I love persistent homology; it's such a weirdo bit of maths that topologists keep trying to make useful. Similarly its bigger cousin, Topological Data Analysis, which as far as I can tell is used by people who love weirdo maths but also want to be paid.
I don't see how much good the persistent topology adds here, though. Why bother to do the abstract birth-death diagram and measure the variance in lifetime of these simplices, when the variance and median of the areas in the Voronoi diagram will give you a much easier and more interpretable result?
> I don't see how much good the persistent topology adds here, though. Why bother to do the abstract birth-death diagram and measure the variance in lifetime of these simplices, when the variance and median of the areas in the Voronoi diagram will give you a much easier and more interpretable result?
Well, my personal feeling as someone who has published math papers is that there is a bit of a pressure in mathematics to continually do things in new ways, even if they are not the best ways of doing things. Topological data analysis seems to be of that sort.
Of course, there could be debate here...but I do think that a lot of mathematics has gone past the point of diminishing returns when it comes to its usefulness or even artistic elegance as an abstract art of the intellect. Yet, the show must go on I suppose.
> a lot of mathematics has gone past the point of diminishing returns when it comes to its usefulness or even artistic elegance as an abstract art of the intellect.
Just because something might have been incorrect 200 years ago does not mean it is not correct now. At some point, the false claims of diminishing returns will turn out to be true. It is foolishness to believe in an infinite supply of wealth from anything, including scientific research.
I didn’t claim it was incorrect. I was just observing that it sounded like an echo of the past, which it does.
…however, surely if we’re reaching some sort of plateau in mathematical understanding, it’s the end of all research — and that is slightly hard to believe.
Do you think we’re nearing a proof of the Collatz conjecture? Or is the theory we have just totally inadequate?
> Do you think we’re nearing a proof of the Collatz conjecture? Or is the theory we have just totally inadequate?
Well, Terrence Tao made a recent advance towards it. It's hard no doubt, but I don't think recent theory is inadequate, except maybe that no one has found any structural link to a body of more advanced math like it was done with Fermat's last theorem, which is why some people think we need new theory to solve it.
Also, I definitely didn't mean to imply we are reaching a plateau of mathematical understanding: there's still a long way to go in proof theory, K-theory, Langlands (a better understanding of orbital integerals, how to compute them symbolically...), nonabelian cohomology even (lots of stuff there seems ad-hoc like definitions of higher nonabelian cohomoogy groups).
What I do mean to imply is that it is getting to the point where none of the discovers at that level really lead BACK to anything that the vast majority of scientists or even math graduate students have much interest in. That's different in cases like evolutionary biology: even the advanced discoveries can still be tied back to things that are interesting for the "every day scientist".
Math has lost that link. It's not running out of problems, but it's running out of interesting problems IMO.
A simple hack used elsewhere is to simply open for voting in select locations a few weeks earlier. If 1/4 or a 1/2 of voters already voted the queues will be much smaller.
Another simple hack is to ensure it’s a Sunday so more people can vote throughout the day and don’t need to vote outside of work hours.
Or let’s vote everyone all at once on a Tuesday and try to solve the queue problem with…math.
If a jurisdiction is reducing the number of election day polling places in an area, they're also going to reduce opportunities to vote in other ways. An egregious example is Houston, where there is now one (1) place to drop off early ballots in a county of 4 million people.
Since moving to Washington, I've discovered just how easy voting can be, and how we can drive voter participation (oh, if only that's what everyone wanted). I always voted when I needed to in person in other states, but now ballots just show up in my mailbox without me even knowing there was an election; it makes having 3-4 elections every year a complete non-issue since all it involves is finding a pen, and making the trek back to my mailbox to drop it off.
I buy that it's rife for abuse in many countries, but the US has such a well-protected (legally-speaking) postal service that it's probably the best country of any I know to do mail-in voting.
Citation needed. For all the claims of massive voter fraud, I’ve seen about three convictions in the news. I certainly haven’t seen evidence of massive fraud in the many, many states that allow mail in voting.
If people believe it threatens the integrity of the election then it already is a problem, whether it actually causes fraud or not.
Holding fair elections has no meaning unless people actually believe they are fair.
Also “abuse” doesn’t necessarily mean voter fraud. It can be as simple as being pressured by a family member to vote a certain way if you do it without privacy. If you vote alone in a booth that’s not an issue (and again - it’s an issue as soon as someone thinks it’s an issue).
Setting up mini polling places where people can cast early votes using the same procedure as on Election Day solves many problems without causing any new concerns. Other solutions have concerns however small.
> early [voting]... solves many problems without causing any new concerns.
You don't trawl political discourse much, do you? Early voting is specifically called out as a problem by people who claim that their political enemies are voting multiple times. Whether or not that's a bona fide concern is somewhat irrelevant.
> Early voting is specifically called out as a problem by people who claim that their political enemies are voting multiple times
I don't understand: what's the difference between early voting and non-early voting in that regard? The last vote made by one voter is the one that counts. If someone votes multiple times under multiple naames they could do so regardless of whether there is early voting.
Are these people suggesting that singlee-day voting and long waiting times help integrity because... it's physically impossible or at least extremely inconvenient to vote multiple times if you have a 3h wait to vote, and even if you try you can only fit so many 3h queue periods into an election day? They seriously fear that if people are given the opportunity of "voting in 5 minutes at the mall" they'd invent 100 different personas and vote 100 times?
It is very difficult if not impossible to catch fraudulent mail in votes. The rules surrounding mail-in and absentee ballots seem like they're actually designed to make fraud easier (ie ballot harvesting).
autotranslation> Chain vote, allows the purchase of votes, the first one who enters to vote, puts another envelope (not the authorized one, but any one). That vote will probably be contested, but they take the valid envelope with them. Then he inserts a ballot from his party into it and closes it tightly, then he can organize a chain of votes making sure that they are in his favor, even if there is a dark room. He offers each person a reward if they bring the empty envelope in exchange for taking the full envelope. Frequently used in low-income areas where political leaders organize the chain.
It's a lot of work to avoid the checks of voting in person. Without those checks it's too easy to force or pay someone to vote for a party and verify it 100%.
There’s an article in GIS for science, (vol 2 I think) by ESRI press which tells the story of students in certain US school using ArcMap to analysis polling stations accessibility, density and distribution. High School Students.
> Porter notes that mathematicians have had success using sophisticated mathematical techniques to quantify gerrymandering, the deliberate skewing of legislative districts.
If only politics followed science, and not partisan loyalties!
In my opinion, wait times for voters of more than 30 minutes should be grounds
for civil suit or impeachment of the election officials responsible. Other variables of interest would include voter dwell time - the time it takes for one voter to cast their ballot - and the likelihood of machine malfunction, whether from inadequate preparation or maintenance, or from active sabotage by voters. Worst case is a polling place with minimal staff, fragile and antiquated machines, and a high proportion of impatient, frustrated, or angry voters. The procedure for repair of machines (never use the word "fixed" during an election) is to mark the machine as out of order, call the elections office, and begin a long wait. For non-Americans, note that US general elections typically involve 2 or 3 dozen contests, so marking paper ballots
just for one party or another is not an effective option in the US.
I'm sorry, but as evidenced by literally the rest of the world, voting wait times are not a research-level mathematics problem, but purely one of resources. Census data and a tiny bit of queuing theory (or alternatively, historical data) will tell you the peak load of a voting booth. Staff accordingly, problem solved.
I don't see how much good the persistent topology adds here, though. Why bother to do the abstract birth-death diagram and measure the variance in lifetime of these simplices, when the variance and median of the areas in the Voronoi diagram will give you a much easier and more interpretable result?