Turing Machines - How Computer Science Was Created By Accident

[@wnh79]

I always feel the sads thinking about how much Turing contributed to humanity and how little humanity gave him in return

[@davidschwimmer8824]

it wasnt "humanity", it was homophobic christians. Lets not paint all of humanity with one brush and hide the christians amongst them.

[@pigeonshak7898]

@dodeca hedron We shouldn't really be blaming any religion based on what happened to Alan Turing. It's more towards society. After all, even in the Islamic society, we are prohibited from being homosexual but we are never taught to put hate on those who commit it. Think of it like the act of premarital sex. Some may think it is a sin but some say it's their right to obtain abstinence or not. It's a matter of our own choice for whether we can accept the person regardless of their sins. We are against the act, not the person who did it. Let's just be grateful for what Turing has done for our generation. (◍•ᴗ•◍)✧*。

[@cronchcrunch]

@dodeca hedron Christianity did not birth science. Up until quite recently in our history, the church had actively suppressed any scientific advancements which went against their false doctrine. While the modern church does a lot of good, it was not always this way. And Christianity didn't do anything on anyone's behalf lmao, everything the church did was to increase their own power and wealth, just like every other empire throughout history. So while I agree that they shouldn't be completely demonized, they should not be praised either. Also, Christianity did not start or even popularise the idea of looking of the poor and orphaned. That and most of what you wrote is false, you shouldn't spew unfounded statements just because you read it somewhere. Comparing science to religion makes no sense, since the one is a collection of stories and rules someone wants you to live by, and the other is just a tool.

[@robertaylor9218]

dodeca hedron It was conservative Christian morals that led to Turing’s treatment. Not society as a whole. Islam has its own problems, but when speaking of Turing, Christian morality of “thou shalt not” (as opposed to “does this action cause harm?”)was the cause (because England was legally a Christian nation), not any societal look into resources.

[@PvblivsAelivs]

In fairness to humanity, most of humanity was not even aware of his contributions during his lifetime. Many were secret and the rest were esoteric. It's a little like finding out fifty years later that your crazy uncle really was protecting the planet from devastation. dodeca hedron: Neither christianity nor christians birthed science. Christians may ultimately have figured out that it was to their advantage to _advance_ science. But the Greek philosophers were engaged in science several hundred years before christianity existed.

[@altrag]

Couple of fun facts: - Lambda calculus is still used a _lot._ In fact, its the basis of many modern programming languages. Lambda calculus is more symbolic and tends to be easier for humans to deal with, while Turing machines are well... machines, and easier to implement as hardware. So the equivalence between the two means we can build compilers to translate from (relatively) human-readable languages based on lambda calculus to the list of 1s and 0s that make up Turing's model of computation. - Quantum computers are _not_ more powerful than Turing machines. They can perform certain classes of computations in polynomial time that a classic computer requires exponential time for, but in terms of decideability (which is what math-y types are usually talking about when they say "powerful,") they are exactly equivalent. That's why its possible to build simulators for quantum computers that run on a non-quantum computer. They just can take a really long time to run (depending on what operations you asked your your "quantum" computer to perform.) Of course, quantum computing is still extremely new and its possible someone will invent a (computationally useful) quantum gate that absolutely cannot be simulated on a classic computer no matter how much time you give it. So quantum computing still has the possibility of becoming more powerful than a Turing machine, but under our current formulations it is not.

[@braveecologic2030]

Yes, I think quantum computing adds a "dimension" to conventional 1D (one spatial, plus time) computing that could yield its own new paradigm. Thus new ideas that can be proven that currently cannot be proved nor disproved. The fact that we have an inkling of something about what can happen with quantum computing, is a strong clue there is something in our own cognitive constitution that can be connected with once we open the quantum gate. That is to say, we probably have quantum element to our own mental cognition, biological brains probably have quantum functions... and maybe others we haven't even started on yet. Imagine when we figure out how to compute in 4 spatial dimensions plus time, meaningfully. :)

[@altrag]

