Skip to main content

Week 6 [19-25.11.18] The Infinite Hotel Paradox

Have you ever thought about infinity? If so, you were not the only one.

In the 1920s, German mathematician David Hilbert developed a thought experiment called an infinite hotel and you will know more about it from this TED animation.

Please, watch the video and answer my two short questions.



1. What is your opinion about this TED video?
2. Do you know any other thought experiment with infinity?

Comments

Unknown said…
I loved it. I have seen it some time ago and thought it is quite a good explanation of the problem of infinity and how hilarious it it.

I don't. Was never interested in thought experiments in field of mathematics. More in general science. Like guy on bicycle going as fast as speed of light having flash light attached to the front of his bicycle.
I ended up with a bunch of errors in my brain while watching it. After rebooting, I came up with another similar example, unfortunately, I do not remember, how it was called, but it was an experiment proving that Achilles cannot outrun a tortoise. You can google it, if you like such paradoxes.

But, honestly, what is a practical usage of those experiments and concepts?
Unknown said…
Mostly for presenting dilemmas and problems of theories. Like Shrodingers cat.
Also it can give a lot of meme material.
1. What is your opinion about this TED video?
I feel sorry for this poor maid, she will have to take care of all those rooms.

2. Do you know any other thought experiment with infinity?
No, I do not know any associated with the infinity, but I do know one which is quite interesting, it is Schrödinger's cat thought experiment - you should definitely check that one.
Unknown said…
I must admit that this video made my brain.exe stop working for a while when infinite buses showed up. Actually, I think that puzzles like this explain the whole point behind the math pretty straightforward and without any unnecessarily complicated theory. Just plain practical approach (although unrealistic) and simple explanation why it is done this way and why it works.
No, I, unfortunately, don't know any other puzzles surrounding infinity. But I found one very interesting and it's called "Gabriel’s Horn And The Painter’s Paradox" which also presents a very interesting "twist" to the whole solution of the problem.
Lukasz Mroczek said…
This was funny and interesting video. I’ve never heard about this experiment and it’s very smart. What’s more, my brain almost died while watching this but after some time it started to work normally. Some time ago I’ve heard about other experiment with infinity. It was saying that monkey typing on keyboard for infinite period would probably write some of Adam Mickewicz’s poems :D It’s also very interesting and it’s only showing us that our brains are very small and have lot of knowledge to gain.
Nataliya Tkach said…
1. What is your opinion about this TED video?
I like to watch videos on different theories or paradoxes.

2. Do you know any other thought experiment with infinity?
Infinite monkey theorem.
The basic idea is that an infinite number of active forces and infinite time will randomly create everything. The theorem is one of the best ways to demonstrate the nature of infinity.
Unknown said…
Curiosities of math are very clever and can help in our live. It shows math can improve daily problem in work. Math is everywhere and this video establish how we can find solution to reduce time which is the most important. Work smart not hard. I really enjoy this short film because sometimes we have to think that fix or iaise our productivity. I feel sorry for personel in this hotel. My brain doesn’t embrace something to infinity. It’s like never ending story which I don’t like. For my any idea or plan to work in fact should be finished. It’s easy to administer not only company but any data. That’s why I don’t know other experiment with infinity.
Unknown said…
Thank you for destroying my brain. Now I have to fin a new one. I just hope the brain store won't make me choose between infinite amount of brains.
Something similar to the experiment with infinity could be the coastline paradox. You can't define the length of coastline, because of its shape. If you try to use fractals, you will receive an infinite amount of fractured numbers. Thus, the coastline could have an infinite length.
Unknown said…
I have a strong feeling that I’ve seen this video before but I think it was too long ago. At some point of time my brain said "Stop. I won’t perceive any information. I need a time to calm down because it’s overly complicated". I’ve heard about some experiment with Pi number and all its digits. Especially that there is a subsequence of your bank account and password or date of your birth and death and lots of other things. This video was really fascinating and made me realize that math is even more complicated that I used to think.
I've also enjoyed video very much.

I've seen some youtube playlist with some kind of Asian mathematics working in USA, but I can not remember name of it :(
Iman Masjedi said…

The video was an interesting piece of study, and showed a very simple and interesting definition of the concept of infinity in math with hotel examples.

