{"id":1800,"date":"2017-08-04T09:54:16","date_gmt":"2017-08-04T09:54:16","guid":{"rendered":"http:\/\/www.cientificos.pe\/?p=1800"},"modified":"2018-04-09T18:58:28","modified_gmt":"2018-04-09T18:58:28","slug":"a-great-battle-approaches-luis-fonsi-vs-wiz-khalifa-goodbye-gangnam-style","status":"publish","type":"post","link":"https:\/\/www.cientificos.pe\/?p=1800","title":{"rendered":"Despacito is the most viewed video on Youtube: An introduction to integral calculus"},"content":{"rendered":"<p style=\"text-align: justify;\"><strong><em><span style=\"color: #800000;\"><span style=\"text-decoration: underline;\">Author&#8217;s note:<\/span>\u00a0&#8220;This article was published on August 4th, 2017. Considering Integral Calculus we predicted that Despacito would reach 4 billion views in october 2017 and 5 billion views in april 2018. Officially Despacito reached 4 billion views on october 11<sup>th<\/sup>\u00a02017 and 5 billion views on april 4<sup>th\u00a0<\/sup>2018.&#8221;<\/span><\/em><\/strong><\/p>\n<p style=\"text-align: center;\"><em><strong>Despacito will reach 4 billion views this year and&#8230;\u00a0<\/strong><\/em><\/p>\n<p style=\"text-align: justify;\">In the <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/08\/04\/a-great-battle-approaches-luis-fonsi-vs-wiz-khalifa-goodbye-gangnam-style\/2\/\">first part of this article<\/a>, published on July 11<sup>th<\/sup>, 2017, using basic mathematical notions we predicted that Despacito would reach 3 billion views after August 2<sup>nd<\/sup>, with a strong probability on the threshold of the second week. Officially it happened\u00a0on August 4<sup>th<\/sup> in America and on August 5<sup>th<\/sup> in Europe and Asia. The route taken was as follow (UTC +2):<\/p>\n<ul>\n<li style=\"text-align: justify;\">Surpassed Uptown funk &#8211; Bruno Mars, on July 14<sup>th<\/sup>, 2017 at 7:30 PM.<\/li>\n<li style=\"text-align: justify;\">Surpassed Sorry &#8211; Justin Bieber, on July 19<sup>th<\/sup>, 2017 at 11:30 AM.<\/li>\n<li style=\"text-align: justify;\">Surpassed Gangnam style &#8211; PSY, on July 31<sup>st<\/sup> at 5:00 PM.<\/li>\n<li style=\"text-align: justify;\">Surpassed See you again &#8211; Wiz Khalifa on August 4<sup>th<\/sup> at 7:30 PM.<\/li>\n<li style=\"text-align: justify;\">Reached 3 billion views on August 5<sup>th<\/sup> at 00:30 AM.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">In this second part, we are going to answer when will it reach 4 billion views and be considered the only song achieving this number. The answer, once again, lies in mathematics&#8230;<\/p>\n<p style=\"text-align: justify;\">Despacito started growing at 6 million views per day in January, increased its rate to 16 million views per day in May, and reached 21 million views per day in July. Will it reach higher values? No, it will not, Despacito\u00a0will decay reaching a stable level in January 2018 (6 months after reaching its highest peak, which was in July), this is likely to happen because other songs have shown\u00a0this outcome. What would this stable value be? Probably around 3 million views per day. Why? Because it has been the stable value of many iconic songs. Here are some examples:<\/p>\n<table class=\" aligncenter\" style=\"width: 694px;\">\n<tbody>\n<tr>\n<td style=\"width: 151px; text-align: center;\">Song \/ Artist<\/td>\n<td style=\"width: 231px; text-align: center;\">Published in Youtube (year\/month)<\/td>\n<td style=\"width: 248px; text-align: center;\">Number of Youtube views per day in 2017\/08 (millions)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 151px; text-align: center;\">Bailando<br \/>\n(Enrique Iglesias)<\/td>\n<td style=\"width: 231px; text-align: center;\">2014\/04<\/td>\n<td style=\"width: 248px; text-align: center;\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 151px; text-align: center;\">Uptown funk (Bruno Mars)<\/td>\n<td style=\"width: 231px; text-align: center;\">2014 \/11<\/td>\n<td style=\"width: 248px; text-align: center;\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 151px; text-align: center;\">Sorry<br \/>\n(Justin Bieber)<\/td>\n<td style=\"width: 231px; text-align: center;\">2015 \/10<\/td>\n<td style=\"width: 248px; text-align: center;\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 151px; text-align: center;\">See you again<br \/>\n(Wiz Khalifa)<\/td>\n<td style=\"width: 231px; text-align: center;\">2015\/04<\/td>\n<td style=\"width: 248px; text-align: center;\">3.5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 151px; text-align: center;\">Chantaje<br \/>\n(Shakira)<\/td>\n<td style=\"width: 231px; text-align: center;\">2016\/11<\/td>\n<td style=\"width: 248px; text-align: center;\">4.5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">This data wil be enough to make a rough estimation\u00a0of the future of the song using Integral Calculus (developed by Isaac Newton and Gottfried Leibniz in the XVII century). Probably in that time, these geniuses had to face a similar problem and that&#8217;s how they developed Calculus, so let&#8217;s go back in time and see what they would have done\u2026<\/p>\n<p style=\"text-align: justify;\">First, Newton would have locked himself in his room, he was a shy person and preferred solitude. Then, he would have drawn a graph similar to the following:<\/p>\n<figure id=\"attachment_1946\" aria-describedby=\"caption-attachment-1946\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" class=\"wp-image-1946 size-medium\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/englishfonsi-300x244.png\" alt=\"\" width=\"300\" height=\"244\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/englishfonsi-300x244.png 300w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/englishfonsi-768x625.png 768w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/englishfonsi-1024x833.png 1024w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/englishfonsi-696x566.png 696w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/englishfonsi-1068x869.png 1068w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/englishfonsi-516x420.png 516w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/englishfonsi.png 1480w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-1946\" class=\"wp-caption-text\">Figure 1<\/figcaption><\/figure>\n<p style=\"text-align: justify;\">Showing that in 6 months (from August 2017 to January 2018) Despacito would fall linearly from 21 million to 3 million views per day (see blue line in Figure 1), reaching a stable and constant value starting february. With this, knowing that beginning august Despacito has 3 billion views, can we derive\u00a0when will it reach 4 billion views? It looks a bit cumbersome, because of this, Newton and Leibniz developed a trick&#8230; Instead of studying the line, they traced rectangles for each month as shown in Figure 1. Why? Because by doing so, things become much simpler, we now can assume that in August Despacito would have a constant value of 18 million views per day, in September of 15 million views per day, in October 12, in November 9, in December 6, and in January 3; hence, considering that each\u00a0month has 30 days we can generate the following table:<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Month<\/td>\n<td style=\"text-align: center;\">Total number of Youtube views each month (millions)<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">August<\/td>\n<td style=\"text-align: center;\">18 x 30 = 540<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">September<\/td>\n<td style=\"text-align: center;\">15 x 30 = 450<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">October<\/td>\n<td style=\"text-align: center;\">12 x 30 = 360<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">November<\/td>\n<td style=\"text-align: center;\">9 x 30 = 270<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">December<\/td>\n<td style=\"text-align: center;\">6 x 30 = 180<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">January<\/td>\n<td style=\"text-align: center;\">3 x 30 = 90<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">Total<\/td>\n<td style=\"text-align: center;\">\u00a01890<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">From the table we\u00a0can see that adding August and September, Despacito accumulates 990 million views, meaning that it would require only 10 million to reach 4 billion views in total. And by the end of January, it would reach 4.890 billion views, requiring then\u00a0110 million to reach 5 billion views in total. Taking into account the exact date in which Despacito accumulated 3 billion views and assuming that after January it keeps\u00a0a stable value of 3 million views per day we can conclude that:<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"text-align: justify;\">Despacito reaches 4 billion views on October 5<sup>th<\/sup>, 2017.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"text-align: justify;\">Despacito reaches 5 billion views on March 12<sup>th,<\/sup>, 2018.