A you know it's costing a lot of money for this which working megabucks only it's about $150000000.00 for about $36.00 billboards so for Netflix you know they spend $8000000000.00 on content a year $2000000000.00 on marketing So $150000000.00 in the scheme of things is just a fraction of their marketing budget how competitive fees Netflix compared to $1.00 of the streaming companies and is it winning the battle Well Netflix has $125000000.00 streaming customers around the world they certainly have the biggest global audience at this point but Amazon and Hulu are also hot in the rays Disney is putting together its own service so it's going to be a battle going forward and that's why Netflix once any education get including you know buying these billboards to show that it remains a dominant force and just finally it obviously digital billboards that which we'll hear about here right now these are old fashioned billboards they're not digital they're like the ones you know you've seen for decades they could they could transform into digital if they wanted I mean that would certainly be an intriguing idea since Netflix is always ahead on technology but as of right now they're just buying static billboards these rich wind there and that's when we have time for thanks for listening and so next time for me Mike Powell and the rest of the B.B.C.'s business team here in London good buy. You're listening to the b.b.c. World news on to Southern Colorado's n.p.r. Station broadcast sun 91.5 f.m. From our studios in Colorado Springs Colorado you can also hear cares you see in the following communities 88.5 f.m. In West Cliff and Gardner 89 point one f.m. In la Hunty 89.9 f.m. In Lyman 90 point one f.m. In Manitou Springs 91.7 f.m. In Trinidad and Raton New Mexico 94 point one f.m. In Walsenburg and 95.5 f.m. In Lake George and Hartsell 95.7 f.m. In saliva Buna Vista and Villa Grove and 105.7 f.m. In Canyon City for questions or comments please call 719-473-4801 during regular business hours you can always become a member of k. Or c c by going to k. Or c c dot o.-r. G. And making your financial contributions safely online. From the b.b.c. World Service with me Bridget Kendall and coming up after the news in just a few minutes Have you ever thought when numbers come from and how it is we humans use them in our everyday lives perhaps you remember learning to count as a child and the effort it took to grasp the idea of big numbers like a 1000000 Not to mention the mysteries of concepts like 0 and infinity so when did people 1st resort to numbers and what came 1st symbols for numbers or ways of writing them down joining me on the forum today to explore the history of numbers with a distinguished British professor of mathematics a Japanese historian of the history of numbers and an American Anthropological linguist who spent time as a child in a remote part of the Amazon with an indigenous group which does not use numbers higher than 3 so do join us for the forum on numbers coming up after the b.b.c. News. B.b.c. News with Su Montgomery confusion reigns in the highest levels of Poland's judiciary the 65 euro death justice smuggler shot against stores has said shoe define a new law coming into force requiring judges to retire at 65 not 70 she said she would turn up for work and weapons d. As usual and called the changes unconstitutional and a purge of the judiciary the European Commission has initiated legal action against Poland saying the law undermines judicial independence from Warsaw I didn't Easton we have a wide range of international legal and human rights groups say this is an attempt to by the governing party to increase its control over the whole of the judiciary so it can get the decisions it wants and we have the government on the other side saying this is judiciary which has become almost like a closed caste and what's more it hasn't been reformed since 1989 when communism fell now there's a somewhat of a floor to that argument because the average age of a judging in Poland in the moment is 38 years old Malaysia's former prime minister Najib Razak who lost power in May is due to appear in court shortly to be charged with corruption offenses the mini's in news agencies says Mr Nunn jury is expected to face more than 10 counts of committing criminal breach of trust linked to a former subsidiary of the state investment fund one m d b he's denied any wrongdoing. Mexico's president elect Anders Manuel Lopez Obrador says he will invite Pope Francis to help restore peace in the country he was speaking after meeting the outgoing president Enrique Pena Nieto. So from Mexico will grant following more than a decade of drug related violence Mr Lopez Obrador said his administration would be contacting the pontiff as well as religious leaders the un and human rights officials to achieve peace in our nation he also said that he didn't intend to have the same tight security detail of previous presidents he's known for rejecting the close security of high profile politicians and traveling in commercial passenger jets rather than private planes in an example of the differences between the 2 men Mr Lopez Obrador appeared at the National Palace for talks with President Pena Nieto in the same white vote Fagen car he has driven for years of course in Ecuador has ordered the arrest of the former leftwing President Rafael Correa for alleged involvement in the kidnapping of a political opponent in Colombia and 2012 Mr Korea has dismissed the case as persecution a judge in Rio de Janeiro has sentenced Brazil's former richest man to 30 years in jail for corruption the judge said I could Battista had paid $16000000.00 in bribes to a former state governor to secure a look at of contracts b.b.c. News. The Islamic state group says that who Dave Badri a son of its leader Abu Bakar are Baghdadi has been killed during fighting in Syria they are I as a propaganda channel said he was killed during an attack on a thermal power station in the city of Homs but daddy's whereabouts are unknown but the wording of choose the statement seems to imply his still alive. 