Both my co-author Sean and I are worried that we're oversimplifying here -- but then, this series is called The Basics!

@moreroidsmoreboys

4 жыл бұрын

Tom Scott nice video

@jack_2000

4 жыл бұрын

Sometimes you just have to simplify things, or else, you'll spend days talking about subjects

@jonsilvestro3359

4 жыл бұрын

Are you going to talk more about BASIC

@Pablo-zu3qj

4 жыл бұрын

Basic Bro

@Axis-bq7uy

4 жыл бұрын

Keep the complexities basic

When you try to solve a mathematical problem so hard that it turns into a philosophical one.

@millomweb

3 жыл бұрын

Was this a mathematical problem ? Was a mathematical computer the right tool to use in this instance ?

@kennyelkhart

3 жыл бұрын

Mathematical proof is based on philosophy

@christianbarnay2499

3 жыл бұрын

It's to opposite. The original problem is philosophical: "Is there a chance, even the slightest, that maybe some day far in the future we will have answers to all questions in the universe?" Maths and logic brought the definitive answer: "Nope. We can prove that it's impossible with just the subset of mathematical questions. And the full set of all questions is far larger than that."

@jasonwillows5239

3 жыл бұрын

Mathematics is actually a branch of philosophy, so... technically every mathematical problem is philosophical.

@kpp28

3 жыл бұрын

Maths is essentially philosophy

Yes. Try to ask my computer why the internet is down.

@theblackwidower

4 жыл бұрын

Surely it can Google the answer.

@laechrysia

4 жыл бұрын

@@theblackwidower well if you have only one internet access then it's not possiblle to google the answer xD

@TauCu

4 жыл бұрын

@AlphaGT r/whooosh

@anatoliyy.7216

4 жыл бұрын

Or just ask the computer to read a captcha.

@laechrysia

4 жыл бұрын

@@TauCu hey thanks I haven't got this in a while

"Is 'no' the answer to this question?" Computer dies

@anshumanagrawal346

3 жыл бұрын

Meanwhile Human: "Yesn't"

@dandynoble2875

2 жыл бұрын

A computer can be made to recognize that "answer" and "response" aren't synonymous. Hell, any automatic grading system already knows just putting text in the box doesn't mean you put the right answer.

@TangoWolf09

2 жыл бұрын

Probably not

@roninnib6635

2 жыл бұрын

It could just answer it in a different language.

@Underpants678

2 жыл бұрын

Definitely.

Fun Fact: you can build a fully functioning Turing machine within the rules of Magic: The Gathering and given a perfect starting hand you can even set it up legally in a tournament game. There’s even a paper on that, for those that are interested.

@kasoy5239

2 жыл бұрын

Could I have the source?

@Beateau

2 жыл бұрын

@@kasoy5239 I believe Kyle Hill did the video Fabian is referring too.

@lomen6694

2 жыл бұрын

@@Beateau link?

@babywjales

2 жыл бұрын

@@Beateau link?

@TheALPHA1550

2 жыл бұрын

@@Beateau Link?

Socrates: "The next thing Plato says will be false." Plato: "Socrates has spoken truly."

@AliKhan-ns5nr

4 жыл бұрын

prints " thats deep " * infinitely *

@sotypme4813

4 жыл бұрын

This is hurting my brain.

@anim8dideas849

4 жыл бұрын

This doesn't seem paradoxical, please can someone explain? It seem that socrates is just wrong here.... Or plato is wrong theres no loop here

@robogaming3045

4 жыл бұрын

@@anim8dideas849 If socrates is wrong then plato is wrong, which makes socrates correct, etc etc

@kly8105

4 жыл бұрын

When two people lie and a third person doesn't understand complicity and deception, then they are truly more stupid than machines.

Me: “this is really complicated” Tom: “sorry for massively over-simplifying”

@LowBudgetJustinY

4 жыл бұрын

That's literally the best flex for every "nerd" to say lmao

@tylisirn

4 жыл бұрын

The core of the idea is simple, proof by contradiction that you can always create. But to actually *prove* that that proof works requires a college computer science course. Hence massive oversimplification. The main takeaway is that a "universal computer" *isn't.* Some things are inherently non-computable. Theory of Computation is then the branch of computer science that tries to figure out what those things are and aren't, among other things.

@Guztav1337

4 жыл бұрын

It is massively over-simplifying. There is a reason why there are half-a-semester course on just this particular subject. If you don't want simplify / to gloss over the details, and actually fully understand the details. Then it takes a very long time to explain.

@LowBudgetJustinY

4 жыл бұрын

@@tylisirn No offense but my brain had a seizure reading this im so sorry for my dumbass not understanding..

@waynedas873

4 жыл бұрын

@@LowBudgetJustinY Computer compute many computations but not all. Smart people compute what computations computers cannot compute.

David Hilbert: "I look very smart and trustworthy. Therefore I will wear this hat to dispel that image."

@abhishek2275

3 жыл бұрын

Was looking for this comment.

@TheAlps36

2 жыл бұрын

I think the hat makes him stand out amongst other mathematicians

@BrBill

2 жыл бұрын

I mean, it makes him quite a bit taller. Probably easy to find in a room.

@kristapsvecvagars5049

2 жыл бұрын

True. The above statement is false.

@BrBill

2 жыл бұрын

We need some symbolic notation to be sure

People don't realize the mindblowing genius that was Alan Turing. Not only did he invent the modern computer in his HEAD. He even went as far to measure its potential when he didn't even know anything about the philosophies of coding, memory management, storage management and general computer science. I think he was a product of an alien species that wanted to push is into the next age.

@ItsGravix

5 ай бұрын

Fr

1:52 That word is pronounced "Entscheidungsproblem" You're welcome.

