Prime Knots - Numberphile 

Can we all just take a moment to appreciate how difficult it must have been for the animator do recreate these knots digitally.

I'm with Brady: having just been explained the minimum number of knots, the idea of compound knots being ignored is revelatory.

Professor: What's your favourite part of mathematics? Student: Not theory. Professor: Me too.

someone drew all 165 knots with 10 crossings, only for them to be on the screen for about 2 seconds.

To be, or knot to be, that is the question (being addressed in this video)

With the help of these videos, I feel like knot theory is actually something really exciting, despite the limited usefulness. It seems to be one of the many places where mathematics and art meet.

"It's a special field of mathematics where you don't need to know much mathematics" ME : SO YOU'RE SAYING THERE'S STILL A CHANCE

Professor Carlo H. Séquin works at UC Berkeley. Does he also teach at the University of Knottingham?

The animators on this channel are amazing! Where do I send the animator money?

Those vectors... :D :D (w,h,a,t) * (e,v,e,r) ;)

I am so thrilled that there is a practical use for the abstract closed looped knots, but it was a surprised about compound knots. Moreover, I wonder if there is a fundamental theorem of knots, similar to arithmetic?

Knot that I want to repeat myself, I mean, I've tied this joke to the last video as well, but I just love doing this. I almost feel like I needle do this. What a yarn.

Those animations are incredible!

Fantastic explanations and animations. Thanks.

Very interesting content and lovely animation! Kudos to you, Brady, and thanks to professor Carlo :)

Hey. can you tie a knot? No, I cannot. Ah, so you can knot... No I cannot knot. Not knot? Who's there? -Rabbit, Piglet and Winnie the Pooh

"Knot realy" - Nice one!

You should have mentioned that there's two trefoils (mirror images of each other), and also that there's always two ways to sum two knots together (depending on their relative orientations).

Love those Topology videos.

This is knotting my brain!

Lovin' the knot videos... more please!

Fascinating stuff!!

that's one subject i've been waiting for quiet a time :)

Glad there's more videos coming about knot theory, somehow it interests me alot and I don't even know why but it does!

Love the new animation

These know videos are great! I'd like more of these....

YAY!!! Now i can classify the level of chaos when my fishing line entangles!!

That is actually pretty interesting food for thought! Thanks :)

Nice explanation.

Not for nought, naughty knots are nuts!

were there more "knot"s or "not"s in this video?

Very interesting!

That's pretty cool... KNOT!!!

4:20 It is the un-knot!

Under 301 club! Wait, that's not a thing anymore...

They play a role in philosophy and theoretical psychoanalysis, too! The biggest example would be the late Jacques Lacan but also better known people like Emmanuel Lévinas, Maurice Merleau-Ponty or people from the Ljubljana School today. Knot theory can e.g. work as a model for topological ontology, subjectivity research or theoretic psychoanalysis. 🌞👍🏻 ❤💙 🪢

5:33 After he said at 2:38 that such cutting and rejoining was something that “mathematicians would never do” ...

That's knot that easy!

Explain why my headphones are always in knots pls. Million dollar question right here

This is knot fascinating.

5+3=9 XD

I feel required to comment because I know Brady will see it. Knots!

There are actually a lot of applications of knot theory in mathematical-physics, specially in quantum mechanics. They could do a Sixty Symbols+Numberphile crossover.

Well you don't need to know calculus for the first chapter, but then you need integration to do Kontsevich integral, matrices to do Seifert matrices and Alexander polynomial etc. And also Fox calculus for some differentials if you count Fox derivative as differentiation.

Does the knot table follow a pattern when you include compound knots?

If you look closely, he's got steam on his task bar. That's freaken cool. :D

why did they use an image of a protein when talking about DNA, i think he meant proteins, right?

Once again I am overcome with math nostalgia.

Quantum Entangled Twisted Tubules: When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. (More spatial curvature). What if gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks. (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are actually a part of the quarks. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Force" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" make sense based on this concept. Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons. Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension? Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons . Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process. Gamma photons are produced when a tube unwinds producing electromagnetic waves.

Which clearly means ....a knot is not just a knot ...a new periodic table based on these...mendeleev would surely lament

I aint no scientist mathematician physicist or anything but this 0:07 should be 8 right?

Is knot-addition well-defined? That is, given two knots, is there only one composite knot, or is it possible to create more than one composite knot? What does it look like if you try and cut up and rejoin a prime knot into two other knots? Do you simply get an unknot and a smaller prime knot? What exactly does a Jones polynomial describe, and how are they computed from the knot? Can it be done by sight only? What happens with the Jones polynomials when you compose two knots?So many questions, such a low probability of it being seen by Numberphile...

