Metric, okay, but does this work in America?

@giin97

3 жыл бұрын

System named after the function, not the function after the system, I would presume. That said, America adopted the metric system in I believe the 1960's, before the UK. Our difference being, cultural adoption was optional, and we ended up defining imperial measures by the metric system and keeping our several million signs listing imperial measures :P The inch is defined as 25.4mm, for example.

@CIorox_BIeach

3 жыл бұрын

@@giin97 I found out recently that there are countries where non metric systems of measurement are banned. An American can't even send a tape measure to France. I was surprised.

@giin97

3 жыл бұрын

@@CIorox_BIeach that's... Bizarre. Of course, we are talking about France, so...

@puckry9686

3 жыл бұрын

@@CIorox_BIeach why is matric horrifying to you

@Noname-67

3 жыл бұрын

@@puckry9686 he didn't talk about that, he said some place banned non-metric system is horrifying

Actually, the metric between (three letter) words is very useful in areas such as auto correct. It is called Levenshtein distance in computer science and it can be calculated through dynamic programming!

@cadekachelmeier7251

3 жыл бұрын

Huh, I think we used that in my computer vision class, but never knew the name. You can use it to correlate points between 2 images and generate a depth map and occlusion map. It's far from the state of the art any more, but it's useful.

@Aaron-ff2ms

3 жыл бұрын

Yeah, levenshtein distance can be handy sometimes but most of the time there are better algorithms for detecting similarity. For autocorrect for example it is better to check the physical distance of the pressed key with the key you'd need to press for a word and to make it extra fancy you even take this distance (and the direction) of the other keys into account for the score. That way you can find out that "gwkki" is meant to be "hello" and the user was just one key to the left, even though there is not one common letter in those two words. The same thing applies to other areas as well, so there might be certain areas where double characters should not play much of a role, e.g. when someone is using something like "whaaaaat?!" to express excitement or any other emotion in the text. Levenshtein distance is not really the best distance to use in pretty much every use case I came across so far.

@mr.knight8967

3 жыл бұрын

Maths problem kzread.info/dash/bejne/nG2ru5Who9KXh7Q.html One time see.

@snippletrap

3 жыл бұрын

Levenshtein distance is useful when comparing DNA sequences too.

@someoneuppingdudetechnical6320

3 жыл бұрын

@@johnrobertson4450 calm down. They just didn't tell him it had a name.

Knight: I takes me 1 move to get to the white square. King: Lucky, I takes me 2 Rook: Luck, I need 3 Black bishop: *_you guys can get to the white square?_*

@kirtil5177

3 жыл бұрын

the surviving pawns on the other side of the board: *you guys can move without dying?*

@9nikolai

3 жыл бұрын

@@kirtil5177 Pawns at the end of the board gets changed out for a different piece

@kirtil5177

3 жыл бұрын

@@9nikolai yes, thats why they are always killed or atleast threatened to be the closer they are to promoting

@chaotickreg7024

3 жыл бұрын

@@kirtil5177 The pawns are sweating profusely waiting for the end of the game like "You guys are allowed to move?! I'm just sitting here and everyone is already threatening me!"

@skelet8337

3 жыл бұрын

@@chaotickreg7024 or 2 pawns locke in a tie till the end of time

The chess metric is very relevant to a lot of endgame studies. They're hard to solve because it's not intuitive to us that the king can move diagonally in the same amount of time that it can orthogonally. Look up the Réti endgame study in particular.

@Doom12384

3 жыл бұрын

I was about to mention the Réti endgame study since it's so famous and relevant.

@mr.knight8967

3 жыл бұрын

Maths problem kzread.info/dash/bejne/nG2ru5Who9KXh7Q.html One time see.

@mate_on_f7916

3 жыл бұрын

Agreed

@chaotickreg7024

3 жыл бұрын

I remember knowing this would mean win/lose in a lot of games. At some point in the late game you need to mobilize your king or else all of their pawns will get to just walk right past you.

@thoop6795

3 жыл бұрын

*Flashbacks to studying the Lucina Endgame*

I really like that you are using the technique of proof by example

@mr.knight8967

3 жыл бұрын

Maths problem kzread.info/dash/bejne/nG2ru5Who9KXh7Q.html One time see.

