The wisdom of the ancients

The software engineering ancients are people like Halstead and McCabe, along with less well known ancients (because they don’t name anything after them) such as Boehm for cost estimation, Lehman for software evolution, and Brooks because of a book; these ancients date from before 1980.

Why is the wisdom of these ancients still venerated (i.e., people treat them as being true), despite the evidence that they are very inaccurate (apart from Brooks)?

People hate a belief vacuum, they want to believe things.

The correlation between Halstead’s and McCabe’s metrics, and various software characteristics is no better than counting lines of code, but using a fancy formula feels more sophisticated and everybody else uses them, and we don’t have anything more accurate.

That last point is the killer, in many (most?) cases we don’t have any metrics that perform better than counting lines of code (other than taking the log of the number of lines of code).

Something similar happened in astronomy. Placing the Earth at the center of the solar system results in inaccurate predictions of where the planets are going to be in the sky; adding epicycles to the model helps to reduce the error. Until Newton came along with a model that produced very accurate results, people stuck with what they knew.

The continued visibility of COCOMO is a good example of how academic advertising (i.e., publishing papers) can keep an idea alive. Despite being more sophisticated, the Putnam model is not nearly as well known; Putnam formed a consulting company to promote this model, and so advertised to a different market.

Both COCOMO and Putnam have lines of code as an integral component of their models, and there is huge variability in the number of lines written by different people to implement the same functionality.

People tend not to talk about Lehman’s quantitative work on software evolution (tiny data set, and the fitted equation is very different from what is seen today). However, Lehman stated enough laws, and changed them often enough, that it’s possible to find something in there that relates to today’s view of software evolution.

Brooks’ book “The Mythical Man-Month” deals with project progress and manpower; what he says is timeless. The problem is that while lots of people seem happy to cite him, very few people seem to have read the book (which is a shame).

There is a book coming out this year that provides lots of evidence that the ancient wisdom is wrong or at best harmless, but it does not contain more accurate models to replace what currently exists :-(

Dimensional analysis of the Halstead metrics

One of the driving forces behind the Halstead complexity metrics was physics envy; the early reports by Halstead use the terms software physics and software science.

One very simple, and effective technique used by scientists and engineers to check whether an equation makes sense, is dimensional analysis. The basic idea is that when performing an operation between two variables, their measurement units must be consistent; for instance, two lengths can be added, but a length and a time cannot be added (a length can be divided by time, returning distance traveled per unit time, i.e., velocity).

Let’s run a dimensional analysis check on the Halstead equations.

The input variables to the Halstead metrics are: eta_1, the number of distinct operators, eta_2, the number of distinct operands, N_1, the total number of operators, and N_2, the total number of operands. These quantities can be interpreted as units of measurement in tokens.

The formula are:

  • Program length: N = N_1 + N_2
    There is a consistent interpretation of this equation: operators and operands are both kinds of tokens, and number of tokens can be interpreted as a length.
  • Calculated program length: hat{N} = eta_1 log_2 eta_1 + eta_2 log_2 eta_2
    There is a consistent interpretation of this equation: the operand of a logarithm has to be dimensionless, and the convention is to treat the operand as a ratio (if no denominator is specified, the value 1 is taken), the value returned is dimensionless, which can be multiplied by a variable having any kind of dimension; so again two (token) lengths are being added.
  • Volume: V = N * log_2 eta
    A volume has units of length^3 (i.e., it is created by multiplying three lengths). There is only one length in this equation; the equation is misnamed, it is a length.
  • Difficulty: D = {eta_1 / 2 } * {N_2 / eta_2}
    Here the dimensions of eta_1 and eta_2 cancel, leaving the dimensions of N_2 (a length); now Halstead is interpreting length as a difficulty unit (whatever that might be).
  • Effort: E =  D * V
    This equation multiplies two variables, both having a length dimension; the result should be interpreted as an area. In physics work is force times distance, and power is work per unit time; the term effort is not defined.

Halstead is claiming that a single dimension, program length, contains so much unique information that it can be used as a measure of a variety of disparate quantities.

Halstead’s colleagues at Purdue were rather damming in their analysis of these metrics. Their report Software Science Revisited: A Critical Analysis of the Theory and Its Empirical Support points out the lack of any theoretical foundation for some of the equations, that the analysis of the data was weak and that a more thorough analysis suggests theory and data don’t agree.

I pointed out in an earlier post, that people use Halstead’s metrics because everybody else does. This post is unlikely to change existing herd behavior, but it gives me another page to point people at, when people ask why I laugh at their use of these metrics.