Socialist Math Textbook Exercises

This post was inspired by an exchange we had in the review of Thomas Sowell’s new book.

You know how bad math classes have become. What makes it worse is that politics have crept into the classroom. Here is an example of an actual math-quiz problem, quoted in Foreign Policy (linked from a story we did two years ago):

In 2004, a bread roll cost 40 cents. For the wheat that went into it, the farmer received less than 2 cents. What do you think about that?

This question might have preserved some semblance to math had it required the student to do some figuring. Where’s the math? I’m not even sure what the politics are, since five percent of the finished, full-retail price goes to the farmer, which is pretty good.

The goal of a good story problem is to make it relevant, to pick topics the student can understand and even—I hate saying this—sympathize with. And if we can make it “socially relevant”, why, we’re doing our part to save the world. At least, that is the attitude of all leading pedants today.

With that in mind, I have begun the creation of highly relevant math problems. The situations are of both world and local importance.

Solving these problems requires the kinds of skills usually taught in “pre-calculus” or high-school algebra courses.

  1. Grand socialist (of both the national and international varieties) schemes were directly responsible for the deaths of at least 150 million, over roughly a 100-year period. If the average height (including babies and the tall) is 66 inches, and you stacked those bodies end-to-end, you could reach about 156,250 miles. Now, the moon is about 240,000 miles away. Assuming the same kill rate, how many more years of grand socialist rule would we need to (A) reach the moon, and (B) return safely to Earth?
  2. The glorious international-socialist Chairman Mao killed at least 50 million people. Assume that for each person murdered, there was one relative who (in secret) cried over that person’s death. Suppose this crying led to a shedding of 3 teaspoons of tears (3 tsp. = 1 tbl. = 0.5 fl. oz.). How high would the walls of a pool built to hold this flood of tears be, if the pool’s radius is 50 feet? Hint: first calculate the base area of this pool.
  3. In 2009, there were roughly 6.9 billion people in the world, each of whom must be fed. 500 million people were fed insufficiently or were starving. Food, of course, comes from farms, 99% of which are conventional, and 1% “organic”. The yield from an organic farm is, optimistically, about 60% that of a conventional farm. If 50% of farms were organic, how many people would be fed insufficiently or would starve? Assume even food and farm distribution.
  4. Farmer Jones has 10,000 acres, on which it is estimated there are 250 vermin per acre. In addition to attending to his other duties, farmer Jones can shoot 50 vermin a day. (A) Assuming the rate of which vermin breed is negligible, how many days would it take farmer Jones to clear his land? (B) Farmer Jones has three boys, each of which is twice as efficient as their old man at shooting vermin. If all three boys and farmer Jones pulled together, how many days would it take to clear the land? (C) Farmer Jones is 60% accurate with his shots, meaning 40% of his shots go astray. His boys are each 80% accurate. How many rounds of ammunition will the family expend clearing their land?
  5. Uncle Ted’s Kill ’em & Grill ’em chain of restaurants serves venison sausage, which, despite its name, is made of 40% deer meet and 60% pig parts. Only 70% of a deer carcass can be turned into sausage, and 95% of a pig’s can. Assume that the weight of both deer and pigs are the same at 150 lbs, and that sausages are 0.5 lbs. In 2009, Uncle Ted sold 2.5 million venison sausages. (A) How many deer and pigs does this represent? (B) If, in an effort to comply with government regulations, Uncle Ted replaced 25% of his venison sausages with soy protein, how many fewer deer and pigs would he have slaughtered?
  6. A murderer is fifty times as likely to kill (again) compared against somebody who has never murdered before. In 2009, there were approximately 2.4 million inmates in all prisons. About 1% of these inmates were murderers. (A) If the murder rate per year for previous non-murderers is 1 in 1000, then how many murders will there be in prison in a year? Ignore all those who are murdered by ex-felons after they are released from prison. Assume there is no death penalty. (B) If the death penalty were exacted for all murderers, how many fewer dead bodies would there be in prison? Assume all executions are carried out in prison. Hint: this one is tricky!

Remember: any problem at this level involves simplifications. Therefore, to criticize a problem for it simplifications is to argue needlessly.

That’s all for now. Suggestions for more? We get enough of these and we can publish our own book! Title: Social Justice Mathematics.