@octosaurinvasion

3 жыл бұрын

@@mr.knight8967 stop spamming

@jasonreed7522

3 жыл бұрын

I believe the mathmatically rigorous proof by example requires you to cover all possible cases, it isn't the cleanest of proofs to do but it is valid and occasionally used (knot types were done this way). He is closer to proof by heres an example to explain it and trust me on all the cases I don't have time to cover. It does work great for teaching concepts though since the best way to learn a concept is in parallel to learning the calculations.

@happysongs4kyrone

3 жыл бұрын

@@mr.knight8967 shut up

@nomukun1138

2 жыл бұрын

Of course, he's not really doing proofs. But TEACHING by example is a very good technique.

Definitions 5:28 2D distance formula 6:01 metric 8:00 taxicab metric 11:35 maximum metric 13:28 discrete metric 14:03 hamming distance

@palmberry5576

2 жыл бұрын

Wish I could bookmark a comment

@wada-wada

2 жыл бұрын

@@palmberry5576 you can actually right click on the time (x month ago) next to my name open link in new tab now you can bookmark my comment

@palmberry5576

2 жыл бұрын

wow I never knew that! thank you so much!

@ZalamaTheDragonGod

Жыл бұрын

​@@wada-wada I see a flag, is it the same thing?

@wada-wada

Жыл бұрын

@@ZalamaTheDragonGod no. that's too far right right click on "2 years ago" next to @wada-wada "open link in new tab"

The chess example gets even more interesting when you consider the default bishop under normal rules. Then the sample distance you pointed out instantly becomes undefined, i.e. "You can't get there from here."

@amphioxusanniversary

3 жыл бұрын

I was wondering if he was going to bring up the bishop...

@sophiegrey9576

3 жыл бұрын

Even a pawn can get there eventually, by walking up the board and promoting to something other than a bishop.

@chaotickreg7024

3 жыл бұрын

There are some pawn cases where a distance is only literal under very specific circumstances, otherwise they are imaginary. A pawn can only move diagonally if there is a piece there to capture which means distance varies by board position. A pawn can also promote and reach any square as a knight or queen depending on need. There are also some distances that are impossible like bishops switching color or moving into check.

@siddharthvikram3054

2 жыл бұрын

it would be very interesting as it will act as a infinite distance point in the metric space

@chaotickreg7024

2 жыл бұрын

@@siddharthvikram3054 A rook can move to any point on a coordinate plane in only 2 moves. A bishop can only reach half the squares in just as many moves. A queen is slightly more efficient than the rook as it can move to diagonal squares in one turn. This geometry gets weird really quick.

I must have missed this one. Changing the background to a city backdrop to demonstrate the different metric is absolutely genius.

Came here when the like to dislike ratio was still infinity

@architjain811

3 жыл бұрын

You mean not defined right?

@Leyrann

3 жыл бұрын

x/0 =/= infinity

@architjain811

3 жыл бұрын

No bro, 1/0 is not defined. 1/(value tending to 0) = infinite.

@pbj4184

3 жыл бұрын

@@Leyrann 1/x is undefined *at* 0, but the right hand limit to 0+ is +infinity

@Enourmousletters

3 жыл бұрын

@@pbj4184 Given that 'likes' are a discrete and not a continuous data set, there is no result between x/1 and x/0. No infinitesimally small decimal to generate near infinity. Original correction holds true. (Unless we start chopping people into pieces and getting individual's sub-sections to submit fractured code semi-like impossibilities. But one should never have to involve cthulhu-esque rituals except on a Monday)

11:00 It's interesting to note that if we drop this requirement from metrics, to get a "pseudometric", we can generate new topological spaces. For example, the function d(x,y) = 0 for all x and y generates the indiscrete space, which is not metrizable.

15:41 It seems pretty applicable for catching misspellings or word suggestions.

14:15 I have actually created a simply autocorrect tool that finds the "distance" between 2 words in a similar way to how you defined it in this video. However, my distance function is more complex than yours: = It considers vowels to be very close to eachother = It considers keys to be close if they are adjacent on a US ascii keybaord; *this part would vary based on keyboard, and should definitely allow users to specif their specific keybaord* = Plus, it allows for letter duplication, and omitting

These uses for rather more complex topics in the realm of mathematics again shows just how important they are to our everyday and abnormal lives. So interesting as always!

@mr.knight8967

3 жыл бұрын

Maths problem kzread.info/dash/bejne/nG2ru5Who9KXh7Q.html One time see.