12 boys and their football coach trapped in a flooded cave in northern Thailand have received their 1st food and medical treatment in 10 days 7 divers including a doctor and a Nurse joined the group inside the cave network the boys and their coach were discovered alive and Monday 9 days after they went missing rescuers are now considering how best to bring the group to safety the authorities say they would take a 0 risk approach. The phone messaging service won't stop her said the dissemination of false messages in social media platforms is a challenge that companies and society should address together here the Indian government did asked what's up to take immediate steps to prevent the circulation of false texts and provocative content false allegations and videos about child abductors and what's up have led to at least 15 people have been lynched across the country India's information technology Ministry said the messaging platform could not evade accountability when its services were abused. In the football World Cup England have gone through to the quarter finals beating Colombia $43.00 and penalties with more details here's Alex Capstick finish one wall and then it went to penalties Jordan Pickford saved one for going to the end it was Eric Dyer who stepped up here to score to to win the game for him and it was a very convincing move it did for the back of the net Q English celebrations they will go on to make Sweden in the quarter final dramatic stuff it wasn't a great game it was a look at times but England have got through by the skin of their teeth b.b.c. News. You know. That's a swear he'll children's song My Way as a cohesive. A short tune that teaches kids to count I can count 123-123-4568 carries Now imagine the world without numbers and think how difficult many Tosk sword be telling people how many siblings you have for instance or counting your wages or fixing a time to meet a friend we take numbers for granted yet not everyone uses them some languages don't have words all symbols for many numbers a tool so today we're going to look at some of the basic questions about when and why humans 1st started counting wedge of the number symbols many of us used today come from and how did concepts like 0 and infinity and much Hello I'm Bridget Kendall Welcome to the forum why experts come together to share that knowledge with us joining me to explore how and why numbers and counting developed through political linguist Caleb Everett from the University of Miami emeritus professor of mathematics at work University here in the u.k. Ian Stewart And joining me here in the studio is writer and historian of mathematics Tama Koch he took our 1st let me ask you will very briefly when did you 1st become fascinated with numbers Ian or probably when I was about 4. Not my mum taught me to read into me to count and I was always kind of interested in. It just over the years it grew by the time I was about 13 I was obsessed with them . What about you and to some extent also when I was about 4 or 5 I saw my parents who were missionaries at the time trying to teach the risk. People can Amazonia number words and number concepts and I saw that these very intelligent people were having difficulty with learning numbers that I had already been learning in school and preschool and so that drew me in and made me fascinated by the concept that some people could not have numbers I could imagine Tomoko what about you which you actually are around the age full I would try to remember the phone number and the time like No 8 does it and you live in does it that with a challenge for me and it looks really nice tellings to take on so I was interested in counting numbers and remembering the numbers Well it's hard to think of getting through even one day of our lives without using numbers why all the same potent Kaleb Well if you think about so much of our lives from how we perceive time to the material world that we construct around us it's all contingent on the invention of this cognitive tool called numbers so if you just think about time hours and seconds and minutes sometimes when talking to undergraduate students they think that something like a 2nd just exists in nature but it's all to mainly seconds and minutes are the by product of a particular number system one that we don't even use anymore really apart from time but that number system still constrains how we think about this very fundamental aspect of our lives in the same is true for other aspects of our lives well counting in numbers do seem to be very much into wind it's quite hard to fathom one without the other so even in the likeness which one do you think came 1st I think counting but it's complicated I mean when kids are counting things early on New You just make straight marks 1234 straight lines they might be when it's 5 you put a slash through that these are cool tally. And it's possible that these go back at least 35000. To. Found in the mountain to Swaziland. And then there's various other bones like Shango bone from 20000 years ago and this has tally marks on it or at least they might be people argue about whether it's some sort of lunar calendar or whether it's some was the multiplication table or whether it's actually just somebody making cuts in the bone so that it'll be easy to grip has a handle for something but clearly if those are telling them what's happening is people are counting just by making 12345 identical marks they're not inventing symbols as such so I think in that sense counting comes 1st and then later on we put names to these things and we even later we put symbols to these things I must pose Tamaqua The difficulty is in knowing how far back early County might go Ok we've got these possible tally marks on these incredibly old bones 35000 years but some mazing the old but how do we know if people were counting before them but not making any marks they could have still been counting right and at the same time in China they used counting rods and rather than they making the mark so they could have been you know many other cultures which wouldn't necessarily some finite right so I think you know it's really a very primitive activities and it could go back I really