We can explain the same example by train and train passengers. For example, the infinite passenger enters a train that has an infinity chair and there is always an empty seat for new passengers.
But one of the real examples of the infinite concept may be the placement of two mirrors in front of each other and the placement of an object between them and the reflection of the image of the object in two mirrors and the creation of the infinite
images.
Kristina Moroz said…
The video is really interesting and interactive for understanding to imaging such thing like infinity. Math is real help in life just like for this hotel manager with hard working in infinite hotel. The other one example of infinite is with mirrors placed parallel to each other and then we can see the infinite reflection of an image.
Unknown said…
The video broke my brain. I understood only that mathematics is infinite. You can count, divide, reduce any numbers. For example, standing in a traffic jam, I sometimes start looking for roots or subtract numbers in car numbers.
No, I do not know of any such experiments. But if you count infinity, then it is likely that infinity is not the limit;)
Piotr Ciesla said…
1)
What an interesting video. The concept of infinity itself is well explained in this video. The difference between countable infinity and real number infinity is awesome. The problem is put in a humorous way I love it.

2)
The is a great video series by 3 blue 1 brown about Hilbert’s curve I highly recommended to you https://youtu.be/3s7h2MHQtxc.
1. What is your opinion about this TED video?
I really like the video. It was an interesting way of explaining infinity however my brain stoped working for a minute.
2. Do you know any other thought experiment with infinity?
No, I don't know any other examples but I think placing mirrors in front of and behind an object leads to infinity number of reflections and that can be good example of infinity experiment which each of us can experience.
Unknown said…
After Discrete Math it hard to find something that broke my brain, but video was interesting. In my opinion animated explanation it’s the best way of explanation, brain and eyes can easier receive and remember topic, than you will read only text explanation.
One time I saw gif in internet with “infinity” plate of chocolate, but I don’t think that it was experiment but only visual deception.
https://www.youtube.com/watch?v=7Yo6mwSB1As
Unknown said…
I find this video great brain exercise and good refresher of some math theorems. As it has already been mentioned after watching it my brain feels a little bit twisted and I needed some time to get it working normally.
Unfortunately I don’t, but I am definitely going to search Internet for some similar experiments as it really helps to improve abstract thinking skills.
Unknown said…
1. I really enjoyed it.

2. Yes, there was one about infinite number of monkeys randomly typing on an infinite amount of typewriters over an infinite amount of time. The possibility of one of those monkeys writing any given book (for example The Odyssey) equals hundred percent.
Unknown said…
I found this video very interesting - I've heard about Hilbert's Hotel before, but this video was a nice reminder about it. Problems like this are always fun to read or watch about, though wrapping one's head around them can be quite difficult. I know about a few other thought experiments involving infinity, for example the infinite monkey theorem and some of Zeno's paradoxes.
Marcin Mróz said…
The video was definitely fun to watch, it's cool when some seemingly complex math theory could be presented in such accessible way. Albert Einstein once said that if you can't explain something in an easy way, then you don't really understand it and this kind of videos are examples of such easy explanation.
Unfortunately, I don't know any other though experiments about infinity.
Marcin Górski said…
Wow, very interesting video. I like this kind of explanation because it's very friendly and funny way. To be honest, after whole day it's very hard to understand everything what happened in this TED video. I hope that I'm smart enough :P No, I don't know any other experiment associated with infinity. Thanks for your presentation.
Unknown said…
1. I think that I saw this movie already before. I knew this paradox from one of lectures in the PJATK. This movie shows this paradox in interesting way.
2. I'm sorry but I don't know any other thought experiment with infinity but you can check paradoxes connected with infinity here:

https://en.wikipedia.org/wiki/Category:Paradoxes_of_infinity
s18716 said…
There is no limit to the human mind. I have always been amazed how people come to the creation of such theories. Very interesting video. I previously heard about several theories related to infinity, but the “Theory about infinite monkeys” I remember most of all. If you're interested, you can read:
https://en.wikipedia.org/wiki/Infinite_monkey_theorem
Unknown said…
I enjoyed the video, it is great and refreshes some old memories about the math theorems. Also it was cartooned in a way like in a Grand Budapest Hotel movie and since i enjoyed that movie. Although i had to stop for 5 minutes because i felt that my brain has a breakdown for some time.

