How The Most Useless Branch of Math Could Save Your Life

Have any lingering questions about knots? Want to hear more knot stories that didn’t make the cut? Derek and Emily (the writer/director of this video) will be hosting a livestream for our Patreons next week! Join our Patreon for more info and a link to the stream - ve42.co/VePatreon

My earphones discover all 352,152,252 knots half a second after entering my pocket.

Veritasium's graphic designer would have become a physicist by now. It must take a lot of understanding on their part to learn the concept first and then visualize how to demonstrate it. It is just mind-blowing.

Although I wouldn't in a hundred years choose to study knots, it never fails to inspire me how people take up these causes, pushing esoteric fields forward for nothing more than a pure love of the game until eventually their discoveries can be tied to other fields to make important scientific advances. Science really is humanities most collaborative sport.

"Not knot" "Who's there?" The Unknot

There is a certain demographic that I hope never finds this extended tribute to knots

I'm in awe at someone having the patience and skill to visually tie thousands of knots and distinguish duplicates. Thanks for another great story wonderfully told.

I don’t think I’ve ever watched a video that I completely understood while, at the same time, I had no idea what you were talking about. It’s like a miracle. Fascinating subject!

Hello internet, welcome to Knot theory

As a Ph.D. student in algebraic topology, I am glad to see that different areas of topology are finally getting the attention they deserve.

Fun fact: making sure you're doing a square knot instead of a granny knot is also very important in surgery. They are taught to alternate the way they secure off the suture.

A buddy of mine is studying knots in projective spaces, called like “knots in the shadow world”; he explained that you can’t necessarily get a well defined projection onto the plane for them (over/under crossings could be the same so you don’t really get a “drawing” of the knot in way that works well).

@31:36 I stiffened knowing the mistake you were about to broadcast as good practice... never do this with any type of cable, but especially cable that contains un-braided stranded wire Ie. Earbuds 3 destructive actions take place when you twist stranded wire onto itself, or even wrapped around a center bobbin. Ie. An extension cord spooled around your hand and elbow. 1. The individual wires that make up stranded wire are equal in length (for many reasons) but as you twist the cable, each individual wire inside the protective insulator is rotating longitudinally, and when you un-twist your cable the inner wires do not completely return to their factory position, so over time they begin to bunch around each other tighter and tighter. since the wires closest to the outside are effectively getting shorter faster, having a farther distance to move with each rotation, they will begin to knot inside the cable first, snapping away from the ends while the inner wire continue to become stiffer, and exerting force on the cable ends in the opposite direction as the outer wires. After a while you will notice that even when you spool out the cable it begins to look wavy as if it had been curled. Since there is less wire making contact with each snapped strand, the resistance slow rises at each end of the cable dropping the voltage... In the case of extension cords you will notice that this makes the plug act like a heating element. With earbuds you will notice that over time the volume decreases, until shortly before one side stops working they only operate at 25%-50% of original volume. You can actually measure it, check output when new, then twist and untwist them 180 times @6 months worth of simulated use, and measure the difference. 2. Friction, you ever had to cut a wire or piece of metal in half, and had only your hands, you folded it several times at a certain point... well a twist is essentially a rotational fold and each crossing point is a fold location since copper is a soft metal, each time you force one side of wire to cover a longer distance than the other side what happens is the two opposing forces pinch the atoms together at that spot forcing them to rub against each other with much more force than they would see during normal use. To figure out how much farther a side has to pinch and stretch to accomplish a twist, take the diameter of the wire then find the circumference for 180 degrees, now using that distance as your radius, double it to find the diameter of the twisted wire, now find the circumference using that diameter for 180 degrees and that is the distance of travel between the shortest side, and longest side. 3. With stranded wires, the insulation is usually not as tough as cable with less strands of thicker gauge, simply for the same reason we use stranded wire in applications where we want the cable to remain easily pliable. So the insulation is easier to damage inside the cable after repeated use, and the insulation be it enamel for earbuds or pliable vinyl in romex, with enough twist, you can find yourself with a cable that is in a permanent state of "dead short" and the big danger being it quickly melts the conductor ending the short, so it gets set aside, and you forget or a coworker uses the cord, plug it in making it live, the rolls the cord out loop by loop and when they get to the place where the damage is, the movement causes their hand to complete the circuit at the damaged location. I tell people all the time the two best ways two best ways to store any cable is do not twist or loop decide on a convenient length and fold the cord back and forth like an accordion then pinch the centers together and tie with a piece of scrap wire or bread tie depending on size of cable. The second way is essentially the same as the first, but instead of a back and forth stacking of the cable, start a spiral on a flat surface with then roll it around itself so that it has no rotation perpendicular to the length like it does when looping, now continue that rolling, until you have four to five passes on the flat spiral. Now start your next roll on top of the first roll at the same size make the same number of passes you did on the first spiral layer, repeat until you have a roll of cord 4-5 passes wide and about the same number of layers high. you will almost certainly be left with a cable end on each side or both ends meeting at same place. You can now place a tie around the finished coil. I almost always use two so that it retains its shape for storage... It I am unclear you can visualize it as being rolled the same way windings on a transformer are.

Math is so incredible. People just study a phenomenon and it reveals a language that describes the world in ways we didn't know of before. Wonder what fields of maths exist that we have yet to study

Derek has been killing it with the math videos lately

I've started to lace my shoes like this ~2 years ago when I realized its symetry and aesthetism, but never paid attention to its tightness. Thank you for this great video, as always !

i love that I never know in which rabbit hole I am going to fall into when I watch your videos but it`s always incredibly fascinating! Thank you for your valuable content!

When it comes to avoiding knots in headphones, my easy way that I have used for years is to simply not allow the endpoints into the storage case. If it is a zippered pouch, just leave the earbuds and the plug hanging outside the zipper. You can just grab the entire length of cable and shove it in the zipper pouch as a massive wad if you want, just leave the ends outside the zipper, and you will have no knots. Same story if you put them in your pocket. Just leave the ends sticking out of the pocket and you get no knots.

In southern India, everyday women create knot diagrams called 'Kolam' in their front porches . The more complicated the knotting the more skilled the person drawing it. This video is when I realized that many such Kolams are actually super complicated, challenging to create, un-knots! So cool to know there is a whole sub branch of math around this! Unknowingly it sounds like these women have been practicing Reidemeister moves on a daily basis in attempts to create ever more complicated knot diagrams! And instead of the p-colourability, these Kolams care more about the areas between the loops which are denoted by simple points. The points are actually laid out first and the knot emerges as a line diagram around them .

This is the most complicated video I've ever watched in this channel. I didn't Understand much but after seeing that our everyday knot can be so interesting to great scientific minds I get excited. 😯