tag:blogger.com,1999:blog-2149943594271779212.post7198671034627400815..comments2023-10-07T00:25:52.264-07:00Comments on A Diary of Numbers: Steven Pinker on the Living and the Deadaaronsantosdotcomhttp://www.blogger.com/profile/09803515727250282449noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-2149943594271779212.post-36586566905627952982014-05-17T20:21:50.390-07:002014-05-17T20:21:50.390-07:00Correction: I'm really sorry Aaron. I got fool...Correction: I'm really sorry Aaron. I got fooled by the post about Steve Pinker. The question, however, stands. Thanks again<br />Wesleywcollhttps://www.blogger.com/profile/13886168184448475636noreply@blogger.comtag:blogger.com,1999:blog-2149943594271779212.post-86786120448524581382014-05-17T20:18:58.536-07:002014-05-17T20:18:58.536-07:00Hi, Steven. I was wondering if there's a way o...Hi, Steven. I was wondering if there's a way of determining a (ballpark figure) for the number of living people born in the 20th century, like you and me, compared to those born and living in this century. A percentage comparison would also work. Would love to know. Thanks and regards. Wesley CollAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2149943594271779212.post-70237556241516865832012-07-16T15:30:01.508-07:002012-07-16T15:30:01.508-07:00It's all good. The inaccuracy is purely my ow...It's all good. The inaccuracy is purely my own, not Pinker's. I only ask guests to supply questions, so it's not their fault in my answers are off.<br /><br />I do like your method. In fact, I may use it for a problem I'll be posting later this week. Feel free comment again if you find something I write innaccurate or a bit misleading.aaronsantosdotcomhttps://www.blogger.com/profile/09803515727250282449noreply@blogger.comtag:blogger.com,1999:blog-2149943594271779212.post-27899411123395853932012-06-19T03:21:42.392-07:002012-06-19T03:21:42.392-07:00Yes my wording was a bit dramatic, but my estimate...Yes my wording was a bit dramatic, but my estimate (which is the best I can think of given my limited knowledge) does differ by slightly *more* than one order of magnitude. That's a big difference when guessing populations. The earth currently has a population of 50 billion, accurate to within 1 order of magnitude. But that is a very very wrong number with which one can get to very wrong conclusions.<br /><br />For example, I propose that there are more than twice as many people currently alive on earth than all the people who died during the 20th century. your former analysis would say - no, there are only about a quarter as many. Take the world's population, and kill them 4 times over. That is how many people died in the 20th century.<br /><br />Steven Pinker himself tweeted this, and that caught my attention. Since we actually have pretty good records of human population we can do a lot better than an order of magnitude guess. But sorry if you became the victim of a famous tweet. From Steven Pinker I expected more accurate guesstimates.<br /><br />It was interesting and got me thinking - thanks for that.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2149943594271779212.post-6780660309203259142012-06-15T06:10:52.371-07:002012-06-15T06:10:52.371-07:00Yeah, that's a fair critique. I like your met...Yeah, that's a fair critique. I like your method better. Though I would argue that your description of it as "hopelessly inaccurate" is a bit overly dramatic considering it's an order-of-magnitude estimate, which is only intended to be good to within roughly a power of ten.aaronsantosdotcomhttps://www.blogger.com/profile/09803515727250282449noreply@blogger.comtag:blogger.com,1999:blog-2149943594271779212.post-56932555788858410992012-06-15T03:56:41.606-07:002012-06-15T03:56:41.606-07:00I'm sorry but your calculation is hopelessly i...I'm sorry but your calculation is hopelessly inaccurate. 2.15^4 × (1.6 billion) assumes the average person is indefinitely fertile, and reproduces every 25 years without dying (until the year 2000).<br /><br />Also, the 2.3 kids might not apply to the developing world, which made up the bulk of the global population increase. See this chart of the real recorded data during the 20th century: http://www.sv.vt.edu/classes/surp/surp96/laughlin/stat/3D_tutor/world_pop.html<br /><br />If we keep with the discrete 25-year generation you propose, and assume a constant fertility over the last 100 years, the successive generations form a geometric series. Let's say if this generation has x fertile (< 25 yr old) people, that the next generation consist of x*m fertile (< 25-yr old) people.<br /><br />Let's assume the fertile population in 1900 is "p". Let's also assume that a given generation basically dies out after 75 years. This is a realistic life expectancy.<br />Then the generations of fertile (<25yr old) people looks as follows:<br /><br />(1850) : p / m^2<br />(1875) : p / m<br />(1900) : p<br />(1925) : p * m<br />(1950) : p * m * m<br />(1975) : p * m^3<br />(2000) : p * m^4<br /><br />In 1900 the world population was then the sum of the generations of 1850 - 1900. Older people were all dead.<br />We also know that the world population was, at that time, 1.6 bn.<br />Therefore p/m^2 + p/m + p = 1.6 bn.<br /><br />Also, we know that in 2000 the world population was 6.9 bn. That was, similarly, the sum of the generations of<br />1950-2000<br />Therefore p*m^2 + p*m^3 + p*m^4 = 6.9 bn.<br /><br />Now we have 2 equations and 2 unknowns, and we can solve p and m.<br />I used Wolfram Alpha to get p = 0.782 and m = 1.565<br /><br />You can verify this model by checking to see if it works for 1950, for which my model predics a population of <br />p + p*m + p*m^2 = 3.3 bn. Looking at the graph it's a little high, but reasonable. Hey, this is a very rough approximation (the effects of 2 world wars and the invention of antibiotics surely makes is much more difficult to model).<br /><br />So let's go with our model. From this you can see that the "average family size" was actually about 2.88 children, not 2.3 assumed. (On average two people produce 2*m offspring)<br /><br />Now look at the final numbers. The total number of people who have lived at some time in the 20th century becomes p * (1/m^2 + 1/m + 1 + m + m^2 + m^3 + m^4) = 9.56 bn. <br /><br />Which means that there were only approximately 2.7 bn deaths in the 20th century!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2149943594271779212.post-40335593382948522012-06-14T08:43:25.277-07:002012-06-14T08:43:25.277-07:00How about wealth created during that time? I suspe...How about wealth created during that time? I suspect that would show that increasing population hasn't had a negative impact on wealth-creation (or, indeed, health or longevity).Troy Camplinhttps://www.blogger.com/profile/16515578686042143845noreply@blogger.com