@@braveecologic2030 > "conventional 1D computing" I'm not sure what you mean by "1D". Computers are real-world devices that exist in 3 dimensions. Maybe you mean the fact that we tend to lay out memory as a 1D array? In which case, there is nothing fundamental about that. We can (and have) built 2D-addressable memory. Not sure if we've ever tried to build 3D-addressable memory but we could in principle (its mostly a manufacturing issue with trying to build electronic structure "inside" a cube). The only reason we don't do that more often is that its not terribly efficient. Its easy enough to compute ((z*ymax)+y)*xmax+x to convert a 3D coordinate into a 1D array index. Far easier than the engineering involved in making the physical array addressable in higher dimensions. (Also, even though we set it up as 1D-addressable, all modern memory chips are physically constructed as a 2D structure on a wafer.. and the wafer is technically 3D but we try to make them as thin as possible and ignore the 3rd dimension due to the manufacturing difficulties noted above). > compute in 4 spatial dimensions plus time, meaningfully We can, and do, compute things in 3+1 dimensions regularly. Some physicists compute in 10+1 (ie: M-theory) and mathematicians even do computations on infinite-dimensional spaces at times. "Meaningfully" is rather in the eye of the beholder though. The computer (quantum or classical) doesn't really care how many dimensions you're using. Higher dimensional work tends to take longer, but computers don't get tired either. The only concept of "meaningful" that's actually well, meaningful, is how obvious any result is to a human's intuition and sadly, its a biological limitation that prevents us from understanding anything higher than 3+1 dimensions - no amount of computing power will ever abridge that limitation. (Well maybe. I guess if we ever get to a point where we can directly interface computer technology with our own brains to the point that we're literally "thinking" on the computer chip, then perhaps it would be possible for our intuition to be extended beyond what pure biology allows.. but we're talking technology that may not even be possible and certainly not within the next few centuries).

[@braveecologic2030]

@@altrag I'm talking about step by step computing (the process) being 1 dimensional. Conventional spacetime can be considered in 5 dimensions, the additional spatial dimension being akin to inward outward and can be readily visualised by viewing a solid object in the centre of your mind and seeing all it's outer surfaces at once, you can then use time to go inside the object for the reverse perspective. I talked about that in my book, Sustainability and how to be a meaningful species in the Cosmos. Taking those perspectives and developing computational systems, processes and algorithms that leverage that, could be pretty cool.

[@altrag]

@@braveecologic2030 Apologies. I had my suspicions but tried to respond as if you were using any form of logic based in reality. I'll leave it to you to figure out how quantum computers (or anything else) should work in whatever woowoo world you believe you're living in.

[@braveecologic2030]

@@altrag There's not really a need to be insulting. I understand current technology and did you know, throughout history there have been people who use their minds to think of new things. Give it a go. While you're at it, don't insult me.

[@peterpike]

I tried to stay in Hilbert's Hotel, but they kept changing my room.

[@seanleith5312]

I majored Computer Science. This is my professor's first slide in Professional Software Development class: Computer Science is not Science, Software Engineering is not Engineering. He was quick right. Computer Science is mathematics, which has nothing to do with science. All engineers require a engineer license, software engineers don't need one.

[@jamesfunk7614]

A job board run by the state of Minnesota has 23 top level categories. One of them is "Computers and Mathematical". When Edsger W. Dijkstra was filling out paperwork for a marriage license, he was asked for his profession. He wrote down "Computer programmer." A clerk rejected that form, saying there was no such profession. He changed it to "Applied mathematician."

[@pedrolanevert570]

You really do have a skills for teaching. This is by far the best introduction to Turing Machine explanation I have ever seen. I can see you work hard to deliver quality content. Great Job !!

[@upandatom]

Thank you :)

[@tolex3]

I second that!

[@empireofpeaches]

@@tolex3 I third that. Or should I say I 11 that.

[@cometmace]

11:18 "Turing realized that internal state tables could be encoded as 1s and 0s..." That could use some additional exposition.

[@upandatom]

yeah but the vid was already 17 mins

[@cometmace]

@@upandatom Point taken. Maybe in a follow-up video -- the whole "hard wired / single purpose" computer vs. the "programmable / general purpose" computer dichotomy.

[@berserker8884]

@@upandatom tbh I was most excited about tgis part and was disapointed. I hope you make a follow up video because your videos are an amazing balance of cute animations and awesome content

[@monad_tcp]

That's the entire area of Information Theory, its a pretty big sub-area of Computing Science. Now go read Shannon

[@mantisshrimp9637]

Up and Atom you make 15 minutes feel like 6.... wonderful video, by the way.

[@williamivey5296]

For the record, the human "computers" did not just perform rote calculations, they often had math degrees, or at least a talent for math, and part of their job was developing efficient algorithms to produce quick and accurate computations based on the requirements and formulas presented to them by engineers and scientists. (These algorithms they developed are why many of them could compute trajectories or orbits in near real time.) Many of the procedures and tricks they developed formed the basis of computer software in later years. (A lot of "computers" ended up programming computers.) "Rise of the Rocket Girls" by Nathalia Holt is a fun read on the computer team at JPL in the 40s to 60s for anyone interested in the subject.

