Gödel's Theorems and IT Governance

Governance in an IT Department aims to remove all uncertainty to reduce the risk for operations. Even if this is a hopeless endeavour the aim is still to achieve predictability of the IT Department service delivery - a deterministic system of IT operations. The question is can governance accomplish to create a deterministic IT system where everything is predictable and randomness is zero?

Until the early 19-hundreds the mathematicians of the world were confidant that they can create a deterministic system of science. For them a system can contain out of predefined axioms from which all activities and conclusions can be predicted. If a unpredictable action or result present itself it was argued that an unknown axiom is at work which only needed to be added to the system to complete it. As with governance in the IT Department they too reasoned that a totally predictable system can be created without any uncertainties and therefore no unknown risks.

When Gödel introduced his two incompleteness theorems to the world of matches, he change the cause of thinking regarding deterministic systems. Of cause it was not just accepted, but after thorough reviews by other mathematician (Alan Turing who built the Enigma machine in the Second World War, was one) the theorems were accepted as fact and is seen today as laws which direct the thinking around systems.

Gödel's theorems state:

First incompleteness theorem:

Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F.

Second incompleteness theorem:

For any consistent system F within which a certain amount of elementary arithmetic can be carried out, the consistency of F cannot be proved in F itself.

Gödel's discovery can be summarised as a natural behaviour of a deterministic system which will start to feed on itself (display inconsistencies) and over time become irrelevant and useless for its purpose. It was also further demonstrated that when inconsistencies appears in a system, that there is only one way to resolve this inconsistency - through an Oracle (think Matrix movie....). An Oracle is an anchor in the reality of the system. Any system's reality is the larger system which contain it. For example an IT Department is a system which exist in a larger system called the Business. In this comparison the Business is the reality of the IT Department. The the Business again live in a larger system called the Business Environment of a region which again live in a say the Global Business Environment - it is fractal in nature. An Oracle is a the ability of the bigger system to guide the smaller system - which it contains - to resolve inconsistencies. Therefore, the Oracle is never a part of the smaller system, but of the bigger system. Because the Oracle is part of the system's reality, the solution provided by the Oracle will not be proof-able in the system. It is like the system needs to accept the resolution in "faith". If the system makes the oracle part of itself to resolve future inconsistencies, it will on stumble on new inconsistencies which the incorporated Oracle cannot resolve and the input of another Oracle from the reality will be needed.

What do we take so far from this explanation. First systems can never be deterministic. This means you can never fine tune a system to run independently and deliver on a consistent basis. The system will from time to time run into inconsistencies where it will not know how to handle an input. The only way how to resolve the inconsistency is to receive the solution from the system's reality how to solve the inconsistency. The solution is not part of the system and will therefore not be understood by the rules of the system. The system needs to accept the solution in "faith" and act on it. The design and build of any system needs to take the need of an oracle into account. If the input of an oracle is excluded the system will over time encounter inconsistencies and start to feed on itself. If these inconsistencies are not resolve through an oracle, the system will only weaken itself and over time become irrelevant for the purpose it was created.

How does knowledge related to IT Governance? The IT Department is a system in a bigger system called the Company. The Company can be regarded as the reality for the IT Department. An adapted incompleteness theorems can be stated as follow:

First Incompleteness Theorem for the IT Department

For any IT Department within a Company which deliver consistent service to the business, will in time encounter requests for service which the IT Department will not be able to deliver according to its value structure.

Second Incompleteness Theorem for IT Department

For any IT Department within a Company the ability of the IT Department to deliver services, the consistently of the service delivery cannot be assured by only looking at the workings of the IT Department self.

As Gödel used axioms in his mathematics examples to demonstrate the incompleteness theorems, a system like the IT Department is guided by a value structure. This value structure can be known or unknown, but it will always manifest itself in the "culture of IT". A request which will create inconsistency in the workings of IT will be where the value structure conflict with itself - a "catch 22" situation. Conflicting values can be the speed of service delivery and the quality of the service. If the quality of the service require a longer delivery time as the agreed Service Level Agreement, the IT system cannot resolve itself as IT cannot make a decision for its business on which value to compromise.

The answer is in an oracle where the reality of the system provides the solution. In this case the IT Department must receive input from its business where to compromise. The IT Department will not understand why business is prepare to compromise on the quality of the delivery time as it is not build into its values how to evaluate it. It also will not help to build in the reason for the business decision into its value structure to be able to handle similar request without business input, as only another "catch-22" situation will occur which IT cannot handle.

The principle of the incompleteness theorems explains the importance of a partnership between the IT Department and its business. The concept is not new, but most of the time the importance of this relationship is not always comprehended. If the partnership does not exist IT can become irrelevant to its business who will find other ways to fulfill its need for IT. It is, therefore, important for IT to establish a partner with business to make sure the work of the oracle is in place to prevent inconsistency in its service delivery.