In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
— Aristotle, Physics VI:9, 239b15
This paradox, as first developed by Zeno, and later retold by Aristotle, shows us that mathematical theory can be disproved by taking the hypothesis to an absurd conclusion. To look at it another way, consider this joke:
A mathematician and scientist are trapped in a burning room.
The mathematician says “We’re doomed! First we have to cover half the distance between where we are and the door, then half the distance that remains, then half of that distance, and so on. The series is infinite. There’ll always be some finite distance between us and the door.”
The engineer starts to run and says “Well, I figure I can get close enough for all practical purposes.”
The principle here, as it relates to simulation like FEA, is that every incremental step taken in the simulation process gets us closer to our ultimate goal of understanding the exact behavior of the model under a given set of circumstances. However, there is a limit at which we have diminishing returns and a physical prototype must be built. This evolution of simulating our designs has saved a lot of money for manufacturers who, in the past, would have had to build numerous, iterative physical prototypes. This evolution of FEA reminds me of…
The uncanny valley is the idea that as a human representation (robot, wax figures, animations, 3D models, etc.) increases in human likeness, the more affinity people will have towards the representation. That is, however, until a certain point. Once this threshold is crossed, our affinity for it drops off to the point of revulsion, as in the case of zombies, or the “intermediate human-likeness” prosthetic hands. However, as the realism continues to increase, the affinity will, in turn, start to rise.
Personally, I find this fascinating – that a trend moving through time can abruptly change direction, and then, for some strange reason, the trend reverts to its original direction. Why does this happen? There are myriad speculations as to why in the Wikipedia page that I’ll encourage the reader to peruse at leisure.
But to tie this back to FEA, think of the beginning of the Uncanny Valley curve as the start of computer assisted design simulation. The horizontal axis is time, vertical axis is accuracy. I posit that over time, as simulating software has improved, the accuracy of our simulations has also increased. As time has gone on, the ease of use has also improved, allowing non-doctorate holders to utilize simulation as part of their design process.
And this is where we see the uncanny valley; as good as the software is, there comes a point, if you use specialized, intricate, or non-standard analysis, where the accuracy of the software falters. This tells us that there will still be needs for those PhDs, and once they get on the design and start using the software, we see the accuracy go up exponentially.
If you need help getting to the door, or navigating the valley, talk to us about our Simulation benchmark process. Leave a comment or click to contact us.