John von Neumann and stochastic simulations

For more on the view that stochasticity fundamentally parallels reality, an interesting read is &quot;The Dawning of the Age of Stochasticity&quot; by David Mumford [1].<p>I also think it&#x27;s interesting that methods like Hybrid Monte Carlo were inspired by a physical-reality-first idea. It makes it seem like this is somewhat of a chicken and egg problem.<p>[1] <a href="http:&#x2F;&#x2F;www.stat.uchicago.edu&#x2F;~lekheng&#x2F;courses&#x2F;191f09&#x2F;mumford-AMS.pdf" rel="nofollow">http:&#x2F;&#x2F;www.stat.uchicago.edu&#x2F;~lekheng&#x2F;courses&#x2F;191f09&#x2F;mumford...</a>

What&#x27;s the current state of the &quot;stochasticity&quot; view presented here? I&#x27;ve always thought of Monte Carlo as being a convenient way to avoid expensive analytical solutions, rather than a reproduction of a stochastic reality, but I&#x27;m not a frequent user of the techniques.