really far given your research what would you say are the reasons for counting in early parts of human activities why would they want to count so that evidence that Ian just brought out about I had of studying the sky for example so to make a calendar you know they obviously need to remember which positions to stars were and also how long it took to move all together so I think you know the. As nest this city came 1st as well so I think you know in that sense that there are many cultures try 900 stand the world in a different ways and counting that's founding common to help you know them to teach Elyse what they're seeing goodness guy so in you were making the point that tally marks on a bone is very different from our actual numbers these aren't really symbols for numbers yet so so how do you move from marks on a bone to the next step there's a very interesting theory which has a lot of evidence for it which is that in Mesopotamia probably 6 or 7000 years ago they were using little clay tokens so it's rather like the counting sticks so if it was necessary to court how many sheep somebody had to say they had a lot of tokens representing sheep and they would put them all inside a clone and break it so that you could be sure that nobody had interfered and change the numbers and then if they if the tax collector came around he would know how many sheep you had and then if they wanted to actually check that they would break open the play on the open and count the tokens after a while they decided it's an awful fuss and bother breaking open the clone so they started writing symbols on the outside saying what tokens were inside. A little bit light but I thought you know once we've done that we don't actually need the tokens inside you can just have a clay tablet with it and you know go a written number symbol system there's even a theory written symbols for would. Initially from symbols with numbers I think the main motivation for doing it was I was. Looking at things happening up in the school but also much more practical things down on the ground how much land of I go How many sheep I go how much tax and. Caleb is as an anthropological linguist it's not the way you say it to. Some extent but for me as an anthropological linguist and as a cognitive scientist what I'm most interested in is how people think about quantities and and how we developed verbal numbers and they're the best evidence is to go to the languages of the world so there are about 7000 languages in the world most of these have number systems not all and if we look at anxious reconstructed languages like Procyon o. Tibet in the ancestral language of Mandarin or proto Indoeuropean the ancestral language of English and many others we see that these languages had Base 10 number systems long before these developments in Mesopotamia so verbal numbers are quite anxious and we don't know this for sure but I would actually guess that the people who did those markings on the Shango and the Bombo bones and some bones that exist here in North America it's quite possible based on what we know from the psychological evidence today and the experimental evidence that those people had number words before they ever came up with those symbols to Mark on as tallies the so much to bear in mind there is no numbers as well as numbers as symbols but going back to the beginning of symbols of course the number symbols that are in use of much of the world now then going to him a. For another few 1000 years we'll be talking about those later in the program the Hindu Arabic numerals but let's look a bit more at some of the earliest civilizations that we know rate down symbols representing numbers there's the ancient Babylonians Tameka tell us how the system watch so ancient by William used base 60 system and this is still in use because we count the hours on Clark and 60 seconds the seconds and 60 Minutes and also like you know 60 is a very very nice number in a sense because it's a very superior composition and that they can be divided by many different numbers so you can cut a pile of higher c.s.s. Exactly I certainly find it easier to look at an analog clock and literally see the visually cart have think about the numbers I find I'm when I think about numbers I find it quite hard to hold in my head I could never do those phone numbers that you remembered but let's just stop for a moment on base systems we've talked about them a couple of times so the ancient Babylonians used to pay system 60 and in much of the world today we use a base 10 or decimal system Ian can you please explain it in very basic terms what is a base system and exactly how it works Ok let's let's think about a race of aliens who have 7 tentacles instead of our 10 fingers so if they were inventing the number system they might well assign a symbol to one tentacle 2 tentacles 3 tentacles 4 tentacles 56 and then when they go to up to 7 they running out of tentacles what do we do when we get to 10 fingers we write 10110 no unit. And then we go to hundreds tens and units so you can represent numbers as big as you like as combinations of your base the base Times itself the base Times itself Times itself the squares the cubes and so on and so we get off thousands hundreds tens units but anybody says possible and the Maya civilization in Central America used by 20 this is another very sensible system some people suggest well maybe they counted on their toes as well as their fingers one of my colleagues today told me that somewhere in the world some tribe used base 8 and they didn't count on the fingers they counted on the gaps between. So you're going to go with a maybe Caleb can shed some light on you know about that Kayla Yeah so there is there are one or 2 cases potentially of base 8 although some of these aren't always very carefully documented we do know of basic systems being relatively common in New Guinea and there are some other bases in Amazonia that are also esoteric and a bit unusual Why would you come to the basics well so the basic system is interesting but it seems to come from the way that some of these groups store yams which are critical to their trade into