Update Two problems were fixed because of ambiguities. Thanks to John Galt for reminding us of one.

27 Comments

  1. Hope this isn’t a duplicate. I think the spam filter got me.

    In 2004, a bread roll cost 40 cents. For the wheat that went into it, the farmer received less than 2 cents. What do you think about that?

    I’d say he got his 2 cents worth. In fact, the farmer got 5% of the gross price. I wonder how much the employees of the baker each got. Oh wait, he got LESS than 5% of the gross. Well, that’s OK then, he’s probably not overpaid.

    Definitely, a socialist type question, though. No common economic sense. IOW: if a bread roll costs 40 cents then everybody involved in its making should get 40 cents in compensation.

  2. Mr. Briggs,

    # 5 doens’t provide enough info. You need to add how much each sausage, deer and pig weigh.

    I remember a really good story problem we had in freshman physics. It started off,

    At some time during the third millenium, a team of solar system engineers discover a solid iron asteroid of radius X and density Y. They set up a conveyor belt to move the iron from one pole to the other and dug a hole of radius Z from one of the poles to the center. We were then asked to find the work necessary to raise the debris from the hole to the surface. We had to calculate the maximum speed of the conveyor. This turns out to be escape velocity. The engineers then complete the hole all the way to the other pole. We were then asked to determine who would win a pole to pole race if one engineer rode the conveyor at max speed and the other jumped into the hole. It was a draw. We also had to demonstrate that if not pulled out at the other pole, the engineer in the hole would execute simple harmonic motion. This went on and we got to know the asteroid very well.

  3. Ontario, Canada utilities pay residents 80 cents per kilowatt hour for electricity that they produce with ‘low cost’ renewables such as solar panels or wind turbines. The electricity price using dangerous and polluting nuclear, coal, hydro and natural gas power plants is 6 cents per kilowatt hour. The utility must charge its customers more to make up the difference. (A) If 50% of customers in Ontario decide to only sell renewable electricity to the utility, what will the new electricity price be for all electricity customers who purchase from the utility? (B) What percentage of utility customers need to produce renewable energy in order for the utility price to double to 12 cents per kilowatt hour? (C) A financially strapped Alfalfa farmer in Ontario decides to cover 10 acres of an existing field with solar panels. The average electric energy produced by the solar array is 600 kilowatt hours per day per acre. How much money will be redistributed from electricity customers to the farmer each year? (D) The farmer received a zero-interest government loan of $10,000,000 to purchase the solar panel system. How many years will it take before the farmer can purchase (with cash) a $15,000,000 ocean-front villa in Santa Barbara, right next door to Al Gore?

  4. If the average acre of forest contains $5,000 worth of timber, and

    if burning an acre of forest in a wildfire causes 10 times that value to be destroyed or damaged (in timber, wildlife, wildlife habitat, water yield, public health, heritage, recreation, and other economic externalities), and

    if the U.S. Government burns 10,000,000 acres of forest every year,

    then what is the total annual cost to the public in terms of total wealth destroyed or damaged?

    Bonus question #1: if so-called “environmentalists” wish to double the number of acres burned every year, then what would the new total annual cost be?

    Bonus question #2: if an irascible forester in Oregon manages to circumvent the desires of so-called “environmentalists” and by dint of his petulant whining gets the government to reduce the number of forest acres burned by half, how much annual wealth would be saved, and how much should we reward said forester for his troubles?

  5. Oh dear: “The yield from an organic farm is, optimistically, about 60% that of a conventional farm.”

    Wheat: The results from a 30 year trial (1940s to 1970s) in central Europe showed a 3% average yield increase from the use of artificial fertiliser. Not enough to cover the cost of the fertiliser, never mind the cost of application.

    Potatoes: Locally (NE Tasmania), yields are around 30 tonnes per acre. In southern Tas on less favourable soil, I regularly get 60 to 90 tonnes per acre using organic, rather than artificial fertiliser.

    Apples: One of my orcharding neighbours asked what I would do to manure an orchard. I said: “Do a leaf analysis first.” The leaf analysis showed no nutrient deficiencies, so no manure was applied that autumn. The yield in the following season was up 50% on expected. The orchards that were given the “required” 8:4:10 showed no deviation from expected yield.