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">These dates do not correspond to the blue line but instead to the approximation given by the rectangles. The curious thing about this trick is that the area of each rectangle shown in Figure 1 represents the total number of views in each month, eg, for August, the width of the rectangle is 30 (days) and the length is 18 (number of views per day), then the total number of views is 30 x 18, as shown in the table above. Oh God!-would have said Newton, who was a fervent Christian, while pulling his hair in his little dorm in Woolsthorpe. Leibniz would have done the same in Paris.<\/p>\n<p style=\"text-align: justify;\">Both were fascinated with the concept of the infinitesimal, to the point that they were immersed in philosophical debates regarding the so called monads. Because of this, both reached a point where they questioned themselves: \u201cwhat if we draw more rectangles and make them thinner, infinitesimally thinner so that they would exactly match the area under the curve (the blue line in our case).&#8221; This simple thought gave a marvelous conclusion: &#8220;The area under the curve, no matter how complicated is this curve, gives us the total number views.&#8221;<\/p>\n<figure id=\"attachment_2015\" aria-describedby=\"caption-attachment-2015\" style=\"width: 640px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" class=\"wp-image-2015 size-large\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/08\/rectangleint-1024x407.png\" alt=\"\" width=\"640\" height=\"254\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/08\/rectangleint-1024x407.png 1024w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/08\/rectangleint-300x119.png 300w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/08\/rectangleint-768x305.png 768w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/08\/rectangleint-696x277.png 696w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/08\/rectangleint-1068x425.png 1068w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/08\/rectangleint-1056x420.png 1056w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/08\/rectangleint.png 1104w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><figcaption id=\"caption-attachment-2015\" class=\"wp-caption-text\">Figure 2<\/figcaption><\/figure>\n<p style=\"text-align: justify;\">To visualize this thought, let&#8217;s consider Figure 2, where we show the actual evolution of the number of views of Despacito from January to August, 2017. As you can see, the behavior is not linear, but Newton and Leibniz showed us that in order to get the total number of views, all we need is\u00a0to find the area under the curve (the area under the green line in this case). By drawing thin rectangles in the month of March (as shown in Fig. 2) and summing up their areas we can obtain approximately the total number of views in that month. The value will be exact if these rectangles are infinitesimally thin, so thin that when they are drawn they describe exactly the area under the curve. This conclusion allowed them to develop Integral Calculus, which in simple words means: &#8220;To find the total area under any curve we just need to sum up the area of infinitesimally thin rectangles.&#8221; For this it is necessary to know the equation of our curve. In Fig. 1 is a straight line, its general form\u00a0was mentioned in <a href=\"http:\/\/www.cientificos.pe\/index.php\/2017\/08\/04\/a-great-battle-approaches-luis-fonsi-vs-wiz-khalifa-goodbye-gangnam-style\/2\/\">the first part of this article<\/a>. In Fig. 2 is more complex but not impossible to determine. In this case we are going to center our attention in Fig. 1, the equation of the straight\u00a0line is given by the function f(t) = 21 &#8211; t\/10, where t represents the time expressed in days.\u00a0This function will allow us to obtain the length of the rectangle and the width will be given by an infinitesimally small value. Therefore, we already have the area of each rectangle and all we need is to sum them up. Mathematically, this infinitesimal sum is expressed as follows:<\/p>\n<h1 style=\"text-align: center;\"><u><img loading=\"lazy\" class=\"size-medium wp-image-1939 aligncenter\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/math-300x89.png\" alt=\"\" width=\"300\" height=\"89\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/math-300x89.png 300w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/math.png 485w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/u><\/h1>\n<p style=\"text-align: justify;\">On the left hand side we have the equation of our\u00a0line, f(t). The symbol in the form of an elongated <em>S<\/em> tells us that we have to add infinitesimally thin rectangles starting on day <em>0<\/em> and culminating on day <em>d<\/em>, date for which we will accumulate 1 billion views. Solving the equation we have:<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"text-align: justify;\">Despacito reaches 4 billion views on September\u00a030<sup>th<\/sup>, 2017.