[@equesdeventusoccasus]

Excellent video as always. I always kinda felt that my college could have spent more time on computer history. Oddly enough, when I was going for my degree in Computer Science, Turing barely got a mention, whereas Lovelace and Babbage were covered in great detail. Lady Lovelace was brilliant as she was writing code for a computer that didn't even exist yet. What's more, it was proven that her code worked.

[@vaibhavjadhav1702]

Professor Alan Turing will be remembered forever for his contribution♥️✨

[@tobybartels8426]

15:00 : Quantum computers can't actually compute anything that a Turing machine can't compute; they're important because they can compute some things _faster_ than any device based on classical physics.

[@jackburton8352]

Depends on the number of qbits although exponential quantum computers have only just over taken the classical computer. Also we are yet to design a reliable method for excluding errors. Still a long way off and even longer before you or i are sat in front of one at home which your grandchildren's grandchildren wont be experiencing either.

[@annaclarafenyo8185]

A Quantum Computer can produce an infinite truly random stream of bits. This can't be computedby a classical Turing machine. The model equivalent to a quantum computer is the probabilistic Turing machine, the one with a perfect random number generator. This is significant.

[@kpk331]

@@annaclarafenyo8185 Can you pls. explain? We can understand extremely chaotic systems / events which may look like truly random events. However they are deterministic and mathematically precise and repeatable and not possible to be considered as truly random. Such systems' components should obey rules of Physics. Such things can not be called random in the true sense of the word. I think it is a giant question with implications for many a phenomenon such as consciousness, free will, which leads - mind or matter, is mind an emergent property of matter just as mass and charge etc....

[@annaclarafenyo8185]

@@kpk331 Your chaotic system model isn't classical computation, but deterministic real number systems. This is not a physical model of computation, you have to convert it to a computer program. When you do this, you end up truncating the real numbers. If you have a deterministic system described by a differential equation (even a chaotic one), one which is simulated on a computer, and you start at a computable initial condition, and you evolve for a computable amount of time, you end up at a computable position. A truly random real number, an infinite stream of random 0s and 1s, is uncomputable with probability 1. This is why the model of random numbers different from classical computation.

[@MeiinUK]

@@jackburton8352 : As of now... a quantum "computer" cannot be truly called a "turing complete" machine, since it is relying on probabilities. For it to be completed, then means that, the quantum bits, and the complete remanifestation of molecules can be created at will, by will. IF that happens, then it can be classified as complete. Right now, we cannot regenerate something from nothing. We have not even begin to create complete machines to do that yet. So far, we have generally recreated and used computers to count. That is all that we have achieved. Can you create an apple purely from pure molecules and atoms? The answer is a "no". So no... no quantum machines exist as yet. We merely have "quantum calculators" (this is a different thing). To truly call something a quantum machine, based on Turing's Completeness' Theory. Then it means that we should be able to make something out of its smallest components. e.g. atoms.

[@stephenpuryear]

The birth of Computer Science as it drops to the ground beneath the Turing Machine was for me a real highpoint. Especially the quivering...I would also like to suggest that other disciplines have fundamental disagreements just as challenging as the ones in Math. I continue to really enjoy where your mind is taking us, Jade!

[@rasandberg]

Fabulous! I appreciate how you take the time to insert additional info, like Turing's relationship to Alonzo and the future potential of quantum computing. Keep up the good work!

[@VaibhavChimalgi]

I sit back now and imagine how they did find all this hard but profound concepts at that period of history and that too so quickly is beyond me. Truly marvellous. Because they were ground breaking.

[@theosib]

I have a PhD in computer engineering, and I approve of this video. 😁 Seriously, Jade did an amazing job.

[@sammyfromsydney]

I have a lowly Bachelor of Science in Comp Sci but also approve.

[@carlg5086]

I have a phD in spotting bullshit. Seriously... shut up.👍🏻

[@robertaylor9218]

Carl G can you provide a link to your graduating thesis?

[@Farreach]

but what was your focus because computer engineering plays better with electrical engineering far more than it does with Computer Science.. I am about to graduate with my B.S. in Computer Science

[@IBITZEE]

?are you sure your PhD is in computer engineering??

[@jindagi_ka_safar]

A great video which is very helpful in understanding the subject "Theory of Computation' , the birth of computers and 'Computer Science' on the whole, . Perhaps this is the best video I have come across on KZbin. Thanks.

[@TheHandOfFear]

Jade, your animations never fail to make me keel over with laughter. Learning something is just an added bonus. Keep up the great work!

[@psilocypher]

I think it’s the other way around..

[@FelicianaDelacruz]

The 2 most influential people of the computer age were Alan Turing and Tommy Flowers. We owe them both so much for their contributions to our current day technology. Thanks for posing such an interesting video.