their to their culture so they store yams in groups of 6 so this is one of the few cases we see where a base system was invented a number system was invented and it wasn't developed based on human anatomy and after we learned to count and when we launched too hard sums like you do is a 10 base system a useful one. Basically from the point of view of counting and even doing some with the symbols base 10 is a perfectly reasonable one but it doesn't really matter as long as you've got a sensible symbol system to work with but some of the early symbol systems are actually rather awkward for working with you look at Roman numerals they are completely crazy system. You have 111-1111 v. But the Romans didn't do this some on paper the way we did they used their system to record the results they did the numbers using an abacus. And the ancient Greeks had a not much better system they'd use the alphabet. Way for use our alphabet Instead the number system would go a b. C. D. E. F. G. H. And that would be the numbers from one to No and then you got to show you that would be 10 k. Would be 20 l.b. 30 and so on and eventually get to $100.00 so numbers become a series of letters which is perhaps a little bit confusing if we look at other ancient systems there's the ancient Egyptians as they used base 10 system right they had one symbol for one a different symbol for 10 a 3rd symbol for 100 and so on up to a 1000000 symbol for 1000000 is lovely it's a man with these and spread wall 8 so it's always appropriate It's like the fisherman with the one that got away it was really really big so we've been talking about numbers but there are also other concepts which are important in the whole story of numbers and counting some of them a bit mysterious some one of them is the concept of 0 and we mentioned the ancient Mayan but they had quite a sophisticated quite an advanced system of mathematics and that included identifying the concept of 0 right Kaleb Yes they did so it depends on how you define 0 again defining it is the numeral that we write down not the concept of nothingness right so a lot of people get that but in terms of something that we write down as a placeholder that facilitates mathematics Yeah the Maya may have been the 1st or at least in Central America and heritage by the my own but for that 0 that we think of a 0 we see 0 developing in the old world in places like India it seems to have developed about 1500 years ago and then made its way east to places like Cambodia which is probably the place where the 1st stone record of 0 was found and then also moved its way westward eventually getting. Europe told you they also had a concept of 0 in China didn't I write well interesting thing is tast 0 in Chinese culture to 1st import it from their India and text so they translate it adult 0 into Chinese text so that the don't 0 could be found in a think tree and also they had the circles there oh so then that appeared in a set in century text and at the same time because China was using counting rods so they had to squint 0 I was about in the European context how soon will these concepts embrace the him 1st of all it comes through Persia by way of a wonderful man called El quo reason me and I'll quote Reason me did 2 very important things he invented out your prayer in pretty much the current form except without symbols and he wrote a book Introducing the Hindu numbers to the Middle East that was translated into Latin and then brought over into Europe but even the idea of using 10 symbols to represent all the numbers doesn't come to Europe until the 1200s negative numbers come in a little bit later. By about 13 or 1400 all of this stuff is well understood often from the Indian or Middle East and sources. And then with the Italian Renaissance mathematics in Europe starts to take off and do new things and it's not the case am that when these Hindoo are written you must 1st came in some people were a bit suspicious and there was even a law passed in Florence in the 1200s forbidding Bankas from using 0 or any of these new Arab numerals because they were too easy to focus of high Well if you do sums on paper and if the person who is watching you doesn't actually understand how to do it's easy enough to fool that was if you do it with an abacus and everyone can watch the that it'll be moving up and down on the wall you can keep track and feel a little more confident so it wasn't such a stupid thing to do there will also competitions between the people who used an abacus and the people who used symbols on paper see who could get the fastest and I think it was pretty much a dead heat why do you think this system eventually caught on and became so popular around the world for one thing we see that it was already popular long before these events in Europe in terms of the verbal numbers around the world including the verbal numbers that existed in most European languages however I should say that there is some debate amongst cognitive scientists whether or not the decimal system in terms of the written numeral system is really advantages or whether this is just sort of a bit of a historical accident that it's become so popular much as our alphabet has become popular much of the world the European alphabet there's not any evidence linguistically suggesting that that alphabet is somehow better but it's more that it was the alphabet and the number system that became so dominant in. Europe prior to the European expansion around the world now we've been talking about numbers whether as written symbols oras concepts and words but when you come to the broader question of mathematics it was of course the ancient Greeks who pioneered the study of mathematics taking ideas from both about millenniums and Egyptians before them and one of the most famous great mathematicians was Python chorus of Python choruses theorem fame he and his followers are very much into numerology ascribing meanings to each number he has an ancient text describing the python Korean's from a translation of metaphysics a key work by the famous Greek philosopher Aristotle they thought they found in numbers more than in fire earth or water