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"text-align: justify;\">Despacito reaches 5 billion views on January 1<sup>st<\/sup>,\u00a02018.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">How accurate are these results?<\/p>\n<p style=\"text-align: justify;\">With time we will know, Despacito\u00a0may decay faster (or slower) than a linear slope, in fact, it will be a chaotic decay, very similar to\u00a0Fig. 2. We are just making a rough approximation, but everything seems to indicate that <strong>the first week of October<\/strong> <strong>Despacito will reach 4 billion views and<\/strong>\u00a0<strong>between January and April, 2018, Despacito will grasp 5 billion views.<\/strong>\u00a0The imminent question is: Is any song capable of beating this record? It is very difficult at the moment. The great advantage of new songs coming by is that the global connection to the internet is increasing; however, if the world population is meant to decrease for any reason in the coming years, most likely Despacito will remain unbeaten for a long long time.<\/p>\n<p style=\"text-align: justify;\"><span class=\"_5yl5\">Christian Ortiz, PhD.<\/span><\/p>\n<p style=\"text-align: center;\"><!--nextpage--><\/p>\n<p style=\"text-align: left;\"><strong>July\u00a011<sup>th<\/sup>, 2017<\/strong><\/p>\n<p style=\"text-align: center;\"><em><strong> Despacito vs See you again&#8230; Goodbye Gangnam style.<\/strong><\/em><u><br \/>\n<\/u><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" class=\"alignright wp-image-1802\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/despacito-ORtiz-300x145.png\" alt=\"\" width=\"400\" height=\"193\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/despacito-ORtiz-300x145.png 300w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/despacito-ORtiz-768x371.png 768w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/despacito-ORtiz-696x336.png 696w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/despacito-ORtiz.png 813w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/>On April 20<sup>th<\/sup> I was in Milan. That night, the first word I heard when I arrived at the Naviglio Pavese was, &#8220;Despacito.&#8221; It amused me, but\u00a0when I heard it again and again in the groups of people that crossed by my side, I realized\u00a0something strange was happening, and I was not mistaken. That day, Luis Fonsi had surpassed one billion views on Youtube&#8230; The next day, I traveled to Munich, and when I arrived the first thing I did was to ask a German friend if she knew the song, she liked rock so she said no, but two months later when I spoke to her again, she told me that she could no longer tolerate it, she has been hearing the song everywhere. Exactly two months later, on June 20<sup>th<\/sup>, Despacito had reached 2 billion views on YouTube. Today, July 11<sup>th<\/sup>, 2017, the ranking of the most viewed Youtube videos is as follows:<\/p>\n<ul style=\"text-align: center;\">\n<li style=\"text-align: justify;\">See You Again \u2013 Wiz Khalifa<\/li>\n<li style=\"text-align: justify;\">Gangnam Style \u2013 PSY<\/li>\n<li style=\"text-align: justify;\">Sorry \u2013 Justin Bieber<\/li>\n<li style=\"text-align: justify;\">Uptown Funk \u2013 Bruno Mars<\/li>\n<li style=\"text-align: justify;\">Despacito \u2013 Luis Fonsi<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Gangnam Style has just lost the throne! However, the question is, how far can Despacito get? The answer lies in mathematics, and that is why today, banks, insurance companies, among other financial groups, are obsessed recruiting mathematicians because they are the new oracles of the world. Able to predict the future and generate strong money gains with their probabilistic stochastic models.\u00a0 In this article we won\u2019t go deep in the theory of probability or mathematics in finance, but we will give some insight about them. To begin, in the following graph we show the evolution of the\u00a0songs in the last six days (or 144 hours), starting on July 4<span style=\"font-size: 12.5px;\"><sup>th<\/sup><\/span>\u00a0at 00:00 and culminating on July 9<sup>th<\/sup> at 23:59 PM (UTC +2).