The Doctrine of Divine Simplicity is itself a simple concept: if God is omnipotent, then He couldn't have been created by anyone/anything or out of anything: He can't have parts. In that sense, He must be fundamentally "simple".
Any engineer will tell you that the more moving parts in an object, the more unreliable it becomes. The problem arises when one compares this with virtually any religion's god(s) and the fact that they exert action or willpower, which seems to require change within them (e.g. a thought or the origin of the desire to act), making the question of how this can be reconciled with the concept of fundamental simplicity of essence.
The Bias of Causality and Experience
The only problem that exists with a God who is entirely simple, yet has a mind with specific actions and will is to be found entirely in our own mind. We can't reconcile the idea of thought without moving parts like neurons, electricity, and so on. Yet that's not a necessary property of reality.
For example, quarks are considered the fundamental part of matter: in fact, they're considered point-like - 0 space - yet still exist. However, they come in not one, but six different types or "flavors" as physicists call them. And they can come into existence as one flavor, but change into another, despite being fundametally simple.
one could object to this by saying that there is something more fundamental and physics isn't exactly complete nor unchallengeable. Aside from the fact that scientists are perfectly willing to accept this simple-but-changeable aspect, there is an equally simple non-constructive proof that the issue with a God who not only has a mind but is three Persons (in Christianity) and fundamental simplicity is no problem.
Take the following assumptions:
If we take the above, we can easily show that simplicity and change are not mutually exclusive. If there is a difference between "something" and "nothing", ultimately this "something" has to be made from something fundamentally indivisible, whether it's the quark or something even smaller. If we assume that it's something infinitely divisible, we don't escape because whatever this infinitesimal is, can be influenced by momentum to change its course (which in the Doctrine of Divine Simplicity objection above equals change).
- Something exists (e.g. matter, energy)
- This something can have its momentum changed (e.g. an object's course is changed by gravity, or a force gets weaker by putting more or less (strong force) distance between its objects)
Despite the fact that if matter's components were infinitely divisible, this "thing" wouldn't be countable, that is, it wouldn't be a "thing", the fact that there's a difference between existence and non-existence would necessitate a fundamental difference, whether that's a particle like the quark or not. This is also shown by the variety in existence as well (different atoms, or forces (gluons)).
The fact that it would be infinitely divisible would technically make its size 0, and therefore its existence non-existent for us. Similarly a black hole's singularity has 0 space/dimensions - a fact that so perplexed Einstein that he denied their existence. However, this doesn't make it nothing, anymore than the fact that points on a number-line make all numbers equal to 0, and are themselves uncountable in the same "non-existent" sense (think of the proof that 1=0.999... exactly: 1/3=0.3333... - multiply each side by 3: 3/3=0.9999...).
It is through this Cantorian property of mathematical validity that the Doctrine of Divine Simplicity can allow for change. This is especially true if we suppose the universe's origin had no cause, which is why Richard Feynman noted that inertia has no known origin: i.e. the direction of objects' motion was not predetermined in any specific way, yet the universe is fundamentally "simple" if it had no cause.