@dpg2652

3 жыл бұрын

@ilimango and he's being sarcastic x3

@dinodoestuff

3 жыл бұрын

ilimango r/wooooosh

@robotplays346

3 жыл бұрын

Ents-schei-dungs-problems

@sircommentthecommenter4501

3 жыл бұрын

Zaymly woooosh has 4 o’s

@nic12344

3 жыл бұрын

@Zaymly r/foundthemobileuser

+1 for vanishing in a puff of logic...

@Maeveyyx

3 жыл бұрын

Alan Turing was also a vanishing puff

@stuartkent383

3 жыл бұрын

careful where you stick the fish

@renardmigrant

3 жыл бұрын

Yes, I'm tempted to make a rude comment about Alan Turing. Just I don't want to.

@lightlysalted7790

3 жыл бұрын

Babel fish go brrrrrr

@bullshitman155

3 жыл бұрын

@@lightlysalted7790 Don't panic

Will this code halt or loop? Quantum Computer: *"Yes"*

@jamielonsdale3018

3 жыл бұрын

Actually, that is the solution. This problem IS SOLVABLE as of 2020, when a team of 5 compscis solved the halting problem using quantum entanglement.

@MegaAgamon

3 жыл бұрын

@@jamielonsdale3018 nice! Do you have a link to the paper, I would love to read it?

@raygreen2134

3 жыл бұрын

@@jamielonsdale3018 lmao no

@jamielonsdale3018

3 жыл бұрын

@@MegaAgamon I'll have a look when I finish my shift :)

@mullerstephan

3 жыл бұрын

well, actually Quantum Computer: "Yes, No, Yes and No"

"Some nerd sneaks into the shop and sets it into a loop" Hey, that's me!

@netkv

3 жыл бұрын

oh so you did it

@art3mis922

3 жыл бұрын

​@@netkv ¬_¬ maybe. And hi btw, imagine bumping into you in the expanse of KZread

@netkv

2 жыл бұрын

lmao

Tom’s way of speaking is always so engaging. You just feel inclined to listen to him and it’s so easy to follow along. Glad this guy decided to become an educator, it’s always a pleasure!

@mtsg3761

4 жыл бұрын

Imagine having him as like a lecturer or teacher. It'd be great

@xbcvideo9751

4 жыл бұрын

I have a video of him explaining things at my school. (edit) it's the one on my channel

@hizon525

4 жыл бұрын

XBC Video Link? Asking for a friend

@jamiesmith8220

4 жыл бұрын

Well said!

@Petar321_GT

4 жыл бұрын

I agree

"Any program that you write in any programming language can be converted into something you can run on a Turing machine." So... Another thing you can run doom on?

@alfred3496

3 жыл бұрын

Well I wouldn't put it past Bethesda to port Skyrim to a Turing machine.

@bathshebahubber614

3 жыл бұрын

Sent from my Turing machine

@7_7_5

3 жыл бұрын

But can it run crysis?

@jimmydiaz1502

3 жыл бұрын

@@7_7_5 Given enough tape, yes, it can

@Ulrich.Bierwisch

2 жыл бұрын

@@jimmydiaz1502 Can a Turing machine overheat? The answer is no. Can any computer run Crysis without overheating? The answer is also no. Run Crysis on a Turing machine - get another paradox.

Tom Scott and James May are the only two people I know who can make topics that don't particularly interest me sound absolutely fascinating.

@Shakes-Off-Fear

6 ай бұрын

That’s the talent of being a good writer and a good presenter

God, what a focus. Explaining this kind of subject perfectly for 8 minutes straight isn't for everyone

I told my computer to try and imagine Tom Scott had a different colored shirt besides red and it exploded

@flouro4782

4 жыл бұрын

paint bucket in photoshop

@QuarioQuario54321

3 жыл бұрын

How much TNT?

@DearSouls

3 жыл бұрын

lmao

@gurjindersingh3843

3 жыл бұрын

You need to download 256 GB RAM to make it possible

@bobstr6224

3 жыл бұрын

420th like

I envy this guy ability to make all this awesome content in just one take

This video really puts into perspective how much of a massive genius Alan Turing was

6:11 "Vanishes in a puff of logic" is one of the best Hitchhiker's Guide references. Computers are logic machines at their core. It's an important class in Computer Science programs, because underneath at the most base level chips just send electrons through AND, OR, NOR, etc gates incredibly fast. And that same logic can bubble up into even high level languages.

@LightRealms

4 жыл бұрын

haha yes I knew I couldn't be the only one to get that reference!

@mondobe

4 жыл бұрын

Also a NetHack reference.

@txrxw

4 жыл бұрын

42

@timh.6872

4 жыл бұрын

Also important, various other forms of logic will sift down from very high level language theories and inform the nature of types and programs, so logic ends up being in both directions when it comes to computers.

@NetheriteMiner

4 жыл бұрын

So that means redstone is technically a computer, because of all those logic gates.

"Are there problems that computers can't solve?" INSUFFICIENT DATA FOR MEANINGFUL ANSWER

@kada0601

4 жыл бұрын

I came here for this.

@v1298

4 жыл бұрын

In the end, there was nothing. Or was it the beginning?

@adityapathak5761

4 жыл бұрын

Is that a SCP reference?

@BertGrink

4 жыл бұрын

@@adityapathak5761 No, it's a reference to Isaac Asimov's short story "The Last Question"

@Ts6451

4 жыл бұрын

It has always struck me that the problem of The Last Question was improperly translated for the Multivac, Adell and Lupov was, after all, discussing having an eternal source of energy and the possibility of escaping the inevitability of entropy, but what they asked Multivac was how to reverse entropy. Rather than working on some way to win "The Game" the ACs were working on some way to replay the same game. So, humanity in that story is stuck in a time loop, one of many trillions of years, but still, they are doomed to replay this one timeline forever. Though, I suppose that is really the fate of any character in any form of linear literature or story telling...