many resemblance is the things which all and become dust such and such an attribute of numbers is just us another is sold online another is opportunity and so on and again they saw in numbers the attributes and ratios of the musical scales a reading from Aristotle's metaphysics written increase about 200 years off to Python died in mobile can you tell us about Python Chris and his followers as a group they had some very interesting ideas didn't they they wouldn't eat beans and they thought of order number says female and even numbers is male I'm quite a lot of other things that we'd find a bit outlandish today yes they were I mean it's hard to disentangle reality from me but some of the stuff the Pi think Koreans did such as the connection of numbers with musical Sco was is actually pretty good they had some seriously interesting ideas which correspond Paley well to the human ear perceives sounds. Some of their other ideas were completely mystical and very very strange They also discovered irrational numbers numbers the fractions the story goes when one of them discovered that the diagonal of a square is not related to the side by an exact fraction they were in a boat crossing the Mediterranean and the others got so annoyed that they picked him up and threw him over. It's probably not true but they would certainly be annoyed because when they talked about everything in the universe being based on numbers they really meant whole numbers and then fractions because that was something you could build out of whole numbers and those seemed all numbers were prank sions Well it turns out the square root of 2 which is the diagonal of the unit square isn't. This musta been rather annoying to discover let's just leap over to the other side of the world have talked a bit about China but trauma care in Japan the study of mathematics interesting new didn't come until much later we're talking about in Europe in the Middle East not to the 1500s Why did that take so long exactly that's a very curious part of my research and Japan had the civil words from 1467 all the way till like the beginning of the 17th century so that education system was not that developed so the one of the oldest textbooks that we can find now in Japan could be the one called The Book of division and then that was published 1622 so at that time because those the words were over in Japan had a new capital built in a door current to talk you know so they killed or there are many people who became jobless so one somewhere more you get decided that he will teach mathematics summerize who are warriors who used to be more years to he established the very 1st mass Academy in kill Oh at the beginning of the 17th century to teach people how to do divisions using a class and also using the chanting methods and so on so for him to teach this technique of division he had to really explain what he meant to introduce presumably from China from Europe both so we opened this book or the Book of division and the preface sais that there were has been no wife at the beginning of the world they picked up a fruit that tasted like peach from a tree and they divided into. 2 parts named their action as a beginning of the operation division so he wrote about this story of the Genesis from the Old Testament and then following up he added that multiplication is like in and in division is like Yan so that if we do both operation that also says the Chinese ancient idea of in and young so that's really perfect thank you all of you so much for the moment to McCurry and Caleb in part 2 we'll look at whether animals can count and examine if infinity is a number and we also look at indigenous groups around the world who still don't use number systems stay with us we'll be back after this news summary. 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Still to come on the forum more on the story of numbers and counting so called a numerical groups of people whose knowledge and comprehension of specific numbers doesn't go beyond the idea of 3 and what about other creatures besides humans come primary some parrots really understand numbers or when they're taught to recite numerals does it only look as though they can count so with me professor in steerage tomahawk it took hour and Caleb Everett will be back after the news b.b.c. News confusion reigns in the highest levels of Poland's judiciary the chief justice Margot Zhao together staff has said she would define a new law coming into force requiring judges to retire at 65 not 70 and would turn up for work and weapons Day Aides to the Polish president said Ms gust of would abide by the new law and a new chief justice had been appointed Malaysia's former prime minister Najib Razak who lost power in May is due to appear in court shortly to be charged with corruption offenses Mr Najib is expected to face more than 10 counts of committing criminal breach of trust linked to a farm a subsidiary of the state's investment fund one m d b the president elect of Mexico under as manual Lopez Obrador says he will invite the pope to help bring peace to the violence wracked come tree more than 200000 people have died in drug related crime over the past decade. A judge in Brazil is sentenced the former tycoon i.q. Battista to 30 years in jail the judge said I could Betty's done had paid $16000000.00 in bribes to a former governor of Rio state to secure lucrative contracts Mr Batista rejects the allegations the Islamic state group says that her day for about 3 a son of its leader Abu Bakar al Baghdadi is being killed during fighting in Syria they I as a mark propaganda channel said he was killed during an attack on a thermal power station in homes b.b.c. News has been told that the official group which campaign for Britain to leave the European Union in the 2016 referendum is expected to be found guilty of breaking electoral law but vote leaves former chief executive said he believed the ducted within the spirit and the letter of the law in the football World Cup England have gone through to the quarter finals beating Colombia 43 on penalties b.b.c. News. This is the forum from the b.b.c. World Service on Bridget Kendall