Overview: A definition of Lindy, discussion of its features and drawbacks, and a sketch of New Lindy that allows us to benefit from the best of tradition and modernity at the same time.
Lindy is the notion that the longer that things have existed, the more likely they will continue to exist.
Running, fasting, being barefoot, lifting heavy objects, eating whole foods, and spending time in nature are all examples of Lindy.
Humans have been doing these behaviors for eons, so it's not hard to believe we'll still be doing them for eons to come.
The fact that Lindy things have survived so long means they're most likely beneficial (either because they're inherently beneficial to humans, or because humans have evolved to derive benefit from them, or a combination of both). And since they're beneficial, it's likely they'll be around for a long time.
Lindy can apply to behaviors (like running) as well as objects (like pencils), and also more broadly to concepts and ideas (like justice, democracy, the scientific method, The Bible, Greek Mythology, etc.).
Longevity signifies robustness, and robustness signifies future longevity. The longer it's been around, the longer it'll be around. You get it.
The name for the term "Lindy" comes from this diner in New York, near Broadway. There, fans of the theater would congregate to gossip about which shows were hits or not. They discovered the general heuristic that, the longer a show has been around, the longer it will likely be around. A show that has lasted already 100 days is more likely to last another 100 days, compared to one that just opened a week ago. 
Some examples of non-Lindy things: potato chips, soda, highly processed foods in general, plastics, the two-party system, reality TV, cars, airplanes, chemotherapy, the internet, and all sorts of technology we use everyday.
Implicit in the concept of Lindy is that old things are generally good for you, and new things are generally not (or at least, we don't know). They simply haven't stood the test of time to prove that they're beneficial over years, lifetimes, and generations of exposure.