Hartree-Fock Theology – Part 2

How a quantum mechanics course laid a new foundation for my faith.

I described the core idea of the Hartree-Fock method in part 1 of this post series. I told how this computational method from quantum mechanics inspired me to apply its principles to worldviews. But to do so, a few points are left to be discussed now. For example, we need to talk about the initial guess that is required and the “form F” that initial guess needs to satisfy. I will address these topics now.

The Hartree-Fock method assumes that the distribution of the electrons around the atom’s core has a specific form which arises from fundamental principles of physics. Demanding the initial guess to be of a form that is compatible with the physics of electrons, ensures that whatever solution comes out of the Hartree-Fock process, is not contradicting any physics. For electrons the form is a symmetry condition of how the sign of the wave function changes when two electrons exchange their positions. What fundamental principles should guide the form for a worldview?

1.Self-consistency. Great fantasy movies or science fiction books stick to their inner logic. Despite the many elements that contradict science, they make an effort to be consistent within the framework of their story. If they contradict themselves, it’s much harder to appreciate them. But there is a deeper problem with inconsistency. Fundamental creeds are like axioms in math. We can build useful mathematics from a set of consistent axioms. But if the axioms are conflicting, the endeavor to construct something useful is set to fail from the beginning. For example there is no consistent summation, multiplication, or ways to calculate a volume with conflicting axioms. Nothing would make sense. Therefore, for something as essential and as fundamental as a worldview, self-consistency should be a necessary precondition.

Of course, nobody can stop you from believing contradicting things. We probably all do this to a certain degree. However, it won’t bring you far in constructing a useful worldview. But what is a useful worldview? This is an interesting question and I will discuss it later. For now, I will illustrate what the symptoms of a not so useful worldview are. Namely, an inconsistent worldview keeps us busy with ourselves just because of the worldview. I claim that the higher the degree of inconsistency, the more energy and personal resources are eaten up by dealing with issues arising from our inconsistent worldview. Naïve 6-day creationism is a good, respectively tragic example. Some Christians believe that God created the world some 6000 years ago in 6 literal days. If God is not fooling us by having done so while creating an entire universe with fake evidence that suggests otherwise, the belief in 6-day creationism is in stark contrast with scientific evidence. Whatever evidence we examine, it suggests a universe aged billions of years. Those who believe in a literal interpretation of that passage of the bible spend a lot of personal resources to deal with that conflict. Resources are emotional and mental capacity, time, money, etc. Those Christians attend seminaries and read books that reassure them in their belief and provide alternative explanations. Emotionally, they need to find ways to deal with the fact that most people - including scientists - believe something totally different than what they do. It is not very reassuring if you face the vast majority of people and science against your beliefs. This can result in social isolation or segregation. This situation binds significant personal resources that could be spent otherwise. Obviously, if these people would believe something else that is compatible with science - for example a Christian version of a billion year-old universe, they would not spend resources on that end.

For the sake of transparency and completeness, I need to discuss another point. Psychology suggests that people who slightly overestimate their capabilities fare better than those who don’t. Indeed, studies showed that depressed people hold the most realistic worldview (here). The studies measured realism in terms of how accurately the participants estimated probabilities and risks. Depressed participants outperformed those without depression. This insight could provide grounds to think: It doesn’t matter what I believe as long as it makes me happy. Why should I strive for a realistic worldview, if it makes me unhappy? Indeed, this is a fair point but not a show stopper for the Hartree-Fock method. Namely, it is convincing that any worldview that makes you happy (or whatever effect you desire) AND is realistic outperforms a worldview that just provides the desired effects at the cost of inconsistency.

2. Adherence to Ockham’s razor. Ockham’s razor is an elegant and powerful principle. It states (simplified) that given two equivalent explanations, the simpler should be preferred. In physics it means if you can describe your system with fewer variables equivalently, you should do so. Ockham’s razor should definitely apply to worldviews too. Especially the framework which goes beyond heuristic science and/or (immediate) personal experience like for example, the belief in an afterlife, should be explanatorily efficient. It is all too easy to postulate an inflated set of beliefs with arbitrarily complex dependencies. As Betrand Russel has convincingly argued with his famous teapot example, the burden of proof lies on the person making an unfalsifiable claim. Some beliefs that are part of a worldview may be hard to scientifically prove like e.g. the existence of god. But this belief has a tangible effect on the person holding it. I am tempted to postulate: Beliefs that do not affect our thinking and likely, ultimately our actions - in other words have no tangible effect - should be considered irrelevant. I might return to this line of thought another time.

I want to stress that holding beliefs that go beyond science do not a priori contradict Ockham’s razor. The belief in an afterlife requires additional variables. A bigger story that comprises the meaning of life before and after one’s presence on earth necessarily requires more complexity than the description of just the life itself. Nevertheless, additional variables should be used sparingly according to Ockham’s razor.

When it comes to applying Ockham’s razor to worldviews, we must be careful to not make ourselves guilty of applying a theory naïvely. This is much like a physicist who requires year-long training to understand and apply physics correctly. Most of the lengthy process of uncovering scientific truths constitutes in identifying the relevant physical parameters at work and their respective relevance. Therefore, worldviews must be diligently evaluated for economic use of variables. I propose to involve experts, e.g., theologians, to adequately respect the self-conception of a worldview.

Finally, complexity is not a necessary indicator of falsity. Notwithstanding the simple principles of physics (e.g., principle of least action) everyday details are very complicated. They are sometimes messy but still the correct description of reality. Most importantly, the complex versions still obey the fundamental principles. The same applies to a worldview as well. We should therefore primarily judge a worldview on its basic assumptions and creeds and not on its details – which naturally become very complex.

Now that I have outlined two preconditions that should be satisfied by any initial guess, we can turn to the initial guess itself. I suggested in the first part that your current worldview can serve as a good starting point - as long as it is self-consistent and adheres to Ockham’s razor. I am well aware that in practice, it is extremely complicated to demand these two preconditions. Nevertheless, seeking consistency has since become a guiding principle for my faith; alongside the three forces of change (science, subjective reality, philosophy) that iteratively refine it.

The final post of this series will address some leftover questions and closing thoughts.