Parade Magazine is a supplement that most newspapers, although not the hoity-toity New York Times, insert into their Sunday edition. Since 1986, nearly every issue has included a brainteaser column by Marilyn vos Savant. Besides her impressive feat of publishing weekly for nearly thirty years, vos Savant may be best known for having once been listed in the Guinness Book of World Records as the person with the highest recorded IQ – an “accomplishment” which, until recently, she trumpeted at the bottom of every “Ask Marilyn”.
Naturally, I read every one hoping to catch her in error. She rarely satisfies this craving but every now and then, like today, she messes up. In fact, when I read her January 25 puzzle, I knew she had presented an almost identical problem before (turns out it was in 1992) and answered it incorrectly. I wondered whether she would tacitly admit her prior error by providing the correct response. She did not.
The question is which is better: A starting salary of $30,000 with (A) an annual $1000 raise or (B) a twice-yearly $300 raise? Now, your immediate response as mine was 23 years ago and this morning is probably (A), right? I mean $1000 more over one year beats two $300 raises during the same period but vos Savant says the answer is (B).
Here’s her explanation:
Say it’s Jan. 1, 2015, and you choose the $1,000 raise at the end of the year. In 2015, you earn $30,000. But if you choose the $300 raise, you earn $15,000 during the first six months and $15,300 during the second six months. In 2015, you earn $30,300. With the $1,000 raise in effect for 2015, you earn $31,000. But wih the $300 raise, you earn $15,600 during the first six months and $15,900 during the second six months. In 2016, you earn $31,500.
Sounds persuasive doesn’t it. The problem is that vos Savant wrongly compresses the distribution of each $300 annual raise such that it’s paid in full in half a year. In fact, the years go as follows:
2015: (A) $30,000 (B) $30,150 ($300 raise is in effect for 1/2 the year)
2016: (A) $31,000 (B) $30,750 ($30,000 + 1/2 X $600 + 1/2 X $900)
2017: (A) $32,000 (B) $31,350 ($30,000 + 1/2 X $1,200 + 1/2 X $1,500)
2018: (A) $33,000 (B) $31,950 ($30,000 + 1/2 X $1,800 + 1/2 X $2,100)
After the first year, the gap favoring (A), not vos Savant’s choice (B), becomes wider and wider. She might respond that because the question provides for either a “$1,000 raise every year” or a “$300 raise every six months” the extra $300 each 1/2 year is supposed to be paid in full within the 1/2 year. This explanation fails because both (A) and (B) assume a $30,000 annual salary so any raise would likewise be distributed over the course of the year.
Marilyn would be on less shaky ground if the employee were offered either (A) $30,000 annually to start with a $1,000 raise each year or (B) $15,000 per 6 months with a $300 raise at the end of each period. But that is not how the question is phrased. She might also have an argument if the offers called for bonuses which, by definition, are paid in full when conferred. But again the question clearly defines the employee’s choice as between two different pay raise schedules. Simply put, vos Savant got the same problem wrong twice over a 23 year span.
Why am I devoting time to this? Well, vos Savant reaches an awful lot of Americans each week who have faith in her reasoning despite the fact that she does make elementary mistakes.
Math errors may be trivial but what about her position on global warming which is prominently featured on her home page and reprinted in full below:
I believe our planet is warming, of course. Although I don’t know how much humans have contributed, I would be surprised if it’s close to 100 percent. So, knowing how vastly the Earth’s climate has varied over its four- to five-billion-year history, I doubt that we can succeed in stabilizing it the way it is now. Regardless, we must try, if only to buy time.
But we can do better than that. I’d like to see our government supporting more adaptive, positive responses to the warming instead of assuming that we must concentrate all of our efforts on scaling back and attempting to maintain the world as it is today. There’s no significant downside to encouraging innovative programs designed to maximize every potential advantage of warming and minimize the disadvantages wherever it’s feasible.
The shift in course would be small, yet I believe that we would be heading in a more productive direction over time. Along with mending our ways, we would be in a safer situation overall if we also develop more coping mechanisms for whatever nature alone may be handing us. Call it “technological adaptation.”
At first blush, vos Savant is taking a reasonable down-the-middle approach. At least she doesn’t deny the basic fact that the planet is getting hotter and hotter. But starting with the second sentence, she descends into absurdity: “I don’t know how much humans have contributed but I would be surprised if it’s close to 100%.” Note what vos Savant does here. She refuses to concede that humans have any responsibility for the approximately 1.4 degrees F rise in global temperatures since 1880 with most of that since 1980. She fails to note that NASA, NOAA, and the Intergovernmental Panel on Climate Change, along with nearly every reputable scientist who has studied the issue, agree that humans burning carbon is the primary reason.
Vos Savant might respond, disingenuously, that because of Earth’s ever-changing climate, it’s implausible that humans are the only causal factor in any observed temperature change. Of course, this is correct. Put more simply, the planet’s temperature most likely would be different today than it was in 1880 even if we were still living before the discovery of fossil fuels. The problem with this argument is that humans might well be responsible for more than 100% of the observed change. In other words, without the heavy hand of industry, temperatures might just as likely be colder than they were 135 years ago rather than 1.4 degrees warmer.
Vos Savant’s dissimulation continues in her “solution”. Rather than focus on “attempting to maintain the [already severely compromised] world the way it is today”, which she claims is impossible given the climactic variations the earth has experienced over its 4 to 5 billion year history, she urges us to “develop more coping mechanisms for whatever nature alone may be handing us”. Vos Savant is silent as to the ways non-human animals and plants, upon which humans rely for our own survival, can adapt to climates for which they are wholly unsuited. Likewise, she appears dismissive of the extraordinary costs of protecting the billions of people living at or near sea level as the oceans continue their inexorable rise.
Due to her ubiquity in Sunday newspaper supplements and her gravitas as one of the world’s smartest people, vos Savant is undoubtedly influential. It is somewhat unfortunate that every now and then she makes careless math errors. It is highly regrettable that she ignores human responsibility for global warming, downplays the existential threat it poses, and promotes highly unrealistic approaches to living on our ever-hotter planet.