I seriously wish all academic subjects could be presented in such a fun and interesting way!

For those who have expressed an interest, the animators were: Henry Paker, Victoria Kitchingman.

@bluegreenplanet89 Yes, it really is David Mitchell :)

Ideas are powerful things, I have always believed. Reality, due to the diverse nature in which it is perceived and experienced, is mostly an idea: reality results from a certain way of thinking and perceiving the things and events around us. Following this course of thought, if we are to change the ideas that we uphold we would also effectively shift the realities that we experience. This is my one passion: to expand our minds and to tear down the walls of traditional thinking that have chained us. By giving the power of new ideas back to people we can excite change where it is really needed. If you think yourself a philosopher or you want to expand your mind: bring me your thoughts and I will bring you mine. Life is no competition; may we learn from each other.

@StrikaAmaru : Another example used to explain this infinite series is that of two people separated by a distance and having to both move half of the distance between them to meet at the centre. Now if only one of the person is willing to move, each half that he/she moves will decrease the distance but would never make it zero as there can be infinitesimal halves between them.

@Hissanrach The paradox is stating he _can't_ move beyond the tortoise because let's say at a certain point in time when he is behind the tortoise (like right after the start because of the advance he gave it) it would take him a certain amount of time to reach the point where the tortoise was at this moment and so once when he reached this point the tortoise had time to move on it's own, thus repeating this process but never coming to an end, ie. Achilles never moves beyond it.

i love his work on "would i lie to you" and "mock the week"

Quantum Mechanics doesn't say that we can't accurately measure because the measurement disrupts it, it says that measurement is simply not predetermined. Wavefunctions are predetermined, but not measurement.

@ShatterSide It's more of a thought experiment than a practical assessment of the possibility of time travel.

@huswsimonbla Here the best way I can simplify it. As they start Achilles is at point A, and the tortoise is at point B. The time it takes for Achilles to reach B is 1. So when Achilles would have reached point B the tortoise will have moved to B+1. Now Achilles have to move from B to B+1, but the time it take to reach B+1 would allow the tortoise to move to B+1+2 (2 represent the time it takes to travel from B to B+1). As you can see this gap can continue to shrink indefinitely.

The explanation for the twin paradox only covers the premise of the paradox. The paradox itself is that from the moving twin's perspective, his twin, as well as his planet, flew away from him and came back (because all motion is relative). The question this poses is why the twin in the ship is the one who ages slower. I don't fully understand the resolution, although it has something to do with acceleration.

achilles & the tortoise is a easy one - when the tortoise moved the achilles have to cover the distance tortoise maked but the speed of the tortoise and chilles doesnt change so while the tortoise is covering distance achilles will cover the distance tortoise maked and the distance making

In response to the Grandfather Paradox, it can be entirely disproved as a paradox if you take into account that time is just a dimension, like forwards, left, and up. Altering one part of the dimensions doesn't change another part along the same axes. Thus, killing your grandfather in the past would have zero effect at all, except if someone else went back in time to that moment, the grandfather would be dead. Of course, assuming you CAN time travel and that time works like a spacial dimension.

Just to clarify why the twin paradox is a paradox, from Bert's perspective his brother's time was slowed and so Al should be younger. This is resolved because while both of them see the other one moving, only Bert has experienced acceleration, which is where all the bookkeeping of relativity catches up with them. This is the issue with GPS, the satellites in orbit experience less acceleration from the Earth's gravity than we do on the ground, and as a result their clocks run faster.

@Pretsal The first one is a bit antiquated, because it was theorized back when we had very little understanding of infinity.

The Chinese Room video, is very witty and sarcastic!

i've known of the schrodinger's cat theory for years but I never realised that it was based on the fact the particle's state decides on whether the cat is alive or dead. good stuff.

@RedDaVincy to your comment regarding 4: I don't thing that's correct. AFAIK, the concept of multiple infinities is generally only used when referring to the cardinality of sets because in the case of sequence this won't help you solve certain other and maybe more extreme "anomalies" (like where "approximating" by cutting-off at terms next to each other can yield totally different results).

I love this. This is amazing. Great work. :)

Interestingly enough, 1/2 + 1/4 + 1/8 and so on DOES end, despite there being infinitely many items in the addition! In fact, the value of that particular infinite sequence is exactly 1!

@OULEARN you guys are the greatest channel on KZfaq.

the turtle one makes little sense ''would have to first cover the distance to where the turtle began'' well the turtle ''began'' from one spot so if the turtle ''started'' 20 yrds into the race and given Achilles is faster than the turtle, and even if the turtle covered an additional 5yrds in the time it took achilles to cover the 20yrds he will obviously overtake the turtle, i feel this was poorly worded or just silly thinking.

