Word Problem of the Week: Bad Pork

One of my fundamental premises is that the themes of algebra problems bear some relationship to the life of the times when they were written. That's why this one from 1857 really caught my eye. Fraudulent practices of this type must have been fairly common in the days before the government had the strength or inclination to regulate them.

As it happens, we know what Cincinnati looked like around that time, at least near the waterfront. There are newly restored daguerreotype images of the city taken in 1848 which have exceedingly high resolution. I mean, high-end digital camera level resolution.

Some of my favorite old problems are the ones that, like this one, combine very specific detail with bizarre contrivance. In this case, the contrivance comes toward the end:

The price at which he sold the pork per pound multiplied by the cost per pound of the chemical process was 3 cents.

 So, what sort of quantity is this, anyway? The unit is "dollars-squared per pound-squared" which is more than a little weird. Especially since he could have just divided the two numbers to get a dimensionless ratio.

But of course, I know why he did it. He needed the equations for solving it to be of a certain type, and having the problem make a little more sense would have upset that situation.

So imagine it said that the selling price p of the pork was 12 times as much as the price c of the chemical process, each in cents per pound. Then we have that the profit, 45000 = the gain - the expenditure. The gain is simply 10000p, and the expenditure is 10000 + 10000c.

So, 45000 = 10000p - 10000c - 10000. Clear the thousands to make it 45 = 10p - 10c - 10. But since p = 12c, This becomes 45 = 120c - 10c - 10 or 55 = 110c. This makes the cost of the chemical process half a cent and the price he charges for the pork 6 cents per pound.

This is a nice little linear system problem. But setting it up the way D. H. Hill did it, you end up having to clear a denominator, making the equation quadratic and introducing an extraneous solution.

In other words, this problem sacrifices some of its plausibility to make a different, harder solution necessary.

Against Humanism

This article argues that Comte's attempt to create a religious humanism failed because we revere individuals and not the species. This is because individuals are the ones who change the way we view the world - greatness is an attribute of individuals.

There is no fixed, unalterable background map of the "familiar facts" that must survive all such shifts, and certainly no fixed schedule dividing real entities from fishy, imaginary ones. Entities like Fate and Progress and the Logic of History and the Hidden Hand of the Market come and go.

Unfortunately for the science of consciousness, Comte's materialism has yet to go:

The search for a "scientific explanation of consciousness" which goes on at the yearly conference at the Center for Consciousness Studies in Tuscon, Arizona still centres not on trying to be scientific in the sense of using suitable methods, but on making consciousness respectable by somehow bringing it within the range of physics and chemistry, mainly at present through neurobiology.

A real robust humanism would have to take the religious tendencies of people into account. Science isn't up to the task of myth-making:

It just works through old-fashioned personification. If there is no purpose and everything is impersonal, how can DNA be actively ruling our destinies? How can it feel "pitiless indifference" and make us "dance to its music"? The Cartesian drama of inert matter and active spirit is suddenly reversed here to show humans (and animals) as helpless objects – passive "lumbering robots" – stage-managed by plotting genes (and memes) that are sometimes helped by other entities such as market forces. The myth-building capacities that surround every new world-view are surely as busy here as they are in established religions. These visions perhaps offer the worst of both worlds – an ontology that is as bankrupt morally as it is scientifically. The imagery of science is used, not, as Huxley hoped, to ground a deep reverence for the natural world but to justify human alienation from it.