Born to do Math 104 – Human Beings as Mathematical Structures (1)
Author(s): Scott Douglas Jacobsen and Rick Rosner
Publication (Outlet/Website): Born To Do Math
Publication Date (yyyy/mm/dd): 2019/01/15
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Scott Douglas Jacobsen: Nature can be described via mathematics. In this sense, as humans are inescapably a part of nature, humans can be described via mathematics, in principle. That is to say, human beings, in some sense, are mathematical structures in the sense of nature existing as a mathematical structure and human beings existing as a part of nature. This seems like an unavoidable modern conclusion of philosophy and science: human beings are mathematical structures.
Rick Rosner: You have mentioned this before. Biology boils down to physics. Physics boils down to quantum physics. Quantum physics is highly mathematical. When you boil it down, it is the physics of information; the physic and math of information. Information is the most featureless thing that you can have.
The most basic information you can have is a choice between two things. But you can probably go below that too, where you have a fuzzy choice between two fuzzy things without a clear choice between two things. But it almost boils down to nothing.
You can build back up from there into humans and the world around humans. The reason that humans do not seem mathematical is that we are so macro. In economics, there is microeconomics dealing with little things like one person buying this stick of gum or this candy bar.
Macroeconomics is the largescale behavior of economic systems. Quantum mechanics is micro with all the weirdness of the quantum world at the micro world. But the macro world makes sense to us because we are macro beings living in the macro world.
I have been messing with micromosaics, recently. Carole likes micromosaics. I guess I do too. They are like these thin pieces of glass, like a millimeter across. Some are less than a cubic millimeter. I think that these things are so small and should not contain so many atoms.
But if you do the math, a cubic centimeter – what’s a mole? 6*10^23, so a cubic centimeter contains 10^23 atoms roughly. A cubic millimeter still contains close to 10^17th atoms. So, even this thing that is as small as you want to deal with in regular macro life, it still contains a billion, billion atoms.
We are super macro. It also that we are organic, i.e., soft, squishy, and wet and mucousy. None of that has the clean sharp purity of math. When you think of math, you think of things that are super symmetrical and pretty well behaved. Things that are limited, perhaps, in extent.
When you think of parabolas, every parabola looks like every other frickin’ parabola. Every circle looks like every other circle. Every ellipse looks like every other with some tilting. You have these simple structures. There is nothing, at least on the surface, on 3. The threeness of something seems simple.
A die, the kind that you throw, is only having 6 different outcomes; unless, it gets wedged against a wall with no face on top. But if you’re throwing craps and one die, there are only 6 possible outcomes. But humans with our huge number of components and 4-billion-year evolutionary history that makes us complicated; there’s not a lot of simplicity in our form, or in our behavior.
It is basically because of our bigness and the number of components. Our duration, our evolutionary history, our extent in time. Everything is macro and macro is messy. You can boil it all down to math. Every single interaction in the human body can be characterized by quantum mechanics.
At the smallest level, you can find these interactions that boil down to simple possibilities. Is this blood cell going to capture oxygen molecules or not? Hemoglobin can exist in two states, generally. Either folded up having absorbed oxygen atoms and expanded, where the hemoglobin has four holes for oxygen molecules.
You put it in an oxygen-rich environment. Under the laws of quantum physics, it will pop open and grab four oxygen atoms. The first gym I ever belonged to; it was owned by a guy who started as a graduate student at the University of Colorado to see if you could actually see the moment when a hemoglobin molecule goes from having grabbed no molecules to having gone open and grabbed four oxygen molecules.
It was something that happened, at least with the technology then, or seemed to happen instantaneously. When the hemoglobin went from empty to full of oxygen, there was never a point when you saw it has two oxygen atoms.
I do not know if that is still the case. Even though, the hemoglobin molecule consists of, maybe, 50 atoms to make this mechanism. But it still governed by laws of quantum physics and can exist in basically only one or two states.
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