[@abnereliberganzahernandez6337]

Von neuman

[@heyk-lee]

I surprisingly never knew about Turing machines before. I really love your animations, and they're great ways to teach visually.

[@gabrielr.7423]

This puts me into contemplative mode... Just pondering the beauty of those ideas, ideas are more beautiful than their realizations to me. And Computer Science is a beautiful idea.

[@vishmaychauhan2863]

Absolutely amazing work. I imagine how hard you may have worked on these animations which are so informative and funny at the same time. Thank you so much for this.

[@sparky7915]

Now in 2022 I learned of the Google Quantum Computer that physicists used to determine that wormholes can exist in space. I love these videos. I am getting much better educated than I ever could in school. You have a talent for making the complex simple!

[@DMB710]

When a Physics major knows more about Computer Science than someone who has been "studying" it for 5 years. Keep making such great videos Jade!!! Love the way you can explain complex topics in such a eloquent manner.

[@cristinasanchez9029]

Great video. Finally someone in youtube explains Turing machines with grammars and languages

[@element118_5]

8:26 "equal" would be a better word here, "even" may mean divisible by 2.

[@pukkandan]

that is how I interpreted it at first. I was thinking why she was using such a weird example b4 realizing that we r looking for equal 1s and 0s

[@X22GJP]

To be fair, the context makes it clear enough. If somebody said to me they had an even number of black cards and red cards, I would instinctively assume that they had the same number of each, not that they had, say, 8 red cards and 6 black cards.

[@steve1978ger]

@@X22GJP - a few weeks of having to deal with programs for a living and I guarantee you will have lost all appetite for such assumptions ;)

[@columbus8myhw]

@@X22GJP Maybe that's a Commonwealth usage? As an American, I would assume that the number of black cards and the number of red cards were each divisible by two.

[@user-zu1ix3yq2w]

No

[@shexec32]

Actually, the model of computing that caught on was the von Neumann model. The von Neumann architecture, with its concept of a CPU, with registers & ALU, reading its instructions from memory, the same memory where data resides (loaded from I/O ports if necessary), allowing programs to be reprogrammable as easily as writing the result of 2+2, was even easier to understand than the Turing model.

[@bjzaba]

I really liked the explanation that shows how you could get from human computers to the idea of a Turing machine. That really helped - I've not seen it explained that way before and it really helped my understanding! I also found it exciting to learn that the goals of consistency, completeness, and decidability went back to Hilbert - these are things that we're often concerned about in the design of programming languages, and it's fun to learn that it goes back that far! Nice to see you giving a shout out to the lambda calculus at the end - I was hoping you would! It's turned out to be pretty influential now in the field of programming language design these days, and is forming the basis of current efforts to formalise mathematics using computers (using type theory as opposed to set theory). :) :)

[@MeiinUK]

I just realised those Dilbert jokes... lol.. It is a parody of Hilbert. LOL...... God...

[@michaelwoodhams7866]

I've done that course, decades ago. Turing machines - you hear about them once, you remember forever. Lambda calculus: you cram it into your brain, it escapes under high pressure as soon as the final exam is over.

[@hikingpete]

I recommend the tree method of solving recurrence relations as a topic. It shows where the formulas in Big-O notation come from.

[@FrankHarwald]

Good idea! But only works for linear recurrences.

[@mnls0]

4:04 Actually, axiom 4 is that all right angles are equal.

[@thebaccathatchews]

Ain't no party Like an Up & Atom party 'Cause an Up & Atom party Explores the Universe

[@AbhishekSingh-pd5cq]

And i just want to say that Jade is a great teacher, she explains every topic very elegantly.

[@ganeshp0001]

Always watch full promotion at the end...out of sheer respect for the creator and the thought put into not bombarding with promotion even before the video. Great content..!!

[@user-or7ji5hv8y]

You are like the teacher that every person wish they had when they were students. Clear with context.

[@braindeadbzh]

I love the fact that, contrary to many youtubers, you seem to film each of your video in a completely random location.

[@martiddy]

Seems like you haven't watched Tom Scott videos then

[@X22GJP]

Hardly random, just different

[@braindeadbzh]

@@martiddy With Tom Scott the place is usually related to the story.

[@braindeadbzh]

@@X22GJP It is random in the sens that she is talking about Turing Machines from a shed or a garage with an electrical box as a background.

[@martinze11]

Thanks, Jade. It gets even more interesting when I realize that I am watching this video using a Turing machine. And that it was made using a series of Turing machines. And also presented using Turing machines.