    Pasture: When I bought the farm in 1981, I performed a soil analysis on the main paddock and also on the next door neighbour’s. The neighbour applied the “required” lime-super every 2-3 years. I applied one light application of a commercial organic fertiliser (Dynamic Lifter). After 5 years, available phosphorus had more than doubled on my patch when compared with my neighbour’s. I suspect this was almost entirely due to a dramatic increase in earthworm population.

    Recently published research in the European Journal of Agronomy and other international scientific publications has indicted glyphosate and Roundup Ready GMO grains for reducing grain crop yields. Over time (10-20 yr), micronutrients chelated by glyphosate become unavailable killing beneficial soil bacteria. This has led to the return of serious diseases such as take-all and other soil-borne pathogens.

    Canadian research has shown that the application of glyphosate one or more times in the three years previous to planting wheat was the most important agronomic factor associated with high Fusarium head blight or scab (FHB) in wheat. There was a 75 percent
    increase in FHB for all crops and a 122 percent increase for crops under minimum-till where glyphosate was used. The most severe FHB occurs where an RR crop precedes wheat in the
    rotation. Glyphosate altered the plant’s physiology to increase susceptibility of wheat and barley to FHB and increase the toxins these pathogens produce.

    Think I’ll stick to organic production somehow…

    Oh yes, for the statistically inclined, every economic analysis I’ve seen so far comparing organic and conventional farming indicates no statistically significant difference in farm income. Anecdotally, many organic farmers said they slept better after conversion because they carried a much lower level of debt.

  6. And you end up paying a LOT more in the grocery store for those foods.

    ‘Pompous’ was well chosen.

  7. Pompous can safely tell everyone his secret that organic production is cheaper with the same or higher yields because all the other farmers (that use non-organic methods) are not interested in higher profit and higher yields. Or perhaps he is just a liar.

  8. Otter said:
    16 May 2010 at 3:36 pm

    “And you end up paying a LOT more in the grocery store for those foods.

    ‘Pompous’ was well chosen.”

    Back when I was growing commercially, most organic produce was sold into the conventional market, there being no organic market to speak of. There is a range of prices paid by the wholesalers based on *quality*. I believe that Chung sold most of my output to the better Hobart restaurants.

    Calling myself pompous tends to take the wind out of sails 😉

  9. Jeffous said:
    16 May 2010 at 4:06 pm

    “Pompous can safely tell everyone his secret that organic production is cheaper with the same or higher yields because all the other farmers (that use non-organic methods) are not interested in higher profit and higher yields. Or perhaps he is just a liar.”

    No I’m not a liar, nor are farmers idiots. Higher yields do not necessarily lead to higher profits. Higher yields *generally* require more inputs and inputs carry a cost. The pasture and apple examples were where applying water-soluble nutrients to the soil reduced the plants’ ability to access nutrients already in the soil.

    No secrets here.

  10. Pomp,

    Forgive my incredulity but I grew up on a small farm. We lost a significant amount to insect infestation and puny yields due to nutritional deficiencies both easily corrected with fertilizers and insecticides. Crop rotation helped but often meant less income for at least one season — one of the prices of farming. It’s hard to see how “organic” farming has higher yields. Good intentions don’t make a good insecticide.

    DAV

  11. DAV, whatever makes you think organic farmers don’t use fertilisers, or insecticides? Paul Mäder et al reported in “Science” 31 May 2002: Vol. 296. no. 5573, pp. 1694 – 1697 DOI: 10.1126/science.1071148:

    “… results from a 21-year study of agronomic and ecological performance of biodynamic, bioorganic, and conventional farming systems in Central Europe… [indicate] crop yields to be 20% lower in the organic systems, although input of fertilizer and energy was reduced by 34 to 53% and pesticide input by 97%. Enhanced soil fertility and higher biodiversity found in organic plots may render these systems less dependent on external inputs.”

    It’s probable (based on my own trials) that had fertiliser and energy use been equal to that of the conventional farming systems in the study that yields from the organic plots would have exceeded the conventional. This is a far cry from Briggs’ “optimistic” claim of organic crop yields being 40% lower.