Even though you’re “oversimplifying” I still have to pay a lot of attention to keep up. The simplification is making the video very accessible to people who cannot code and who doesn’t know much about computers

As someone who has TAed an intro Theory of Computation course several times, this was a really good layman's explanation. Of course one funny thing I like to point out is that for any computer that we can ever possibly hope to build, the halting problem is actually solvable. This is just because unlike a Turing Machine, computers we can actually build don't have infinite memory. They're not Turing Machines, they're finite automata. This means I can look at the "state" of a particular computer executing any program (the contents of its registers, memory, disk, etc) and wait until either the the program halts, or I see the same state appear twice (in which case I know the program will loop) In practice however, this is obviously infeasible. Just considering 8GB RAM for the moment, that's 2^(36) bits so 2^(2^(36)) possible states. Also, interestingly, some low-level languages like C aren't in fact Turing-complete because the C standard defines a finite constant for the width of a pointer in bytes and the number of bits in a byte, which implies that the amount of addressable memory, and hence the number of possible states the program can be in, is finite. This doesn't actually rely on the hardware limitations i mentioned before. Or rather it demonstrates that those limitations are built into the C abstract machine. Another funny consequence of this is that all C programs that halt run in O(1) time. Since they halt, their runtime is bounded by O(2^(2^(CHAR_BIT * sizeof (void*)))) which is a constant (albeit typically a very, very, large one)

@sushant2664

2 жыл бұрын

interesting take on the subject

@ejasmith

2 жыл бұрын

I mean, if talking real world, it would eventually halt given the heat death of the universe (or a power cut) but this doesn't solve the logic question

This actually ended up being an extremely important discovery, as ever since this there have been many other problems that have likewise been proven to be uncomputable, most often by finding a way for "If we CAN compute X, then by doing Y and Z we can then use X to solve the Halting Problem." But as we know that's impossible, then X must ALSO be uncomputable.

@TheAkashicTraveller

4 жыл бұрын

I wonder is that has resulted in people ruling out things that almost solve the halting problem.

@user-vn7ce5ig1z

4 жыл бұрын

It wasn't a discovery; philosophers had already contemplated the "this statement is false" concept long ago; Turing merely framed it in computer terms.

@misterscottintheway

4 жыл бұрын

@@TheAkashicTraveller it is definitionally impossible to solve the halting problem. You can't almost solve something. It's a binary thing: either it's solved or not. An unsolvable problem isn't unsolvable because it's difficult to solve, it's unsolvable because it is a logical impossibility. The problem inherently contradicts itself.

@CousinWuKaLok

4 жыл бұрын

@@user-vn7ce5ig1z Keep in mind though, there are a lot of ways to resolve this "this statement is false" "paradox", but you can't do that for the halting problem

@willowarkan2263

4 жыл бұрын

It reminds me of np problems and how you can convert from one to any others, so that if you show one np is p, then all are.

"It's a paradox, there is no answer!" -A Computer Says To Another Computer In Portal 2

@wingboy0

4 жыл бұрын

@real gamer hmmm... TRUE

@kittyNya38

4 жыл бұрын

Um... I’ll go true. Eh that was easy

@DarkAudit

4 жыл бұрын

Nice try, but my head was built with paradox-absorbing crumple zones.

@aaclovern9804

4 жыл бұрын

I AM NOT A MORON

@nonchip

4 жыл бұрын

@@duncanhw that was a quote ;)

the editing on these videos always amazes me

This feels like Russell's "Set of all sets that don't contain themselves", but on a computer.

@martinsmolik2449

2 жыл бұрын

Yes, exactly. Russell's or Cantor's "diagonal argument" was very likely the inspiration for this proof.

Tom: "The, uh. The... Uh. The. Decision Problem" Me: (laughs in german)

@oswaldtime

3 жыл бұрын

same

@jefferu2577

3 жыл бұрын

Same lul

@richardpureveen6040

3 жыл бұрын

Laughs in Dutch

@xexpaguette

3 жыл бұрын

*laughs in bilingual*

@jonavuka

3 жыл бұрын

germans laugh?

"Vanishes in a puff of logic" The bablefish really was far too convienient

I can simplify the answer even more. Any problem can be solved as long as you can put it into a form the computer can parse. On the topic of the example paradox, if the program is capable of causing a paradox, then it _MUST_ loop. If the code does not loop, it cannot recur to create the paradox. That's actually built into the code itself; the code loops as long as it would stop, but it also just stops if it should ever loop, once the code stops, it is no longer running to cause the paradox but it had to loop at least once to reach that point. It's like the +1-1 ad infinium "paradox," the answer could be 1 or 0 depending on whether infinity is odd or even, but 0.5 is also an answer.

Hilbert, Turing and Gödel lived great lives and impacted much of maths. I recently read a book called The music of the Primes by Marcus de Sautoy with chapters on them. Definitely worth a read.

"And that boss, is why I didn't bother checking my code with different cases, 'cause what's the point eh ?"

@m4d_al3x

4 жыл бұрын

10/10

@mousermind

4 жыл бұрын

Case in point.

@bayzed

4 жыл бұрын

hahaha best comment!

Me: *German* Tom: *staring at "Entscheidungsproblem"* Me: where's the problem Me: oh

@TheXAlexus

4 жыл бұрын

haha, same :D

@tertrih9078

4 жыл бұрын

Me too :D

@amyj4106

4 жыл бұрын

What's the joke😂

@pixobit5882

4 жыл бұрын

Ich dachte mir exakt das selbe 😂

@eddydrouet1888

4 жыл бұрын

@@amyj4106 that it's a long and complicated word to say for those who don't speak German fluently 😂

ah, i hate when my belongings disappear in a puff of logic

This has been the clearest statement of the P NP and the halting problem I’ve seen. Thank you.

@RoeiCohen

2 жыл бұрын

You mean R and RE

One of my college math professors with "Scott" in his name introduced this problem to me, and another professor with "Sean" in his name taught me about Turing machines. Now I'm seeing a script written by someone "Sean" and some "Scott" talking about those topics on KZread. What a moment.

@ardaozcan98

4 жыл бұрын

You are the lucky pigeonhole in the pigeonhole problems

@DragoniteSpam

4 жыл бұрын

This compliments the concept of the "opposite" machine bizarrely well

2:37 The guy who animated this "computer" deserve respect)

@antonwestergaard5211

4 жыл бұрын

yes indeed

@zaicol850

4 жыл бұрын

Tom has one of the best editors in his crew)

@jamisonbreeding7181

4 жыл бұрын

Looks like it's William Marler

6:07 can someone explain this better to me? If it thinks it will halt, it will loop. But that just means it will loop given this specific input. Of course, if we take all of this again and take it as another input, fair enough it will halt, but I don't see where the self-contradiction comes from, since we never stated that we refeed its output infinitely

@cerealkilla378

2 жыл бұрын

Clearly this went right over your head...

@Yash-ML-Sharma

2 жыл бұрын

@@cerealkilla378 What an explanation!!!

@dan_man3087

2 жыл бұрын

The program goes in infinite loop of halts and loops within itself. That's the contradiction. It's like in time machine paradox: after developing time machine and killing yourself in the past using it - what will happen? If you die - you can't create a time machine. Then you wouldn't travel in the past and won't kill yourself. But that means that you will be alive. Which mean that you will make time machine in the future and will kill yourself. But that means that you are dead and can't make time machine, go back in time and kill yourself. But that means that you are alive... And so on. The Opposite starts a loop similar to this: if the "inserted" Opposite is running - then the "main" Opposite will stop. But since the inserted program have ability to stop, the main Opposite must run forever. It's somewhat resembles the superposition: because the inserted program can do both infinite looping and halting, the main Opposite must looping and halting simultaneously too. Which will break it, until someone deliberately breaks this loop by makig some changes to how both programs should work.

@cerealkilla378

2 жыл бұрын

@@Yash-ML-Sharma I have my moments.

@danya023

Жыл бұрын

One way to think about this is to observe that in order to have a machine that can answer a query, the query must be finite: for example, a program that finds the largest number does not exist, because it would need to be "x = 1 + (1 + (1 + ...))". If a question is impossible, so is the answer. To get OPPOSITE to halt, you ask it "do the opposite of (a program that prints something rude forever)", and to get it to loop forever, you ask it "do the opposite of (a program that prints hello and exits)". But when you feed in its own source code, you are asking it: "do the opposite of (a program that does the opposite of (a program that does the opposite of (...)))", and this query expands infinitely. A machine that answers an infinite query cannot exist, therefore OPPOSITE cannot exist.

One of the best openings I have seen in entire KZread that summarize the rest of the content.

you know tom is working hard when the pinned comment was 4 hours ago instead of 2 weeks to a month

Finally watched a Tom Scott video that isn’t from 3 years ago!

@mikumutual

4 жыл бұрын

This comment's gonna be really funny in 3 years.

@anawesomepet

4 жыл бұрын

Yum.

@NurulArifin49

4 жыл бұрын

I know that feeling

@suryatejasunny

4 жыл бұрын

Ive started from 10yrs ago video, watched a bunch of 3yrs ago video and i m here now and this comment makes sense

@denorod1

4 жыл бұрын

I can totally relate to this

I love the energy you gave to the disclaimer for the computer scientists

"Any program in any programming language can be converted into something that can run on a turing machine" Cyberpunk 77: _Oh, you're approaching me?_

"and then it vanishes in a puff of logic" Is that a Hitchhiker's Guide reference I see?

@Blue-Maned_Hawk

4 жыл бұрын

God says "I shall never prove that I exist, for proof denies faith, and without faith I am nothing." Then, People discover a thing, something which could not have occurred naturally, something which could only be created, but which nobody but God could have created. People show this thing to God and say "But this thing clearly shows you exist. Therefore, you should not exist, for we have found proof of your existence that would deny the faith which keeps you existing. Q.E.D." And God says "Ah, crap. I didn't think of that." and vanishes in a puff of logic. Afterwards, People, feeling full of itself, goes on to prove that white is black and subsequently dies at the next zebra crossing.

@lawrencedoliveiro9104

4 жыл бұрын

As opposed to a toke. Which might be ... I don’t know ... Cheech & Chong maybe ...

@molotera8789

4 жыл бұрын

I mean his team in that BBC program named themselves Hitchhikers bc of that

@mistbornlazarus2611

4 жыл бұрын

@@Blue-Maned_Hawk I kinda have the need to read Hitchhikers Guide now To be fair, it was already on my list.

@jamesthaimassage

4 жыл бұрын

@Blue-Maned Hawk The Babel Fish, a fish that feeds on brainwave patterns and excretes a telepathic matrix that allows you to decode any speech you hear if you stick one in your ear... a naturally occurring creature so mind-bogglingly useful that it was widely considered to be the final proof of the Nonexistence of God. (No doubt you knew that, Blue-Maned Hawk; I just thought I’d elucidate a bit!)

"This statement is false!"; "New mission: refuse this mission!"; "Does a set of all sets contain itself?";

@sphynx7242

4 жыл бұрын

Pinocchio comes from school and explodes

@tonydai782

4 жыл бұрын

NO, the last one is true, the set of all sets, by definition contains itself, the paradox however, is Does the set of all sets that don't contain themselves contained within itself? If it is contained in itself, then by definition it isn't contained within itself, etc.

@Moh4mmed_gh

4 жыл бұрын

@@tonydai782 I was quoting a video game's reference known as Portal. It is always cool to know about these paradoxes. The real question however is, can a computer solve such paradoxes?

