P vs. NP and the Computational Complexity Zoo 

Let's say a specific problem expected to be NP turns out to be P, but with a ridulously high power, say N^100. How does that help? It still requires approximation methods that find local optimums, like genetic programming.

@@TheGandorX Well none of the np complete problems have ever been found to =p. Thats the problem, but its has yet to be proven that they cant = p either.

True af

Only Indians were interviewed

@PotatoTornado You cant turn a P problem into a np complete problem.

I prefer "If I had more time, I would've written a shorter letter." ;)

Behind simplesty there is a long story

Mark Twain is possibly my favorite writer. Very intelligent and wise.

@@nathan3721 Indeed!!!

True, thing is most of us agree that P is most likely not equal to NP Still, non deterministic polynomial algorithms for such problems can still be faster or slower compared to each other and there's a lot of work that goes into making them as fast as possible, usually in the form of SAT-solvers (a nice keyword for you to google more detail there)

Curing cancer is almost an impossibility but averting cancer through a healthy diet is possible. You people constantly blow my mind. I would like to ask you people one question. Why are you people not vegan? That is how to almost eradicate cancer. That is how to end the worldwide obese epidemic. That is how to stop our species degenerating. That is how to save the planet and all the species on the planet. That is how we will evolve. I do not understand the complexities of mathematics. That is what you people excel at but could you people please go vegan and then direct your brilliant minds to building a vegan world. Time is running out for planet earth and all the species that live on it. Thank you.🌱

Math is wild

Ivan R yea man I enjoyed it

@LeDjipy Just watch it with subtitles and slower speed, figure out with vocabulary first and pronunciation. There is a settings -> playback speed.

I didn't get most of it

Music only distracts. Your brain has to process one extra task - the music. So no, music is not what makes you focused. Your attention is.

No it's not! it is bewildering.

no this is halting problem

ITTM-undecideable

They voted Brexit/ Trump

The reason why someone may dislike this video is because this video doesn’t inspire. And no, it’s not simple. The video is lots of art, sure. But no viewer with coding experience will think, “ok, here is the goal, let’s take it step-by-step” because a model was not first developed.

@@danielmontaigne1219 There are no smart Brexit/Trump supporters. People who think different than me are dumb and I'm better than them because I liked this video. Quite a way to think, eh?

having a phd doesn't mean you're smart or bright or creative

@@mojo5093Thank you for your enlightening contribution! Oh wait...

@@celkat He's not wrong

@@mojo5093 Your comment has no relevance to what I said. I mentioned the PhD to imply that I have been introduced to / introduced the P = NP problem dozens and dozens of times and much more often than most people,, and this is the best presentation I've seen of it. I was congratulating the video producer on a job well done. Then you come onto a conversation, misunderstanding why something has been stated, and leave a snarky "rebuttal" to a claim I never made? That's a pretty strong indication that you're not particularly smart, bright (synonyms), or creative. Do you feel better about yourself now? Your comment supports that there is a growing general disdain against education. If this was a conversation about a football topic and had I come in here and said I was on the college football team as QB and this was one of the best explanations I'd heard of that topic, Im willing to bet that you wouldn't have opened your mouth to make a comment about my mention of being QB; however, since my claim is academic instead of physical, you feel some strange need to come in here and be snarky.

@@rope435 HIs comment has nothing to do with the conversation. I mentioned that I have a PhD in combinatorics not to give myself authoritative validity or imply that I'm smart or bright or creative, but to say that I've seen and studied the P=NP problem more often than most people since it's in my field of study and I use it at work. Then I used that to give a much deserved thumbs up to the author for giving the clearest, concise, easy-to-understand description of the P = NP problem, at which point, MO JO lasered in to my mention of my PhD, inferred that I was implying a whole bunch of things that I was not, and contributed nothing of value or even on topic to the conversation. See my reply to him on this thread. I don't know if you have a disdain for education, but there is certainly a growing one. My personal hypothesis is that it's pure Dunning-Kruger.

If you keep doing this you won't be a simple man for too long

Me too 😂😂😂😂

curiosity

Run out of clicks pretty soon.