    Of course insects don’t respond to “good intentions”, but they will happily respond to fertiliser inputs. Water soluble N generates lots of uncombined amino acids in plant sap which makes aphids and other sap-suckers very happy. When organic farmers apply N in protein form (nearly always as animal manures) the aphids find very few uncombined amino acids, mostly there’s just whole protein chains that they find indigestible.

    Note that this doesn’t necessarily eliminate aphids, but it sure makes their control less of an issue. The local ladybird population takes care of mine except on the Brussels sprouts. Then it’s time to resort to (shock, gasp, horror) an industrial chemical commonly known as soap! I prefer soap to Malathion mainly because it’s several orders of magnitude cheaper and considerably less toxic.

    Much of what has been learnt about successful organic farming over the last few decades is about plant and animal nutrition. [See Humic, Fulvic and Microbial Balance: Organic Soil Conditioning : An Agricultural Text and Reference Book by William R. Jackson]. It’s possible to push yields to considerably higher levels with compost than is possible with water-soluble fertilisers. But as I said before, there’s a cost to this. One of the arts of successful farming is contributing to your bank balance at the end of the day and that requires balancing input costs against income.

  12. It’s been sixty years since I did high school math, but —

    1. We would need 230,400,000 bodies to reach the Moon, or 153.6 years total — (A) an additional 53.6 years. (B) No more; climb back down the stack to return — but there is no way to return “safely” to a place of grand socialist rule.

    2. Missing information: fl. oz. => cu. ft. conversion. From online conversion.com: “1 gallon [US, liquid] = 0.133 680 555 56 cubic foot”. We know there are 128 fl. oz. in a gallon.
    25 million fl. oz = 195312.5 gallons = 26113 cu ft
    The area of the pool is 7,854 sq. ft. It would need to be 3.325 feet deep to contain the tears.
    On the other hand, assuming an average of six cu ft per body, a pit of the same diameter as the pool would have to be 7.23 miles deep to bury the corpses.

  13. Wait–there used to be a joke going around the internet that sounds exactly like your bread roll exercise. Are you telling me there are TEXTBOOKS out there with these types of problems in real life?

  14. John Wheeler, Princeton, namer of black hole, asked his grad students in a final, “How far does the wild goose fly?”

  15. Coincidentally this problem was discusses on “Breaking Bad” on Sunday. Walt has stuck a deal with the chicken man to cook 200 pounds of meth per week, for 12 weeks with the option to extend the contract. He will be paid $3 million for this contract. Jessie, Walt’s partner, calculates that if meth wholesales at $40,000/pound, Walt and Jessie are underpaid.

    Organic farming — I have no expertise here, but that has never stopped me, before. I remember a college class where we discussed Amish farms vs. conventional farms in Pennsylvania. The Amish have about twice the yield per acre as the conventional farms. But the Amish are also putting in several times the man-hours. Conventional farming doesn’t attempt to maximize yield per acre, but instead, maximizes ROI.

  16. Corrollary to question 2: when all those tears evaporate, thereby increasing water vapor, a powerful GHG in the atmosphere, what will the average global temperature rise (or fall) in degrees C be? Don’t forget to compensate for all the GHG that would have been emitted if the 50 million were allowed to live. Did Chairman Mao love or hate the Earth?

  17. Doug M said:
    17 May 2010 at 10:16 am

    “Organic farming — I have no expertise here, but that has never stopped me, before. I remember a college class where we discussed Amish farms vs. conventional farms in Pennsylvania. The Amish have about twice the yield per acre as the conventional farms. But the Amish are also putting in several times the man-hours. Conventional farming doesn’t attempt to maximize yield per acre, but instead, maximizes ROI.”

    The interesting question then is *does* conventional farming maximise ROI? Back in 1990, we had an international sustainable agriculture conference in Adelaide, South Australia. One of the farm walks was on Sam Jericho’s sheep/wheat farm on the Eyre Peninsula. Now Sam isn’t organic in the legalistic sense; he uses herbicide and therefore, according to Green ideology, like The Git, an Evil Enemy of The People.

    Back in the 1920s, Sam’s dad had planted out a significant portion of the farm to trees and Sam continued the tradition. The Jerichos also went to considerable trouble to maintain soil organic matter by growing green manure crops. At the time, the district was in drought, but Sam’s farm was producing 30 bags of wheat per acre and his treeless neighbour’s 10 bags from there worn-out soil.

