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| | ==Explanation== | | ==Explanation== |
| − | This comic pokes fun at millions of advertising tricks, analyzing them mathematically. | + | This comic pokes fun at some advertising tricks, analyzing them mathematically. |
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| − | *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}}). | + | *"Up to 15% or more" is a reference to the {{w|Geico}} car insurance commercials: "15 minutes could save you up to 15% or more on car insurance." "Up to" means "less than or equal to," so the phrase means "less than, equal to, or more than 15%," which is a {{w|tautology}}. |
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| − | :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 first line uses notation from {{w|set theory}} and 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}}. |
| | + | :Below is a {{w|number line}} (with the numbers being interpreted as {{w|percentages}}) the black dot indicates that the number 15 is included, and the white dot indicates that 15 is not included, but only strictly bigger numbers. |
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| − | :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. | + | :Geico's ad is also referenced in [[42: Geico]] |
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| − | :(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%.) | + | *[http://thepiratebay.se/search/some%20things/0/6/0 Some things] in life are free. However, typically not those aggressively advertised, with a capital "free!" splashed right over the ads, followed by a small asterisk, indicating the presence of a {{w|fine print}}, ensuring that they are only technically not guilty of {{w|false advertising}}. (Get a '''FREE'''* drink!) |
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| − | :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]]. | + | :The little formula [[Randall]] gives, is to calculate the least amount of money that they expect to make from you. The suggestion is that they expect their income from the ad to be more than what they paid for it. <small>(*with the purchase of a $6 meal)</small> |
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| − | *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. | + | *Some sales 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!" This is of course nonsense, as "spending" is the opposite of "saving", and the deal is there to make you spend more. |
| | + | :Note that an alternative phrasing "The more you buy, the more you save" is not strictly a contradiction. In some situations, the total number of items you intend to buy may place you just below the spending threshold that would qualify you for an additional discount; you can strategically buy additional items to place you just past the threshold. Despite buying a greater quantity of items, after the discount is applied, you will have spent less money, and thus saved more. (Though savvy retailers will attempt to avert this by placing this exploitable range higher than the cost of what any consumer reasonably needs, forcing them to spend more to qualify for the discount.) |
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| − | :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.
| + | For those who don't celebrate Christmas, {{w|Santa Claus}} is a mythical person responsible for delivering presents to good children on Christmas Eve. Randall explains in the title text that the first flaw in mathematically annoying advertising (that there will always be someone who profits from said advertisement in some way) is what led him to realize that Santa isn't real. Although most small children are traumatized after learning this, it is a testament to Randall's level of geekiness that he is more concerned with the first revelation. |
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| − | :(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.)
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| − | *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).
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| − | :(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].)
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| − | The title text compares Randall's realization of the "FREE"-fraud to the revelation that {{w|Santa Claus}} is not real.
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| | ==Transcript== | | ==Transcript== |
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| | :When discussing real numbers, it is impossible to get more vague than "up to 15% or more". | | :When discussing real numbers, it is impossible to get more vague than "up to 15% or more". |
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| − | :["'''FREE!'''*" in large text, with substantial illegible fine print.] | + | :["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)) | | :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)) |
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| | {{comic discussion}} | | {{comic discussion}} |
| − | | + | [[Category:Math]] |
| | [[Category:Charts]] | | [[Category:Charts]] |
| − | [[Category:Line graphs]]
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| − | [[Category:Math]]
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