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More is more complex.
Having more lines of code, methods, classes, packages, executables, libraries etc. always means also to have more complexity (which is bad). This means that given the complexity of the problem is fixed, a suitable compromise for the number of methods, classes, etc. has to be found. Reducing the number of statements per method typically results in the introduction of further methods. Reducing the number of methods per class can be achieved by dividing the class into several smaller classes, etc.
Note that it is actually not the number of lines, methods, classes, etc. that is relevant but the effective number of items that have to be kept in mind for the purpose of understanding. So reducing the number of lines by placing several statements in one line does not help. Neither the introduction of an additional obvious private method exceeding the limit will do any harm. MIMC is just a rule of thumb stating that the introduction of further modules (and the like) usually has a higher complexity as a drawback.
The capabilities of the human mind are certainly limited. If it is necessary to keep a large amount of modules or lines of code in mind, it is difficult to understand. Furthermore if a module is large, it takes a long time to read (and thus to comprehend). And if there are many modules, looking for a particular module takes a long time. And the longer the searching process takes, the more one will have forgotten what has been read previously. This results in worse readability, understandability and this maintainability.
See also section contrary principles.
The phrase “more is more complex” is new but can be regarded trivially intuitive to every developer.
Examined: As a specific aspect of MIMC, complexity through deep inheritance relations is known to reduce effectiveness and efficiency of maintenance. There are controlled experiments showing this1)2). On the other hand these results are limited as there may be many factors which are neglected by the experiment. Most notably in these experiments maintenance tasks where carried out on systems with artificially constructed inheritance hierarchies. It is undisputed hat there are good ways and bad ways of using inheritance. And it is doubtful that there are several equally good solutions for the same problem only differing in the depth of inheritance. So there is some evidence but no “proof” that deep inheritance hampers maintenance.
Note that many principles are contrary to MIMC as they favor the introduction of additional modules. This means that it is worthwhile to consider MIMC when considering one of those. Nevertheless this does not mean that this is true the other way around. When considering MIMC, one wouldn't want to consider all principles that have complexity as a disadvantage. So here are those needing consideration: