Time Will Run Back (30 page)

Peter realized that he had allowed his mathematics to become a trifle rusty. He decided to start from the beginning. He read for a couple of pages and stopped when he came to this:

6. Let us represent among the data the quantities of the different kinds of capital...

“What do you mean by ‘capital’?” he asked.

“I am using the word in what I think is the same sense as Karl Marx used it, Your Highness. By capital I mean capital goods of all kinds—including cigarette packages because they are the medium of exchange—”

“What do you mean by ‘capital goods’?”

“By capital goods, Your Highness, I mean all the produced means of production.” Peter looked at him quizzically. “By the phrase ‘the produced means of production,’ Your

Highness, I mean to exclude labor and land, though I include the value of the improvements made on land, and I mean to include all capital goods—that is, all the goods that are used for further production. I mean the tools of production put in the hands of the workers. I mean the machines put at the disposal of the workers, and the factories that house the machines, and the raw materials that go into the finished products, and the railroads that transport the raw materials, say, from the mines to the smelters, from the smelters to the finishing mills, from the finishing mills to the factories, from the factories to the stores. And by the railroads I mean the value of the railroad beds, and of the locomotives and freight cars and depots. And I also include the capital goods and motor trucks that deliver goods, and the roads over which the trucks travel—”

“You mean the same thing by ‘capital’ as you do by ‘capital goods’?”

“Well, yes—practically, Your Highness.”

“Don’t you think the use of such an abstraction as ‘capital’ for concrete things like capital goods might prove confusing and misleading?”

“Not if it is used carefully, Your Highness. It’s a sort of shorthand. Just as we use the abstract word ‘labor’ to mean all the workers, or the services of all the workers.”

“The workers are not the same as the services of the workers?”

“No, Your Highness.”

“The services of the workers are a commodity, but the workers themselves are not?” “That distinction is correct, Your Highness.” “So the same word—’labor’—to cover both, is ambiguous, and might lead to confusions?”

“Yes, Your Highness.”

“So perhaps we’d better be equally careful, Comrade Baronio, in using the abstraction ‘capital.’ Now I like your phrase ‘capital goods,’ but I have difficulties with it. Take railroads. Take a locomotive pulling a passenger car. If the passenger car contains His Highness No. 3—Adams here—who is going, say, from Moscow to Stalingrad to inspect factories in his capacity as head of the Central Planning Board—then the locomotive and the car are capital goods, that is, goods used to promote production. But if the same locomotive and passenger car are pulling No. 3 to some resort on the Black Sea where he is merely going for a vacation, then they are not capital goods but consumption goods?”

“I suppose that would be strictly correct, Your Highness.”

“And if the rooms in a certain house are used as business offices for commissars, that house is a capital good, but if those rooms are used simply for commissars’ living quarters, the house is merely a consumption good?”

“Yes, Your Highness.”

“And if the rooms are used as offices in the daytime, and to sleep in at night, the house is a capital good by day and a consumption good by night?”

“That is right, Your Highness.”

“So ‘capital goods’ is a rather fluctuating concept?”

“I suppose it is, Your Highness. But perhaps only for a few things.” “How would all this affect your equations?” “It might make them less exact, but I don’t think it would invalidate them.”

“I have other difficulties with this same phrase,” continued Peter. “You write of ‘the quantities of the different kinds of capital.’ What do you mean by ‘quantities’?”

“Why, eh... I thought the word ‘quantities’ was selfexplanatory, Your Highness. You see, I go immediately on to write here: ‘Let the different kinds of capital be
S T
... to
n
terms. The total quantities of these existing in the group will be
Q
_s
, Q
_t
...’ “

“You don’t seem to get my point,” said Peter. “I am asking you what you mean by the term ‘quantities.’ By the relative ‘quantities’ of these goods do you mean the relative
values
of these goods as measured, say, in terms of the value of some homogeneous third product, like cigarette packages? For example, suppose a locomotive is worth 600,000 packs and a freight car 25,000 packs, then does the locomotive count for 24 freight cars in your equations?”

“Yes, Your Highness.”

“Then your equations already take for granted precisely the thing we are trying to find out,” said Peter. “As I understand your paper, you are trying to work out by mathematics what prices the Central Planning Board ought to put on production goods—in order that costs of production might correspond with values of consumption goods in the market—so that we can be sure that labor and capital goods and land are not being wasted or misdirected in making the wrong things or the wrong quantities of the right things. But if your equations
assume
that we already know the values of the means of production, then they assume that we already know the prices that ought to be put on the means of production. So your equations tacitly take it for granted that we already know the answer to the very problem we are trying to solve....”

Baronio was silent for a while. “I gave the wrong answer to your question, Your Highness,” he said finally. “By ‘quantities’ I simply mean physical quantities.”

“As measured by what?”

“By weight.”

“You mean that you add so many pounds of abstract or homogeneous locomotive to so many pounds of abstract freight car to so many pounds of homogeneous drilling machines to so many pounds of abstract sand to so many pounds of homogeneous watches?”

“But in my paper I already differentiate between different
kinds
of capital, and I don’t multiply any of these by price until—”

“You mean you weigh each ‘kind’ of capital separately?”

“Yes, Your Highness.”

“Then your equations assume homogeneity within each ‘kind’ of capital?”

“Yes, Your—”

“So an old or defective lathe is considered to be worth as much as a new or perfect lathe—provided it weighs as much?” “I suppose we would really have to count them as two different ‘kinds’ of capital, Your Highness.”

“But then every lathe would be a different ‘kind’ of capital, depending on its individual age, state of wear and repair, efficiency, et cetera?”

“I suppose so, Your Highness.”

