I appreciate the point being made---that we're too reductive in how we view a healthy human body---but calling Patrick Mahomes "one of the greatest athletes on planet earth" is laughable. He's more healthy than many adults, but he's no means an outlier amongst _athletes_. Compare that claim to this header [1] by Cristiano Ronaldo. He jumped 2.6 meters, at pace, perfectly timed, to score a goal, in his mid-30s.
And more generally, I would take almost no health advice from American footballers, many (most?) of whom will go into old age with ailments and injuries due how they treated their bodies.
Are you sure? Compare before/after for the main affected regions (Holland Tunnel, Queensboro) versus the unaffected regions. We definitely need more data, but I think there's an immediate reduction in the obvious places.
"Before" and "after" are generic terms. A car might stop before the crosswalk (space). You might eat dinner after work (time). But "ex ante" and "ex post" specify a relationship to an (random) event or to specific information. For example, a data scientist might compute a quantity "ex ante". This means that the quantity was estimated using only forecast data. No historical data was used. It would not make sense, however, to say that a car stops ex ante the crosswalk.
I could have easily said "afterwards" and "beforehand", but I like "ex post" and "ex ante" when referring to before/after having access to specific information.
I don't think so. My problem was that I had a weak grasp of many basics concepts, and more critically I did not know in which areas I was weak. So while it's easy ex post to say "I could skip such and such section", it would have been impossible to make this judgment ex ante.
And in fact, I think a failure mode many people make is trying to predict which things they already know and then skipping those. This allows for blind spots to persist.
I suppose the one way to skip things correctly would be to have a coach. But that comes at a new cost ($), but maybe that works for some people.
Maybe 5 years ago, I was in a similar place. I had a particularly embarrassing moment at work when it clicked that I just... didn't know the basics. I was, to use an overused term, "mathematically immature".
So I made a commitment: I decided I would work through Khan Academy math for 1-hour a day for 1 year. I started with pre-K [1] (specifically counting) and watched every video and did every single exercise in order. I focused on mastery. I didn't rush myself, and I did not continue until I felt completely confident in the material. I just did this for a year. I think I go through roughly algebra 2. In my mind, it is critical to combine explicit knowledge (watch videos) with tactic knowledge [2] (do exercises). For example, you need to understand what a logarithm is conceptually but you also just need to do problems to get a feel for it. So this is fundamentally different than learning-by-grazing or just reading a book.
I could go on and on, but let me just say that it changed my relationship to math in a deep way.
And more generally, I would take almost no health advice from American footballers, many (most?) of whom will go into old age with ailments and injuries due how they treated their bodies.
[1] https://www.youtube.com/watch?v=rMZ1O6uFdAE