<img loading=\"lazy\" class=\"aligncenter wp-image-1861\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khalif1-1024x713.png\" alt=\"\" width=\"440\" height=\"306\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khalif1-1024x713.png 1024w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khalif1-300x209.png 300w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khalif1-768x535.png 768w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khalif1-100x70.png 100w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khalif1-696x485.png 696w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khalif1-1068x744.png 1068w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khalif1-603x420.png 603w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/>In the vertical axis we show the number of Youtube views and in the horizontal axis the time interval expressed in hours. Clearly, we observe that as time evolves, Luis Fonsi grows much more than the others. Moreover, Wiz Khalifa is very close to surpass\u00a0PSY. Maybe you cannot see it well, so here we show a zoom of PSY vs Wiz Khalifa:<img loading=\"lazy\" class=\"aligncenter wp-image-1862\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khali2-1024x713.png\" alt=\"\" width=\"440\" height=\"306\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khali2-1024x713.png 1024w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khali2-300x209.png 300w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khali2-768x535.png 768w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khali2-100x70.png 100w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khali2-696x485.png 696w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khali2-1068x744.png 1068w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/khali2-603x420.png 603w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/>We have to recall that the graph shows the evolution of Youtube views from July 4<sup>th<\/sup>\u00a0\u2013 July 9<sup>th<\/sup>, that is, when PSY was in the first position. Why I\u2019m convinced from the graph that Wiz Khalifa will surpass\u00a0PSY? The truth is that I should not be; I\u2019m simply predicting the future based on a &#8220;mathematical hunch&#8221; where I study the historical behavior of the number of Youtube views to project future data. In order to do so, it is necessary to estimate the slope of each line using the ordinary least squares method, and then, consider\u00a0the trendline equations (given in the form f(x) = mx + b) in order to predict the future in which my hypothesis will occur. In simple terms, we will extend our lines in the graph and see where they intersect, with this we can deduce the exact moment in which Wiz Khalifa surpasses\u00a0PSY and Despacito becomes the video with most views on Youtube. Mathematically, e.g., if the trendline equations of\u00a0Wiz Khalifa (w) and PSY (p) are given by:<\/p>\n<p style=\"text-align: center;\">f(x<sub>w<\/sub>) = m<sub>w<\/sub>x<sub>w\u00a0<\/sub>+ b<sub>w<\/sub><br \/>\nf(x<span style=\"font-size: 12.5px;\">p<\/span>) = m<sub>p<\/sub>x<sub>p<\/sub><sub>\u00a0<\/sub>+ b<sub>p<\/sub><\/p>\n<p style=\"text-align: justify;\">The exact moment in which Wiz Khalifa dethrones PSY is given by f(x<sub>w<\/sub>) =\u00a0f(x<span style=\"font-size: 12.5px;\">p<\/span>). We will not make this cumbersome so here we show the final result (UTC +2):<\/p>\n<ul style=\"text-align: center;\">\n<li style=\"text-align: justify;\">Wiz Khalifa dethrones PSY on July 10<sup>th<\/sup> at 2 PM.<\/li>\n<li style=\"text-align: justify;\">Luis Fonsi beats Bruno Mars on July 14<sup>th<\/sup> at 8:30 AM.<\/li>\n<li style=\"text-align: justify;\">Luis Fonsi beats Justin Bieber on July 18<sup>th<\/sup> at 9:30 AM.<\/li>\n<li style=\"text-align: justify;\">Luis Fonsi surpasses Khalifa and Despacito becomes the video with most views on Youtube on July 31<sup>st<\/sup> at 6:30 AM.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Can you guess what would happen if instead of talking about songs the graph would show the value of company shares? Many, if not all, would invest in Luis Fonsi\u2019s company because they would be convinced that beginning August\u00a0these shares will become the most expensive ones, and therefore will generate greater profits. However it is not as easy as it seems, because in the financial world the graphs are more complex and depend on many factors, both endogenous and exogenous. In this sense, the most sophisticated models that predict the future behavior of an event consider variables as stochastic, that is, random variables (non-deterministic) exposed to external shocks that can change the &#8220;normal&#8221; course of history. In this example, the number of views is a random variable, because I do not know exactly how many people will watch the Youtube video one hour after