    The ABC Radio journalist who interviewed Sam for the Country Hour asked Sam: “Would you have made more money farming in your neighbours’ way than you and your dad’s?” Sam’s reply: “yeah, but I’d only have spent it.”

    We were all impressed by Sam’s long-term profitability while his neighbours were all crying and asking for government handouts to stay in business.

    Here’s a profile on another “socialist” organic farmer, my recently deceased friend, Bert Farquhar:

  18. Hmmm… WordPress seems to have deleted the URL. Try Googling “Bert Farquhar”. The story is at “ABC Rural Legends: Bert Farquhar”.

  19. Pompous Git,

    The spam filter (WordPress + Akismet + Bad Behavior) are sending an increasing number of valid posts to the spam box. I have no idea why. My spam rates do not appear to have increased. Sorry about that.

  20. Hi Briggs, I stumbled across this because I follow math news and trends in education. The question you quote piqued my interest.

    Interesting conversation between PG and the others. I don’t have a take on the relative merits of organic gardening, but as a math curriculum expert working with UK and US math standards, the particular example that prompted your post seems suspect.

    Can you provide the full quote from the FP piece?
    The article is subscription-only.

    But reproductions of the piece here:
    http://www.ipa.org.au/library/publication/1210833458_document_60-1_theil.pdf
    or here: http://network.nationalpost.com/np/blogs/fullcomment/archive/2008/02/11/stefan-theil-europe-s-crusade-against-capitalism.aspx

    …don’t feature the example you quote. In fact, the reproduced pieces don’t refer once to mathematics. The emphasis of the original article seems to be on economics, not math.

    I don’t doubt that standards have shifted in math teaching, nor that politics can creep into economics education (which is the subject of the piece).

    I don’t also doubt that individual teachers can impose their political will on their students, but I’ve never seen a formally-set and published math question phrased even remotely like this. Besides, math teachers are not expected to mark such open-ended questions.

    Show me that the question came from a published math test in Europe or the USA and I’ll get some salt, pepper, a knife, a fork, and my hat. If this comes from an economics paper, I hope you’ll agree that the question, whilst leading, is legitimate.

    In the meantime, explain why you’ve taken the tongue-in-cheek leap from apparently ‘socialist’ ideology (discussing fair pay for farmers) to nazism and communism. You’re either being cheap for the sake of a laugh, or you’re making an honest mistake that a high-school history student would have avoided.

  21. Briggs wrote:
    17 May 2010 at 3:44 pm

    “Pompous Git,

    The spam filter (WordPress + Akismet + Bad Behavior) are sending an increasing number of valid posts to the spam box. I have no idea why. My spam rates do not appear to have increased. Sorry about that.”

    My dear Briggs, no need to apologise for that which is out of your control 🙂

    I too have a recalcitrant spam filter that I cuss at from time to time.

  22. Duncan,

    Actually, that high-school history student would be the one making the error, not I. The national socialists of Germany were, at times various, holding hands with the national socialists of Italy, and the international socialists of Russia, and at other times bickering with them over whose socialism was purer; the international socialists said theirs was, and that anybody who disagreed was “right wing.” Now, since the educators and news people of this country were (and are) sympathetic to the international variety of socialism, they adopted the “right wing” phrase.

    We do remember that “nazi” is German shorthand for “national socialist”, do we not?

  23. Briggs, presumably you have read Ayn Rand’s book, Capitalism: The Unknown Ideal. In it she (or none of the other contributors; perhaps even Allan Greenspan) describes government systems as follows:

    1. Socialism: Government ownership (of property), government control
    2. Capitalism: Private ownership, private control
    3. Fascism: Private ownership, government control.

    From this comes my notion that what Hitler, Stalin and Mussolini had in common was a belief in Despotism, rather than Socialism. It is I think a bad assumption to take Hitler and Mussolini’s claims that they were socialists to be true. Similarly, it’s a bad assumption to take Green Socialist claims to favour organic farming over conventional as implying organic practitioners to be socialist.