@martinshoosterman

4 жыл бұрын

If a set of all sets existed then of course it would contain itself. That isnt really where the issue lies.

@Deguiko

4 жыл бұрын

@@martinshoosterman Yes, in some exotic set theories, there is a set of all sets, and they work just fine.

The editing is top notch in every video.

I have worked on Computers my whole life and I never knew this, thank you.

AC at the end of the Asimov story: “Ah, the one unsolvable problem. How annoying. Lemme jus infer the answer from available data, test it, reject if wrong, loop infinitely till solution reached, Let There Be Light and done” Edit: what the hell happened down there guys

@iaminterface0101

4 жыл бұрын

INSUFFICIENT DATA FOR A MEANINGFUL ANSWER

@Spazmonkey625

4 жыл бұрын

@Xeno Phon Can you explain what an optimal trade distribution and currency system would look like?

@macsnafu

4 жыл бұрын

@Xeno Phon Do you want a society you actually enjoy living in, or do you just want to be a cog in a societal machine? Besides, no computer can decide what you really need or desire. What about new innovations and changes? Do we even *know* what all the resources in the world actually are? We don't really have enough information to even give as input.

@rastkodragic4120

4 жыл бұрын

@Xeno Phon ok commie

@petros_adamopoulos

4 жыл бұрын

@@macsnafu Maybe being a cog in something can make one happier than anything else. You are making assumption after assumption, any of them can be mistakes. But we're just supposed to trust them.

I’ve never seen someone who looks so old yet so young at the same time

@Yaptomizer

4 жыл бұрын

agreeedd!!

@EderSalcedoCastro

4 жыл бұрын

Hahaha

@czechmix221

4 жыл бұрын

Like a very wise teenager

@mitchahbw

3 жыл бұрын

Maybe he's a paradox! 😳

@neomika92

3 жыл бұрын

It seems you do not know the German politician Philipp Amthor :D

thank you for saving me a day before my presentation on undecidable problems!

Would be fun to hear Tom's full lecture series on it

This just reminds me of GLaDOS's failed effort to disable Wheatley by telling him "This sentence is false."

@AidebHerb

2 жыл бұрын

Um… true, I’ll go true. Huh, that was easy.

@guilhermetorresj

2 жыл бұрын

Don't think about it.

@YosheMC

Жыл бұрын

same, i was thinking that too lmao

I'm glad you mentioned that this problem is _mathematically_ impossible to solve. The two other videos I've watched about the halting problem made it sound like it was only impossible for computers specifically, when really it's a logical paradox, impossible for everybody.

@shadowxxe

2 жыл бұрын

exactly a more human friendly representation of this problem would be "if true then false if false then true"

@cmyk8964

10 ай бұрын

Human analysis (and in fact, computer analysis if you know how to write it down in a program) can detect some infinite loops, but it’s not possible to solve whether ANY program halts.

@Ripred0219

3 ай бұрын

I don’t get it. The opposite function loops or halts depending on its argument. If we feed the opposite function to itself without any arguments then isn’t the answer just undefined?

I'd hope that computer scientists would know that you're giving a simple explanation to people that you'd likely confuse or lose going really into depth on coding and internal workings of a computer, This form makes it so much more accessible to people like myself who have an interest or curiosity.

Coming back to this after Vertasiums latest video talking about decidable and undecidable math, this video prepared me for that!

@sinpi314

3 жыл бұрын

Same!

"This sentence is false!" "Umm... true. I'll go true."

@moved8575

3 жыл бұрын

Is the answer to this question no?

@vendybirdsvadl7472

3 жыл бұрын

Its an paradox. THERE IS NO ANSWER!

@Mate_Antal_Zoltan

3 жыл бұрын

too stupid to realise that it's a paradox, or, in other words... blissfully ignorant

@jumbledfox2098

3 жыл бұрын

@@vendybirdsvadl7472 This place is gonna blow up if I don't get back in my body!

@aleph6707

3 жыл бұрын

@@moved8575 In classical bi-state logic it does not have a value, you could say that it isn't actually a proposition which can have a truth value attached to it (again, in bi-state logic)

It's like the "everything I say is false" paradox but for computers

@imveryangryitsnotbutter

4 жыл бұрын

"Ummm... 'true'. I'll go 'true'. Eh, that was easy. I'll be honest, I might've heard that one before, though."

@MatthewBaka

4 жыл бұрын

@@imveryangryitsnotbutter "For God's sake, you're boxes! With legs!"

@louisdurand4567

4 жыл бұрын

I don't think this is a paradox since this statement could be false without contradicting the negation of "everything you say is false" which is "it exists something you say that's true". If the statement is false, maybe another statement you said could be true, who knows. A real paradox should be more specific to the statement like "This sentence is wrong."

@MatthewCampbell765

4 жыл бұрын

For what it's worth, the answer to that paradox is that they're lying to you. Not /everything/ they say is false, just one statement. It should also be noted that most paradoxes are less logical contradictions and more "failures of sentences to form a concept" or failing to take into account a 'third option'. To use an example of the latter: What happens when an unstoppable force meets an immovable object? They pass through eachother. The force does not stop, the object does not move. To use an example of the former: "Can God draw a square circle?" No, because the term 'square circle' doesn't actually mean anything. Similarly, God could not create a tornado over water, because then it'd be a water spout.

"vanishes in a puff of logic" is a phrase I will start using in my own proofs by contradiction

1:28 so Turing's halting problem. Got it. Don't need to watch the rest of the video but I will anyway because I like your explanations 😃

"Are there problems Computers can't solve?" Captcha surveys: _"Now this looks like a job for me"_

@ShivamSan

4 жыл бұрын

𝘴𝘰 𝘦𝘷𝘦𝘳𝘺𝘣𝘰𝘥𝘺 𝘫𝘶𝘴𝘵 𝘧𝘰𝘭𝘭𝘰𝘸 𝘮𝘦

@joeyjojo91

4 жыл бұрын

Fairly sure these are more efficient at filtering out humans than machines *NOW SELECT All SQUARES WITH BUSES. FIFTY TIMES.*

@Bizarre-Daniel

4 жыл бұрын

@@joeyjojo91 This one has 1/8 of a bus showing do i count it? Yes What about this one that's the exact same thing? NO HOW COULD YOU THINK THAT WOULD WORK.

