Editing 870: Advertising

{{comic
| number    = 870
| date      = March 9, 2011
| title     = Advertising
| image     = mathematically annoying.png
| titletext = I remember the exact moment in my childhood when I realized, while reading a flyer, that nobody would ever spend money solely to tell me they wanted to give me something for nothing. It's a much more vivid memory than the (related) parental Santa talk.
}}

==Explanation==
This comic pokes fun at millions of advertising tricks, analyzing them mathematically.

*In the first panel, the phrase "up to 15% or more" is examined, and shows to encompass all real numbers. While intended to entice to customer with savings of 15%, the savings could be lower or even not at all. The phrase ultimately means "less than, equal to, or more than 15%," which is true no matter whether you save anything or not (it's a {{w|Tautology (logic)|tautology}}).

:The equation at the top of the panel expresses the same thing using {{w|set theory}} notation.  It reads out as: The {{w|Union (set theory)|union}} of {{w|Set (mathematics)|sets}} A and B equals the set of all x, such that x is {{w|Inequality (mathematics)|less than or equal to}} 15, or greater than 15, which equals the set of all {{w|real numbers}}.

:The same is expressed again with a {{w|number line}}; the numbers being interpreted as {{w|percentages}}.  The first range ending with a black dot indicates that everything below, as well as the number 15, is included ("up to 15%").  The second range beginning with a white dot indicates that it only includes numbers strictly bigger than 15 ("more than 15%").  The two ranges combined clearly cover the entire number line.

:(The way humans interpret language, as well as the realities of economics, makes this expression somewhat more meaningful in practice.  No reasonable consumer would experience savings of 0% or less from such a promotion [as they would instead simply stick with whatever they'd been using beforehand], and the phrasing of "up to 15%" as the primary portion of the phrase implies to a human listener that they'd be most likely to get some positive amount of savings between 0% and 15%, with the secondary "or more" interpreted as referring to a lesser chance of a greater reward.  Thus, in practice, "up to 15% or more" would be interpreted as meaning that most consumers would be able to realize positive net savings of approaching 15%, with a lucky few getting savings in excess of 15%.)

:The phrase "up to 15% or more" may be a reference to the {{w|Geico}} slogan at the time: a phone call lasting "15 minutes could save you 15% or more on car insurance." However the reference is unclear, as the words "''up to'' 15%" are not actually used by Geico. Though Geico's advertising is also referenced in [[42: Geico]].

*Second panel: Whatever is advertised with a big capital "FREE!" splashed over the ad, most likely does not belong to the things truly free.  The small asterisk, indicates the presence of a {{w|fine print}}, ensuring that the advertisers are only technically not guilty of {{w|false advertising}}.  The conditions attached in the fine print typically reveal how they will (try to) make money from you.

:We are even given a little formula to calculate the average amount of money they expect to make from the readers. The assumption is that they expect to generate at least as much income from the ad as what they paid to print and publish it in the first place.

:(It should be noted, however, that, in many, if not most, cases, it ''is'' possible, with some careful examination of the fine print, to partially or completely dodge the seller's attempts to impose ancillary costs.)

*The third panel relates to sales tactics that are based on a scaling percentage rate - for example, all items are 20% off, but if you spend more than $200, you get 30% off instead, and so on. These are almost universally proclaimed with a phrase like "The more you spend, the more you save!" In absolute dollar terms, this is of course nonsense, as "spending" is the opposite of "saving", and the deal is there to make you spend more.  The graph shows this interpretation - spending zero money implies you have saved all your money (the dot where it intersects the X axis), whereas spending all your money implies you have saved none (the dot where it intersects the Y axis).  There is a linear relationship between the two: the amount of money spent, plus the amount of money saved, has to add up to a constant number (your original savings).

:(However, if "the more you spend, the more you save" is interpreted as referring to the proportion of the list price that the  consumer now doesn't have to pay due to the ''x''%-off promotion, the expression ''does'' make sense, as the discount ''as a proportion of the list price'' does indeed increase the more you spend.  For [relatively-]nonperishable goods, this makes it a good idea to take advantage of these promotions to make large bulk purchases, as the scaling discount rate makes the cost per unit of merchandise lowest for very large purchases, making these a much-more-efficient use of one's money than frequent low-volume purchases [especially as a large proportion of these low-volume purchases would be at times when there was no ongoing promotion, meaning that they wouldn't be able to take advantage of even the lesser discount rate of these promotions].)

The title text compares Randall's realization of the "FREE"-fraud to the revelation that {{w|Santa Claus}} is not real.

==Transcript==
:Mathematically Annoying Advertising:

:A ∪ B = {x:x ≤ 15 or x > 15} = ℝ
:[line graph representing the above equation.]
:When discussing real numbers, it is impossible to get more vague than "up to 15% or more".

:["'''FREE!'''*" in large text, with substantial illegible fine print.]
:If someone has paid $x to have the word "free" typeset for you and N other people to read, their expected value for the money that will move from you to them is at least $(x / (N+1))

:[Graph representing inverse relationship between "amount you spend" on the y axis and "amount you save" on the x axis.]
:It would be difficult for the phrase "the more you spend the more you save" to be more wrong.

==Trivia==
Randall changed the image name from advertising.png to mathematically_annoying.png, since adblocking extensions interpreted it as an ad and made the comic blank. He had the same problem again just three months later with [[906: Advertising Discovery]].

{{comic discussion}}

[[Category:Charts]]
[[Category:Line graphs]]
[[Category:Math]]