I didn't see any, but this topic made me feel interested and i will definitely search for some more examples.
Unknown said…
This material was very educating, I always learned something new. I didn’t know that TED does such great animations. I think I will see more of them, in a very simple way, seemingly difficult matters have been presented.
Unfortunately, I don’t know any experiments with infinity, but I would love to know them more.
Quite unusual topic, it seems to me that David Gilbert first of all wanted to say that it is impossible to realize the concept of infinity, and in this impossibility lies all infinity
The assumption of the possibility of bringing the quantity to infinity is purely mathematical, but not actual. In any case, the hotel has a place to be, but what happens when the first endless bus arrives to take visitors to the hotel?
Personally , I don’t know any experiments with infinity, but I would defiantly look for some interesting articles concerning this topic.
Unknown said…
It was quiet fun - I kind enjoyed it, but I'll tell You, that it doesn't bring me any further to understand maths - I feel less smart right know :D
I like this kinds of video, with visual representation of a problems. Animations were good and funny. Unfortunatelly I don't know any other videos about infinity :((
Unknown said…
Thank you for your comment. For me, it was also hard to understand everything in this TED video.
Unknown said…
It is fun to destroy your brain with this kind of calculation.
Infinity numbers are one of the most interesting think to discuss.
Thinking how to solve mathematically this kind of puzzles is fun :)
Unknown said…
As Rafał said, the main purpose for it is to present dilemmas and problems of theories. I have heard about Achilles and tortoise experiment, I think it was presented by Mrs Turska.
Unknown said…
Yeah, I also feel sorry for her.
I've heard about Schrodinger's cat and as far I remember I was reading about it but will definitely read it again.
Unknown said…
It was my pleasure.
That's interesting, I will definitely read about it. Thank you for it.
Unknown said…
Maths is beautiful :D
I find this video interesting and I agree that it's really hard to understand the infinity.
It's hard because no one have experienced it and we can't define the end.
I don't know any other experiments connected with this topic but I'll look for some.
I’ve seen this TED video before and I really like it. It’s a perfect example that complex problems can be explained in an approachable way if done by a qualified team or individual.

I know other thought experiments (e.g. Schrödinger's cat) and other paradoxes about infinity (e.g. infinite stairs), but I don’t know any other thought experiments about infinity, unfortunately.

Popular posts from this blog

Week 12 (12.01-18.01.15) Are you an early bird or a night owl ?

Owls are nocturnal creatures. They’re wide awake at night and they sleep during the day. If this sounds like bliss to you, then, like about 20 percent of the population who find themselves most active at around 9 pm, you may fall into the same category as our feathered friend. Night owls often have difficulty waking up in the morning, and like to be up late at night.  Studies of animal behaviour indicate that being a night owl may actually be built into some people’s genes. This would explain why those late-to-bed, late-to-rise people find it so difficult to change their behaviour. The trouble for night owls is that they just have to be at places such as work and school far too early. This is when the alarm clock becomes the night owl’s most important survival tool. Experts say that one way for a night owl to beat their dependence on their alarm clocks is to sleep with the curtains open. The Theory is that if they do so, the morning sunlight will awaken them gently and natura...

Week 11 [03-09.06.2019] The problem with ecological cars emission in UK

The problem with ecological cars emission in UK Since the adoption of the European Emission Allowance Directive in the European Parliament, all car makers have tried to submit. Since 1992, the Euro I standard has been in force, which limited the emission of carbon monoxide to the atmosphere. The Euro VI standard currently applies, which limits the series of exhaust gases. These include: hydrocarbons, nitrogen and carbon oxides, and dust.   The most significant change was brought by the Euro IV standard. For the first time it introduced the limitation of nitrogen oxides, which are responsible for the harmful compounds of smog.   What is smog?   Smog consists of sulfur oxides, nitrogen and carbon. In addition, solid substances such as suspended dust (PM). Dust suspend in atmospheric aerosols may be in liquid and solid form. These can be particles of sea salt, clouds from the Sahara and artificial compounds made by people. These compounds...

Week 4 [06-12.11.2017] This is what happens when you reply to spam email.

James Veitch is a British comedian. In today’s Ted Talk James with characteristic for himself a sense of humor shows how he deals with spam emails and why responding to junk messages may be sometimes dangerous. Questions: What do you think about James’s  way of dealing with spam? Why are junk messages legal, even though it sometimes may be a fraud? Dou you have a problem with spam? How do you deal with with it?