It doesn't mean anything. The point is that the language of lean, and its proof derivation system, are able to express (and prove) statements that do not correspond to any meaningful mathematics.
I feel obliged to mention that this does feature prominently in Kim Stanley Robinson's Red Mars trilogy. The single most important piece of infrastructure on Mars is a space elevator, but not everyone on the planet is happy with how the owners of the space elevator are running things.
Not only does Southwest exclusively fly Boeing aircraft, they exclusively fly 737s, which enables their unusual routing style. Essentially every pilot and crew at Southwest can fly any aircraft the company has for them.
Presumably this gives Boeing a strong incentive to keep making new 737s that push the engineering envelope, instead of making a new narrowbody aircraft.
That strategy makes some sense in the short to medium term, but I always wonder what the end game is supposed to be. Convincing Boeing to just keep making 737 variants forever so Southwest can keep flying a single aircraft type seems like it will lock the two in a death spiral where they slowly become less and less competitive due to forced reliance on an increasingly aging airframe. The MAX is an obvious example of the types of compromises that need to be made to try to keep pace, but it sees unlikely it will be the last. At some point both Boeing and Southwest need a path to replace the 737 entirely.
Other airlines have switched from exclusively Boeing to exclusively Airbus - eg Easyjet did in the early 2000s, and operated a mixed fleet for about a decade.
You're right that switching airplane models certainly seems possible, even for airlines that operate one model exclusively. I wonder if Southwest being such a huge airline by fleet size (much larger than EasyJet for example) would make that harder or easier.
Either way I was thinking less about Southwest jumping ship to Airbus and more switching to an entirely new model from either manufacturer. I wouldn't see Southwest going through the trouble of switching to the A320 for example, but maybe to an A320 or 737 replacement. The A320 may be a newer platform than the 737, but it still dates to the 80s (admittedly better than dating to the 60s). I doubt Southwest would want to go through the hassle of changing models just to end up on a 40 year old airframe that they might have to transition away from again in the not-too-distant future.
I imagine Airbus does have a chance, although like I said in a sibling comment, I think they'll need a new plane to do it. The A320 might be newer than the 737, but it's not really that new. I don't see a company like Southwest planning a generational shift to an airframe that itself is nearly a generation old. Whichever company comes out with the next generation single aisle might end up with the business though.
The expected value of this distribution goes up with every iteration, there is no such Kelly point. You could try this with
heads: double your money
tails: lose all your money
in which case the expected value is always $1, as you have a 1/2^n chance of having $2^n dollars after n rounds, and 0 otherwise.
The point of discussing ergodicity here, however, is whether you can describe the behavior of the iterated distribution deterministically if you exclude a portion of that distribution which has measure zero.
The "average" of the distribution goes up as you increase the number of rounds, but the probability that you get an average or above value when you sample that distribution once goes to zero as the number of rounds increases.
If you repeat this game n times (as n goes to infinity), you will have Θ(n) pairs of (heads, tails) and O(sqrt(n)) unpaired wins or losses, except for a vanishingly small fraction of the time when the results fall outside of any fixed number of standard deviations.
The point is that you as an individual playing a repeated game don't get to meaningfully sample the expected value of the distribution. You only get to sample once, and you will almost surely (i.e. with probability approaching 1 as n goes to infinity) sample a point in the distribution where you lose nearly all of your money.
Absolutely. The individual is long-run guaranteed to be wiped out. But I disagree with the original author’s way of concluding that fact (ie, that it arises from “losing 5% per round”, which is just false).
I believe the entire point of the ergodicity question here is "If you apply this process n times, with n approaching infinity, obviously the result may depend on what point in the n-times iterated distribution you sample, but if you choose a volume of vanishingly small measure to exclude, can you make a single concrete statement about what the process is doing without taking an expected value over the different outcomes"
And the answer is yes - with probability approaching 1 as n increases (ie excluding a portion of the distribution whose measure decreases to 0), the random process matches a deterministic process which is described by "you lose 5% each round".
I should admit I'm being very generous to Peters here - I came to the conclusion that this is what he means only because the math of ergodicity (https://en.wikipedia.org/wiki/Ergodic_theory#Ergodic_theorem...) talks a lot about "except on a set of measure zero". He provides no explanation of how he moves from "the time average of values in a particular run of the process" (which is ergodicity) to "what does a typical process round do, with probability 1" (which is perhaps what someone computing a utility function cares about).
I asked a friend who is an econ professor "Why does this Peters guy explain this so poorly" and his response was more or less, yes, all of economics has been wondering that too since he first published his Nature Physics paper on this a decade ago.
This quote tells you all you need to know about the author's ability to understand things:
"my second criticism is more severe and I’m unable to resolve it: in maximizing the expectation value — an ensemble average over all possible outcomes of the gamble — expected utility theory implicitly assumes that individuals can interact with copies of themselves, effectively in parallel universes (the other members of the ensemble)."
