The Calculus Crossroads of Policy Pyramid

We (the collective “we”) should have an integrated view of the various components of the Policy Pyramid in order to create a comprehensive framework for IT management.

So what can we take from mathematics to develop a better understanding of the interrelationships between the layers represented via the Policy Pyramid?

Calculus' derivatives and integrals provides a crossroads of mathematics and cybersecurity that allows for the development of new solutions and perspectives to the challenges of information security. Derivatives and integrals are the two main concepts of calculus.

“A framework is a construct to formulate theories.” - Carroll, Sean M. The Biggest Ideas in the Universe: Space, Time, and Motion. Dutton. September 20, 2022.

How do derivatives and integrals help us?

Let's assemble a framework with the Policy Pyramid and derivatives and integrals. There are 6 orders, or levels, of derivatives. Starting with the 0th order derivative, we have the function itself. Let's use position as the 0th order.

The 1st order derivative would then be velocity, the 2nd order derivative would be acceleration, the 3rd order derivative would be jerk, the 4th order derivative would be snap, the 5th order derivative would be crackle, and the 6th order derivative would be pop.

The Policy Pyramid

The Policy Pyramid is a common information security concept within medium to enterprise-sized organizations. What can we take from mathematics to develop a better understanding of the interrelationships between concepts, relationships, and dependencies represented via the Policy Pyramid.

The pyramid works well, but let's go with the following pyramid for our working model (or framework). This pyramid model has been expanded to bring in additional layers, so we have layers of policy, process, standard and procedure.

Putting it All Together

Using our framing of calculus for the pyramid, we can then apply derivatives or derivation. We derive information for higher layers from lower layers. This means we integrate higher layer content into lower layers.

Ask yourself what you can derive from lower layers, and what you can integrate from higher layers. Also have a bit of fun with the fantastic naming of physics derivatives inspired by eating Rice Krispies. :)

Derive from below, integrate from above.

We'll pick up here in our next session.

- The Phenom Security Group