Ok, so there are knots that are less or more complicated, can be connected and cuted in half.... but what can i use this for expect tying up a boat or something like that?

2:00 BEAUTIFUL! I MUST HAVE THAT STUFF!! Where can I but it!??

I'd like to learn more about matrices... I've learned how to add them, etc, but I've never learned how they apply to real life, or what they are even supposed to be

Just read this in book "Things to make and do in 4th dimension"

The knot at 4:05 is a unknotted loop I'm pretty sure, I didn't actually build it physically I just kind of did the unravelling mentally but I ended up with a loop with no crossovers.

Prof Seguin misspoke when he said the sum of a 7 crossing knot and a 6 crossing knot was not a 13 crossing knot. What he no doubt intended to say is that it is not a 13 crossing prime knot.

i am knot amused :-D

Where can I get one of those plastic bendable knots, like in the video?

If I take two prime knots and glue them together, is it possible for them to cancel out in some way? i.e. the resulting composite knot can be simpler than what you start with?

I have to correct Prof. Séquin a bit: When he is talking about DNA strands and cells he is actually talking about proteins. But since the terms DNA strands and genes on a linguistic level and the terms genes and proteins on a biological level are pretty much interchangeable and cells are made out of proteins this errors are understandable.

I really was knot expecting there being prime and composite ones ;_;

These knots are all three dimensional structures being looked at as a two-dimensional representation with "over" and "under" notations. How would knots be calculated (done?) in more than three dimensions?

My question is how can you ensure that your knot is always in its simplest form

yes this is good

This is one of those videos were visual aid is mandatory.

Oh my Knot!!!

it's a 0 crossing knot!

I've always been able to look at a diagram like that and 'unravel' it in my brain. Why didn't my Maths teacher tell me that was a useful skill?

I like his accent

Hey, I was wondering, is it possible to link two knots and end up making a compound knot that is actually simpler than the previous two? Great video! :D

@0:06 tears....

What are the criteria for whether a knot can be 'cut' to make two simpler knots? Surely any knot can be reduced in this way? I thought that if it can't be reduced _without_ cutting it, then it counts as a knot in its own right.

My brain is knot able to hold all the information at once which is required to "unfold" a complicated knot.

Adjoin two un-knots to yield, again the trivial 0 crossing knot. Is this knot neither prime nor composite, like the number 1? Also is connecting prime knots as shown at the end of the video akin to multiplication, or is it just a nice metaphor? Also, does for example a given prime 8 crossing knot have prime 8 crossing knots that are naturally it's neighbours contrasting to prime 8 crossing knots that are less related?

4:26 It's the unknot!

The second knot example reduces to 5 crossings is that right?

Numberphile If you can combine these knos ... is it possible to unknot a knot if you combine it with another knot, that has a special property?

Seems like all the compound knot that can be untwisted into the same prime knot can form a group on something...? But which operation is this group on, or, is this really a group?

Very interesting! Where can I get one of those amazing red plastic bendy knot toys from? It would make a unique gift for my 6 year old godson and maybe get him into knots?

These jokes are knot funny.

What's the biggest prime knot ever found then?

Where do the baromean rings fit in on the knot table?

What family are the fractals in the background?

What type of knot is the ABC TV'S knot?

he was going to say "explode the universe". you heard it.

this guy is so punny

Knot checking works as a one-way function? easy to check in one way, hard on the other? That could be useful in cryptography

What about knots in higher dimensions? I can see that knots are basically circles linked together (or with itself) to prevent them from separating. How about doing that with spheres in 4-D? I was trying to think of how that could work, with criss-crossing spheres and imagining that the intersections were in different places between the spheres within the 4th dimension. Then I played around with where the rest of the objects were in the 4th dimension. No matter what I did there was a way to separate the spheres. Is it possible to knot up higher dimensional objects in higher dimensional spaces? How would you do it?

knotty! i feel like ive been lied to about the number of knots now.

But can n crossing prime knot glued to the m crossing knot form a n+m-d knot wherw d>=1?

Okay when they were speaking about DNA a ribbon model for a protein came up... Also Proteins are more likely to be in a knot than any eukaryotic DNA, which is linear. The only DNA that should match the mathematical definition of a knot is that of prokaryotes, which would be a 0-knot due to their circular chromosomes. (Edited due to silly grammatical errors as I was tired when I wrote it the first time.)

Kinda boring......knot! Great presenter :-)

5+3=9-1

He has Steam opened.

1:00 is the non-existence of the ether proven?

It's knot what it looks like

I knew immediately it was a 3 not. I don't know how, but I knew.

I solved 4:07 in my head :D (notice me senpai)