@Daniel_WR_Hart

4 жыл бұрын

When you need to select all squares with cars, but it's a photo of a truck

@georgf9279

4 жыл бұрын

@@Daniel_WR_Hart In this case you shouldn't select it. In this kind of captcha the pictures are not the filter. The filter is how long it takes you and how you move the mouse. The pictures are only there to train image recognition AI. You are stating "This truck is not a car." And after some number of people (50-100?-idk) solved the same picture in the same way, it is fed into the AI as training data.

It's interesting to see that the English word "computer" comes from 'compute' + -'er' (person or thing doing an action). - In Swedish, we have the word "dator", which is a portmanteau of 'data' and 'motor'; an engine that runs through data. Quite clever.

@Yotanido

4 жыл бұрын

In German it's Rechner and basically means calculator, or... well, computer. Although the Anglicism "Computer" is more common nowadays.

@unicornspilot

4 жыл бұрын

In Chinese it literally translates to "electrical brain"

@mikespearwood3914

4 жыл бұрын

@@unicornspilot That makes sense. Although the irony is human and animal brains are electrical too. Not sure about tiny things like bacteria though.

@fieryweasel

4 жыл бұрын

That construct exists in most language. The concept is called (in English, of course) the 'active agent' form of a verb. The do-er.

@DLBBALL

4 жыл бұрын

Mike Spearwood I guess “semiconductor brain” doesn’t have as much of a ring to it?

This went completely above my head

Humans: Computers can't solve paradoxes Computers: Well humans can't too.

They really paid Turing back for his help.

@sword7166

4 жыл бұрын

Oof. Happy pride month :/

@TestarossaF110

4 жыл бұрын

The minds we lost to discrimination of any kind.... sad world.

@irandom419

3 жыл бұрын

No good deed goes unpunished.

@TheKazragore

3 жыл бұрын

@@TestarossaF110 And a lot of it founded in some religious doctrine of one form or another.

@d779

3 жыл бұрын

@@TheKazragore oh no not religion! Imagine blindly accepting a proposition, that certainly doesn't apply to anyone here.

If I remember correctly, it would only pring "SOMETHING RUDE" horizontally like that if you included a semicolon on the print line, otherwise it would just print one per line.

@MarrsAttax

4 жыл бұрын

Spot on. Was that you I saw in Dixons?

@RhysWilliamsEsq

4 жыл бұрын

Came here to make this comment 😄

@richardsmall5514

4 жыл бұрын

Yep, you’re right. 😎

@Paul-sj5db

4 жыл бұрын

Or if you had a trailing comma it would insert a tab afterwards.

@jsrodman

4 жыл бұрын

the better troll is to load up a legitimate pong game or whatever that only every few minutes prints a few pages of obsenities then goes back to the game after clearing the screen.

I'm gonna write this into a riddle for DnD. This might be the nerdiest idea I've ever had.

wow the animations are amazing

Now this is a way of starting off my morning.

@Lattamonsteri

4 жыл бұрын

This video made me kinda sad tho. But it's Monday so what did I suspect xD

@ThaSingularity

4 жыл бұрын

Same

@crystal_royal3405

4 жыл бұрын

In India its night

@poncho4068

4 жыл бұрын

@@crystal_royal3405 no

@hiareeb

4 жыл бұрын

l'll say "What a way to end a Monday"

My computer can’t solve why it sounds like jet engine when I open 2 tabs.

@CharalamposKoundourakis

4 жыл бұрын

How is it starting the calculation? Is it custom software or?

@chrisspellman5952

4 жыл бұрын

It's just having an identity crisis. It think's its a jet not a computer. Put little wings on it, might make it happy.

@Ammarirfanofficial

4 жыл бұрын

Use the new Microsoft edge it really helped me had the same problem Never looked back

@JimboRustles

4 жыл бұрын

clogged fans

@lawrencedoliveiro9104

4 жыл бұрын

Could it be one of those pages has a cryptominer hidden in it?

great explanation of theory of computation

Thank you again Mr.Turing.

QUESTION: Can computers solve the question of where David Hilbert got that sweet hat style?

@hiiamelecktro4985

4 жыл бұрын

Solve? no. Discover? Yes ( ͡° ͜ʖ ͡°)

@Otzkar

4 жыл бұрын

Do you mean brian david Gilbert?

@johnmcdaniels9231

4 жыл бұрын

@@Otzkar BDG is actually the oldest immortal. That's why hes Like That.

@Felixr2

4 жыл бұрын

@@Otzkar Do you mean Hugh Brandity?

"vanishes in a puff of logic" Nice reference.

@Jont828

4 жыл бұрын

What's the reference to?

@TheArchsage74

4 жыл бұрын

@@Jont828 Hitchhiker's Guide to the Galaxy

my simple ass brain: "its opposite day" "that means its not opposite day" "but by not being opposite day the statement 'its opposite day' is in fact true and it is opposite day." "but that means that its not opposite day"

@someoneyoumightknow4375

3 жыл бұрын

boom, 6:32 theres your paradox

I asked Chat GTP wether it could solve the halting problem and it made the decision to tell me: "no".

“Are there problems computers can’t solve?” The Balkans.