[@ericgoldstein4734]

Hi, I really enjoyed your video. You might be interested to know that in the 1990s, Hava Siegelmann proved mathematically that there is a range of computation from Turing and one end to the most powerful form, which she called Super-Turing computation. She published a really interesting book in 1998 on the subject, “Neural Networks and Analog Computation: Beyond the Turing Limit. Siegelmann is a really brilliant mathematician and computer scientist. While “Hypercomputation” is essentially a vague group of conjectures by philosophers, Super-Turing computation is a mathematical fact and is currently the basis for a new generation of computation being spearheaded by DARPA (the government research agency). Siegelmann, in fact, is the head of the L2M (Lifelong Learning Machine) program there. Her project has taken the first steps toward computational systems that alter their programs in real time based on input from the environment. Her book is an excellent place to start. You might want to do a video on Siegelmann and the L2M program.

[@annaclarafenyo8185]

Her work is incorrect. It is based on the false idea that atomic systems like in the brain can do "analog computation". They can't, because of the Landauer bound. To work with a bit of data at temperature, to keep it from thermalizing, you need a certain amount of energy, roughly kT log 2 per bit, where k is Boltzmann's constant. There cannot be analog computations in brains, as the real valued quantities in brains can only be read out to finite precision by the biological mechanism, and the rest of the precision is lost to thermal and quantum jitter.

[@Trouble1354]

I am not that familiar with Siegelmann's work, but as a former mad scientist at both NASA and DARPA, I do know that Turing machines can simulate Neural Networks (been there done that) AND that Neural Networks can simulate Turing Machines (most obviously in Turing's head, but I think it's been mathematically proven, at least for integer weights). The big question is whether it is a 1-1 correspondence? I suspect that being able to solve the generalized Halting Problem requires something more powerful than a Turning Machine. However, SonarQube today can solve the Halting Problem on your laptop for many instances of Java code. Can it's abstraction model be extended to "understand" code samples well enough to solve *ALL* classes? I simply don't know. I don't even know how many possible classes exist. I do know that I can't run them all, and my day job does not pay me do this kind of abstraction. I suspect and fear that it's turtles all the way down-i.e. just as SonarQube can solve the Halting Problem for some classes of code samples, adding another layer of indirection may solve more classes of code samples, but others will remain no matter how many times you abstract the relevant features of the abstracted code. The question I would have (especially for Siegelmann) is what additional abilities emerge in Neural Networks when weights are not just integers, but Rational numbers? Or Real, or Transcendental numbers? The number of states is obviously going to get ridiculously larger, but so what? After all, math allows us to work with big numbers fairly easily. Ignoring efficiencies, is there anything that Neural Networks (like our brains) can do that Turing machines can't? In a finite universe, in which efficiencies do matter, I suspect so. However, our brains are only made of quanticized atoms, so why can't machines (in the worst case), just simulate them?

[@brianmontgomery6184]

Excellent break down of the issue! I had an undergrad professor that was a student of Church's, but had no idea that he was Turing's advisor as well. You've taught this philosophy PhD something new.

[@mheermance]

Not a comment, just bragging. I am the owner of the world's only stuffed toy Turing machine! My daughter made for me as a Father's Day present about a decade ago.

[@NoahSpurrier]

Video or it didn’t happen!

[@mheermance]

@@NoahSpurrier LOL, I've been meaning to put a video of it on my channel for close to a decade. But I've been kinda lazy about it.

[@SISSYPUSS]

@@mheermance Can you do it now? It's Saturday!!! 👸

[@mheermance]

@@SISSYPUSS OK, here you go kzbin.info/www/bejne/kJrKgmSfaLurj5I

[@mheermance]

@@NoahSpurrier kzbin.info/www/bejne/kJrKgmSfaLurj5I

[@MysuruBharath]

The is amazing, Jade has explained the Turing machines is such a succinct manner.

[@Uncle-Mike]

If Alan Turing could visit us today, he'd be amazed beyond belief that computers have become chess masters - and maybe a little sad that so few people play chess, even against a computer. Awesome video as usual! You make everyone want to learn.

[@twitertaker]

Hardware wise every computer can be described by the Von Neumann architecture, software wise everything a computer does cna be described by a touring machine. The simplicity of these models (which open up an endless world of uses) is beautiful.

[@nehamotwani6477]

Computer science is quite new to me and i am glad you decided to explore this more from now on. This story was great! Probably i enjoyed watching this video the most😊 Feeling excited for upcoming videos✌️

[@upandatom]

thanks!

[@americanexploring7440]

Should've mentioned Kurt Gödel. It was Kurt who showed math is broken through his incompleteness theorems.

