Joel M. Hoffman, PhD

Finding the Similar in the Dissimilar

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The Important Difference Between True and Real

Posted on by Joel M. Hoffman

Lots of things are true but not real.

For example, if a village has 100 families with 150 children, there are one and a half children per family. That’s true. But that doesn’t mean that there’s such a thing as a half child.

Unfortunately, especially when it comes to physics, many people don’t appreciate the difference between true and real.

So they learn, for example, that a quantum-mechanical description of the world is non deterministic and assume that that necessarily means that the world is non deterministic. It doesn’t. The non-deterministic nature of quantum mechanics may be like the fractional child — a useful part of a useful model that doesn’t directly represent anything real.

A clear example comes from coordinate systems. A point in space can be described by Cartesian coordinates $(x,y,z)$, but that doesn’t mean that there’s any reality to $x$, $y$, or $z$. The same point can be described by polar coordinates $(\rho,\theta,\phi)$, but, again, it’s not as though a point actually has a radius and two angles. Both of these systems are true. Neither one is real.

Similarly, from the Heisenberg uncertainty principle we know that $\Delta x \Delta p \geq {\hbar}/{2}$. Or, more popularly, the more you know about a particle’s position, you less you know about its momentum, and vice versa. But, again, we don’t know that particles have momentum at all, any more than they have an $x$-value or a radius. (They may not even have position.) Just like Cartesian or polar coordinates, perhaps Heisenberg’s principle tells us something fundamental about the universe. And perhaps not.

More generally, it’s a mistake to leap from truth to reality.

© 2019 Joel M. Hoffman, PhD


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The Starting Point

Even apparently dissimilar complex systems have similarities that are important, interesting, and useful.

We can learn about the world by studying the brain, learn about the brain by studying countries, learn about countries by studying the body, learn about the body by studying companies, learn about companies by studying computers, and learn about computers by studying the world.

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