@silviapetrova8562

4 жыл бұрын

хехе

@crazyhorse9298

4 жыл бұрын

press 'Launch'

@adamduck7988

4 жыл бұрын

Europe's most dysfunctional family

@shutupMaji

4 жыл бұрын

Just bring a bottle of rakija with you and all the problems are solved

@Lambullghini

4 жыл бұрын

oh wow that's...yea. I feel like an idiot now 🤔

I am a computer science engineer and, yes, *I do appreciate your "deliberate semplification".* May all of us be able to explain things like you are. All with that commendable, pervasive sensation of you having actual cognizance of what you are talking about. Happy recent subscriber of yours.

@jasonreed7522

2 жыл бұрын

As an Electrical Engineer my take on deliberate/oversimplification. If you cannot explain a concept without using math or hyper technical jargon then you don't understand the concept. Basic example, the Fourier Transform, it is defined with integrals and dummy variables and complex numbers and all this junk that takes at about 1.5 years of college to be able to perform. But what does this painful math actually do, it converts songs from audiofiles to sheet music (assume instrumental only). Obviously this isn't all its good for or even exactly what it does, but the full answer takes litteral years to build up to. A more accurate description is that is converts functions from time domain to frequency domain, but those aren't universal concepts like instrumental only music and sheet music. (I assume everyone is forced to do atleast a little bit of music theory in elementary school)

i dont understand most of the things you are saying, but i still enjoy those videos so much i cant stop watching

Great editing btw.

2:36 - Was impressed the pre-recorded movements lined up with the post-production graphics .... twice! Also a nice touch that the buttons 'depressed' simulating being pushed.

@mewheni

4 жыл бұрын

chrisjlocke It's almost as if the post production graphics editor could see the pre-recorded footage and had the ability to line it up with onscreen Tom! The pinnacle of video editing, I say! :D

It's not a Tom Scott video without a pinned comment at least 4 hours ago.

@zoophiliaphobic

4 жыл бұрын

yes

@mytrangly458

4 жыл бұрын

And the red shirt

@TheElvisnator

4 жыл бұрын

And the moving gestures?

@B-RaDD

4 жыл бұрын

I'm new to the Tom Scott page... Is the 4hr pinned comment a regular thing?

@crayfray

4 жыл бұрын

@@B-RaDD It can range from hours to weeks at times.

i love how tom just does away with entscheidungproblem

The editor of this video should get a raise. By that, I'm sure it's Tom himself. Give yourself a raise Tom.

"then it vanishes in a puff of logic" Hitchhiker's Guide reference?

@sanscipher9166

4 жыл бұрын

Tom was a leader of a team Hitchhikers on Only Connect.

@ultrio325

2 жыл бұрын

haven't -heard- read that part yet

"Is the answer to this question no?" Computers: "uuuhhh"

@Nulono

4 жыл бұрын

Computer: "Yesn't."

@OriginalPiMan

4 жыл бұрын

"It is not."

@FrustratedProgrammer

4 жыл бұрын

You: "Is the answer to this question no?" Computer: "Nah m8, of course it isn't"

@pieman12345678987654

4 жыл бұрын

This sentence is... False

@lawrencedoliveiro9104

4 жыл бұрын

Bertrand Russell’s answer was “bottom”. No, that wasn’t a more polite way of saying “bum”, it was the name of the “⊥” symbol for the (non)result of a nonterminating computation.

I watched this video a few times before and was always amazed at the "you just booted straight into a programming enviroment". Why don't we have that anymore? Today I looked at the linux terminal I've been using daily for all these years and realised bash/sh is exactly that

I've been thinking about the problem a lot and I find a great way to simplify it is this: Computers are logic machines and can only take in logic and give out logic. A paradoxical problem is by definition not adherent to logic and therefor can not be computed, because for a problem to be computable it needs a logical answer. The issue with the halting problem is therefor not that computers simply can't solve it, it is that it has no logical solution

"We take its code." The fact that we can do that is very important. It seems obvious talking about programs but this is the hardest step when you try to do this with other things like Gödel did with proofs over natural numbers.

@jpobi9880

4 жыл бұрын

Wouldn't the code for opposite that is fed into the program opposite, require itself another parameter in order to be run/analysed?

@11matt555

4 жыл бұрын

@@jpobi9880 That's where I'm confused as well.

@JohnnyAdroit

4 жыл бұрын

@@jpobi9880 You're right. A slightly less simplified proof uses the hypothetical program HALTS(P, I), which takes a program P and input I as parameters. This program answers True if program P will halt when given input I and False otherwise. Then, you create OPPOSITE(P) which takes a program P as input and runs forever if HALTS(P, P) returns True and halts otherwise. That is, OPPOSITE uses the program HALTS on program P using the same program P as input. Finally, you analyze what happens if you run OPPOSITE(OPPOSITE). This will run forever if HALTS(OPPOSITE, OPPOSITE) answers True. But, wait! HALTS(OPPOSITE, OPPOSITE) answers True only if OPPOSITE(OPPOSITE) halts. So, OPPOSITE(OPPOSITE) will run forever if OPPOSITE(OPPOSITE) halts and vice versa. This contradiction means that the program HALTS(P, I) cannot exist. More accurately, any version of the program HALTS(P, I) that can be written cannot determine the correct answer for all programs, only a subset.

@HenryLahman

4 жыл бұрын

@@jpobi9880 I've thoroughly confused myself: it probably doesn't matter and if we do need to we just pass the simplest code like the assembly `HALT` or the C style `return`

@CollinRapp33

4 жыл бұрын

@@HenryLahman It does matter; refer to JohnnyAdroit's explanation above.

I'm German, so when there was "Entscheidungsproblem" appearing and Tom paused I was like, huh? What's the issue? And then I noticed that it's not English 😂

@julius5632

4 жыл бұрын

Jep

@luka_8

4 жыл бұрын

Same. And then I remember that such long words must look really intimidating to pronounce for someone who doesn't speak German. I'd have loved to see him try tho

@calum5975

4 жыл бұрын

@@luka_8 Break it down, it's actually a very simple word to say. Most long German words are

@luka_8

4 жыл бұрын

@@calum5975 for us germans yes, but I've seen *so* many people have problems with the harder pronunciation of longer German words

@huawafabe

4 жыл бұрын

@@luka_8 Tschechisches Streichholzschächtelchen.