1:30 3rd to Bedford seems the shorter distance; plus, it has fewer turns.

@whahala555

3 жыл бұрын

A jet pack is also faster.

@mr.knight8967

3 жыл бұрын

Maths problem kzread.info/dash/bejne/nG2ru5Who9KXh7Q.html One time see.

This absolutely made me go nuts, I've been just introduced to this topic and seeing everything that I used to see come alive is just awesome, if possible can you do a playlist for it, or can you suggest some books that talk more about the intuition that you gave us a gist of...😅

@mr.knight8967

3 жыл бұрын

Maths problem kzread.info/dash/bejne/nG2ru5Who9KXh7Q.html One time see.

The max(dx, dy) metric is used, for instance, in Doom, when calculating the distance to apply splash damage (e.g. from a exploding rocket or barrel). It gives square-shaped damage areas.

This is a nice topic to discuss with special friends. Many of them were suprised by the shape of a "circle" using different metrics!

@mr.knight8967

3 жыл бұрын

Maths problem kzread.info/dash/bejne/nG2ru5Who9KXh7Q.html One time see.

@bryanreed742

3 жыл бұрын

Yeah, it turns out you can have a square circle!

@ispiderguy6505

Жыл бұрын

In the discrete metric a circle would be the entire plane

Distance is super fun and important. In robotics, we commonly use heuristic functions to guess at the actual distance between two robot positions. Those have some fun properties too! Another fun thing that popped into my head: sometimes, in robotics, distance (we actually tend to call it cost, because it behaves ever so slightly differently) *isn't* symmetric, and that actually forms the basis of my grad research :) Love metrics!

Great! I recently went through the first chapter of Barnsley's 'Fractals everywhere' where he introduces metric spaces. When studying in the book I really thought that I need a tutor and more visuals, to speed up the process of understanding this topic. So this is exactly what I needed! In the book I spend a lot of time looking at formulas and reading definitions over and over again, while this video does it in a fraction of that time!

This reminds me of my Data Mining course at university. Learning about the Lp metric, cosine distances etc was really fun.

This is the first video of yours that I've watched, and i think it's really good. It's very relaxing to watch since you explain everything in such great detail.

Great, now criminals seeing this video will use the equation to minimize their probability of getting caught.

Your “shortest distance using streets”, near the start, was not the shortest distance using streets.

@acr1327

3 жыл бұрын

i noticed this as well, can't say it fills me with confidence

@aidanmays7825

3 жыл бұрын

Who cares

@dbldekr

2 жыл бұрын

You aren’t taking into account expected traffic

@jeremyashford2145

2 жыл бұрын

@Jeb Could be you are confusing distance with travel time. Years ago I was scolded by an Englishman for telling him travel times when he asked about distance. I thought it was only we antipodeans who do that. Maybe he was just a pedant.

Thank you for ur video. I'm a Vietnamese student who can't understand lectures from my teacher. Then I came here and this video clear my brain 100%. Hope u will make more useful videos like this

Then there are two distances. 1: absolute distance (units of space between two points) 2: traversable distance (units of space that must be traversed for an entity/object to get from where it is to some other unique point)

i really like the formulation of metric space at the beginning before you start examining diff functions/metrics . thank you for making this video , i really have learned alot !

Thanks for this brilliant and fun explanation - and yes, Lumberjack Feinman's lectures are good too :)

Briliantly explained!!! Thank You.

It’s crazy to see a serious video from one of my favorite comedy skit KZreadrs, my mind is blown.

They can also define the P-adic numbers... Can't believe you didn't mention that! It was crucial in proving Fermats last theorem

Great video, it covers so many concepts I learned in different lectures in a very applicable way, which is really refreshing

Was nice for me to see this video since I'm currently taking the course 'metric and topological spaces'

@mr.knight8967

3 жыл бұрын

Maths problem kzread.info/dash/bejne/nG2ru5Who9KXh7Q.html One time see.

Great topic and great video :)

This is exactly what i was looking for 👌

Interestingly, "it's symmetric" sounds similar to "it's a metric"

I don't have anyone to talk to about math, so I really enjoy watching your videos. I know it's a lot of work to make them and maybe sometimes you question your sanity and if it's worth it. Please know that many of us really enjoy them to a great extent. You don't know it, but you're our closest math buddy, for all of us.