[@meswag1233]

Me: reads title Also me: now I am not sad about realizing I am a mistake

[@baka120y4]

Really nice vid. Love the location and the way you filmed it. Tom Groenestyn's animations are just amazing! Everything is so well timed and spot on. The dialog is soooo interesting! You guys produce exactly the kind of stuff that gets me thinking and improves my knowledge and makes me want to learn more. Thank you, thank you :)

[@williams-g4846]

Me: Watches a bunch of videos about the Turing Test. 10 mins later: This video comes out Me: :o Jade is stalking me

[@anujarora0]

It's called frequency illusion also known as Baader-Meinhof phenomenon if you are interested here's the video link www.google.co.in/url?sa=t&source=web&rct=j&url=m.youtube.com/watch%3Fv%3DGesduY4Fizg&ved=2ahUKEwimnOOHj7jnAhVWQH0KHelrCMcQt9IBMBJ6BAgKEDg&usg=AOvVaw0Yzq3UUbqRAj1sdFjZv1Cm

[@Fudmottin]

Relax. The presenter is a computer program. Just like KZbin and Google. And, of course, this commenter.

[@AgentOccam]

From about 0:51 - God I love that music! It''s like a warm "Everything will be explained" hug, in sound somehow.

[@jesusfernandoliraperez7210]

I was waiting Gödel when you mentioned "formal system" :)

[@upandatom]

he's coming. he gets his own video :)

[@alvaros.]

Me too :)

[@RobertWF42]

Yes Godel showed there were problems with a consistent math proving it's own consistency & being complete.

[@pepelemoko01]

@@upandatom Thank God.

[@gerritgovaerts8443]

@@upandatom I actually fail to see what Turing proved (you cannot write a program that can predict for every other program whether it will ever stop) that was not proved already by Godel's incompleteness theorem . For me this just another way of stating Godel's theorem

[@jancsi-vera]

The FSM example provides a very concise insight into the Turing machine - this is brilliant 🎉

[@nokanol45]

I would like to see a video which goes more in depth about formal systems, and the subsequent proof that a sufficiently powerful one is necessary incomplete by nature by Godel. I think it is an interesting alternative perspective of how to answer Hilbert's questions about mathematics.

[@rayderrich]

I often use a Turing Machine based module in my Eurorack synthesizer case, and now I finally learned the reasoning behind this, so thanks.

[@laurilehtiaho9618]

One of the probably nerdiest thing I have done, I once spent an inordinate time with pen and paper programming Turing machines doing different operations.

[@Trouble1354]

Pen? I hope it had erasable ink! (otherwise it would have been a lousy Turing machine).

[@jarnoldp]

I know this is random. I have a MS in physics with 8-10 years of teaching. You are very good at explaining complex concepts and breaking them down. I would love to know how you make these videos. Finally, you are very sweet, and you look lovely in blue. It goes well with your eyes and hair. :)

[@dudeabideth4428]

Computer science is about computers as much as astronomy is about telescopes.

[@johnvonhorn2942]

If Microsoft implemented a Turing Machine they'd load the program into high memory and only allow a finite space for the data and Steve Balmer would come out on stage shouting at how lucky we were to have 640 kb and what a great feature this was.

[@vixi2819]

Amazing! You're the best UwU And you're animations are also the best!!

[@stephenhanna1436]

You are the best math/science teacher on the internet! Your explanations are always understandable, well-motivated, and (drum roll, please) accurate! Keep up the good work!

[@Reliquancy]

I’d like to see the state transition graph for calculating square roots... I’ve never seen anything but really really simple algorithms in Turing machine form.

[@pgoeds7420]

Do you mean to limited precision (square roots of primes being irrational)?

[@Reliquancy]

pgo eds I don’t even know what’s involved in representing a decimal point on a Turing tape, but I imagine you represent the number you want the root of on the tape and the algorithm replaces it with the root going deeper into the decimal places getting more precise and you just stop it at some point?

[@pgoeds7420]

@@Reliquancy How about this for representation? kzbin.info/www/bejne/hou1emR_m7inj5I

[@photinodecay]

You don't want to use a turing machine to do any kind of serious programming

[@Reliquancy]

Rahul Jain I know, just wondering what a nontrivial program would even look like. That that’s so hard to do is the reason we don’t use them I guess.

[@klam77]

The concept of "Effective" procedure touches on your "P=NP" video; related themes.

[@SophsNotes]

I don't know about you, but I'm feeling 22... Gonna go create computer science

[@vonkaiser6817]

Might be a bit harder than that, but you do you

[@santoshparker8681]

Mathematicians gave birth to entire computer science. (Alan turning, Ada Lovelace, charles baggage, John von Neumann and many more )

[@hansisbrucker813]

From the movie "Hidden Figures" I didn't get the impression that those human computers were just mindlessly performing tasks. They had quite some input in solving the problems iirc.

