Our theme for the month of March is “Ask the post calvin.” We’re taking on questions submitted by readers and offering our best advice.
Dear the post calvin,
I’m bad at math. I still do basic addition and subtraction on my fingers. I have to really stop and think about how much a pair of pants costs if it’s 20% off. I try not to rely on my phone/calculator too much because it’s probably good to keep flexing that muscle, but I’m just embarrassed sometimes when I’m counting points on my fingers during board games. How can I get better?
First, as somebody who likes math, I want to clarify: what you’re describing is being bad at arithmetic, not necessarily being bad at math. I think of arithmetic to math as spelling to poetry; you can be a very good poet without being a perfect speller, and you can be a very good mathematician without being perfect at arithmetic (just be sure to double check your spelling and/or arithmetic before you publish anything). Indeed, having sat through many math classes in my life, I can say with confidence that even people who have dedicated their lives to studying math can still make arithmetic errors. I say this not to shame you for using the wrong word, but to encourage you to explore math, because it is an interesting field.
Now to your question: the annoying truth is that it will require practice. Fortunately, opportunities to practice are myriad. When you watch the news and they say that malaria deaths have fallen by 29% from 603 thousand per year, try to estimate what the number of deaths is now. When somebody says their car gets 22 miles to the gallon, try to estimate how many gallons it would take to drive the 176 miles from Grand Rapids to Chicago. People talk about numbers all the time, so practice some mental arithmetic, then check it on a calculator.
That said, there are a few little tricks that can make mental calculations easier. There are a bunch of cool but mostly useless tricks that you can find online. If that’s your style, go for it, but here are some less cool but more useful tricks that I like to use (in approximate order of importance):
- Break it down. Multiplying by 135 is hard. Multiplying by 100 isn’t that hard, multiplying by 30 isn’t that hard, and multiplying by 5 isn’t that hard. But here’s the thing: just add together all the answers from the second sentence and you get the answer from the first sentence. Same goes for percents: figuring out 20% is hard, but figuring out 10% is easy (just move the decimal) and multiplying by 2 isn’t so bad. This also works with fractions: computing two-fifths is the same as multiplying by 2 and then dividing by 5.
- Just try to get close enough. Most of the time it’s not necessary to get the exact answer. For instance, when you’re shopping it’s usually fine to get a good estimate; there’s no need to get exactly the right number of pennies you’re going to need. So, for example, you can often ignore everything after the first digit or two. Figuring out 29% of 603 is hard. Figuring out 30% of 600 is easy (especially if you “Break it down™”). And guess what? 29% of 603 is 174.87, and 30% of 600 is 180. You simplify the problem substantially and get an answer that is very close to the right one.
- Reframe it. Figuring out 20% is the same as dividing by 5. Do whichever is easier in your context. Figuring out 70% is the same as subtracting 30% from the total. Do whichever is easier in your context. Figuring out two-fifths is the same as multiplying by 2 and then dividing by 5 or dividing by 5 and then multiplying by 2. Do whichever is easier in your context.
- Guess and check. This is especially useful for division. Division is hard. Multiplying isn’t that hard. But division is just the inverse of multiplication: if you can solve one, you can solve the other. Say I wanted to know 429 divided by 3. Well, 3 times 100 is 300, so it’s more than 100. And 3 times 200 is 600, so it’s less than 200. And 3 times 150 is 450, so it’s less than 150, but we’re getting close. Then you can keep doing that until you arrive at the answer (or an answer that you think is “close enough™”).
Dear the post calvin,
What’s the best way to study for the GRE?
Grad School Bound
(I’m assuming you’re referring to the general test rather than a specific subject test.)
Lauren Boersma has some advice here. One of her pieces of advice is to consult me, so you’ve come to the right place.
That said, my advice for the essay section is “don’t worry about it; it’s dumb and highly subjective,” and I did quite poorly on that part, so maybe don’t take that advice.
I have a bit more to say on the objective portions. The advice I got from a professor I worked for was “answer all the questions correctly.” This was extremely good advice, and I followed it as well as I could. I recommend you do the same.
For the verbal section: Unless you already have an enormous vocabulary, you should spend a lot of time studying vocab flashcards. Physical flashcards are cheap (or free if you can get them from a friend who has recently taken the exam), and there are many free vocab apps, so there’s no excuse not to study. For the reading comprehension stuff, I think the main limiting factor is time, so practice example questions with example readings in a timed environment until you find a good balance of deep reading, skimming, and answering questions.
For the math section: Don’t do ANY math practice outside of practice questions that have been on actual GREs. They always ask the same types of questions that require the same types of tricks, so don’t bother studying math in general; study for the GRE specifically. The biggest hurdle with the math section is that they’re actively trying to dupe you. For instance, they love to ask questions like “which is bigger, 2 or the square root of 9?” and your first instinct is to be like “well the square root of 9 is 3 which is bigger than 2,” but you should think “well the square root of 9 is 3 or -3 which could be bigger or smaller than 2.” They’ll specifically give possible answers that prey on the incorrect first instinct, but they do so in predictable ways. So learn their tricks from previous exams and don’t let yourself get fooled.