Great timing. My real analysis homework on metric spaces is due today lol

was curious and decided to check this out. wasn’t disappointed, it was very interesting 👍🏼

Metrics in spacetime work a little differently, though. The distance between two points (or the "interval" between two "events", to use the correct jargon) can be zero, or even negative. There is an equivalent of the triangle inequality, but it's a little bit more complicated than the version used in these examples.

@robertmorrison1657

Жыл бұрын

Then it is a topological space, not a metric space.

Thank you for the amazing videos zach!

Before you said "discrete metric" I was thinking "teleportation metric".

Good lord, this title makes me think of college!

@mr.knight8967

3 жыл бұрын

Maths problem kzread.info/dash/bejne/nG2ru5Who9KXh7Q.html One time see.

Literally so many of your comedy videos have been recommended to me, and watched by me. Now here I am in a non euclidean rabbit hole and youre about to teach me some real shit. MY MAN!!!!!!!!

I’ve learned a lot from this video! Thanks!

Great video! I would like to see a continuation of this topic talking about pseudo metrics. :)

Deep respect, Zach Star!

I'm still in the 12th grade , and I really like your videos , it basically helps me alot and also give me some of encouragement that university is gonna be good , is gonna be different, is gonna be challenging, is gonna be fun , and I also really appreciate all your work in these informative and useful videos , specially the videos where you talk about university, the applications of what you study etc, your own experience in it I'm searching for a good niche in engineering and your videos are always helping! Keep up your awesome and noble work Zach! Goodluck!

@User-jr7vf

3 жыл бұрын

His videos inspire you while money keeps flowing to his money account heheh

@Enourmousletters

3 жыл бұрын

First rule of life: Nothing is free. But some things are delicious, like Zach Star

Thanks for this amazing video that made my day, it helped to my homework

Excellent Video!

Awesome as always. Thanks.

You should do more videos on hyperbolic/spherical space they’re rly good

1:26 "Instead, the useful distance would be the shortest path, using streets" >doesn't draw the shortest path

This was awesome!!

Dude you’ve really outdone yourself with this video, probably my favorite ever of yours. I’ve been wondering what a metric is and you explained it so clearly. I’d love more videos explaining fancy math terms.

@mr.knight8967

3 жыл бұрын

Maths problem kzread.info/dash/bejne/nG2ru5Who9KXh7Q.html One time see..

I don't know about you guys, but just a few of days ago I was thinking about how to create non-euclidean spaces and how to calculate distances from point to point. I wont say why but I will say I think it's crazy how sometimes I think about something and a few days or even weeks later I'm recommended a video about it here on youtube.

Zach I'm planning to get a PhD in Industrial Engineering & start a business. I think you should get a PhD in math. You clearly love it and keep learning. That's how I found my love of engineering statistics and manufacturing. Keep it up, I love your videos bro.

Cat-->Cot-->Dog is also like the detour point being on the line segment for Euclidean distance because on a line segment AB we will encounter every point on the line segment going from A to B just like how Cot (or any other detour word than keeps the distance tge same) comes up in the process of converting Cat to Dog (for a particular order of changing letters).

I'm not sure if you've covered this or not, but I would love to see a video on convex sets and their applications to concepts such as optimization.

15:00 fun fact: detour can only increase the distance by an even number

Great video

I LITERALLY WENT OVER THIS IS CLASS YESTERDAY!

The Taxi Cab geometry is great for the game of Snakes! (The cellphone one where the snake gets a treat and grow long)

The simple complexities of the obvious, greatly explained and interesting ! Sounds good for a sub =] Thank you

Good work 👍 Thank a lot

I think I saw the use of distance in position encoders as well. By making sure the 'distance' between any two adjacent positions is only 1, they avoid imperfect transitions where the encoded position momentarily 'jump's because not all the bits change state exactly the same moment. Grey codes I believe they are called. Read a book years ago on 'taxi cab geometry' this video triggered me to go dig that out and read it again. :)

Dmaps is called Manhattan distance BTW. (Geographer here.) In a universe as hologram or 2D surface on the event horizon distance is a bit of an illusion. Well our conventional 3D distances anyway!

bruh nice upload time i'm literally working on a DG assignment right now

@UncoveredTruths

3 жыл бұрын

let's fucking go

@PapaFlammy69

3 жыл бұрын

1111111111

@UncoveredTruths

3 жыл бұрын

@@PapaFlammy69 u r a meme virus

@aarongabraham6179

3 жыл бұрын

DG ?