and today we're looking at the invention of numbers from markings on Bones thousands of years ago I believe to share the earliest evidence of humans counting through differing numbers systems created by the ancient Babylonians Mayans Egyptians and Greeks to India and the number system that most of the world uses today the Hindu Arabic numerals still with me in steerage emeritus professor of mathematics at Warrick University in England writer and historian of mathematics Tamaqua Kitagawa and Caleb Everett and anthropological linguist from the University of Miami now we've been hearing how various civilizations and vegetarian ways of counting based on different based systems and using different symbols but there are indigenous groups in the world today who are a new American in other words they don't use numbers and care that you were explaining at the top of the program you spent a lot of time as a child with your parents who were missionaries in Brazil and they discovered that the indigenous community that you were living with had no word for numbers. So yeah my parents realized this in the early eighties I guess it was and they were trying to teach outside numbers and numerals to these people and they were having a lot of difficulty and so one of the things that they realized was that these words that people had thought of before as being number words in this language Peter were not actually precise in terms of what they referred to so there was a word that people had previously thought was the number 2 but it actually is closer to something like what we mean when we say a couple of so it has this sort of diffuse imprecise meaning and the same holds for the word that had been translated as one also the language lacks singular and plural distinctions so it's really a numeric just telling us a little bit about this group Peta ha yes they live in a remote part of the Armisen and a saucy who are our traditional hunter gatherer is just that. Is that's fair and so you could argue that they don't have any need for numbers but there are many other hunter gatherer groups that have some numbers and so there seems to be something specific about the peta that they are not that interested in numbers you could argue that it's because they're generally somewhat ethnocentric they don't really want that many things from the outside world they're pretty happy with their lives but they're not the only group that's a numeric or at least close to a numeric there are some other groups in Amazonian particular that really do not rely on numbers much if at all why am I right in thinking that was a test to see how they would respond to the concept of numbers than 12 or 3 so the most basic task to test whether people can get this key numerical concept called one to one correspondence is just to line up a series of objects in front of someone and then so if you line say spoils of thread and then you give them another set of objects the empty rubber. Balloons and then you have the match one balloon for every spoil of threat right what we find is that they're very good with if there's one object or 2 object or 3 objects out but just the mere discrimination of say 5 versus 6 or 6 versus 7 spools of thread is very difficult or at least we start to see errors creep in after the quantity of objects exceeds 3 and this is similar to what we see with pre-linguistic children before they've learned number words. In some ways this is similar to what we see in other species although not not exactly but there are some clear parallels there where we like other primates are very good at distinguishing 12 and 3 but then when the number gets larger than that even that just the mere one to one correspondence seems to become difficult for us in the absence of number words and this is this is true in the peta harm but it's also true in the other groups that this has been tested it's really fascinating this because when you think about 3 often in kind of cultural context. Stories of county games and things it often has a big significance I mean think about it in Christianity apart from anything else but when you're talking about the being a conceptual difficulty of seeing beyond 3 why do you think this is something special about 3 and. It seems to be the case that our sort of our brains are sort of naturally predisposed to discriminate $12.00 and $3.00 and we have what some have referred to as an exact number sense for these smaller quantities there are various reasons that it could be the case one is it just relates to our memory storage so we can naturally recall 3 objects what psychologists sometimes refer to as our object file system we can file away 3 objects in our memory even if they're moving around but if you get more than that it gets a little bit tricky another key thing though is that we can discriminate all quantities even before we can count if the ratio between the quantities is sizable enough so for instance the Pieta ha can easily tell 8 things from 16 things right because the ratio is one to 2 and similarly that might be why we're very good at discriminating one and 2 and 3 because the ratio between them is quite large. Now you mentioned other animals Caleb and whether or not they can count a tool Here's a clip from a 2015 documentary numbers by nature on b.b.c. Radio 4 and here presenter Alex by loss is talking to Dr Irene Pepperberg an American scientist who worked with an African Grey parrot named Alex for nearly 3 decades teaching him the numbers one to 6 when did you start to realize that he was exceeding your expectations in a simple number tasks and was going to carry on breaking new ground we started giving him multiple sets of objects soon for example they were like 3 keys into quirks and the fact that he could tell us the subset was a real breakthrough because young children have real trouble with that they just want to tell you the total amount Here's a recording of Alex presented with a tray of objects with different colors and shapes on the tray how many are you walked. How many are you was very very good. Ok we'll get you. Can you tell me how many are you block how many orange block. Very