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*Creator*
Jade Tan-Holmes
*Script*
Thank you to script writer Simon Morrow for your work on this video.
simonmorrow.com
*Animations*
Tom Groenestyn
*Music*
https://www.epidemicsound.com/
*Sources/Further Reading*
The History of Zeno’s Arguments on Motion: Phases in the Development of the Theory of Limits by Florian Cajori
Paradoxes: Guiding Forces in Mathematical Exploration by Hamza E. Alsamraee
https://seop.illc.uva.nl/entries/paradox-zeno/#ParMot
Zeno’s First Paradox of Motion: A Cartesian Perspective
BBC Radio 4 – In Our Time, Zeno’s Paradoxes
Calculus: A Liberal Art | WM Priestley
Source
Outstanding job!
Where is that music coming from? pauses the video that's weird. Not enough volume to recognize anything, but enough to be noticeable background.
I'm in love 😡
Where have you been? Everything alright? We missed you so much. Please don't leave youtube. 🤞🙏😍 We love you ❤️
Ha! Good one. Draw a square. Draw a line that cuts the square in half. Draw another line that cuts one half in quarters. Draw another line that cuts one quarter into eighths. Another line that cuts one eighth into sixteenths. Continue on as small as you can. Add up the sum of the areas, 1/2 + 1/4 + 1/8 + 1/16…… Graphical proof this series sums to 1 no matter how small you go how many half blocks you draw. Its a simple pattern to generate and I wonder why we don't see a lot of examples in things like tiles, textile patterns, architecture and so on.
I'm absolutely blown away by your intelligence and spunky energy,… Please tell me you have an identical twin sister who just can't say no to a good old Canadian boy?? 🤠
Lol, if my past "luck", is any indication,… I couldn't be that fortunate,… 😫
Good luck on future videos and happy new year from Canada,…
Zeno's dichotomy paradox and others led to Calculus, limits and the concept of infinity. Infinity doesn't exist in the physical world, though, otherwise any motion couldn't reach the end point. So, calculus can't explain motion, and continuity is a mathematical concept, not to be found in the physical world. If you imagine going down to atoms, then particles, continuous motions can't be possible either. That means that particles' motion is discrete. Physicists know that quantum waves allow for particles' motion. This has to imply that these waves have a continuous motion, meaning that waves are continuous–no breaks in them. So, waves can't be made of particles. Since waves are electromagnetic, this implies that the electromagnetic field is continuous. So, not composed of particles, but of virtual particles which are a release of energy. These are not real particles, that is, they don't move in space since motion is discrete. They constitute space, then. Summary: quantum particles move discretely in continuous quantum fields.
Uhhhh hey
You are good. Thank you and happy new year
She looks like my college angel .Turned to be a Sniper with a knowledge gun.
Just think… if we could truly comprehend infinity, we wouldn't need any of this!
So, you aspire to be like Hannah Fry one day… too late, you're already there! She is great, and so are you. !!!
Regarding the narrowing of the rectangles under the curve and the statement "The open space near the curve has decreased". As a maths graduate I know intellectually that the statement is true however I always find this part of the explanation of calculus a little glib.
As an example of why I do not think that this argument is sound consider a discussion about calculating the distance from the origin to some point (p, p). I suggest that an initial calculation could be made by considering a route from the origin along the x-axis to (p, 0) and from there, parallel to the y-axis up to the final point of (p, p) giving a distance of 2p. I then go on to suggest that we could refine this estimate by halving the distance along the x-axis, (0, 0) to (0, p/2) then consider the path from the x-axis to the y=x line at point (p/2, p/2) then from there to the x=p line at (p, p/2) and from there to the final point at (p, p) creating a zig-zag line to the destination with each step of the path parallel to one of the axes. I then go on to suggest that if we continue to halve the distances in each step then our estimate of the distance from (0, 0) to (p, p) would get increasingly closer to the actual distance. Except it doesn't. It doesn't matter how many times you halve the distance in each step the total distance calculated is always 2p and not p√2 as we would hope for.
In short I do not think that it is sound logically to argue that narrowing the width of the rectangles leads to a better solution even though it does.
Sorry, just had to get that off my chest.
Be careful!!! Zeno's paradox is not disproven by calculus!
If space is continuous, then movement is impossible. This is because an infinite number of steps cannot ever be completed, even if we can identify a "limit" or asymptote.
Another way to see this is by switching the argument around:
"To move some distance, one must first move half that distance"
By phrasing it this way we can see that you can never even begin moving!
This paradox arises when we incorrectly assume that space is continuous. If we instead believe space to be discrete then we avoid this problem entirely. Recently, many of the best minds have been converting to a discrete view of spacetime as computationalism gain traction.
Hey great video! A year ago you had a big existential crisis and you were asking yourself a lot of questions in the last minutes of your video on anthropic principle. Could you PLease do another video and share answers you found and how you found a way to deal with it? I am really curious to know everything about it. So please!
Your explaination is as beautiful as you.
θɹiː ˈpæɹəˌdɒksɪz ðæt ɡeɪv ʌs ˈkælkjələs
It’s funny because the concept of infinitesimals which calculus is named after is what we try and avoid when doing mathematical analysis
Excellent except for the BCE nonsense.
Her awesome hair makes me angry and jealous. And I kind of want to braid it.
7:49 the inconsistency in rectangle alignment bothers me more than it should. Some of them use the left corner to determine their height and some use the right corner.
Great video. Not feeling the outfit though
Power of distribution and transformation is in decay
It is very deceptive
That's the easy part. What I found difficult was categorizing equations to find out what method was appropriate to symbolically integrate. It felt like I am supposed to find the result before I know the question.
No, the name calculus (small stone) comes from the idea of pebbles being used to count and do calculations with.
I am not a mathematician, in fact I am absolutely horrible at math. But, I have an interesting story related to Zeno's paradox:
I remember the first time I heard of Zeno's paradox. The conclusion I came to was that the infinite series of fractions that result in purely mathematical sense are restricted in reality by the bounds of what the subject travelling or the object being moved is capable of. Example: Say you have to travel a distance of ten meters. You can travel half distances between yourself and the goal only to the point where the difference in the distance you have left to travel and the minimum distance of your stride coincide.
I have no idea if this made any sense whatsoever, but… there it is.
wonderful
Very informational! New sub here
Math is about the infinite extension (as pi with its infinite precision) of physics (where pi(n) is self constructing, depending on the finite number n of particles inside our observable universe which is growing because intersecting more matter from the infinite universe, pi(n) tending towards the mathematical pi. Don't forget the pretty good idea from Einstein, that the geometry depends on what it contains!). So there are some paradoxes in Math because working with the hypothesis continuum while, we are still wondering how, our physical world only appears continuous. As long as these paradoxes are not contradiction, Math are coherent but it may appear contradictory to some finite minds because inifinity is physically unreachable. So, to these minds, keep in mind that the Mathematical infinite precision, as in the calculus of aeras, is unreachable and consider only big numbers, as if we were doing an instantaneous picture of our observable universe, stopping its growth, and do the approximation of the infinite with big numbers. Keep in mind too, that scientists are still looking for the Graal, meaning the way to link the little world of particles, which appears to work with some most little elements, not dividable, and the big world, which appears to work some most big elements, then these two element being necesarily linked
The sharp teeth creep me out and make me laugh simultaneously😬
my favorite way to say it; one was invented and zero was discovered.
Thanks
👍🏻