To explain the first theory, Achilles wouldn't be able to catch up with the tortoise as when he reaches the spot here the tortoise had started, the tortoise would have already moved. Then when Achilles reaches the second spot where the tortoise had moved to, he would again have moved. So basically everytime Achilles moves to the new spot the tortoise had reached he would always have moved even if it's the tiniest fraction of length. Remember it's just a theory :)

@pancakewafflebacon agree, the paradox disregards time and distance, and only factors in the space between the two. it makes a point, but with a nonsensical argument.

The OU is conducting a survey investigating how people use our free content. The aim is to provide a better free learning experience for everyone. If you are interested in giving your views please copy and paste this link into your browser - bit.ly /ouytsurvey - (you will need to remove the space before /ouytsurvey in order for the link to work)

This is like college all over again, gives me the chills seriously I miss college that much.

@TeamJulene it wasn't explained here, but it actually is a paradox. If we treated Earth as an intertial frame of reference, the twin in the rocket might be treated as stationary and we could say that earth is moving close to the speed of light, hence the paradox, we wouldn't know which twin should age faster. However, Earth isn't in fact an inertial frame and therefore we know that the guy who stays on earth has proper clock...

Hello. I'll give it a shot. Rooms: 1, 2, 3, . . . n, n+1, n+2, . . . and so on so, there is always a room at the "end" of the sequence. It's kind of like trying to think of the "biggest" number. What's the biggest number you can think of? A billion? 10^87? Graham's number? Whatever number you say, you can always just add one to it. And there's a bigger number. So, if there were a hotel with an infinite number of rooms, there would always be one more room. :-)

4. Infinity is not a number, it is a concept. 6. The only way to observe a particle that small is to hit it with electrons. You can't just take a microscope and look at it. By hitting it with other particles, the unknown changes.

Zeno's paradox is basically built around the mathematical idea that you can divide any length of space an infinite number of times. Essentially, Zeno showed that, taken literally, that principle means we cannot move anywhere, even though such a principle is very important for math and geometry. Both his paradox and Hilbert's hotel shows how the concept of infinity is logically bonkers and hard for us puny humans to understand.

If anyone is interested in theory of mind and artificial intelligence, I'd recommend reading "The Mind's I" by Hofstadter, and Dennett. It's fairly old, but it is a collection of essays, including the Turing test and Chinese Room experiment, both discussed here. With commentary from the book's Authors. Brilliant way to familiarise yourself with the field, without getting bogged down with too much jargon. And real interesting, and thought provoking!

this was amazing! and opened my eyes to a lot of things I don't quite yet understand but would like to learn about. thank you for this!

What's so hard to understand about no. 4? What paradox? Infinite is infinite, it never ends, we all know that, I don't get what's so strange about that. And about the no. 1, it's all fun and games until Achiles is 1 cm from the turtle and he takes a step 1 meter long. Schrodinger's cat: the engine only does one thing or another, depending on the particle's state. The answer: the engine needs to to something when the particle is in the superposition state. I liked the time machine one :)

@595o Yes I understand that, but what I still don't get is that if you actually applied this problem to real life Achillies would just speed past the turtle. The problem assumes that Achillies is forever moving to close the distance between him and the turtle, but for the idea to work he would have to slow down as he reaches the turtle. In reality, he would not, especially if it was a race to a predetermined point. This only makes sense if Achillies was phyiscally unable to reach the turtle.

@PyroGuideToHappiness Never in my life have I read a more awesome sentence. Bravo, sir.

@jmarrvin This is where the whole "Challenging our perception of reality" part of quantum mechanics comes in...

i think with schrodingers cat the geiger counter would just break the poison anyway because there is one raidioactive state present which it detects because it's not a smart enough geiger counter to handle them both

@Tanglephish If you could count to infinity, you would be able to count each of these lists. However, the list of all real numbers or even all real numbers between 0 and 1 is bigger than those, because of Cantor's diagonalization argument, which I won't go into here.

@jimmyt3411 yea, but i guess this is the point it stands to prove. infinity is not a fixed integer and must, in itself include all of the available units to remain a valid expression. as soon as there is the possibility that there are more people to add, they are suddenly already in the hotel!

They're moving at the same time, but the experiment is easier understood what Zeno was thinking the way it is demonstrated in the video.

@timen1986 That's not the way you want to think of it. You have to think of it as 1 is paired with 2 and therefore 2 is paired with 4 and so on. This would make them the same level of infiniti i.e. countably infinite.

Rather than being the 'basis' of GPS, relativistic effects are a small correction necessary to ensure the accuracy of GPS.

Locouk's Padadox: An infinite is such a big number it becomes a paradox in it's own right, but if you put that infinite number in a box.. You know the box will have 4 sides, even though you'll never reach a corner on that box.