I publish this article, but I can dare to say a number with a certain level of significance, that is, the prediction I make is subjected to a margin of error that depends on the model I use. In the example outlined at the beginning, where we estimated the slopes of the lines, we omitted a number of exogenous factors that affect the number of Youtube views, such as people\u2019s routine, internet access, each individual\u2019s diminishing marginal utility (e.g., the fact that songs soon or later become annoying), among other factors. How long does it take to get bored of listening the same song? We do not know, each song has different behaviors. We only know that at some point, we will get bored of listening the same thing. If we want a slightly more sophisticated model, where we can use additional variables, statistical concepts such as &#8220;Bayesian Theory&#8221; and &#8220;Time Series&#8221; are needed. Yes, sounds complicated.<\/p>\n<p style=\"text-align: justify;\">To understand the basics, let\u2019s focus on Despacito. This song was released on January 12<sup>th<\/sup>, 2017. 97 days later it reached a billion views on YouTube, which means that on average it accumulated 10 million views per day from January 12<sup>th<\/sup> to April 20<sup>th<\/sup>. With this data, can we infer what will happen next? Not necessarily, because the behavior is stochastic, then there are exogenous factors that can alter trends. One of these factors has a name: Justin Bieber. On April 17<sup>th<\/sup>, he altered the probabilistic data with his Despacito remix. This alteration gave a positive shock to the number of views, because Justin Bieber, due to the number of fans he has worldwide, transformed the probabilistic growth of Fonsi, who became more popular in english-speaking countries. This does not imply that Fonsi could not have done it himself, perhaps yes, but it was Bieber the external variable that gave a push to the song. On June 20<sup>th<\/sup>, Despacito reached 2 billion views, that is, in 60 days (from April 20<sup>th<\/sup> to June 20<sup>th<\/sup>) it accumulated 16.7 million views per day. Now, what is happening in the last weeks (until\u00a0July 9<sup>th<\/sup>)? The following histogram\u00a0shows us:<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" class=\"aligncenter wp-image-1885 size-large\" src=\"http:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/lastenglibar-1024x385.png\" alt=\"\" width=\"640\" height=\"241\" srcset=\"https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/lastenglibar-1024x385.png 1024w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/lastenglibar-300x113.png 300w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/lastenglibar-768x289.png 768w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/lastenglibar-696x262.png 696w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/lastenglibar-1068x402.png 1068w, https:\/\/www.cientificos.pe\/wp-content\/uploads\/2017\/07\/lastenglibar-1116x420.png 1116w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><\/p>\n<p style=\"text-align: justify;\">Although the song can be considered old, Fonsi, within the last weeks,\u00a0is enjoying its highest peak, reaching on average 21 million views per day, with peaks beyond 24 million views on weekends. Can Fonsi grow beyond these values? Probably no. Although the calculations are not shown here, so as not to make the discussion cumbersome, one can estimate that Fonsi has reached stable values and is likely to decrease &#8220;despacito&#8221; and &#8220;poquito a poquito&#8221;\u00a0in the coming weeks; nonetheless, there will always be exogenous factors that will alter the result.<\/p>\n<p style=\"text-align: justify;\">To finalize, it is important to mention that in the last days (until July 9<sup>th<\/sup>)\u00a0the Youtube views are growing as follow:<\/p>\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td style=\"text-align: center;\"><strong>Number of views per day (millions)<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">W. Khalifa<\/td>\n<td style=\"text-align: center;\">3.5<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">PSY<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">J. Bieber<\/td>\n<td style=\"text-align: center;\">2.3<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">B. Mars<\/td>\n<td style=\"text-align: center;\">2.3<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">L. Fonsi<\/td>\n<td style=\"text-align: center;\">\u00a024<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Because these are weekend values, they correspond, on average, to the highest values that each singer can achieve.