good Ok last question how many green the lock how many green a lot. More good for a good parrot Ok. Dr Irene Pepperberg and how parrot Alex from the b.b.c. Radio 4 documentary nature by numbers in 2015 Alex stands for avian learning experiment in case you were wondering what you make about Caleb. Yeah Irene's work is excellent and really fascinating and one of the things that it demonstrates and she's written this very clearly in her own work is that African great parents like Alex can learn some of these quantitative distinctions if they are taught numbers which is really interesting because it suggests that the power of numbers extends beyond our species and we see some evidence of this with primates in some other species where if they're taught how to count with sufficient care they can start to make some of these quantitative distinctions fairly consistently but 1st they too have to be given handed this cognitive tool of numbers what do you want thoughts on this and. It's certainly true with humans that without the number words or the symbols or something we can sort of hold you know minds to represent specific numbers as we do run into trouble I believe some people can just look at things and tell you the number I think this is related to the business of lightning calculators there are some people who can instantly do sums in their heads the rest of us would find much too complicated so it's partly the way the mind is what up but for most of us we need this linguistic symbolic crutch to help us do the sums Well I suppose one linguistic crutch that we all rely on for a rather ambiguous concept is the word infinity the largest figure rule. When did mathematicians start talking about infinity and is it even a number. It goes right back to the ancient Greeks I was still who the great Greek philosopher. Distinguish 2 kinds of infinity He said there is potential infinity which is a process that can go on as however far it's gone you could always go. Or there's actually infinity which is kind of what would happen if you could just continue all the way with the process and as far as I was total is concerned and the infinity of the Counting Numbers is a potential infinity given any number there is always a bigger one and children find this if you ask young children what's the biggest number they'll say a 1000 and then another one which I know not a 1000000 because they know a big one but eventually they start saying that there isn't one because whichever number you give me I can stick another north on the end and make it bigger so there is no biggest number is a kind of philosophically just a way to say there are infinitely many numbers and I was startled rather objected to the idea that you could have a completed infinity so infinity isn't really a number in the normal sense but mathematicians have found it convenient to extend the number system by throwing in something that they called Infinity just going from that I'm back to you Caleb and the same numerical groups or indigenous people you've worked with in Amazonia you just think what an enormous gap there is within our contemporary world between one way of thinking and another what impact does it have coming into contact with this is Saatchi that uses numbers how does that affect them. Well we see this we've seen this various times historically in a lot of different parts of the world where people that don't have numbers or have only a few numbers come into contact with people that have a robust number system and I see this for instance with one of the groups that I've done research with called the cut each Iana who are friends of mine who have a number system in Amazonia but as they've encountered Brazilians and had been forced into economic trade with Brazilians They've adopted the Brazilian number system because it's a lot larger and they don't get swindled in trade that way and you see this time and again so trade is a really critical thing here that people don't want to be taken advantage of and so they realize that there's a certain usefulness to these quantities or in some cases they're essentially forced to adopt these quantities because outsiders want things from them and want to be able to want them to be able to count those things so a lot of times it's it's a pretty forceful thing not always but it's certainly something that is is a fairly dramatic difference in terms of what we how we're handling quantities depending on the numbers that we have in our language but I should point out it's sometimes tempting to think of these a numeric groups or groups that don't have numbers as the odd ones out the truth is we're kind of the weird ones here right so these numeral systems that moco and that he and I've been talking about they primarily date to the last few millennia and for the vast majority of our history as a species which states back well over 100000 years as long as we've had numbers they've probably been fairly simple and maybe decimal based in some cases but we haven't had these written numerals and we certainly haven't quantified things like time in the ways that we do now. But people like the peta hunter gatherer groups that don't rely on numbers at all or don't rely on them much are probably a better representation of our of the history of our species right only recently have numbers every become so number obsessed in ways that have benefited medicine and history and all these things but in ways that you could argue have also taken away from taking us away from the more typical human experience which is probably that of people who don't have numbers or don't have many numbers and it's not such essential it's part of their experience. It's interesting you say that because when you think about. Modern systems actually they've sort of got more sophisticated but in a way they've gone back to simplicity and I was thinking Tom occur about what you said about Chinese number numerical systems and the binary system of being young and young and when we look at the development of the computer it's back to the binary isn't it exactly it's very surprising fact that binary at the end of the day makes sense or any