Wonderful animation and a delightful educational tool. I hope these fun videos will lead viewers to crack a book or two to learn more about the topics. Also, it would be nice if the Open University adds the name of the animator who created the video.

This was really fun, MOAR MOAR MOAR.

It's interesting to note that when the first GPS satellites were being launched General Relativity was still up in the air, though supported by theory and experiments. The folks programming the satellites had to gamble on whether to correct for it or not.

It's brilliant how the top comments differ so much.

Twin paradox is not a paradox. When rocket-twin turns around to come back, he changes his direction, which means he is accelerating. Non-constant velocity means special relativity does not apply.

Is this voiced by david mitchell?

As far as I know, Turing didn't say that the machine can be said to think if it passes his test or any other test.

@xBreeTannerx Subatomic particles can be in two states at once, Kind of like your computer being on and off at the same time. While this is true at the sub atomic level, it is also true at the human level (i.e. The cat being dead or alive) in the confines of this experiment. The point being that only when an observation is made does the state change from both possible positions and becomes one definite position. (i.e. the computer is on)

Yes, it seems paradoxical, but there are indeed different "sizes" of infinity (And yes, infinity does POSSIBLY exist outside of the mathematical realm). Imagine it like this: Imagine a mathematical set containing all integers (1, 2, 3, 4, 19, -22, 1564, -29552, etc.), and another set containing all real numbers (1, 2, pi, 4/9, 77/4, -1, sqrt(3), etc.). Both sets contain an infinite number of numbers, but the second should be larger than the first.

The thing with the tortoise is that you always look at smalller time spans. that's the whole trick to this.

Once anyone adds infinity to a calculation they have made a mistake. Infinity is a concept, not a number or variable. You cannot use infinity for practical applications.

The first one isn't really a paradox if they are racing over a finite distance. Greek philosophers are not all they are marketed to be!

the grandfather paradox can however be replied to by the simple argument of time being a fixed axis instead

@pancakewafflebacon no it doesn't, even if he is always moving forward its impossible to divide the distance between them past zero. so logically he can never catch up to the tortoise because the distance between them can never reach zero.

Whenever people talk about the twin paradox they never explain WHY is it a paradox. It's a paradox because movement is relative, you could say the earth is moving close to the speed of light compared to the rocket and therefore the person on earth should be the young one. (however thats not how it works just like you can catch up to something who started before you).

If you graphed the position from origin of each on the same axes, then the point where the lines cross... The Y-value would be the "where" and the X-value would be the "when"?

@BinghamVlogs like the Hizenburg Uncertainty principle, the two would try to slow down/speed up to understand the other

@iranakamura This is only possible mathematically. Realistically it is not true - which is why it was stated it is a paradox, and also why the video contained the caption: "NB: Movement is possible".

I love all six of those！！！

The guy who though about the grandfather paradox died when back to the future was created

Its easy to understand, but when you really start to think about them your mind gets blown. :P

@BastardMan91 Peep Show was created/written by Sam Bain and Jesse Armstrong, not David Mitchell or Robert Webb. He did, however, write for The Mitchell And Webb Situation and That Mitchell And Webb Look.

@AgentHD123 They're not riddles, they're paradoxes. You can't solve it. The Achilles and the Tortoise paradox deals with the fact that infinite series can add up to whole numbers. In reality Achilles *would* catch up to the tortoise, but when you look at it as a series of steps, Achilles would just barely never catch up.

@lampofhell By definition, Searle's Chinese room operator has a book of instructions and no semantic relation to the ideograms. What is he to remember? If he remembers "I've seen this sequence of inbound symbols before and produced this sequence of symbols in reply," and concludes "that's a bit fishy," then the operator has added meaning - which is a fail for Searle's hypothesis that the operator has no semantic relation to the stream. Memory is where meaning lies. Searle requires no memory.

Love that a comedian is somehow qualified to comment on physics and mathematics perhaps because he has an interesting, intellectual sounding voice . . .

Yeah, but that's just the problem. Any extra room you can imagine adding on, already has somebody in it. Think of the problem: person 1 moves to room 2, forcing person 2 to move to room 3. This goes on for ever and ever, forcing one person to be out of a room at any given time. The process never ends as there's always somebody without a room. Moving the people to twice their number solves that problem. Nobody moves to a room that's already occupied, so the process has a definite end.

@A55ma57er My point, is that he's not a "jack-off" for saying multiple dimensions don't exist, because there's no evidence for or against it. He didn't even say anything about another dimension, he said something about a parallel universe. Learn the difference. The String theory is also still what it says it is, a theory. While it seems plausible, it still isn't a hard fact.

Zuse was the first who build a "Turing Complete Machine" but Turing was the guy who invented the mathematical construct.

