"In this they were undoubtedly wise, because I should not have been able to tell them."

Firstly, a quote about counting from Titchmarsh:

"Little children easily learn to count. Very early in their lives, they notice the existence around them of recognizable objects. As soon as they can speak, they learn to say the names of some of these. Almost at once they notice that some objects may be classed together, as being obviously of the Same kind. In particular they notice the existence of pairs of objects, and learn to use the word "two". When I speak of two hands and two feet, the child realizes that the set of my hands has something in common with the set of my feet. When I turn on a light and then another light, the child says "two lights". This is the beginning of counting.

Soon other numbers three, four, five and so on are learnt. The use of the word "one" probably comes later, the existence of single objects, being at first too obvious to call for a special name. "Nought", the negation of the existence of any objects of a particular class, is a comparatively abstract idea, which only occurs to us when we are used to counting. Some ancient races had no symbol for "nought", which they did not think of as the same sort of thing as "'one" or "two".

Older children learn the routine of counting up to quite large numbers. Beyond thirty or forty this must soon cease to have any particular meaning for them, but the rhythm of counting (twenty-one, twenty-two, twenty-three) makes it rather like saying very easy poetry. Children sometimes even count backwards to amuse themselves.

It soon becomes obvious that the process of counting can go on a very long way. I once overheard my children discussing the question, "What is the largest number?" One of them thought that it must consist entirely of 9's. The second thought that it must be possible to get it by using all the words "hundred", "thousand", "million", and whatever else there might be, in the most favourable way (the idea of repetition not being thought of). The third objected that one could never count as far as that, supposing apparently that to make it fair one ought to be able to count through all the numbers up to the largest. They all agreed that the subject presented serious difficulties, and passed on to other topics.

They did not ask me what the largest number was. In this they were undoubtedly wise, because I should not have been able to tell them. I should have been faced, like any other mathematician, with a serious dilemma. Either there is a largest number, and when we get to it we must stop; or we go on for ever, and the set of numbers is endless, or, as we say, infinite.

It might be said that, as all the numbers which are ever actually used or thought of individually form a finite set, we might as well confine our attention to such a set, and avoid the necessity of trying to think about infinite classes of numbers. Perhaps it would be possible to do this, but it would really make the practice of mathematics more difficult. Not only should we be condemned for ever to the trivialities of finite arithmetic, but almost every statement in mathematics would be limited by a condition that the numbers involved must not be too large. Of course in our minds there is no barrier to endless counting. However far we have got, we can always count one more.

Practically all mathematicians agree that there is no upper limit beyond which counting must cease; that is, they agree to regard the numbers which begin with one, two, three, ... , the primal elements of mathematics, as an infinite class. Such an agreement, or declaration, which is itself incapable of proof, but which is a necessary starting point for further thinking, is called an axiom. The axiom about the set of numbers going on for ever is called the axiom of infinity."

I thought of counting when I read this post in Reason by Matt Welch:

"The L.A. Times on Sunday updated the numbers on 2008's historic (and historically awful) round of bailouts, and came out with a shiny new figure: $8.5 trillion. It's a useful piece of journalism, so I almost hate to complain, but the lead-paragraph framing is really annoying:

With its decision last week to pump an additional $1 trillion into the financial crisis, the government eliminated any doubt that the nation is on a wartime footing in the battle to shore up the economy. The strategy now -- and in the coming Obama administration -- is essentially the win-at-any-cost approach previously adopted only to wage a major war.

What a godawful mix of imprecise, played-out metaphors ("wartime footing," "battle," "major war") and couldn't-possibly-be-accurate absolutism ("eliminated any doubt," "win-at-any-cost approach," "only"). As in the inaccurate, propogandistic usage of "rescue" over "bailout," this paragraph conveys the impression that the financial crisis can be likened to a finite, singular goal, one that can be accomplished if only you marshal enough resources. Neither are true. Globalized economies are organisms that evolve constantly, not stationary mountains that can be climbed with enough sherpas. And by definition, not all government interventions into a national economy get you closer to the goal of allaying a capital-C Crisis, particularly when key elements of said Crisis (politicized lending practices, moral hazard caused by federal guarantees, cheap monetary supply, mark-to-market accounting rules) were caused by...government intervention!"

Hold on mate! I agree, but apoplexy isn't the answer either.

"Anyway, the rest of the article is actually about that latter conundrum, which is another reason to read it. Here is a section devoted to sanity:

Once the financial crisis eases, higher interest rates and soaring inflation will be risks. If they materialize, they could dramatically increase the government's borrowing costs to meet its annual debt payments. For consumers, borrowing could become more expensive even as the price of everyday items rise, holding back economic growth.

"We could have a super sub-prime crisis associated with the meltdown of the federal government," warned David Walker, president of the Peter G. Peterson Foundation and former head of the Government Accountability Office.

My only quibble there being with the word "if," since we will have bailout-triggered inflation, mes amis."

Where's the bit about sanity? My only quibble is with the phrase "mes amis".

"And here's a quote that scares me:

"You just throw everything you have at the problem to try to fix it as quickly as you can," said David Stowell, a finance professor at Northwestern University's Kellogg School of Management. "We're mortgaging our future to a certain extent, but we're trying to do things that give us a future."

Submitted for your approval, Matt. I thinks it's the word "mortgaging" that scares him. He's afraid it's Subprime.

"As the economics journalist Amity Shlaes told Nick Gillespie in a January 2008 interview, such kitchen-sink problem solving, and the uncertainty it creates, certainly prolonged the Great Depression. A selection from that interview:

Both the Hoover and Roo­sevelt administrations (but especially the Roosevelt administration) were so unpredictable. That hurt the economy very much, and when I went back and saw the extent I was astounded. Uncertainty is a factor that I thought needed to be explored. There were lots of people who said, "I will not invest 'til I know what's going to happen."

During the Depression, you heard the phrase "bold, persistent experimentation" all the time. We've been taught that was good. Somebody had to do something, was what we learned. But what I saw was this enormous cost, especially during the second half of the 1930s."

The Kitchen Sink approach. Yikes.

What really bothered me was the number $8.5 Trillion. What's the point of keeping track? Originally, I thought that it was a good idea to keep track of what the IMF was doing in this crisis, so I got in touch with Brad Setser and Calculated Risk ( Who've had a very bad day today, I'm sorry to say ), but neither took up the gauntlet.

Then, I thought for about a microsecond about keeping track of layoffs, but that was beyond awful to contemplate.

Finally, this Trillion Dollar number. There's a great graph on shopyield.com and Jesse's Cafe Americain, with lots of great colors, which normally entrance me like an infant, but the numbers, as I'd already said to Stacy-Marie Ishmael, were a terrible bummer pour moi, ma cherie.

So, here's my comment on Reason:

Don the libertarian Democrat | December 1, 2008, 11:58am | #

Who's counting?

Not me.