Mony Chesterton discussed on BBC World Service

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Mice people join a gym but on this show I waited to challenge your mind only mony Chesterton and when I say we I mean mainly this panel of highly intelligent experts in the studio with me I'll introduce them in just a moment let's dive into the sort of thing they'll be talking about the biggest question ever coming out from corn Carlos hiker in science I am from god was telling us Maurice from Peru I may have some questions about the infinity is he the number are some feet is bigger than others and why does that minor in reality thank you find call us I just want to mention that as a show that takes on your questions crown science often becomes a dialogue inspiring more questions and Quinn coalesce was one of several listeners he got in touch last year off we made a show about the relationship between maths and reality you can find it in a pot costs back catalog but his reminder of the effect it had on us the time I do everything with you I do ads with people with the city she so the blood if you live that is about to make that was doctor Ellen knocks philosopher of physics at king's college London and I'm very happy to say that she's back with us now ready to blow our minds again welcome Elena thank your cuts Elena off to the side I have to say that loads of listeners certainly want put off in fact they also a whole load more impossible sounding questions about maths physics and reality and also here to help us on to them is doctor Allday Faisal and you're a scientist and engineer who leads the brain and behavior lab at imperial college London he's actually joining us from a studio in Germany hi elderly hello now that you were previously on a crowd science where we were asking about brains and whether they were better than computers we've got a question on brains coming up so we're very pleased to have you on board and last but by no means least we have doctor Katie Stickles here in the studio Casey is a mathematician Royce and lecturer from Manchester welcome Katie hello and we have plenty of coffee and snacks and orange is essential for working on difficult problems on a dreary January often name site let's start with you Katie can you help us with one Kallis's question about infinity just to recap he wanted to know whether infinity is a number if some infinities a bigger than other infinities and whether any of this action is in reality so to go to the first space I think I'm happier with the idea of infinity is a concept from the number yeah it's definitely not a number and I think mathematicians a very cautious not to call it a number mainly because it doesn't behave like one if you take any normal number and add another number to it something happens to it where is if you've got infinity and you whatever this might mean aft one to it you would still have infinity so it kind of doesn't behave the way you'd expect to number two okay so that's nice definitive answer the first part of one Kallis's question streets on to his next question all some infinity is bigger than others yes No there are different types of infinity which is interesting because I guess people quite used to dealing with the one kind of infinity that you can get your head around which is what we call countable infinity so you use the counting numbers starting with one two three going up towards on that goes on forever so there are infinitely many of them but it's accountable infinity because you can put them in order and count them starting from one going up puts and what's interesting is that sought same council infinity for not just all of the numbers one two three four five but even if you just said say for instance the old numbers all the even numbers they're still infinitely many of them and thus also cancel infinity okay so I talked to Elena knocks can I bring you in here it sort of seems like infinity that you get from counting in whole numbers might be bigger than the infinite see that you get if you counted two four six eight so you it's complete understand we might think that but actually the same kind of intimacy accountable infinity is countable infinity this all goes back to this business of infinity not being a number I'm behaving not like numbers as such so maybe to get a handle on what about infinity it's helpful to think about Hilbert's hotel this was a sort of xterra proposed by mathematician and what he thought is that suppose you have an infinite hotel with an infinite number of rooms and money much near the receptionist and catches up okay this is five star infinite hotel right you're gonna do your best okay we don't tell it's full useful okay anybody not rooms okay can you accommodate unicast will not because I'm full but what if you take every single gas and you bump them up from seven guess among a server number two I such exception got room one free okay affinity is strange so you don't have to go to the ends to find the lost free room and the reason you spend the first few rooms that that relates this fact that if you had one to infinity to still get sick but now suppose you have an infinite number of guests show up in infinite limousine right right really stretch let my liver and they all want to be accommodated at once yeah what can you do no because I can get my head around one person turning off and I just ask everyone who's in the just move out one written that's fine but an infinity of people turning up is where I probably put the back in ten minutes sign on the reception and given a call I can curl it but if you think about your question about the even number for the space you do the following things guest room one and you put it into into the custom in two and you put her in for and so on and so on all the way up the chain so you even though you have her second frontier guest user it doesn't double the number of cast you still just got the same affinity so if you add infinity to infinity you still get in Finnessey for Katie you were saying there's different kinds of infinity yes of the infinity that you think about with the hotel is accountable infinity because you can count the rooms in the hotel you can count the people getting off the infinite limousine but if you have things that you can't count so you can't put them in order line them up against the numbers one two three four five then you end up with an uncountably infinite set of things and the the classic example of this is what we call the real numbers you imagine a number line so whole numbers within that fractions are in there as well but if you take not just fractions but also numbers that can't be written as a fraction as the things like poly which is number that people will have heard of and and it's a number which I think most people are what has an infinite string of decimals going on after it three point one four one five nine two six five three five eight nine seven nine etcetera right talking I'll check out I know more than that but not infinitely many digits which I guess no one knows and you could do that with any sequence of numbers and if you take all of the numbers that you can make by putting an infinite string of digits after something then you get the real numbers and this is an uncountably infinite sets I guess if you think about it there's no way you could even start to list all those numbers because even if you're starting with zero what's after that is it no point one is at no point no one is at no point not not one like that whatever number you think of the something in between so if you've got accountable infinity and an uncountable infinity let's go back to crime Kallis's question is one bigger than the other yeah I think uncountable infinities definitely bigger than countable infinity Elena and the things front of items yeah I mean his way of thinking about it every single number in the council infinity is there in the uncomfortable infinity uncountable infinity is not the biggest infinity yeah so for the first two infinity I have no recollection of a seminal someone that unit and they were like this council that's on council and then there was like a whole slide what foods just continued with all these different infinities we were like what it's ridiculous at this point I'd like to bring in the last bit of crime Kallis's question why does all of this actually Massa in reality and I'll tell you can I ask you about this because I think you work at the Brandon behavior lab is quite practical it involves engineering in solving real life problems do you need to understand different kinds of infinity for that so for many problems and signs pulls in engineering you need to have some form of mathematics that you can apply in very often if you want to solve mathematical problem used to simplify it in the only way off into simplified is to take things to the limit of infinity very often the mathematical models that underlie technology that we're using today like your mobile phones require us to operate in limits of infinity however I've never encountered to the situation where we need to work with and I'm comfortable infinity but what I find very fascinating is that our brains that are made out of countable many molecules and cells and so forth can even thinking conceive such a thing as I'm comfortable infirmity so well done our brains I'm we don't have an infinite amount of time to discuss infinity so I'm going to leave it that because we need to get on to our next question which is about quantum mechanics and the nature of thought hold on to your hats hikers science my name is we fail Flores from or Louis my question these are my targets affected by quantum uncertainty because there is uncertainty at the atomic level I'm because our brains are made of atoms does this affect the decisions we.

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