of you can begin to basics are basis of everything and it's really interesting notion or the way to think about numberless And also we're talking about this know they can it's in numbers Chinese or East Asian clock has to do diac associating with numbers so instead of using numbers we all will always have like say Well it's 5 o'clock that means like not the hour of the monkey you know we go to the bed like you know maybe midnight and it's the hour of . Right and then getting up at 6 and then that's the hour of hair and it's just like they bake but you know to communicate the numbers in that manner was still I can see some places that you know a number is has been replaced by the very basic I.D.'s and a very basic you know ideas associating with animals were coming towards the end of the program but before we go let me ask you what's the connection between the number 2147000000 483647 this song or band got another star. Well that was of course the South Korean pop star sigh and his 2012 hit Gangnam Style here in lightness on the link This is the song which broke You Tube you counter. What happened was so many people had viewed it and every time somebody viewed the counter ticked up one and the total number of viewing got to 2147000000 483647 and that was the largest number that the 32 bit signed register in the computer could store so when the next person viewed it the computer didn't get the right number anymore it didn't know what to do so. This is something that showed up in various other ways an area and space rocket crashed because of this problem. So if you're programming a computer to count quite large numbers you have to make sure large enough you have to make sure that it can store the numbers big enough to do the job you want and there have been a few failures with this overflow problem that the the computer cannot handle the numbers that are the big numbers that actually come up usually because it never occurred to the programmer that this would happen I mean do you really imagine that somebody song on youtube will be viewed more than 2000000000 telling us Well nowadays you do but when they were writing the software they didn't well when it comes to capacity we were never going to do more than scratch the surface when it came to the history of numbers the same much to say and explore and I think that's all we do into this episode of The Forum but to finish very briefly from each of you where do you think numbers and counting will go next came up. Well I think for one thing the vast majority of the groups in the world that don't have numbers will continue to adopt numbers or I should say don't have many numbers will continue to adopt the decimal system numeral system that that we all sort of take for granted Tomoko I think it's a very interesting concept and now we can rethink and rethink all the time to create new Thanks the number I think we just a lady think like you know it's existing and it's all the you know of but I think you know we really have to rethink about the concept itself and big. This is the buzzword for collecting huge amounts of information and analyzing them on a computer. It has the potential to unlock quite a lot of medical secrets for example it also has the potential to be actually rather nasty. You could have artificial intelligence is analyzing everybody's daughter and taking over the world so I hesitate to recommend it but this is one of the directions numbers are going Many thanks to all 3 of you Ian Stewart Tom and Co get your go or I'm Caleb Everett to join us next week on the forum and in the meantime there are lots of other topics to explore as Don led us free podcasts from our website just had to b.b.c. World Service dot com forward slash for him so enjoy the programs and be back with you soon. Hi I'm David Edmonds of the b.b.c. World Service and this is the big idea I found the most fascinating ideas around and the people who thought them up and I don't do my best to explain them. Take my word for it today's big idea is warning the decline in trustworthiness. Tonight and the man called the biggest swindler in history is sent to jail in New York in 2008 Burnet made off was arrested like he confessed to operating a fort of staggering proportions he says he's sorry and ashamed of the taking $50000000000.00 clients when are counting the cost made of was not a man to trust but what is trust and Nora Neil is a philosopher who I've been reliably informed has what Nick's pensively about trust trust is a judgment that somebody else can be relied upon or but some institution can be relied on it isn't proof trust is what we do when we need a shortcut Why is it so important. There isn't time in this life to go and get complete evidence and a proof for everything we often have to rely on other people so we have to have quick and reasonable ways of judging whether they can be relied on for a particular purpose so it lubricates life it makes life easier quicker easier quicker friendlier all sorts of good things but the downside is if you misplace trust if you place trust in somebody who is untrustworthy. Society can't function effectively without trust. So does that mean the more trust the better well not according to a Nora Neil we have another word which is gullible and if you simply place trust indiscriminately without making a judgment about whether the other person or institution is trustworthy then just trusting to luck as we say is probably not a virtue so if I trust Bernie Madoff for example that wouldn't be a sensible thing to do it would not because he would make off with your money but lots of people did trust it we don't want more trust says O'Neill but we do want more something else trustworthiness all trustworthiness is what the person or institution the time trying to assess house all our acts an individual or organization is trustworthy if they can justifiably be trusted to be trustworthy they need 3 ingredients 1st honesty people have to be able to believe what they're told 2nd competence for example you have to think you're going to go to the dentist you do want a competent dentist if I would just say I know chaplain Gary stone.