\u00a0These data enable us to forecast the trends of Khalifa and Fonsi, the future leaders of Youtube. Removing exogenous factors, we can intuitively guess that in the near future W. Khalifa will drop\u00a0to 2.3 million views per day because these are the stable values \u200b\u200bof Justin Bieber and Bruno Mars. In the end, these results put \u201cSee You Again\u201d as the most viewed video on Youtube in the month of July.<\/p>\n<p style=\"text-align: justify;\">In our first analysis we said that W. Khalifa would reach the first place on July 10<sup>th<\/sup> at 2PM (UTC +2). Officially he did it at 11:30PM (UTC +2). This confirms all what we have just said, it is nice though to realize that in the most basic analysis, our prediction remained very close to reality. Additionally, we mentioned that Luis Fonsi would surpass\u00a0W. Khalifa on July 31<sup>st<\/sup>. This won\u2019t be the case\u00a0because, as we have said, Fonsi has reached stable values, declining &#8220;poquito a poquito&#8221; in the coming weeks. So, what will happen on July 31<sup>st<\/sup>? Most likely, Luis Fonsi will step on the feet of W. Khalifa, perturbing fans of both singers, this perturbation will become an important exogenous variable in the month of August, as we don\u2019t know what fans may be capable of.<\/p>\n<p>The pending question would be, which song will become the first to reach 3 billion views?<\/p>\n<p style=\"text-align: justify;\">The curious thing about this question is that if we use the graphs shown at the beginning, on July 31<sup>st<\/sup> W. Khalifa and L. Fonsi would reach 2 964 829 089 views. Meaning that they would require 35 million views to reach the historical number of 3 billion views. This can be achieved by Luis Fonsi in a couple of days if he keeps a\u00a0trend of 21 million views per day. That is, on August 2<sup>nd<\/sup>, at best, Despacito would become the first video clip to reach that number. It would be a historic moment in the internet world&#8230; but it won\u2019t be the case. As mentioned, Fonsi will hardly keep his\u00a0growth unchanged until July 31<sup>st<\/sup>, which means, and here is the funny thing, that it may happen that W. Khalifa and L. Fonsi together will reach 3 billion views at a later date.<\/p>\n<p style=\"text-align: justify;\">Granting to Wiz Khalifa a lower bound\u00a0of 2.3 million views per day (as given from the previous table),\u00a0it can be deduced that he will reach 3 billion views, in the worst case, on August 24<sup>th<\/sup>. Therefore, we can conclude,<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><strong>First reaching 3 billion views<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">Luis Fonsi &#8211; Wiz Khalifa<\/td>\n<td style=\"text-align: center;\">\u00a0August 2<sup>nd<\/sup>\u00a0&#8211; August 24<sup>th<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Everything seems to indicate that in August Luis Fonsi and W. Khalifa will make history, with a high probability on the threshold of the second week, this is, finalizing the first one\u00a0and starting the second one.<\/p>\n<p style=\"text-align: left;\"><span class=\"_5yl5\">Christian Ortiz, PhD.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Author&#8217;s note:\u00a0&#8220;This article was published on August 4th, 2017. Considering Integral Calculus we predicted that Despacito would reach 4 billion views in october 2017 and 5 billion views in april 2018. Officially Despacito reached 4 billion views on october 11th\u00a02017 and 5 billion views on april 4th\u00a02018.&#8221; Despacito will reach 4 billion views this year [&hellip;]<\/p>\n","protected":false},"author":9,"featured_media":1948,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[142,149,143],"tags":[],"_links":{"self":[{"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=\/wp\/v2\/posts\/1800"}],"collection":[{"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1800"}],"version-history":[{"count":69,"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=\/wp\/v2\/posts\/1800\/revisions"}],"predecessor-version":[{"id":2859,"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=\/wp\/v2\/posts\/1800\/revisions\/2859"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=\/wp\/v2\/media\/1948"}],"wp:attachment":[{"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1800"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1800"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.cientificos.pe\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1800"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}