Watch it. It's about 25 minutes long. There are many important messages here; please listen with your eyes opened. Ms Lewinsky is a brilliant and thoughtful woman with impressive speaking skills and a life experience from which we can learn much about our culture, about the era of electronic communications and about the torture of public humiliation.
Ms Lewinsky refers to herself as "Patient Zero" in cyberbullying. Over 20 years ago, information about her life changing event spread rapidly and internationally over the internet. Her image, along with negative labels and sordid stories and commentaries, was spread with never-seen-before speed. Her story was likely exaggerated through repetition (ever play "telephone" as a kid?) and carpeted the globe. Her name became household; she was recognized on the street and grocery store. She claims, likely accurately, to be the first to be publicly humiliated in this extreme manner and at a time before "cyberbullying" was a word. Since then, bullying on the internet has become lethal. Take a deep breath and process that idea, google if you'd like. We will now sanitize her heavy message and look at just the math.
So if you have not already watched her TED talk, then stop reading MY blog now, click on the link above to her TED talk, and watch her full talk. Then return to this page and continue.
Again, let's separate ourselves from her personal humiliation and look at the spread of information on the internet. We will start slowly, and with an unrealistically simple model to set the stage. Our first model will minimize the spread but will still illustrate how rapidly information is passed from person to person electronically. We'll put a name to this kind of growth. Let's start by working by hand. You'll need full-sized graphing paper , some regular lined paper for some work, and at least two writing implements of different colors. (The link will take you to free graph paper; you can choose your size. Choose Cartesian Graph Paper. Let your size be 85x11 inches. Choose millimeters. Measure in 5 cm units. You are lucky, though, I've copied some of this paper for you to use for this exercise. )
With a ruler or straightedge, darken a horizontal line one unit upwards from the bottom of your graph paper, oriented vertically. This will be your x axis. Each PAIR of blocks will represent an HOUR time interval. Then darken a vertical line one unit to the left of the left side of your paper. This will be your y axis. Each block will represent the number of new people who receives the information. Label your axes with words and with numbers; labeling will help you keep track.
The parameters we will set include a limitation that you all might agree is very conservative. Let's say that each time a person receives this juicy information, they forward this information -- a simple "click" -- to only 3 different people. Let's say that folks send on information not continuously or within seconds, but once each HOUR. (Ok, so in reality, it could be shared on any social media account where potentially HUNDREDS of people would learn the information with a single instantaneous "click," but we are working with a simpler and far more conservative model. We are starting by spreading the message slowly and to three additional people at a time. Do you agree that we are really really slowing down the spread of information?)
At time = 0 (x=0, therefore the y intercept), have 1 person know the information. Then after 1 hour (x = 1), that person "clicks" the mouse to send the information to 3 people (so the coordinate is (1,3) ) Then at t = 2 (2 hours later), those 3 people each send the information to 3 more people (so the coordinate is (2,9)) At 3 hours, each of those 9 people send the message to 3 more new people: the coordinate is then (3,27). On your lined, paper, make a chart that represents hours in one column and number of new people who receive the information in the second column. You'll want to use your calculator and likely round appropriately. Find the numbers for up to 15 hours. (Use scientific notation if you need to!) This is, remember, just over half a day.
When you are done with the chart, plot the points on your graph paper. You might have trouble plotting some of the points on this single graph paper. You have nearly 40 blocks on the x axis, so you can represent 18 hours on your graph; let your chart be complete for each hour up to 15 hours. Record your observations, in writing. Here's the start of your blog.
Then find an equation that fits your data points. (in the form y = _______) Of course, Khan Academy parallels what we are doing nearly perfectly in a two minute video. In this video, you'll learn the name of these kinds of relations. So if you have not already watched Sal Khan in the video link above, stop reading this blog now and watch the Khan Academy lesson now then return to this page to continue. Be sure your BLOG TITLE includes the name of these relations. (Hint: begins with "e.")
Now let's adjust a single parameter. What if information is transferred only once each hour, but instead of only 3 people getting the information, 10 people receive the information? (This is still pretty conservative, in light of the fact that each "click" could spread the information to hundreds of your friends.) Re-do your chart on your paper. Plot the new points on your graph in a different color. Find the equation that fits your data points. Record your observations.
By now, you likely get the idea. What would happen if information was passed on -- more realistically -- once every 15 seconds? What if information was passed on to 100 new people with each "click" each person makes? How does the graph change for each adjustment? Report your understanding in your blog. Be expansive and thoughtful and creative. At some point, we can cease to understand the magnitude of the numbers our calculator reports: the numbers are simply too large.
On February 21 (Feb 22 for period 4), I will collect your charts and graphs and expect your blogs to be uploaded into canvas.
Our next blog will consider a different graphing strategy so we can graph more information about the large numbers that appear in these functions.
No comments:
Post a Comment