Overall: Buy and use some practice books—especially for the math section, but both are worth practicing. They don’t need to be the newest edition (a few years old is perfectly fine and typically much cheaper). Do a couple practices in a timed environment. Being timed is scary. Try to get used to it and develop strategies to use time well (this isn’t just going as fast as possible; good time usage involves slowing down sometimes and focusing on one question rather than flitting back and forth between many questions).
Dear the post calvin,
Why are corporations given the same rights as people when it comes to free speech and political contributions, but not when it comes to jail time and legal consequences? Help!
An American Person
Dear American Natural Person,
To clarify: corporations are not given the same rights as people when it comes to free speech and political contributions (e.g. corporations are not allowed to give money directly to candidates or candidate committees, but people are) and are subject to legal consequences like lawsuits and fines. One could (reasonably) argue that the differences in campaign contribution laws are immaterial and legal penalties are insufficient, but they do exist. And they highlight an important point: American law does have distinctions between natural persons (human beings) and juridical persons (a non-human entity that can act as a single legal unit).
I think a lot of the public discourse about corporate personhood treats it as a weird boogeyman because “corporations aren’t people.” But it’s obvious that corporations aren’t natural people, and it’s extremely convenient to treat them as juridical people. Treating corporations as single legal units allows us to substantially simplify contracts and other activities at the intersection of business and law. This isn’t limited to private interest; issues of public interest like taxes and regulations are made possible (and/or substantially less costly) through corporate personhood. Obviously it isn’t a complete panacea for the public good and it can introduce problems of its own, but it has a reasonable justification.
In fact, I’d guess that most people would say that the corporate right to free speech is reasonable (at least in some circumstances). For example, I think most people are glad that press corporations have the right to free speech (e.g. famously The New York Times and The Washington Post). So, I don’t think corporate personhood (or the corresponding right to speech) is the central problem that people have with corporate money in politics.
Another issue that people discuss is the treatment of restrictions on political spending as restrictions on free speech. This goes back to a 1976 Supreme Court Case in which the majority argued that “a restriction on the amount of money a person or group can spend on political communication during a campaign necessarily reduces the quantity of expression by restricting the number of issues discussed, the depth of their exploration, and the size of the audience reached.” Some people interpret this to mean that “money is speech,” and they disagree. A more direct reading is not that money is speech but that restricting money is restricting speech, and it isn’t the government’s business to restrict speech unless there is a direct public interest in doing so.
This brings us to (what I think is) the core of the problem that people have with corporate money in politics: money in politics can lead to corruption, and there is a direct public interest in preventing corruption. If this is your bugaboo with corporate money in politics, then it’s worth noting that it doesn’t hinge on corporate personhood or the right of corporate persons to free speech, and it doesn’t hinge on whether or not restricting money is restricting free speech. Instead it is a question of whether or not this money (because of its source or its quantity or any other reason) leads to corruption. This is an important point; Justice Stevens used variants of the word “corrupt” at least eighty times in his dissent on the Citizens United decision.
(Many points in this answer were discussed with people who have legal expertise. Most insights are theirs, and all errors are mine. Also, states and countries vary; I’m talking about American federal law.)
Dear the post calvin,
How do I seize the means of production and overthrow the bourgeoisie when the means of production have been outsourced?
Dear Muddled Marxist,
Marx’s emphasis on the physical means of production as the main drivers of profit and capital accumulation has become pretty outdated in most developed countries. The output of labor in twenty-first-century, developed countries is usually intangible services rather than tangible commodities. The means of producing services are the minds and bodies of the people performing them, and I don’t think anyone claims that the bourgeoisie literally own any minds and bodies (certainly not in any legal sense). Instead they own the intangibles that give them access to the surplus generated by this labor: intellectual property rights, etc. Perhaps most importantly they own the legal right to corporate decision-making and profits in the form of stocks and other financial products. If you want to see the contemporary bourgeoisie in numeric form, look no further than Table 10 of this paper: Household Wealth Trends in the United States, 1962 to 2016: Has Middle Class Wealth Recovered? An overwhelming eighty-four percent of stocks owned by Americans directly or indirectly (e.g. by retirement funds) are held by the wealthiest ten percent of Americans (with similar numbers for other investment assets). So I think if you’re going to seize something, you have to seize some legal rights.
Tony graduated in 2012 with majors in mathematics and economics. He now lives in Chicago and is pursuing graduate study in economics. He also has a very good cultural trivia podcast called “Here’s My Number, So Call Me Ishmael” available on Libsyn, iTunes, and Google Play.