“That would require a lot of equations for the Central Planning Board to set up and solve, wouldn’t it?” Baronio was silent. “It was very good of you to come, Comrade,” said Peter at length, “and I appreciate the ingenuity and zeal with which you have worked on this vitally important problem. You at least realize that there
is
a problem—and you understand pretty clearly what the problem is—and No. 3 and myself have certainly got no further than that ourselves. Suppose you leave copies of your paper with us to study.”

Peter studied Baronio’s paper carefully that evening.

“I don’t know whether I am impressed more, Adams,” he said the next day, “by Baronio’s cleverness or by his blindness. I’m afraid he doesn’t realize that his equations tacitly take for granted precisely the things he is trying to find out. What his equations are really saying is that
if
we knew the value of
x
and
y
we could find out the value of
z.
And then he tacitly assumes that he
does
know the value of
x
and
y
—or, as he puts it, that he does have the same number of ‘independent equations’ as he has of ‘unknowns.’ “

“I read the other copy of his paper that he left with us,” said Adams. “I freely confess that the mathematics of it was over my head. But I noticed that his paper referred to a No. ME-13-742—otherwise known as Comrade Patelli—another clever Italian in the Central Planning Board whose work inspired Baronio. So I have taken the liberty of bringing Patelli with me. He’s waiting in the anteroom, if you should care to see him.”

“By all means,” said Peter.

Patelli was ushered in. Peter had never seen a more intelligent face. He told Patelli about Baronio’s paper and his own difficulties with it.

“I’m afraid your misgivings are right, Your Highness. I’ve been fascinated by the consumers’ goods market, and trying to see whether we could solve by mathematics the problem of finding out the correct prices for producers’ goods. I think a system of simultaneous equations
could
be used to explain what determines prices on a market. But I have concluded that we couldn’t actually arrive by that method at a numerical calculation of what the correct prices ought to be.... Let us make the most favorable assumption for such a calculation. Let’s assume that we have triumphed over all the difficulties of finding the data of the problem and that we already know the relative preferences of every individual person as between different amounts of all the different commodities, and all the conditions of production of all the commodities, and so on.”

“That is already an absurd hypothesis.”

“Precisely, Your Highness; that is just the point I was about to make. Yet even if we went on this hypothesis, it would not be enough to make the solution of our problem possible. I have calculated that in the case of 100 persons and 700 commodities there will be 70,699 conditions.”

Adams laughed.

“Actually,” continued Patelli, “if we took into consideration a great number of circumstances that I ignored, that figure would have to be increased still further. But on these simplified assumptions, we would have to solve a system of 70,699 equations.”

“And could we?” asked Adams.

“No, Your Highness. That practically exceeds the power of algebraic analysis.”

“Assuming that we have only .700 different commodities,” said Peter, “the actual world population for which we have to plan is not 100 persons but about 1,000,000,000. So how many equations, under your simplified assumptions, would you have to solve to get the correct prices of commodities for this world?”

Patelli threw up his hands. “Oh, well—when you get into the neighborhood of seven hundred billions... and even Your Highness’ assumption is terribly oversimplified. There are so many different grades of each commodity, and different places—”

“And wouldn’t you have to change your equations at least every day,” pursued Peter, “because supply and demand and everybody’s preferences would be constantly changing?”

“Yes, Your Highness.”

“So even if one could really know all these equations, it would be beyond human powers to solve them?”

Patelli nodded.

“I suspect that you can’t put millions of different items and the preferences of millions of different persons into any meaningful mathematical equation,” said Peter. “And I’ll go further. Putting aside the bewildering multiplicity of these equations, I suspect that
all
of them would be purely hypothetical; we could never say with confidence that any
one
of them really described a fact. For we can never in fact know what the constantly fluctuating preferences of any one person will be, even if that person is ourself. So I suspect that, tempting as the idea might be, we can’t predict human choice and human action by mathematics. This appearance of precise results is delusory. I believe it was our great Russian mathematical logician, Bertravitch Russelevsky, who once defined pure mathematics as the subject ‘in which we never know what we are talking about, nor whether what we are saying is true.’ And so all these impressive-looking equations that you and Baronio have put together merely seem to me to say, in effect, that
if
we knew so-and-so to be true, then such-and-such would necessarily follow. But—”

He paused eloquently.

Patelli shrugged his shoulders in resignation.

“Anyway,” Peter said, “we are grateful for the light you have thrown on the problem.”

HE walked along the line of haggard creatures, in their filthy rags, and stared intently at each vacant face in turn. He had now seen hundreds, thousands of these faces of what had once been men and women. But neither Edith nor Maxwell was among them.

He had not really expected to find them. He did not know whether he feared rather than hoped to find them here. But anything was better than sitting at his desk and getting negative second-hand reports that he did not trust. At least he was doing something himself. He had slipped secretly away from Moscow for a week, left his responsibilities there in charge of Adams, and visited every slave camp in the region that the time allowed. It had all been in vain. This was the last camp, the last line-up.

“I don’t understand you, chief,” said Adams when their afternoon conferences were resumed. He had been talking of Peter’s “negative attitude” toward the proposals of Baronio. “You have this passion for reform, and yet you reject one proposed reform after another without even trying it.”

“Would I have to jump out of this window,” Peter retorted, “to find out whether or not I would get hurt?”

“No doubt there are some things, chief, that one does know about in advance without trying them—usually because something very much like them has been tried before. But you can’t know
everything
that would happen under a particular proposed reform until you try it.”

“That used to be the very thing you objected to, Adams. My efforts to introduce personal liberty and real democracy were both wretched failures. And especially while Bolshekov is around, I can’t afford any more failures.”

“But your freedom of exchange for consumers’ goods was a great success!”

“Well, what experiment would you want me to try now?”

“You criticized me severely, chief, for proposing a system that provided harsh penalties for managers but no incentives. Well, why don’t you suggest or try some incentives for managers?”