    [Aside] One Green told me that they preferred Biodynamic to organic, because Biodynamic farms were animal-free. Steiner’s Biodynamic system is entirely dependent on dairy farming. It’s difficult to comprehend the notion of dairy farms without cows 🙂 [/Aside]

  24. William is right .
    The national socialist doctrine is a socialist doctrine .
    Of course to go in detail would necessitate that people be familiar with both Marx/Lenin and Hitler writings as well as with the history of both movements .
    As this is generally not the case , we won’t go in detail .

    So only 3 points :

    – nazi actually means “national socialistische deutsche ARBEITER partei” . There had been an explicite reference and claim to the workers’ origin of the movement since the beginning . (Arbeiter=worker) . This is equivalent to the claim in the Communist Party Manifest by Marx .

    – “Der Nationalsozialismus ist eine Weltanschauung, die in schärfster Opposition zu der heutigen Welt des Kapitalismus und seiner marxistischen und bürgerlichen Trabanten steht. ”
    =
    “The national socialism is a world concept that stands in the strongest opposition to the capitalist world and to its marxist and bourgeois satellites of today .
    Wrote the person who formed Hitler’s economical thinking (and was a socialist btw) .

    – Economical and political writings from both marxist or national socialist variations can be exchanged for each other with a minimum of modifications .
    Interestingly the marxists hated the nazis and the nazis hated the marxists .
    Probably as it is said – the deepest hatreds happen in family .

    Follows that socialism/marxism and national socialism actually disagreed only in small irrelevant details .
    The main of which was the question which of both would be the master of the world .
    Events in 1945 ruled that the master would be the socialims/marxism variation because , as Stalin said “the quantity is a quality on its own” .
    It’s since then (who would dare to contradict the Stalin’s definition of quality ?) that it became fashionable to describe oneself as being “socialist” while “national socialist” has become harshly prosecuted .
    Such are things that history does – even if both doctrines are still conceptually equivalent in 2010 because they didn’t change , they are sharply differentiated by the law .
    Claim one and you’ll be interviewed by CNN and implored to deliver your deep thoughts , claim the other and you’ll go to jail .

  25. Tom,

    Thanks! Technical question. My German is, of course, schlecht (assuming that I have the right word). So how do we create acronyms/words in German? That is, how did we go from “National Socialistische Deutsche Arbeiter Partei” to “Nazi”?

  26. Yes, thanks Tom. My maternal grandfather read Mein Kampf several times and when asked the reason said: “Know your enemy”. He was a committed socialist and always attended the national workers’ conferences. My grandmother said to me, some years after he died, “Arthur never knew, but I always voted conservative”.

    When I was 17, I read Mao’s Little Red Book and Ayn Rand’s Capitalism: The Unknown Ideal. I’ve considered myself a libertarian ever since.

  27. Schlecht is indeed right William – if you want to convey the idea that your german is not on a par that is 🙂
    German has the particularity that you can create words by gluing together several other words what gives to it the distinctive character of both accuracy and long words .

    For a simple example – Unkameradschaftlichkeit which is composed of :

    un : prefix signifying negation (like “un” in unspeakable)
    kameradschaft : root noun meaning comradery (itself composed from kamerad and schaft)
    lich : allows to transform a noun in an adverbe (kameradschaft = comradery kameradschaftlich = “comraderily” – I am not sure if that word exists in english)
    keit : allows to transform an adjective or an adverbe in a noun

    The end result is a noun expressing a property/characteristic of a person who doesn’t exhibit a comradely behaviour .
    You also notice that this single word is very accurate yet I need a sentence to (imperfectly) translate its meaning in english . Literally it would give “uncomeraderilyty” .
    While I have selected on purpose for the example a process that uses processes very similar to english in every individual step , the accumulation of steps is common in german but uncommon in english .
    And of course I have taken a simple root (kameradschaft) while I could have taken a root which is itself composed of several nouns .

    As for nazi , it’s the opposite .
    “Z” is pronounced “ts” in german and national has the same sound – it should have been written nazional but isn’t .
    Hence the whole name (NSDAP) was abbreviated to its first 2 syllables as it is pronounced :
    NA-ZI (onal) .
    Of course not NA-TI because that would be pronounced with a “t” and not with a “ts” .
    In the same vein , socialists are called Sozis in germany (same “ts” sound) because of So-zi-alismus , the difference being that here Sozialismus is correctly written with a “z” and not with a “t” .

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