You are simple, you can’t even come up with an original joke

I would say "could be Mozart" would be less biased, because P=NP only implies that for every problem whose solution can be easily checked (NP), there is a method that can systematically resolve it (within only a polynomial number of step). But not that being able to check a solution would automatically imply discovering that method.

@@youri76000 Exactly

@@youri76000 Yes, this is slippery. There is the intermediate case you allude to.

@@worldnotworld which one?

@@youri76000 It is a little bit biased. But it is reasonable for deterministic problems, because you can always (1) randomly generate some answer by RNGs and (2) check if it's correct, both in polynomial time, all intention to "discover a method to systematically solve a problem efficiently" would end up to be just as good as "guessing the answers".

ikr

+behnamasid2 yah. did he, like, die?

For Real.

I will pay money to watch more videos!

Welch Labs you also great explianer.

How is this in your Algorithms class? dont you have a couple Computational Theory classes?

Six Millions waiting there :)

Wish he could have cited the fundamental papers for each set then provided he own sources via link to wikis or books.

If you solve P=NP, the others are easy

Luiz Felipe Except if you solve it by proving P≠NP

Someone truly understood the video

You also as a programmer, have to give some thought as to how long an operation might take to be performed. If it often takes too long, then the user needs a progress thermometer, so that it does not appear that their computer software has just frozen or crashed for no apparent reason, then they start doing drastic things that could cause problems, such as force-quitting. Also, any data file updates should be done in such a way, that if the program becomes interrupted, the data is quite unlikely to become corrupted. Thus, perhaps the old state of the files is maintained as the current version, completely until all updates have been completed. Thus, the worst-case scenarios is simply starting the process over again, and not catastrophic data loss. BTW, I notice that some progress thermometers, initially have no idea how long the process will take. Rather, they self-calibrate and will estimate how long, based upon the rate that it is progressing so far after a short wait going into doing the process.

@@yosefmacgruber1920This is what RAID controllers are for. Also the reason progress bars start out without an accurate estimate is because that calculation itself is quite complex. So you need a download bar for the download bar...

