https://www.explainxkcd.com/wiki/api.php?action=feedcontributions&user=173.245.55.229&feedformat=atomexplain xkcd - User contributions [en]2022-08-18T23:38:59ZUser contributionsMediaWiki 1.30.0https://www.explainxkcd.com/wiki/index.php?title=Talk:1299:_I_Don%27t_Own_a_TV&diff=54294Talk:1299: I Don't Own a TV2013-12-04T16:28:19Z<p>173.245.55.229: The graph in the comic is the negative second derivative of a logistic function.</p>
<hr />
<div>Annual Data for households between 1958-1970<br />
http://www.tvhistory.tv/Annual_TV_Households_50-78.JPG<br />
<br />
Plotted next to a fitted logarithmic function<br />
http://imgur.com/aVWmQ9z<br />
<br />
The negative second derivative of this function<br />
http://imgur.com/xywpEJZ<br />
<br />
If someone can find more data for television ownership I'd love to see it :) {{unsigned ip|173.245.54.12}}<br />
<br />
Can someone explain why Randall believes smugness at not owning a television is decreasing? [[Special:Contributions/199.27.128.138|199.27.128.138]] 08:31, 4 December 2013 (UTC)<br />
<br />
Because as TVs become less relevant, people don't feel smug for not owning one. [[Special:Contributions/141.101.99.216|141.101.99.216]] 11:44, 4 December 2013 (UTC)<br />
<br />
;Current explanation - logistic curve<br />
<br />
The current explanation is total bullshit. The thing with the negative second derivative is just saying, that the more embarrased people are, the more the change of the TV ownership rate will increase, which just means, more and more people will get themselves TVs.<br />
The other point of view is, the more smug you will look like for not owning a TV, the more the change of the TV ownership rate will decline, which means, that less and less people are buying TVs.<br />
<br />
It has nothing to do with a logistic curve. The function, which second derivative is depicted in this comic is totally irrelevant.<br />
<br />
[[Special:Contributions/108.162.231.19|108.162.231.19]] 08:34, 4 December 2013 (UTC)<br />
<br />
I have the strong feeling he is talking about a sine wave, not a logistic function. It fits the curve in the comic as well as the condition of f"=-f. <br />
Also, it makes way more sense for the smugness to behave like this over time as for the first 30 years TV is culturally extremely significant and you therefore would want to own one in order to participate. But with declining quality of television and the emergence of the internet you might feel as if you were extremely progressive by not owning one anymore.<br />
<br />
[[Special:Contributions/108.162.254.189|108.162.254.189]] 09:25, 4 December 2013 (UTC)<br />
<br />
Yes, it definitely could be a sine curve. (see: [http://www.wolframalpha.com/input/?i=d%5E2%2Fdx%5E2%28sin%28x%29%29 http://www.wolframalpha.com/input/?i=d%5E2%2Fdx%5E2%28sin%28x%29%29]). If one would neglect the beginning of the function for simplicity, this could be a solution.<br />
<br />
[[Special:Contributions/108.162.231.19|108.162.231.19]] 10:07, 4 December 2013 (UTC)<br />
<br />
We bid a tearful farewell to our friend the line break. [[Special:Contributions/141.101.99.216|141.101.99.216]] 11:50, 4 December 2013 (UTC)<br />
<br />
http://www.wolframalpha.com/input/?i=sin%283*pi*x%2F100%2Bpi%2F2%29+from+1945+to+2014 [[User:Xhfz|Xhfz]] ([[User talk:Xhfz|talk]]) 12:02, 4 December 2013 (UTC)<br />
<br />
I agree with the commenter who said that the current explanation is bullshit, but I think he has the cause and effect reversed. Randall is saying that you feel more smug about not owning a TV as a result of observing how quickly TV ownership is becoming more or less trendy. In the 1950's, TV's were catching on quickly and becoming more popular, so you would feel embarrassed for not owning one. Later, the trendiness would start to decline as more people owned one, and you would head towards being smug. In the 2000s, people are giving up TVs because the internet makes them unnecessary. As this happens more and more, there's no point in feeling smug because you're no longer bucking a trend at all. --[[User:Kazim|Kazim]] ([[User talk:Kazim|talk]]) 12:49, 4 December 2013 (UTC)<br />
<br />
In my view the title text joke is that smugness is defined as a function of TV ownership when in reality TV ownership is a function of smugness. [[User:Ralfoide|Ralfoide]] ([[User talk:Ralfoide|talk]]) 15:18, 4 December 2013 (UTC)<br />
<br />
Hold on, the logistic curve gives very reasonable graphs both for ownership of TVs and for the negative second derivative. TV ownership easily fits a logistic curve, as it starts at zero and has to approach some upper limit. The negative second derivative has a very similar shape to the graph in the comic. Here's Wolfram|Alpha for the negative second derivative of a generic logistic curve: <http://www.wolframalpha.com/input/?i=-%28+d%2Fdx+d%2Fdx+%28100%2F%281%2Be%5E-%28.1x%29%29%29%29>. This would suggest that as time goes to infinity, people's feelings about TV ownership approach neutral; they do not oscillate like a sine function. This makes sense, because for the negative second derivative to be a sine function, TV ownership would have to be too, yet TV ownership is unlikely to be periodic. [[Special:Contributions/173.245.55.229|173.245.55.229]] 16:28, 4 December 2013 (UTC)</div>173.245.55.229