[@ssarkar2996]

I agree. This meme of "mindlessly performing tasks" has been pushed probably because they were women.

[@calinnilie]

CompSci grad here, I think this video would've been incredibly useful in my 1st year of Uni. Great work!

[@nehamotwani6477]

3:20 🤣🤣🤣 Hilbert made me laugh crazily

[@jimbert50]

That was Dilbert. 🤣🤣🤣

[@nehamotwani6477]

@@jimbert50 😂😂

[@vonkaiser6817]

He still haunts me at night

[@vonkaiser6817]

I don’t want no axiomatisation, get your witchcraft out of here.

[@sporg]

Hi -- great video: always nice to see Turing being recognised for his seminal work. Won't your 'even number' TM get stuck (looping forever in state B or C) if there's an uneven pairing of '0's and '1's? If you add a path from B or C to a 'Reject' state, which is taken when the reader encounters a space (i.e. ran off the right end of the tape), then it'll stop when it runs out of one or the other symbol... Of course, getting stuck forever is an interesting comment on completion: the TM in the video never tells you that a tape has an uneven number of symbols, because it never stops...

[@malandradispersound]

Came here to comment exactly the same

[@nederlandsefrhd]

I literally just started learning computer science in school yesterday

[@AbhishekSingh-pd5cq]

I admire Alan Turing a lot and i just read a book called The imitation game in which I learned lot about his life, contribution in winning the world war second and many more struggles of the great Alan Turing.

[@jorgerangel2390]

Remarkable how Turing machines are the basis for compilers and parsers.

[@garryslocombe]

That's a fabulous area - parsing and compiling algorithms - for Jade to explore in her computer science videos. LL Parsers for example. They are an incredible insight into equations, but also language.

[@genesanborn2367]

Von Neumann's Universal Constructor in a Cellular Automata was equally impressive, and employed a Universal Turing Machine at it's heart, and was the inspiration for the Von Neumann architecture of computers.

[@UserName-mn5rx]

Great work, but I can't stop looking at the equipment on the wall behind you.

[@billdunsmuir2467]

Jade, your teaching is first class. Very engaging and, of greatest importance, just simply so enjoyable to watch. I hope you continue with this stuff!

[@GarrettPetersen]

If I were going to go back in time and re-start my life at age 18, I probably would study computer science.

[@Heylow1]

Never too late. And hobbies are a thing too. Try Brilliant and maybe look into Scratch coding

[@GarrettPetersen]

@@Heylow1 I code as part of my job now. But I'm impressed at how much faster the comp sci majors were able to start their careers. Plus the theory is interesting.

[@GarrettPetersen]

@jtg42n42q iuq3irqn My PhD in econ is actually very employable.

[@OL9245]

I am amazed by the clarity and conciseness of your video. A true pleasure even for the ones already fluent in this topic.

[@shaileshrana7165]

Bruh moment for Hilbert

[@dgw1970]

I'm very proud to be the first Head of Computer Science at the school where Turing went at school. I always get emotional when I teach Turing machines.

[@junaidesse]

Hippie alert - There is so much beauty about all this. Thanks for making us understand all this in such a simplified manner excitable one!

[@michaelcoll433]

Great video. Some day, I hope that you'll take a look at sewing looms and adding machines. These are mechanical computers at their heart.

[@rkara2]

Computing isn't an accident, it's deliberate. Georg Cantor deliberately tried to get to the bottom of infinities, and it drove him mad. He thought that mathematics or set theory is deterministic. Hilbert didn't like the fact that mathematics couldn't be determined, and he wanted a theory or way to prove that it was. Turing comes along and deliberately shows that mathematics can't be determined, hence circular and circle -free machines. The real discovery that you are not pointing out is that all three men are describing the same thing or phenomena, a constant energy source. Computers only exist because there exists a constant circular state that they are subscribing too. It's not possible for computers to exist if the world wasn't circular or non-determinism to begin with. !DA

[@d3consultancyservice12]

crystal clear, amazing talent for explaining complex science based subjects, you go deeper than most of the others creators

[@manishmayank4199]

*Calculations exist* Programmable computer: I can do this all day

[@theyellowmeteor]

More like: Problem that's impossible to compute: exists Programmable computer: I can do this all day

[@moguldamongrel3054]

3:54 Chess however has a problem that I discovered playing a great old timer in jail against. One of my fav strats was to double or triple stack defenses on pieces I was moving to attack with. No piece ever moved that didn't have backup. I always made sure once the engagement started that one of my pieces won that engagement. However I wouldn't attack, I'd just press. The guy mirrored my strat. All across the board we moved not attacking but reinforcing. Pressuring. Stacking defenses. Eventually though the their was nowhere I could move without attacking. Because of the finite number of moves on a chess board. I was finally forced to attack with a piece that wasn't triple defended and thus would lose that engagement. All across the board exchanges happened. Everything escalated so quickly that pieces where dying left and right. I lost that match because of the finite number of moves that one can make on a chess board. One of the best games I've ever had the privilege to play. Hope the og is doing ok.