A neat counterexample: Write a simple while loop of searching for zeros of the Riemann zeta function where the break condition is finding a zero which is not on the critical line, thus disproving the Riemann hypothesis. If the program halts we know that Riemann was wrong, and even if it takes billions of years that would still be a mathematical precise result. But if we could simply "tell" or use a "halting machine" to determin wether it will ever halt... then this would classify as proof of teh Riemann hypothesis. You could re-phrase this procedure for basicly every math problem. Computers can find counter examples, but they can (almost) never proof an infinite logical pattern. The only exceptions i know of where computers actually prooved the thing without any human understanding what they did in fulld etail is the proof of the four-colour-map-theorem and Hales proof of the Kepler-conjecture. Both showed results, but you gain no insight on the topic by knowing something is true. You gain insight by understanding why something is true; an insight a computer may never be able to give.

The steps for troubleshooting a specific computer issue typically involve the following: 1. Identify the specific problem - Determine exactly what the issue is that you are experiencing. 2. Break down large problems into smaller ones to make them more manageable. 3. Consider the scope of the problem and who or what is affected. 4. Ask the right questions to quickly discover the root problem. 5. Document the troubleshooting process, including both successful and unsuccessful fixes, for future reference. These steps are part of a structured troubleshooting approach that can help you effectively address and resolve computer problems.

1:55 It's pronounced 'Entscheidungsproblem'

@ooo629ooo

4 жыл бұрын

aw gee thanks for the help

@TheAPlayd

4 жыл бұрын

End-shy-dunk-s-problem

@timothyharris7288

4 жыл бұрын

Thanks I was stuck on that

@lugga9113

4 жыл бұрын

Thanks

@garrybogdanho

4 жыл бұрын

Haha very funny jokez

As a software engineer, I can say that your simplification is reasonably adequate :-). BTW, Kurt Goedel basically arrived at a similar conclusion with its two incompleteness theorems. A brilliant work.

@guilhermetorresj

2 жыл бұрын

Gödel's Incompleteness Theorem also follows this self-referential principle to arrive at paradoxes, but the consequences are even deeper. The fact that it implies that any set of mathematical axioms either produce truths that cannot be proven by those axioms alone, or that they outright contradict themselves, is amazing. Just imagine how many problems we have right now that are worth a million dollar prize, some of them might literally be true, yet have no formal mathematical proof. It makes my head spin.

@efulmer8675

2 жыл бұрын

The big problem that I know of that could be this way is the Riemann Hypothesis. However, if we could prove that the Riemann Hypothesis is unsolvable from the axioms of math, then that means that it is true because if it were false we would have a way of proving it false from the axioms.

@watchm4ker

2 жыл бұрын

And the thing is, the paradox is a deceptively simple "This sentence is a lie." formulation. It almost seems silly that this could tie logic up in knots, but there you have it. The fundamental flaw in formal logic.

@TheBraude

Жыл бұрын

@@efulmer8675 That doesn't mean it's true, it means it can be both.

@efulmer8675

Жыл бұрын

@@TheBraude Numberphile has a video on Godel's Incompleteness Theorem and they mention implication that the implication that the Riemann Hypothesis is true if it cannot be proved true from the axioms.

This video should be played in every lecture of Theory of Computation

2:12 Hilbert’s optimism is engraved in his gravestone: it says “We must know, we will know” in German

"Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic.

@ankitaishwarya5586

4 жыл бұрын

That sounds like something Terry Pratchett would write

@nicholasfinch4087

4 жыл бұрын

I love The Hitchhiker's Guide to the Galaxy

@benfll

4 жыл бұрын

@@ankitaishwarya5586 it's actually from Douglas Adams' The Hitchhiker's Guide to the Galaxy

@durdleduc8520

4 жыл бұрын

ahaha! I get that reference!

@shawn6745

4 жыл бұрын

@@ankitaishwarya5586 Also dry, brtish and satirical like Douglas Adams, just on the fantasy side of things :P

Weirdly enough, though this was only tangentially related, it helped me better understand how Magic the Gathering can be used as a Turing Machine.

@hyperspeed1313

4 жыл бұрын

Do enlighten me

@jonathanw1106

4 жыл бұрын

Because Science already has a video doing exactly that

@birdrocket

4 жыл бұрын

Same with microsoft power point, same with HTML5+CSS3. The important thing to know is that a Turing machine can compute *anything* given enough time. Turing machines (aka computers) are actually quite powerful

@brent_peterson

4 жыл бұрын

Chris Wyllie Did you watch the video?

@shadiester

4 жыл бұрын

@@birdrocket Correction: A turing machine can compute anything that is computable

Love the Hitchhikers reference there

Small technical detail at 1:32: It is possible to determine if a program will loop (do the same thing over and over again) forever. Halting is not solvable because of those programs that keeps on doing new things forever. Small but important detail that can be very hard to put into a 7-8 minute introduction but it is an important detail that I have to mention.

@NStripleseven

10 ай бұрын

Doing a new thing like, say, looping and incrementing a counter every time (yes I know hardware limitations on number size and so on but in theory)

@sung-ryulkim6590

10 ай бұрын

@@NStripleseven That particular thing is actually determinable, even without hardware limitation. I myself have simplified here, because the word "new" has to be more precisely specified. Here, "new" means, even if you write any possible set of determining methods (any program or Turing Machine), there is always something missing, as long as the set is finite.

@NStripleseven

10 ай бұрын

@@sung-ryulkim6590 Yes, clearly, I have no reason to dispute the proof here, that was just an example that could be missed by some naive solution attempt.