Category Archives: Math

Give Me a Pallet and I Can Move the World

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The Single Most Important Object in the Global Economy

Companies like Ikea have literally designed products around pallets: Its “Bang” mug, notes Colin White in his book Strategic Management, has had three redesigns, each done not for aesthetics but to ensure that more mugs would fit on a pallet (not to mention in a customer’s cupboard). After the changes, it was possible to fit 2,204 mugs on a pallet, rather than the original 864, which created a 60 percent reduction in shipping costs. There is a whole science of “pallet cube optimization,” a kind of Tetris for packaging; and an associated engineering, filled with analyses of “pallet overhang” (stacking cartons so they hang over the edge of the pallet, resulting in losses of carton strength) and efforts to reduce “pallet gaps” (too much spacing between deckboards). The “pallet loading problem,”—or the question of how to fit the most boxes onto a single pallet—is a common operations research thought exercise.

I'm in my Prime

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Prime Number Patterns

For each natural number n, we draw a periodic curve starting from the origin, intersecting the x-axis at n and its multiples. The prime numbers are those that have been intersected by only two curves: the prime number itself and one.

What Kind of Question Is That?

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“Is Algebra Necessary?” Are You High?

Towards the end, Hacker’s reasoning gets just bizarre. He keeps emphasising how important “citizen statistics” is. I’m baffled as to how one could teach statistics in any useful way without the material he wants to throw out! Prerequisites: we needz them. “Is Algebra Necessary?” If you want to do statistics or economics, yes, it is.

One thing Blake doesn’t address (perhaps it’s in one of the links he provides) is part of the larger picture: the idea that because students are not graduating, we should lower the bar. Which makes a diploma quite meaningless; they are not simply participation awards.

edit: PZ Myers does bring it up in his post

A Zero-Sum Game

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Causes of death: 1900 and 2010

Interesting chart; one can see where we’ve made significant progress in reducing diseases like tuberculosis and making the world safer so that accidents account for fewer deaths per unit population. Fewer deaths implies progress. But an increase is not so clear.

We’re doing great on kidneys, but hearts not so much.

As they might say up in New England, you can’t get there from here. Death is a zero-sum game; sorry if this comes as a surprise, but everybody dies. So if you are going to drastically reduce the number of deaths by one method, then those people will eventually die via another. If you eliminate childhood diseases then average lifespans will increase and those spared will die of something else. I can recall a comment in a medicine-related blog post recently, wherein the commenter claimed that something is wrong with the system because the instances of cancer were increasing, as this chart shows. But given some probability of getting cancer as an adult, you expect that increase: if your chance is 25%, then (roughly speaking) every four childhood deaths prevented should give you an additional adult cancer death. Similarly for heart-related deaths. The chart also doesn’t tell you at what age the deaths occurred (though the decrease in rate implies that death is occurring later, on average). So a heart attack that killed a person at 50 in 1900 might translate into avoiding or surviving that attack in modern times, and finally succumbing to heart disease at 70 or 80. That would not be a lack of progress. You simply can’t glean the necessary details from the graph.

Were We Vealed in the First Place?

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America Revealed: Pizza Delivery

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AMERICA REVEALED takes viewers on a journey high above the American landscape to reveal the country as never seen before. Join host Yul Kwon (Winner of “Survivor: Cook Islands”) to learn how this machine feeds nearly 300 million Americans every day. Discover engineering marvels created by putting nature to work, and consider the toll our insatiable appetites take on our health and environment. Embark with Kwon on a trip that begins with a pizza delivery route in New York City, then goes across the country to California’s Central Valley, where nearly 50 percent of America’s fruits, nuts and vegetables are grown, and into the heartland for an aerial look at our farmlands. Meet the men and women who keep us fed – everyone from industrial to urban farmers, crop-dusting pilots to long-distance bee truckers, modern-day cowboys to the pizza deliveryman.

I'm Also A Drachma Short

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June 19, 240 B.C.: The Earth Is Round, and It’s This Big

Eratosthenes knew that at noon on the day of the summer solstice, the sun was observed to be directly overhead at Syene (modern-day Aswan): You could see it from the bottom of a deep well, and a sundial cast no shadow. Yet, to the north at Alexandria, a sundial cast a shadow even at the solstice midday, because the sun was not directly overhead there. Therefore, the Earth must be round — already conventionally believed by the astronomers of his day.

What’s more, if one assumed the sun to be sufficiently far away to be casting parallel rays at Syene and Alexandria, it would be possible to figure out the Earth’s circumference.

et al, Brute?

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Top Wrangler

When I was in the navy, we (well, me, mostly) used to joke about doing a movie about Nuclear Power School in the format of Top Gun. (Top Chalk?). Similarly, there’s a reason they never do movies like that. (Not having call signs was but one of many fatal shortcomings)

One, Two, Three, Many

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This is a concept I can recall astonishing me, and also steering me away from majoring in math. I knew the abstract rabbit hole would go much deeper.