[@Antarjyoti-c3i]

Who is here after watching the imitation game movie?

[@Dyslexic-Artist-Theory-on-Time]

Well made video, Turing work on chemical morphogenesis is really interesting also!

[@Adraria8]

Don’t forget my boi Charles Babbage

[@JohanHolmbergMalmo]

Also, Shannon!

[@josh34578]

Bharles Cabbage.

[@cometmace]

And, *exactly* what did Ada Lovelace do.

[@michaelprozonic]

@@cometmace Ada Lovelace is the Goddess of computer programming. Not to be confused with her sister, Linda Lovelace

[@bgg4865]

Or Jacard, who invented the punch card system and had clogs thrown at him for doing it.

[@balthazarbeutelwolf9097]

I see the difference between Turing-machines and lambda-calculus a bit different. TMs are more clearly identifiable as a machine-like model of computation, and following (executing) the instructions is a tad easier that to compute with lambda-calculus terms. However, coding with TMs is a nightmare, as there is no form of abstraction whatsoever; to code with a TM you have to work at a meta-level. The lambda-calculus has abstraction built-in; coding in the raw thing is rather tedious, but it is actually doable.Even for theoretical study the lambda-calculus is used more commonly than TMs.

[@juzoli]

If anyone complaints that abstract mathematical theories are useless in real life, I will just show them this video...

[@upandatom]

exactly!

[@SMA265]

For me, it is 'If A Turing Machine Can't Compute It, It's Not Computable'. Had a lot of fun studying this course as grad student.

[@themandalorian7352]

No one: No one ever: Hilbert: slowing shakingly approaching Kant with cutely angry face xD

[@Macieks300]

10:50 I know it's pedantic but for your solution to work completely you need to draw two additional arrows from the state B and C to the reject state if they encounter a blank.

[@GrowlingM1ke]

True but I think point of the video is to demonstrate the concept as simply as possible.

[@Asaritwo]

Your eyes are sooo Engaging

[@zakuro8532]

her whole expression is very engaging

[@mowbrayfelix2041]

Ok simp

[@AdrianColley]

I thought I already knew this topic well, but this video gave me a new clarity of understanding of it. Great explanation!

[@KcKc-bh6lu]

Would you do the Information Theory by Claud Shannon?

[@upandatom]

I've done a video about that!

[@michaeldougherty3737]

Interesting. I've heard of Turing Machines, but Havn't really heard anyone talk about them before. Thank you.

[@Pongowl]

My brain: Ok let’s procrastinate studying for tomorrow’s math test Also my brain: Ok let’s watch a video about math

[@darylallen2485]

Thanks for making this video. I enjoyed it.

[@NavidIsANoob]

This is the video that made me understand the Turing Machine. Thank you!

[@jeremycastro5401]

*Hmmm...while I don't think primarily in numbers* but, in philosophical terms I found that mathematics has nothing to do with numbers at all. In my research on the etymology of _mathematic_ I came to a beautiful find! It comes from the the Greek _mathematike tekhne_ literally "the art of knowledge, learning" from _mathema_ "that which is learnt"; from _mathenein_ "to learn"; from Proto-Indo European root *mendh-* "to learn". I found similarities in _arithmetic_ from the Greek _arithmetike (tekhne)_ "(the) counting (art). *Therefore mathematics* has more to do with the art of knowing that something is or isn't and less to do with numbers or logic, which, are simply tools to help us make sense of the knowledge entering into our minds. *In conclusion* _mathematics_ is the art of knowledge which seeks to prove what we intuitively know to be true or false.

[@TheLowstef]

I love, love, LOVE history of science. Not just what the discovery is but how it came to be. LOVE it!!!

[@oguz_new]

very clear explanation. i learned how the turing machine works and what is an algoritm

[@literallylegendary]

3:46 Taking the opponent's king is not allowed; instead you must checkmate the king by putting it into a position which the king is in your area of attack such that the opponent can't move to make it so their king is out of the area of attack. Any move which puts your king in an area of danger is not allowed by the rules of the game.

[@dirkhoekstra727]

Very cool, easy-to-understand, informative video presentation! Tibees (Toby Hendy) did a great video on Alan Turing too.