Virginia O'Hanlon

Santa Claus (Lt. Col. Jerry Lobb) waves to members of the 908th Airlift Wing family (Air Force photo/TSgt. Jay Ponder)

On the existence of Santa Claus and that of unique solutions to the Navier-Stokes equations - respectively

You may ask yourself: What on earth is this article about? Probably more that you can imagine, simply because it reflects my imagination and not yours (it would be the same if I listened to your imagination). The essay is about subjects like happy Christmas sentiments, parenting, engineering education, the yet to be unleashed power of mankind, running a successful business and the future of Computer Aided Engineering (CAE, a.k.a. "simulation"). For that reason, my company website offers you a possibly less confusing entry into that multitude of subjects. One where you can pick one subject at the time.

A word of comfort, possibly: Before presenting this material to you, I have - to the best of my ability - had it sanity-checked piece by piece by experts in the various fields. As also stated at the very end of this article: Happy Christmas!

The existence of Santa Claus

Through the years, mathematicians have proved the strangest things, dealing with non-existence as well as existence. Proofs of the existence of Santa Claus are rare. However, in 1897, the American publicist Francis Pharcellus Church constructed a proof which you can read here:

Church's proof contains two interesting features: It is transparently frugal with respect to assuming the existence of anything beforehand. Its basic assumption is the existence of Virginia. One must assume that Virginia did not object to that when hearing about the proof. Another feature is an implicit negotiation with Virginia: The Santa Claus which Church offers to Virginia is a Santa Claus that nobody will ever see. If Virginia does not accept this deal, Church has not lifted the burden of proof requested by Virginia. This could have led to a disappointment based on honestly conveyed information.

Church's proof lives on because we all assume that Virginia was happy to keep the essential part of Santa Claus: That he is able to convey to all children the same happiness that he conveys to Virginia. We all assume that Church enabled Virginia to keep her joyful belief in Santa Claus instead of immediately losing it.

This is education at its finest. Every child and every adult should be allowed to receive knowledge and experience at a pace which will optimize the joyful outcome of their education. If you truly love and understand your fellow human being, you wish that Virginia kept her virginity exactly as long as she needed it. There is no reason to believe that Virginia did not let go with her belief in Santa Claus when the time was right.

The existence of unique solutions to the Navier-Stokes equations

Above, you have seen Francis Pharcellus Church's attempt to educate a young girl. Below, you will see my attempt to educate newcomers in the essentials of fluid mechanics:

I call my approach "From scratch to RANS in 1000 words". The 1000 word limit is important because of the expected attention span of a never before seen group of newcomers: those that start off using low-cost, high-performance offers like SimScale.

Why settling on RANS as the target of this crash course of mine? Because believing in the truth of a RANS solution will have the same effect on a student as believing in Santa Claus will have on Virginia: Peace and (at times false) understanding as long as those emotions are needed in order to progress. When the student does not need these emotions anymore, she or he can peacefully and informed focus on the full Navier-Stokes equations instead.

A RANS approach will in the eyes of a newcomer have these properties:

  1. Doing it is an immediately available option (SimScale and similar offers)
  2. You obtain nice and stable solutions (because the turbulent viscosity is at the right places much higher than the actual viscosity)
  3. These solutions are not wrong for low Reynolds numbers. For low Reynolds numbers, the inherently wrong turbulent contribution to the total viscosity vanishes in comparison with the actual viscosity.

I claim that the standard progression of fluid mechanics education lacks alignment with today's conditions. Therefore, I suggest a modified approach.

And now for something completely different...

The world is full of nails that need to be driven into walls. The normal thing to do is to use a hammer. I will use a hammer as a metaphor for "belief" in the barest, most stripped-down sense of that word.

As stated, most people use hammers when driving nails into walls. It is, however, possible to imagine a man who can drive a nail into the wall with his bare hand. This person will see a hammer as something which simply does not relate to him. He will, however, embrace the existence of hammers as something which enables many nails to be driven into many walls without involving him. He will also have no problem respecting people who need hammers to drive nails.

Self-declared "hammer addicts" should have no problem respecting a man who can ostensibly drive a nail into a wall without a hammer. If they meet an unknown man who is going to drive a nail into a wall with his bare hand, it will be an act of care and respect if they tell that person that according to their experience, that man's intent will lead to unhappiness. In case the man realizes that his first attempt failed, he may then decide to use a hammer for his second attempt.

Belief, care and respect may live happily together if we decide to do it right. Happy Christmas.

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