&gt;<i>I disagree that math is that great. A mathematical model is a formal description of some sort, but a mental model is just a different kind of ontological descriptor; both are merely machines to process inputs and produce some sort of output.</i><p>That doesn&#x27;t say much though.<p>A cheap numeric calculator (not turing complete, the plain type) and a high end PC are both &quot;merely machines to process inputs and produce some sort of output&quot;.<p>It&#x27;s the precise kind of machines that each is and the exact kind of processing that it can do that&#x27;s important -- not just their general similarities.<p>&gt;<i>You might argue that it&#x27;s better to be able to observe and tweak the mathematical model than to use one built on purely human semantics, but, mathematical models, by virtue of their simplicity, are generally poor at dealing with complexity</i><p>Yes, but they&#x27;re very good at dealing with very precise formulations. It&#x27;s not necessary when doing an analysis of field X to deal with the whole of X&#x27;s extend and complexity at all times. A very specific answer to a small non-complex part of X can be very worthy itself.<p>(The same way Newton&#x27;s theory is very good to determine the angle of cannon shots with even if it&#x27;s a bad model for anything really complex speed and mass wise -- only in this case, the &quot;less complex&quot; theory gives more precise answers for its subdomain, whereas with Newton vs Einstein it&#x27;s the inverse).