment above I suggested arising of a question of existence of god due to relevance of man made things in nature. I have tried to design mathematical models of some industrial systems. After putting a lot of effort and time, I as able to achieve something. Now that system is still nothing as compared to any natural system. My point of argument here is that even after lot of hard work, I created something imperfect and far away from any natural system. May be not God but there is a person sitting somewhere who isn't tied in the boundaries of time and space. Or I could frame it like if we are able to escape the boundaries of time and space that we proudly use as a reference every 'moment' then we will be in a position to create a being just like us who will address us as gods!
Thanks for giving some time to read what I wrote and to reply what you felt!
Where are you.... again????
But isn't "how good it sounds" completely subjective? How is tgat even a measurable thing?
Another good question!
Maybe when two different species are having a discussion. Aliens might prefer different ratios. However, human ears do math and they like simpler ratios.
A ridiculous claim. We built math based on what we see in the universe around us. Then we say the universe runs on math? That's like saying water on earth = life, therefore we need to find water elsewhere in the universe to find life... NO, humans happen to be made of water, who are we to say no other life form can exist without it?
wait, priest and scientist?. 6:15. something's messing with me.
Interesting right?
RIP
7/6 is relatively simple, but alright
Pythagoras of Samos rules
The reason Math describes our universe so well is because that's how we designed it. The video holds up Euclidean geometry as an example, but ignores Non-Euclidean geometry as counterexamples. Hyperbolic geometry is logically consistent, but doesn't describe our universe. If our universe was hyperbolic (or hyperbolic enough that we'd see it on a smaller scale), we'd be holding it up as "proof" that math has uncanny abilities to describe the universe.
Great points! Any references you recommend?
But then it turned out that our universe is actually described by non-Euclidean geometry in the form of general relativity. And similarly Lie groups turned out to be the perfect description of gauge symmetry now used to describe the standard model of particle physics. It's true that a lot of early math like Euclidean geometry sprang up to describe the universe by design, but then proceeded to go off on purely theoretical tangents, simply looking for, as you put it, logical consistency. The surprise is that many of those logical consistencies turned out to describe our universe in a way they weren't designed to.
Maybe the fact that math, or logic itself, even exists where it's structure is independent of the physical world is enough that "NOTHING" is impossible, thus *something* has to be possible (no matter how remote) so given a non-universe, with no time or anything, the mere possibility of something becomes a necessity and BANG ! -> instant universe.
Please.... subtítulos in Spanish
Mer-sen
Not "the univerce is built from math", it's "math is built from the univerce". We created math to be related to the real world. If math wouldn't related to the real world we would change it.
идея в том, что мы создали простые концепции в математике -- числа, сложения, умножения и т.д. -- а потом оказывается, что какие-то законы природы могут быть выражены очень удачно той математикой которую мы придумали. мы не придумали её специально для того, чтобы выражать это законы, просто так совпало, что они могут быть выражены с помощью нее. и это совпадение -- одна из причин, по которым пифагорейцы (и даже некоторые современные физики) считали, что вселенная построена на математике. это конечно весьма спорное утверждение, т.к. не совсем понятно даже, что значит "построена на математике".
This was really misleading. It wasn't "How to Science", it was "How to use a solution manual". Anyone who earnestly tried to solve the problem from last video is still in the dark. What methods could Pythagoras have used to find this answer from that table if you didn't already know the answer?
He did demonstrate that, although briefly. He took out one row of the table, and then searched for what the numbers in green had on common. Perhaps he tried adding them first, then subtracting, and finally dividing, which revealed the pattern. I agree he could've gone more in depth here though.
He went right to showing the answer on a single row. It would of been cool to see the answer on all rows. We have to take the single row answer as fact with no real way of knowing why.
Check out the pdf! :)
Use a Pendulum.
The back ground music is very distracting.
btw Very nice and comprehensive series on imaginary numbers. Nothing even close to it in all of UA-cam. Thanks!
I would rather claim that humans built maths to understand the universe