How to Science [Part 2: Our Universe = Math?]
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How to Science [Part 2: Our Universe = Math?]


Last time we left off with a mystery what is the mathematical connection between the links and tensions of strings that sound good together? Let’s start with length The simplest pattern I see is that strings with the same length sound good together This is not too surprising since these strings are at the same tension and have the same length They should make pretty much the same sound Now what about our other pairs of strings that sound good together? if we look at the third row of our table we see that our second string is fixed to a length of 60 centimeters And the lengths of our first string that sound good with our second are 60 45 40 30 and 20 centimeters Now what do these numbers have in common? Well if we divide the length of our first string by the length of our second string we see that the strings that sound good together do have something interesting in common The ratio of their links all reduced to simple fractions while the ratios of the lengths of strings that do not sound good together do not reduce to simple fractions This was the first discovery of Pythagoras String sound good together when the ratio of their lengths is simple Now let’s have a look at tension, maybe the same simple ratio rule applies If we divide the tensions of our first string by our second We see that the tensions that sound good together do result in relatively simple ratios However some string tensions that don’t sound good together such as three point six and one point eight kilograms also reduced to very simple ratios So it seems that the hidden mathematical relationship between string tension and sound must be a bit deeper If we have a closer look at the tensions of strings. That sound good together. We may see a hint of a deeper pattern Notice that quite a few of our good sounding tension ratios are exactly equal to the ratios of perfect squares Following this hunch let’s take the square root of our tension ratios remarkably this simple transformation snaps our problem into focus Our new square roots of ratios are simple when our string combination sound good together and complex when our strings don’t sound good together This was Pythagoras is second remarkable discovery string sound good together when the square root of the ratio of their tensions is simple This information was helpful for early instrument makers, but what’s really interesting here is how these discoveries change the way we humans think about the universe we live in These discoveries along with another interesting Pythagorean discovery involving right triangles really got Pythagoras and his followers thinking Why is it that mathematics is able to predict what we observe in the world around us? Division square roots fractions, and even numbers kind of seem like human inventions Why are they showing up so clearly in triangles and vibrating strings? These mysteries were compelling enough to convince the pythagoreans of something that might sound a little far-fetched today That our world is literally built from mathematics This may sound ridiculous, but we don’t actually have to look very far to find very bright modern day physicists who believe this Now whether or not our universe is built from math is still open for debate But what I think is really interesting here is what we do with this mystery For the pythagoreans this was basically it Why does mathematics show up in vibrating strings and triangles because the universe is built from math mystery solved? It would take a couple thousand more years for us humans to really start probing what I think is the more interesting question How deep does the connection between mathematics and our universe go If we can predict when two strings sound good together? What else can we predict? In the case of our vibrating strings, what actually makes our strings sound good or bad together? Can we use math to really understand what happens when a string vibrates? Answering questions like this required one more piece of the scientific puzzle that the pythagoreans never really committed to experimentation It may seem obvious to us now, but it took quite some time for us humans to accept what is perhaps the most important idea in all of science if it disagrees with experiment? It’s wrong! In that simple statement is the key to science It doesn’t make a difference how beautiful your guest is it doesn’t make any difference how smart you are who made a guess or what his name is If it disagrees with experiment Wrong. That’s all there is to it. When this idea finally started to catch on in 16th century Europe Scientists were finally able to dig into all kinds of mysteries including the vibrating string The first real progress came in the form of an educated guess from the Italian scientist Geum Battista benedetti Benedetti suggested that musical sounds travel through the air as a series of rapid pulses and how high or low a note sounds to us. It’s pitch is a direct result of how frequently these pulses arrive So if Benedetti suggestion is true then the sound we hear from a vibrating string is a direct result of how frequently the string moves back and forth Also known as it’s frequency of vibration This idea raised all kinds of new questions How is the strings frequency of vibration connected to its length and tension does anything other than length and tension affect a strings frequency? How can we measure the frequency of real strings when they vibrate back and forth way too quickly for us to see? The late 1500s around 50 years after Benedetti guessed that pitch was a direct result of frequency the great Italian scientist Galileo Galilei turned his attention to these questions guided by the work of his father Vincenzo Galileo made some well-informed guesses at our first two questions. That would ultimately turn out to be correct However, Galileo also claimed that since strings vibrate too fast for us to see actually measuring their frequency was impossible Meaning that he had no experimental means to test his guesses but fortunately for us Galileo was wrong within 30 years of Galileo’s work the French priest and scientist Myron Marcin did measure the frequency of vibrating strings and was able to experimentally confirm Galileo’s guesses Marcin was even able to use his methods to compute the frequency of pipe organ notes with around 90% accuracy So how did mersin do what Galileo said was impossible? What do you think? Given the technology available in the early 1600s. How would you try to figure out how the rate of vibration of a string its frequency? depends on its length and tension How would you prove Galileo wrong? For a small hint and some other cool stuff check out the PDF linked in the description below Good luck, and thanks for watching

100 thoughts on “How to Science [Part 2: Our Universe = Math?]

  1. 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.

  2. 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.

  3. 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

  4. 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.

  5. 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

  6. 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.

  7. 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?

  8. 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…

  9. ~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

  10. 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

  11. 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.

  12. 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.

  13. 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?

  14. 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)

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. I wouldn't say that the universe is made from math, but rather that the human invention 'math' was made by observing the universe.

  20. 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

  21. 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

  22. 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.

  23. 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

  24. 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).

  25. If you use Reddit, you should find a subreddit to post links to your videos. I think that many, many people would enjoy your style!

  26. 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.

  27. 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?

  28. I would stick the string in my ass and count the vibrations. I could get the frequency with 99% accuracy since my anus is really sensitive.

  29. 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)

  30. 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.

  31. 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

  32. 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.

  33. 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

  34. 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 🙂

  35. 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.

  36. 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!

  37. Its been well documented that mathematics is the language used to construct the universe. A modern person not believing this does not make it wrong, it only makes the modern person less than the greater minds that came before

  38. 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

  39. The back ground music is very distracting.
    btw Very nice and comprehensive series on imaginary numbers. Nothing even close to it in all of YouTube. Thanks!

  40. 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

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