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11/12/2005: "Joy's Law"

So Doc quoted me, but I think he missed the point I was trying to make.

I've seen Joy's law expressed in print lately as: "Most of the smartest people are never in your own company"- or ""No matter who you are, most of the smartest people work for someone else.", but the original I saw in 1990, when I was still a Sun employee was:

smart(employees) = log(employees)

Note that the base of the logarithm is unstated. Joy allowed that the base could be changed by the management style, culture or reward structure of the company. Still even if the base is quite small because everyone is getting rich and management gives daily hot oil massages to all the programmers, the results are not pretty. In this short table, the first column is the number of employees, the second is the log of the number of employees (base 10), the third is the natural logarithm of the number of employees, and the last column is uses a highly improbable base of 1.1

1.00 0.00 0.00 0.00
10.00 1.00 2.30 24.16
100.00 2.00 4.61 48.32
1000.00 3.00 6.91 72.48
10000.00 4.00 9.21 96.64
100000.00 5.00 11.51 120.79

Now, there are several interesting things happening. First, if you are the only employee, there are no smart people in your company. 'Nuff said about that. However at 10 employees, if your management team is epending all their efforts at keeping the smart people happy, there are 24 equivalent smart people. Likely your company is kicking ass and taking names. Note what happens as soon as your company has 100 employees though. Now less than half of them are smart, even under improbable conditions.

This is the diminishing returns I spoke of in the piece that Doc quoted.

Now, Google had 4,183 employees as of June 30, 2005. Microsoft has 61,000

4183.00 3.62 8.34 838.04
61000.00 4.79 11.02 1107.36

As you can see, Microsoft still has the potential for a few more smart folks, all other things being equal, though I find it likely that Microsoft's base is much larger than Google's. Its also interesting to note that the world's population is 6,446,131,400 and running the same test yeilds:

6446131400.00 9.81 22.59 2269.95

So Microsoft, which employs 1 in every 100,000 people of the total world's population may have about 1/2 of the smart people, and google has grabed a subtantail fraction of the rest, leaving the world with only 325 "smart" people who don't work for Microsoft or Google. This explains why the "law" doesn't hold outside of organizational boundries. Joy's law is really a criticism of the dynamics of corporations, especially those engaged in high-tech.

My point is that both Google and Microsoft make outrageous claims about having hired "only" smart people, but anyone who understands the dynamics of the hiring process knows that this can't happen as the company grows. Joy's law states this quite simply. For any company of more than a handfull of employees, hiring the next smart person get exponentially more difficult with each new hire.

Herein lies one of the secret strengths of the "open source" development process. Not all the smart people have to work for you, or even closeby. If the distribution of smart people is approximately uniform, it really is true that most of the world's "smart people" will never work for any one organization. The so-called "Open Source" development process understands and leverages this very fact. Anyone can contribute, and the contributions tend to stand on their own merit.

wnj, as those who know him refer to him, had another "Joy's law" once, it expressed that computing power of the fastest microprocessors, measured in MIPS, increases exponentially in time. The expression I saw was that the number of available VAX 11/780 MIPS (essentially a SPECmark of 1.0) was equal to 2^(year - 1984). Its late 2005 now, and so we should have 21 years of doubling, representing approximately 2,097,152 VAX MIPS equivalents.

The fastest SPECint2000 benchmark I find is 1771. Of course, the reference standard has changed, but I still don't know if a modern single-core Opteron is 2 million times as fast as the 11/780 I used in 1981.

I do know that an 11/780 would produce about 1700 Dhrystones, and this is what is often known as a Dhrystone MIP (one DMIP = 1700 Dhrystones), so that VAX 11/780 was good for one DMIP.

Recent postings of Opteron show that single core can produce 9191 DMIPS, or 15,624,700 Dhrystones.

If we were on-track with Joy's (CPU) Law, we should have much, much more.