@ithaca2076

3 жыл бұрын

DG?

The min function at 11:22's metricness can also be disproved with the "point c" requirement. If point a is (0,0) and point b is (3,3), the distance=3(for both x and y). If you place a point c at (2,1), the distance a to c=1 (change in y) and the distance c to b=1 (change in x).

@asherporter2119

Жыл бұрын

*triangle method

I just realized the "French railway metric" isn't as popular outside of Germany as I thought it was. Imagine a railway system where every single train is going through the main station, but the only place to change trains is the main station. Either your destination happens to be on the same track going through the main station as your starting point, or you have to take one train to the main station and then another train from the main station your destination. With the French railway metric, the distance between any given point a and the origin is calculated using the euclidean metric, but for two points a and b, the distance d(a,b) is either ||a-b|| or ||a-origin|| + ||b-origin||, depending on whether a and b are on the same straight line through the origin.

A nice application is in (admissible) heuristics, in particular solving the 15 number sliding puzzle.

I'm enjoying contemplating the discrete metric unit circle.

An Inspiring video indeed!

Great video. Thanks Zach. Love all your videos. What is the software you use to animate points on the graph?

Reminds me of what was used for movement with the board game Star Trek Ascendancy.

The fact that d_maps is less than d_euclidean for some spaces is revolutionary!

"Most of you would say 5" Yes i definatly thought that and wasnt immediatly thrust into a distant stare at the sight of numbers.

I like the visual aspects of maths but not the numbers and such, so this kind of stuff really hits that sweet spot

I see a Zach Star video, I watch. Simple.

Please make a video on what is mechatronics and it’s future

@uttamkumbhat7991

3 жыл бұрын

Even I want to know

Amazing thanx alot

Nice vid 👍 , can you make another part exploring metrics as H-norms and L-norms

15:43 Good timing, just watched 3b1b's Video on Hamming codes a couple of days ago :D

Hey Zach Star, Please upload a video about the application of set theory.

I found this channel by watching a bunch of his comedy skits first, so I thought this was a setup for another sketch. Imagine my bafflement when I'm 5 minutes in, there haven't been any jokes yet, and I realize "hang on a fucking second this is just an actual lecture"

At 13:34 Well, that's a very appropriate name for that!😆

could you do a video on how time would be effected by a negative gravity well?

I think everybody is correct because you need to explain more. Like Knight is 3 spaces away, or Knight is 1 turn away, or the distance between knight and (space) is (idk).

fun fact: Dungeons and Dragons uses taxicab distance for spell ranges, movement, etc. D&D by necessity is played in a non-euclidean world.

One of the best channels ever!

12:50 fun fact: Magnus Carlsen, currently the #1 ranked chess player, has never been able to remember this rule, and has through his entire chess career resolved to calculating end games when he could've easily seen the outcomes using this rule.

3:20 it depends what your anser is in, if you said "its 3 squares away" then the distance is 3 but if you say "its 2 moves away" then the distance is 2

2:01 as a chess player i gotta tell you, its a knights move in distance. anything else such as a number is wrong.

it is useful to say the rook travels 3 or 7 squares in the chess example because, unlike the knight, the rook can be obstructed. It's just that the rule is the rook can travel an infinite horizontal/vertical line.

You should check out Hyperbolica and Hyberblock

Your first example has 3 turns and you could do it in 1 turn ;) Straight down 3rd Street and take a left onto Bedford Avenue. Same distance - quicker travel time. Yes that's about all I am capable of :p

Reminds me of sailing where a straight line from point (a) to point (b) isn’t always the fastest way across.

I see your spherical geometry and raise you: cylindrical geometry. Space behaves like euclidian geometry in one direction, and behaves like spherical geometry on the other.

@MudakTheMultiplier

3 жыл бұрын

This would be useful for non-Euclidean VR because the floor would still stay under you after you rotate your head.

Wait, wait. No. The spacetime interval does have the idea of distance but it is clearly not a metric. It can easily be negative for timelike events. That is the entire inside of the light cone we can see and interact with

hamming distance is quite a useful metric and something that is rarely thought of as a "distance". Edit: nevermind 15:50

OH HE'LL YEAH, AWESOME!!!