They prove a new upper bound to a combinatorial quantity that controls the worst-case running time of an algorithm of Dadush, not an upper bound to the optimal value of a given ILP instance.
If they wanted to see their ideas work in practice, they could implement Dadush's algorithm in light of these new bounds, but this would be unlikely to outperform something like CPLEX or Gurobi with all their heuristics and engineering optimizations developed over decades.
Otherwise, and this is the sense of the quoted sentence, they could go deep into the bowels of CPLEX or Gurobi to see if their ideas could yield some new speed-up on top of all the existing tricks, but this is not something that makes sense for the authors to do, though maybe someone else should.
The exponential curve does look like a line when you zoom in very close to a point. For example, f(x) = e^x looks linear with slope e^x near x. You can see that, for small epsilon, e^(x+epsilon) - e^x is approximately epsilone^x, with an error term of the order of epsilon^2 e^x
The analogy would be that if your friend Bob asks you for a $1k loan, you could tell him "done, I am loaning you $1k and for now I am keeping it safe for you; just tell me when you need it".
Now you have all the money you had before, and you friend "has" an extra $1k, so you have "created" money.
If Bob then tells you hey, I need the $1k to give it to John, you say no worries, and you go to John and says hey, here is $1k from Bob, and for now I am keeping it safe for you; just tell me when you need it. And so on.
If at some point John actually wants the $1k in cash then you actually give him the money, you cannot create it. Maybe at some point you have just $1k of real cash with you, other people owe you $9k, and yet other people have $10k of "created" money that you are keeping for them. If all of the latter want their money in cash, you are going to be in trouble.
Same with a bank, if a lot of depositors want their money back, the bank has to give it out of its reserves, it cannot "create" it to give it to them, hence the phenomenon of "runs on the bank" (because at any given time, the sum of all depositor balances in a bank is a lot more than the actual reserves) and why we need a federal insurance program to protect depositors.
You can see that the market deviates from the model and accounts for the fact that the Brownian motion model of Black-Scholes underestimates the probability of big moves: typically, options for the same security and the same expiration date have different IV, with options ATM having a lower IV and options deep ITM or deem OTM having larger IV.
If the market believed in the model, options for the same security and the same expiration date would all have the same IV, which would be whatever volatility the market thinks the security is going to have.
I don't think that this is how it works. In Italy almost all sushi restaurants are run by Chinese immigrants, but we definitely don't think of sushi as Chinese food.
The article ends with a reference to Trout Tickling, https://en.wikipedia.org/wiki/Trout_tickling, that sounds like some kind of Urban Dictionary euphemism, but is instead exactly what it sounds like
I understand that diamonds are the kind of Veblen goods for which people are willing to spend a lot of money because they are expensive, in a logic-defying circular way, and that the presence of a cartels- makes prices artificially high, but there are still two things that I can never wrap my head around:
1) That if someone wants to sell a used diamond, they get pennies on the dollar. It's reasonable that they would sell at a small discount compared to wholesale prices, because of the extra work of authenticating it, the small volume etc., but the difference is so great that one assumes that some businesses would step in and take advantage of the arbitrage opportunity
2) That there is any difference at all in prices between mined and lab-grown diamonds. They are literally the same material, and lab-grown diamonds are as "real"as the mined ones
Just consider gold. You can sell used gold at a small discount compared to spot prices, and if there was a cheap way to make "lab grown" gold, I am sure it would sell at exactly the same price as mined gold
If they wanted to see their ideas work in practice, they could implement Dadush's algorithm in light of these new bounds, but this would be unlikely to outperform something like CPLEX or Gurobi with all their heuristics and engineering optimizations developed over decades.
Otherwise, and this is the sense of the quoted sentence, they could go deep into the bowels of CPLEX or Gurobi to see if their ideas could yield some new speed-up on top of all the existing tricks, but this is not something that makes sense for the authors to do, though maybe someone else should.