Friday Focus: Satisfying the laws of conservation

headshot of a man
UAF photo by JR Ancheta

Oct. 29, 2021

— By Dan White, chancellor

I happen to really like equations. Mathematical formulations for how the world works. Engineers borrow these equations from the basic sciences to understand or design our built and natural environments. The gift of mathematical formulation has allowed us to predict or forecast natural processes such as ice growth on a lake in winter. A mathematical representation of the science of phase change from liquid water to solid ice. With just that one calculation, the life-risk of trial and error has been greatly reduced. Of course, every fall and spring we see the process of trial and error play out as Chena River ice bridge enthusiasts take a drive across the thin ice. But that is not about science.

Having taught water resources and environmental engineering at UAF for many years, my favorite equation (well one of them, ‘cause it is kind of hard to choose) was the continuity equation. It is one of the “laws of conservation” that allows us to solve a million problems. Simply put, the continuity equation just says that the water going into a pipe is equal to that coming out. That’s right. What goes in comes out and you don’t need a PhD in engineering to conjure that one up.

So the flow rate of water into a pipe is equal to the velocity of the flow times the area of the flow assuming it is an incompressible fluid and the pipe has rigid walls. So if one end of the pipe is smaller than the other, the same amount of water going in the big end will come out the smaller end, but watch out ‘cause it will be coming out with a lot higher velocity than it went in. (Hence the expression “sipping from a firehose”). And there can be no missing water. If what is going in and what is coming out is not equal then we are either not talking about water or we are not talking about a pipe and then we have bigger problems. Even a balloon has a limited amount of material that can go in before it explodes and everything goes out (ultimately satisfying the continuity equation).

The laws of conservation are powerful and are harmonious across the fundamental forms of science: mass balances, force balances, charge balances, and energy balances are used all the time in physics, engineering, and chemistry. The extension of these basic balances give us great leverage to solve complex problems – even including the grand biological and ecological challenges that range from nutrient cycling and metabolic energy production to global carbon cycles and climate change. And they hold true – as long as we are not talking about nuclear reactions or travel beyond the speed of light, which for the most part we are not.

The laws of conservation are an elegant reduction of our universe. The one problem is, they don’t describe me, as a human very well. How could they? I am a complex organism with feelings that cannot be modeled by math. I am way too complicated for a law of conservation. Unless I am not. I am, after all, part of the universe. 

There is an expression, “I have forgotten more than I know.” This expression plays on the fact that at this point in my life, my memory does seem to obey the continuity equation. If something goes in, something else goes out. And over time, the amount that has gone in and out is more than what is in there now.

What is going into our hearts and minds feels to me like it also behaves like the laws of conservation. In some ways I really like this idea, goodness shown to me should be passed on in goodness shown to others. What good is done if I alone don’t obey that law of conservation? The same is true about stress though too. If stress is just coming in and not getting out, we’ve got a problem.

Most of you know that I play music in a band. There is nothing more satisfying than playing for a crowd at a bar, gathering, or event. You can see stress going out and goodness going in. I know when I am on the other end of that equation and listening to live music, watching a volleyball game, or a theater performance, I start setting down all that stuff I carry that adds to my net stress burden. Somehow we have to ensure that our hearts and minds satisfy the continuity equation too.

COVID has denied us humans many opportunities to satisfy the laws of conservation. Whether it is love and care coming in that is out of balance with what we give, or the amount of stress we take in without the usual stress relievers letting it out (in a constructive way). Letting out stress by enjoying the company of others, listening to music or running a race is needed to satisfy the fundamental laws of the universe. We are not out of COVID, whatever that looks like, but there have still gotta be ways to balance the laws of conservation.

Please figure out a way to ensure that the laws of conservation are functioning in your heart and mind. It’ll do you good as well as those around you. Have some fun, for this too shall pass.

Friday Focus is a column written by a different member of UAF’s leadership team every week.