@@deoxal7947 The calculation is quite complex, due to factors beyond the computer's control. For example, the hard drive or even USB flash drive has its own computer controlling it. You can't tell it to hurry, it takes as long as it takes. The computer doesn't even know how long it takes, unless it can find that data in the device driver or in some database, other than by testing or bench-marking it. Some devices are faster, some are slower. Or if downloading, the speed of the internet and wifi links, affects it, and maybe the server is running slow today. When progress bars start without an estimate and take several seconds or more to estimate, that is because the computer is trying to get a small test percentage done, and it times the progress against its own internal clock, and then extrapolates "At the current data flow rate, 2 minutes are remaining." If then it becomes 3 minutes and 5 minutes, it is because some weak link in the data flow, is slowing things down. There are a few self-explanatory progress bars for progress bars. The empty bar appearing, and meaningless movement or gradients flowing in it, before it starts properly advancing. Some progress bars never properly advance, because for some reason, it doesn't even seem to know how big the file is, and so it just shows progress, but not the percentage of completion. It could be because of a gap in the programming, that it is not fully compatible, so some of the progress calculation data is missing. Sometimes, well especially in a free or beta version, it is more important that it works, than just how great its performance level is. The circle going around, that often means, hold on for a moment, I actually am doing something. And to have better self-explaining error messages would be helpful. "Internet connection is not responding, attempted to reset the connection." "Re-requesting the file, due to request time-out." I get so tired of crappy software, in which the circle or beachball goes round and round, and you walk away for a minute and come back, and still nothing has happened. Surely a computer can diagnose when no progress is occurring or when the data link has gone down and do something appropriate about it. Not just tease the user and pretend to be working on it. When I was in college long ago, and the Macintosh lab was jam-packed with users, I tried a curious experiment. I needed to make a copy of an 800K Mac-formatted 3.5" disk. Problem was, I had no Mac. I had an Apple //e computer with a mail-order 800K disk drive. Hmm. Both computers made by Apple. Both 800K, both using the same type of disks. Hmm. I suspected they could be undocumentedly compatible, even though supposedly they were not. I ran a disk copy. The copy disk verified noticeably faster than the Mac original. Wow. Really? An improvement? Not so much. I knew enough about how they work, to know what had happened. My Apple //e used the wrong sector interlace ratio. It used 4 to 1, and it was supposed to use 2 to 1 for Macintosh. 4 to 1 only optimized it for use on my //e and not on the Mac. That incorrect ratio Mac disk would run slower on a Mac. 4 disk spins would be required to load the entire track, where otherwise it would only need 2. That was back in the days, when most all the work was dumped onto the CPU. The //e was so slow, that it needed a 4 to 1 ratio, to have enough time to process the disk data before it could be ready to read the next sector. The Mac 2 to 1 ratio was causing it to miss the next consecutive sector, and so it had to wait for an entire turn of the disk to read the next sector. My copy disk worked just fine on a Macintosh. That told me in theory at least, that an Apple //e computer could technically be programmed to see, load, copy Mac files, as it was actually capable of reading and writing the data. (My interest was in writing my own OS, and also in being able to use Mac fonts on my //e.) The compatibility problem was not critical, as it did not keep it from working, only messed up the optimization. Better software could have chosen the correct ratio for Macintosh. But I guess cross-platform programming wasn't quite as big a thing as it is now? Another interesting experiment, slightly related. I liked the music on a PS1 pinball game CD. Since the PS1 often used actual CD tracks for game music, I once put the CD into my car CD player. It didn't play at first, but I pushed the next track button, and it easily played the game music. Apparently it was some sort of hybrid disk, with a game data track, and standard CD audio tracks. I doubt that that would work on later video game console disks, because I think their music tended to be some sort of compression. And earlier CD-ROM drives were actually CD players as well, meaning that they have actual audio outputs that were connected to the motherboard. I suppose if the computer crashed and froze up, the music would keep on playing? I think they may have moved away from that now, as computers became faster, perhaps the computer actually does the work of playing the CD/DVD, streaming the data, and doing all that drawing of the movie image to the computer graphics memory. And where is that "audio connection" when your optical drive now has no connection at all to the computer other than a USB cable? Surely is it 100% computer data now? Normally, I am not much bothered by a progress thermometer. They usually fill up fast enough. I just want to see that it is progressing and that the computer hasn't crashed or froze up. I had an experimental program that I wrote on my graphing calculator, that had to momentarily display a graphic image on the screen, so that it could use it as efficient storage to load all of its graphic icon variables. My little progress thermometer filled in just a second or two. Just drawing/updating the progress thermometer, probably slowed down the load by 30%?

Very interesting read, I didn't expect such a long post. I heard about playing audio from CDs with other content on them from this video about malware. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-4eM4wjgXsJI.html Also I found this xkcd about progress bars. www.xkcd.com/612

I forgot to ask, what was the program you made for the calculator? Do you still have it? I'd like to see it if possible.

He said the nature of the problem is same, the computational complexity of solving sudoku and curing cancer through solving protein folding problem is same, a computer that can solve one such problem can also solve the other.

because it came from the warm, loving, heart of Computer Science, not the cold, emotionless, beast known as mathematics

Glad I'm not the only one; I finished watching it and had a profound urge to cry.

@@TheAlmightyCon this is a math subject, computer science is about wrestling with dumb syntax that makes no sense

I can't explain why but this quote moved me.

who said this

@@wongpentelglobal Jack Kerouac

"Simple." - Jack Kerouac

@@wongpentelglobal watch the video from beginning to end 👿

Adam Katav good one 😀

I think this rap battle would have ended with P and NP having an existential crisis, not being sure whether they are one. "Am I you, are you me?"

🤣🤣🤣

Epiccc rap battle of historrrrrrryyyyyy

Yooooo send it to me lol

Your prof is there to further their research, teaching you is just sidework. The maker of this video is highly incentivised to communicate the concept clearly and in an engaging way. Yet only one is considered to be a valid form of "education." The world's a funny place

DeanoTXR53 I would like to think that a professors first priority is to further a students education and passion. I would like to think they are “highly incentivized” to create meaningful and easy to understand lectures since they’re getting paid 6+ figure salary.

