Editing 1299: I Don't Own a TV
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 16: | Line 16: | ||
The title text suggests that whether people feel embarrassed or smug doesn't depend directly on what percentage of the population owns TVs (TV ownership rate) or even on how quickly this percentage is growing (derivative of TV ownership rate with respect to time); instead it depends on how the change in this percentage is speeding up or slowing down (second derivative of TV ownership rate with respect to time). Specifically, as the rate at which people adopt TV ownership accelerates (positive second derivative of TV ownership rate with respect to time), people who don't own one feel embarrassed (negative smugness); and as the market is saturated and the rate at which people adopt TV ownership slows down (negative second derivative of TV ownership rate with respect to time), people who don't own one feel smug (positive smugness). If people feel twice as embarrassed/smug when this rate of acceleration/deceleration doubles, then we have Randall's formulation: "smugness is proportional to the negative second derivative of TV ownership rate with respect to time". | The title text suggests that whether people feel embarrassed or smug doesn't depend directly on what percentage of the population owns TVs (TV ownership rate) or even on how quickly this percentage is growing (derivative of TV ownership rate with respect to time); instead it depends on how the change in this percentage is speeding up or slowing down (second derivative of TV ownership rate with respect to time). Specifically, as the rate at which people adopt TV ownership accelerates (positive second derivative of TV ownership rate with respect to time), people who don't own one feel embarrassed (negative smugness); and as the market is saturated and the rate at which people adopt TV ownership slows down (negative second derivative of TV ownership rate with respect to time), people who don't own one feel smug (positive smugness). If people feel twice as embarrassed/smug when this rate of acceleration/deceleration doubles, then we have Randall's formulation: "smugness is proportional to the negative second derivative of TV ownership rate with respect to time". | ||
β | As evidence for this, the adoption of TV ownership should theoretically follow a {{w|Sigmoid function|sigmoid curve}}, which is the graph of something that starts small, grows in a spurt, and then approaches a maximum capacity (in this case 100%). | + | As evidence for this, the adoption of TV ownership should theoretically follow a {{w|Sigmoid function|sigmoid curve}}, which is the graph of something that starts small, grows in a spurt, and then approaches a maximum capacity (in this case 100%). The negative second derivative of a sigmoid curve looks very much like Randall's graph. |
==Transcript== | ==Transcript== |