Understanding Rob Pike's book incineration example

In Rob Pike's talk 2012 talk, Concurrency is not Parallelism (it's better), he has a running examples of a group of gophers working together to incinerate a pile of books.

On slide 15 (video 6:58), there are three gophers at work:

1. One loading books from a pile into a cart.
2. One moving the filled cart to the incinerator (and later returning the empty cart).
3. One moving the books from the cart into the incinerator.

On slide 16, four gophers are working together on the same problem:

1. One loading books from a pile into a cart (as before).
2. One moving the filled cart to the incinerator.
3. One moving the books from the cart into the incinerator (as before).
4. One moving the empty cart back to the pile.

Pike says that this performs more work but will run faster. Why? It seems like the same amount of work, shared by more gophers.

The trick is that there isn't just one cart, there are multiple carts. One being filled, one being moved to the incinerator, on being emptied into the incinerator, and one being moved back from the incinerator. This means that each gopher should (as long as things are working reasonably and the completion time of each task is relatively similar) always be busy.

The assumption is that the gopher carrying the loaded cart has to perform some kind of cleanup or communication after removing the books from the cart. Now he can do that while the other gopher carries the empty cart back. Therefore, the loading gopher doesn't have to wait as long for the cart to come back.

Consider a round trip for a cart load.

In the first case we have:

• One moving the filled cart to the incinerator (and later returning the empty cart).

That is:

• Gopher 1: Move the filled cart to the incinerator.

• Gopher 1: Move the empty cart back to the pile.

In the second case we have:

• One moving the filled cart to the incinerator.

• One moving the empty cart back to the pile.

That is:

• Gopher 1: Move the filled cart to the incinerator.

• Gopher 1: Walk back to the pile with no cart.

• Gopher 2: Move the empty cart back to the pile.

• Gopher 2: Walk back to the incinerator with no cart.

Although we have extra work, it may run faster for several reasons, for example, division of labor.

> Of the Division of Labour
>
> To take an example, therefore, from a very trifling manufacture, but
> one in which the division of labour has been very often taken notice
> of, the trade of a pin-maker: a workman not educated to this business
> (which the division of labour has rendered a distinct trade), nor
> acquainted with the use of the machinery employed in it (to the
> invention of which the same division of labour has probably given
> occasion), could scarce, perhaps, with his utmost industry, make one
> pin in a day, and certainly could not make twenty. But in the way in
> which this business is now carried on, not only the whole work is a
> peculiar trade, but it is divided into a number of branches, of which
> the greater part are likewise peculiar trades. One man draws out the
> wire; another straights it; a third cuts it; a fourth points it; a
> fifth grinds it at the top for receiving the head; to make the head
> requires two or three distinct operations; to put it on is a peculiar
> business; to whiten the pins is another; it is even a trade by itself
> to put them into the paper; and the important business of making a pin
> is, in this manner, divided into about eighteen distinct operations,
> which, in some manufactories, are all performed by distinct hands,
> though in others the same man will sometimes perform two or three of
> them. I have seen a small manufactory of this kind, where ten men only
> were employed, and where some of them consequently performed two or
> three distinct operations. But though they were very poor, and
> therefore but indifferently accommodated with the necessary machinery,
> they could, when they exerted themselves, make among them about twelve
> pounds of pins in a day. There are in a pound upwards of four thousand
> pins of a middling size. Those ten persons, therefore, could make
> among them upwards of forty-eight thousand pins in a day. Each person,
> therefore, making a tenth part of forty-eight thousand pins, might be
> considered as making four thousand eight hundred pins in a day. But if
> they had all wrought separately and independently, and without any of
> them having been educated to this peculiar business, they certainly
> could not each of them have made twenty, perhaps not one pin in a day;
> that is, certainly, not the two hundred and fortieth, perhaps not the
> four thousand eight hundredth, part of what they are at present
> capable of performing, in consequence of a proper division and
> combination of their different operations.
>
> An Inquiry into the Nature and Causes of the Wealth of Nations, Adam
> Smith, 1776.