My point isn't that it lacks utility, it's that the proofs are not relevant (maybe they are to the teeniest tiniest number of people but I'm not sure of even that - most research is about speeding up calculations on computers). It's that practically it amounts to a library of computer functions. I can type the date function on the command line, how it works behind the scenes is not relevant.
What is the criterion you would give an astrologer? I'm not equating them with astrology, but simply pointing out the countless billions wasted on mathematics that narrows to the rarefied "breed" of pure mathematician earning a salary is as much of a waste as if billions were spent on buggy whip boys. Some things are just meant to fade into museums and history books.
If you're solving DE's by hand you were probably just in a class taught by members of the Mathematician-Teaching Complex (allusion to Military-Industrial Complex).
Hate to do this (but will have to anyway because you're misrepresenting that authors article),
- you've mixed in with nonlinear phenomena (most physical processes) with linear, and there's less and less reason to pretend linearity with increasing computer speeds (although in fairness you alluded to models being wrong)
- poo pooed spreadsheets without explaining why (you alluded to QM etc. but they don't care about useless proofs in linear algebra unless they're pencil pushing time wasters)
- implied infinite-dimensions is practically useful when it isn't (unless you're a mathematician/theoretical-somethingist seeking to extract tax-payer money)
There's little need to get linear algebra in you unless you want to waste time.
Newborns don't come out with all knowledge in their heads already. I'm simply alerting younger people to facts, there's absolutely no reason to get mods involved. Otherwise most of HN should be banned (since a lot of it is not completely fresh news). Why alert the mods, are you a scared pure mathematician?
The intelligent way to do that nowadays is to use automatic differentiation followed by optimization "plugins". And that has little to with proving theorems unless you consider all computer programs as proofs and all computer programmers as mathematicians.
The Shannon theorem is basically voided by compressive sensing. But all of this (shannon+compressive) was a waste of practical people's time anyway. It's justification for pencil pushers who don't want to do real work.
The computer industry wasn't built on Turing completeness. It's an evolution of practical technology starting with the invention of textile machinery (but you can also kind of argue it started with abacuses or even lines drawn in sand).
That's just a few parameters that you avoided having to tune, a few milliseconds of computer time. I'm not great, just questioning basic assumptions that have been handed down from a time before computers were around.
Learning a few functions that deal with spreadsheets is a lot more simpler and faster (and hence useful to a lot more people) then doing linear algebra courses complete with proofs and 18th century symbols.
What will have more societal impact? Should anyone wishing to use a wordprocessor be required to understand turing machines and computer architecture?
The example you've described (radio signals) is just a method of winning an argument. It doesn't actually help you, you practically do it by writing a computer program that tries out different parameters to get the right one.
I might be missing something big, but it seems like linear algebra is then just an overly complicated way of describing what should be a simple toolbox of spreadsheet manipulation functions, kind of like an extra module for python. Why is it given such special emphasis then, it would be like teaching the datetime or sched modules.
If that's the case, things are so efficient that things will spill over in those ways, why not open the exchanges to everyone. Anyone should be able to list a company for zero cost, and anyone can purchase stock in anything for zero cost and no net worth requirements. The competitivness of the market will sort it all out.
Well, if you want to brush everything off like that (including how you make predictive model from daily data when there's so much volatility when you actually want buy/sell) then you're clearly trying to win some type of "argument". Have at it boss.
By that reasoning, HFT are parasites too. More generally, the stock market exists to allocate resources. Is society already so efficient that millisecond allocation needs to occur?
I didn't say long-term investment. I said limit trading to once per day or week. Then resources will go towards creating predictive models in the longer time range than milliseconds/seconds etc. Even limiting to monthly would be good. Most real world projects (that directly benefit soceity) occur on days/weeks+ timescales. There's no reason for stock trading to occur faster than that since it's ultimate purpose is to finance those projects.
Is it as easy as possible? Can you borrow straight from the central bank at the low interest rates? The more regulations/expenses you put in the way the less competitiveness there is and the more unfair it is (hence giving free money to the powerful). (Also, will I get a bailout?)
If there's more data, then it's more costly to deal with it - simple as that.
What if there's a little appliance that you plug in which makes predictive models (you can think of it as installing software on your laptop). What if millions of people want this appliance but it costs a $100 a month but could have made about $100 dollars a month? They will choose not to invest.
This might seem contrived, but it's also the scenario behind the web (lot less blogs when it cost $100 per month).
The net effect is that less predictive models of the economy are created. This is bad because that's how capitalism allocates resources.
The larger framework is that competition increases quality. Any barrier to business decreases competition.
Well, the costs add up. You have to process that data as well afterwards. And all those resources are being diverted away from collecting other data and making longer term predictions. Multiply that by the millions who could be trading but don't (a few hundred dollars a month is a barrier to a lot of people, that might have been the profit of a small strategy that worked).