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.
(author of the blog post) I would have loved to take into account each comic's age and compute some kind of normalization/weight but never got around to doing that. It's hard to do this kind of normalization correctly since HN's population size isn't a constant over time.
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
I don't know if it's still there in the revision, but in chapter one of the earlier draft of the California framework it said, in a prominent place "we reject ideas of natural gifts and talents"
Edit: in the new version it has been changed to "high-level mathematics achievement is not dependent on rare natural gifts, but rather can be cultivated"
> "high-level mathematics achievement is not dependent on rare natural gifts, but rather can be cultivated"
I mean, I would hope this is true.
I'm not "naturally" gifted at mathematics, but like reading, writing, and other things, I can learn them in school and got quite good at them.
Public education is like mass transit. Not everyone gets their own Lamborghini. Most have to take the bus. Its goal should be providing the best general education it can for all people and making as many people as possible productive.
If you looked at society 500 years ago you could assume that only certain people were smart enough to read and write.
It really depends on how you define "high-level". Yeah the attitude that some people "just can't do math" is not good, I don't disagree with you there. But that's not the same as acknowledging that some people may pick up math more quickly.
Holding kids back is really the opposite of cultivating mathematical achievement. To use the reading analogy, do you think a kid that can read at 4th grade level should be forced to only read 1st grade books anyway because that's what their age is? I'm not sure what that accomplishes.
It'd be one thing to make a resource allocation argument but that's not even what this is. This curriculum is clearly a philosophical statement and personally I don't get it.
> But that's not the same as acknowledging that some people may pick up math more quickly.
Certainly some people are better at things than others - but so what? I know plenty of people that excelled in math in grade school and struggled in high school, also many more that excelled in high school and struggled in college. Some, like myself, struggled in grade school and excelled in high school. The difference was motivation.
> Holding kids back is really the opposite of cultivating mathematical achievement. To use the reading analogy, do you think a kid that can read at 4th grade level should be forced to only read 1st grade books anyway because that's what their age is? I'm not sure what that accomplishes.
And how many brilliant kids moved just a bit too fast and lost interest? The thing is you only view things one way. You forget that a fast ramp-up in difficulty can turn away many students who could've turned out to be brilliant scientists and engineers.
> It'd be one thing to make a resource allocation argument but that's not even what this is. This curriculum is clearly a philosophical statement and personally I don't get it.
I don't agree that it is a philosophical statement, having read it, it seems pretty straightforward. The alarmism about the woke mob is overstated.
As mentioned by OP:
> in chapter one of the earlier draft of the California framework it said, in a prominent place "we reject ideas of natural gifts and talents"
The people that wrote said publicly available draft are still involved with this plan, and have not personally nor explicitly backed down from the statement. It's a good sign that some moderation has been introduced to the text, but it seems clear to me there are still some pretty extreme beliefs amongst those leading this thing.
Whether the "woke alarmism" is over the top or not, I don't think it should be controversial to say that a philosophical statement is at the root of this plan. I wouldn't be surprised if the Equitable Math folks would agree with that assessment even.
I also don't think that criticism of a specific model of leveled courses should be used to dismiss all leveled courses. You talk about kids that are rushed ahead or that perform differently at different points in their math "career" - which could certainly be problematic if levels are rigid throughout the educational timeline and leave little choice to students.
Yes sometimes it is implemented that way. But it is not impossible nor even particularly impractical to implement a more flexible levels system that would mitigate those concerns. There are schools that have done this well, California school system was not one of them. This proposal is throwing out the baby with the bathwater.
I don't see a problem in that statement. The opposite would mean that you are born with ability and can't grow or improve it, which is absolutely false. The idea behind the statement is basically: people do not have to be naturally gifted to be good at math.
> I also don't think that criticism of a specific model of leveled courses should be used to dismiss all leveled courses. You talk about kids that are rushed ahead or that perform differently at different points in their math "career" - which could certainly be problematic if levels are rigid throughout the educational timeline and leave little choice to students.
But arguing for a gifted track IS rigid - it basically says "you must decide now if you're good at math, or not." That is deeply flawed. You can't add flexibility - you need algebra and geometry to do calculus. If you decide or become motivated too late (even if naturally gifted!), you have no recourse, as the "gifted track" starts before you can even know. The current system and system you advocate for could be removing huge numbers of potential STEM graduates from the mix.
> Yes sometimes it is implemented that way. But it is not impossible nor even particularly impractical to implement a more flexible levels system that would mitigate those concerns. There are schools that have done this well, California school system was not one of them. This proposal is throwing out the baby with the bathwater.
Not really - as is said in the framework, most foreign nations that outperform the US have a standard curriculum. So the problem isn't flexibility.
"The framework builds on the strategies used in a number of high-achieving jurisdictions (e.g., Estonia, Finland, Japan, and Korea) that pursue an integrated curriculum—connecting the domains of mathematics with one another as students collaborate in using data to solve real-world problems. These countries pursue a common curriculum in elementary and middle school, supporting more students in reaching higher level mathematics. The framework illustrates how this integrated approach with many different kinds of supports can be used to expand the number of students excelling in mathematics and heading for science, technology, engineering, and mathematics (STEM) careers."
If you define "natural talent" in such an unconventional way sure I guess. But the existence of innate potential does not imply that abilities cannot be improved. Derek Jeter has natural talent. Derek Jeter worked his ass off to cultivate those skills. There is nothing at all mutually exclusive about these things.
Schools spend a lot of time reviewing things over the course of the academic year, including things from prior years - I disagree that it is not possible for students to move tracks with a well thought out curriculum plan. But regardless the proposed curriculum eliminates material that would be covered in upper track courses, and explicitly states it does not aim to have students prepared to take calculus during high school. This is like putting all students on the lower track, which is a hell of a solution to the problem of students getting stuck on the lower track.
Japan's model is much more like putting every student in the high track, it is not comparable to what is being proposed here. Japanese high schoolers are able to take intro analysis in 11th grade, here is a translated textbook that would be extremely rare to see a US 11th grader cover the same material (even with standard tracks you'd be lucky to cover it all in 12th):
https://bookstore.ams.org/mawrld-11
I'm not familiar with math education in those other countries mentioned, but I imagine it is more similar to Japan than the US. Hilariously there have been some recent pushes in Japan to be more like the US education system as far as flexibility is concerned, in order to take some of the pressure off of students.
Actual math is irrelevant to this whole argument, just as actual literacy was irrelevant ~500 years ago. This isn't about math ability, it's about the fact that STEM is an obstacle to woke bureaucrats' projection of power.
I'm not sure if I buy the woke-alarmism that is rife on HN. Reading the framework, I don't see any of this "wokism."
It seems like any other guided/misguided attempt to improve the school system that has already taken feedback into account.
This entire HN thread is filled with "back in my days" and "wokism" but no one actually is disputing the content of the framework itself with actual evidence.
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.