@Bubbiea yes, time actually doesn't exist. The idea that you simply age slower because you "go real fast" is beyond preposterous.

@sdifs The problem is that Achilles cannot logically beat the tortoise, but at the same time that tortoise cannot complete the race because in the end hes not moving at all ( and ofc Achilles wont be moving at all either, relative speaking). If you divide their speed an infinite time they will both stand still and no one will complete the race, thus Achilles won't beat the tortoise.

@Hissanrach The paradox assumes that both move at constant speed.

Hey, I'm learning about the Artificial Intelligence in my philosophy class now.

@jmarrvin its a probability. You don't know for sure until you collapse the system ( measure it).

The preeminent goal of philosophy should be that of encompassing a maximum of epistemological concepts through logical deduction with a minimum of hypotheses or axioms. That is, to take all of the philosophical isms out there and create the understanding of them all by the usage of one hypothesis or axiom, don’t you think?

Very interesting....thanks...many are historically philosophical paradoxes.

Wait, in #1, the Tortoise was given a head start. Then it was stated that Achilles had to catch up. By then, the Tortoise had already moved. Then Achilles had to cover that distance. But isn't it weird that that meant that Achilles had to SLOW DOWN for that one and only purpose of covering the distance the tortoise made? He could have easily overtaken if he didn't slow down every time the Tortoise would move.

the difference isnt in the infinity, its in the countable or not countable infinity. with integers you get to count them and they all have an order. real numbers are uncountable you will ever be able to squeeze one extra in. both are still the same infinite.

@bodyheals quite an eloquent refutation you just gave.

The Schrodinger's Cat theory was postulated more as a joke/poking fun at quantum mechanics, yet everyone took it seriously.

These are brilliant thank you!

@RawkBanderz Just appearing in the past would cause an air displacement which would eventually change the weather patterns of the future, meaning thousands of people lived that would have died and visa versa. Why would you have to kill your father when just being there would break the future. Even just breathing would be enough.

1. Well, ok, but say that if the tortise and Achillies were moving towards an established point then this would be invalid. The same goes for it Achillies is allowed to move beyond the tortise, where it seems to be that he is for whatever reason unable to.

@leafblight27 Trolling via semantics? Don't know. The idea isn't that you age slower, it's that from the frame of reference of the sedentary person, they view time moving slower for the person that's moving. The traveller won't notice a difference in regards to his own clock: it will appear to be moving at normal speeds.

6. -Schroedinger's cat: why do only 2 of 3 (stylized) animated electron shells show an orbiting electron?

@Bubbiea going real fast won't slow down the flow of time, now matter how many big words you try to use to explain it.

@Hawkknight88 Have you played the game? It's like standing between two mirrors, but they are portals instead which when you go in one you come out of the other, and they are closing up towards you like a sandwich.

XXX Thought is Precious XXX Thinking in it’s most part is Behavioral Activity. Behavioral Activity can be programmed. Using language as a mind software we permanently are repeating our desired goals through spoken words, just like a mantra. This way we are establishing a specific pattern of information and literally downloading as well as programming the subconscious mind, which in response will trigger the programmed action. Our subconscious mind works like a computer. It turns commands..

@BinghamVlogs Yes. However the means of communicating would be very complex, with the ship moving at speed close to speed of light, you can confirm this by another simple mind experiment. If you went on a 10 year old journey in that space ship and you had the "skype" window open all the time, you would need to see the other end sped up, otherwise when you return, there'd have to be a sudden leap of time and where would that time difference go?

Since there are no comments on the Chinese Room argument, I would like to offer a personal refutation of it. Searle's Chinese Room isn't convincing, because it has no memory: it can't learn, and it can't identify repetitive behavior. This is sufficient for it to fail the Turing test, and means that it is not sufficient to show that Strong AI is impossible.

@maliceit reddit isn't limited to the US. This kind of action has a global impact.

As you zoom closer and closer the the distance between them, you are also showing smaller and smaller bits of time, or 'snapshots' of the race. You will never see the completion of the race, just as you will never see Achilles overtake the tortoise when viewing the race in this manner.

@hla27b yes, it is :)

Main issue with the first is that people and tortoises move at different rates so actually Achilles will overtake

Schrodinger didn't make the cat in the box thought experiment to make sense of nor to explain the quantum superposition theory. He made the thought experiment to make fun of the idea, because he thought it was absolutely ridiculous and made no sense. The point of his experiment was "So the cat would be alive AND dead! Isn't that STUPID!?"

I've learnt more in a 6:41 YT video than I did in school.

@Fuzzy192006 Yes, his voice is perfect for this.

@bloximonkey you would be cut off inbetween dimensions where space and time do not exist; in other words, you will fall into a black hole, meaning you will be crushed by extreme amounts of/ infinite gravity. So don't do it haha