@@scotthofbauer5448 I would "like" to think that too... But sadly that's not the reality of why they are actually being paid that 6 figure salary. They are actually being paid for the non-classroom work/value they bring the university

@@DeanoTXR53 Not always true. There are plenty of professors who don't do much research. This is especially true at smaller, libear arts schools

@@blownspeakersss We are both correct. The ones you're talking about aren't grossly overpaid. The ones who publish research and books usually are because they offer more reputational value to the institution. Not saying it should be this way. But sad facts are sad facts

Anwser is3584

@@foobarmaximus3506 not true, E=mc^2, or more generally, E^2=p^2c^4 2+m^2c^4, is used all the time. The energy and mass in it are both well defined, and can be thought of as emerging from lagrange mechanics due to symmetries (noethers theorem).

Jon I think we are on round O(n!). But I can't tell when P vs NP is supposed to halt.

FrankenPC Also, this round is EXP.

@@metachirality: That's one of the best comments I've seen in a long time right there

+hameed lol

+hameed Someone get this man a dunce cap

+hameed What are you going to buy first with $1,000,000?

lol that is not one it means

+Noah Reichert prove it.

lol XD!!!

hahahahhahahah damn underrated comment!

he didn't accept both the 1M $ and Fields Medal

Tony Raubenheimer i respect that guy alot

Refusing a prize doesn't mean it hasn't been awarded.

grigori perelman

@@Theo_Caro if I try to award you a prize for being a dbag and you refuse it would you go around saying the prize was awarded?

Exact my thoughts. It could have been one of the greatest RU-vid educational channels ever. What a loss.

Maybe the next video is a follow-up, with a proof for P Vs NP

Maybe finding a good idea for their next video turned out to be an NP problem...

What happened?

hey bro i can't find him😣

Back again :)

Life got busy! I've been working on writing a new one recently.

Hey, I don't usually comment on videos much but I have to say that this video is one of my favorites, as a recent Computer Science graduate and Software Engineer. Glad to hear you're making another! :)

Please do, take your time, not polynomial time please ;) There is some other topics em computer science closer to the subject that if explained using this form of explaining, visual, entertaining and simple can be really helpful and even fun to watch.

Hey, that's awesome to hear! Thanks for all the time you put into these.

Can't wait

Helder Ribeiro Thanks! I've got another one coming for sure.

@@hackerdashery Still Waiting...

@@SK-yo5nl Still waiting! What ever happpened to this guy? Two great videos, then nothing more...

I don't get why he declined the fields medal. Guess he really doesn't care lol

@@iiRenan Maybe? He gave reason that he is not worthy of it. His proofs were based on guidelines set by Hamilton years ago, he just followed the path paved in front of it. Really respect for this guy.

nothing wrong with living with a mother in almost all non-western countries

***** Thanks for the correction! I researched this somewhat casually, and looking deeper it seems my sources were incorrect.

+B. Michael Zimmermann Irrefutable proof that one cannot flim flam the zim zam. Additionally, I, too, subbed.

+hackerdashery I am greek and i dont agree with B. Michael Zimmermann's correction. polynomial in greek does not include the word "nomos", since the word in greek is "polyonimo" ("nomos" cant be changed into "οnimo"). By googling it in greek sources, it turns out to be a half greek half latin word from greek poly=many and latin binomium = binomial (which makes perfect sense) and comes from F. Vieta.

+stkyriakoulisdr I also think Michael is wrong. All the sources I find say that polynomial was formed by analogy from binomial. And binomial was derived from Latin nomen = name. To add one more clarification: the Latin word was binomius, which became binomial in English (the -al ending is for making nouns in English).

+B. Michael Zimmermann 'polynomial' was modeled after 'binomial', coming from Latin 'binomius', or "two-named". source: polynomial and binomial on etymonline.com

@@foobarmaximus3506 NP problem bud

Mutantcy1992 Now you have to solve for P.

Rooket6 P is defined, so problem solved.

Mutantcy1992 I'll give you that one. P = NP CONFIRMED!

Divided by a variable. Error in proof. >|

Yumita kun P is a known set. It can be divided >

..or any engineer

Just gonna throw a random quote that doesn't even complete.

@@snafu2350 3 stand for pi

+David Oliveira On his discussion page, he said that he's been extremely busy.

Also, thank you for providing me with affirmation that math terminology is largely unhelpful. It feels great to know that others agree.