Reductions are painful because they specify a sequence of ordered operations. Runtime is O(N), where N is the sequence length, regardless of amount of hardware. So you want to work at a higher level where you can exploit commutativity and independence of some (or even most) operations.
You can reduce in parallel. That was the whole point of MapReduce. For example, the sum abcdefgh can be found by first ab, cd, ef, gh; then those results (ab)(cd), (ef)(gh); then the final result by (abcd)(efgh). That's just three steps to compute seven sums.
No, you can not. Your example is correct only if addition is associative. And it is not always associative. Hence the need for higher abstractions, where you model commutativity and associativity of certain operations.
You're right it's primarily a runtime + compiler + language issue. I really don't understand why people tried to force functional programming in environments without decent algebraic reasoning mechanisms.
Modern graph reducers have inherent confluence and aren't reliant on explicit commutation. They can do everything parallel and out of order (until they have to talk to some extrinsic thing like getting input or spitting out output), including arbitrary side-effectual mutation. We really live in the future.
I hate articles like these. They get 10% right and the remaining 90% is just some random filler. I don't have time to write a lengthy comment but do note the LACK of SCIENTIFIC EVIDENCE. There is no evidence that jacking kids cell phones and swapping digital articles for physical books improves anything. It's part of the perennial right-wing message: "Kids are so unruly these days! We need to discipline them harder!"
That was standard practice for much of recorded history. Surrender now or we will kill you all. Alexander the Great did it to Tyre and Sidon. The Romans did it to Jerusalem. The Israelis did it to Gaza. The orange madman and his henchmen have made it very clear that they don't give a shit about the rules of warfare.
Magazines published lists of phone numbers of bbses you could call with your modem. Long distance calls were very expensive so you could only call those within your local area. Prices were significantly cheaper during evenings and nights so that's when I called. BBSes were mostly for warez, porn, messages, and games. It took forever to download. Settlers I think came on 12 floppies and it took days to download due to quotas. Porn were jpegs or gifs, often magazine scans that loaded top to bottom. You needed way more patience than I had... Turn-based bbs games were quite fun because you played them over several weeks or months. Especially those that synchronized with neighbor bbses so you could team up with local users on a bbs to fight rival bbses.
Amiga bbs were 3l373 and PC bbses were for n00bs. However, Amiga bbses were all ASCII while PC bbses had way better ANSI graphics.
My bbs alias was "interrupt". I had no idea what it meant but I thought interrupt handlers were cool (they are!).
Someone wrote there wasn't politics but as I recall there was lots of bickering and quibbling. Things like "X banned me from his bbs for Y. He is a turd! Spread the message." Some people registered under others names and acted as pricks. I used the "sysop assistance" paging feature to wake up sysops in the middle of the night. Got me banned from more than a few bbses. :p
Does the data reject the null hypothesis? If you group people into hundreds of groups (occupations) and measure something (Alzheimer's rate) variance ensures that the means of the measurements will vary. Some groups will have low means other will have high means. The distributions may be equal but due to random chance there will be outliers.
There are many researchers who already avoid US conferences. The risk of arbitrary arrest, being denied entry, or general asshattery from border guards who want to snoop through your social media is just too high. The needless and unjustified war against Iran is just the final straw.
This comment is devoid of data. There have been less stoppages and detentions than you can count on one hand of scientists and mathematicians. There are hundreds of thousands classified via various levels of visa. None have been arrested in some unlawful manner, and the onus is on you to define "asshattery" in a way that is defensible. Foreign adversaries have been embedded within the US academic institutions before the Cold War. Just because the current US president is a divisive convicted felon doesn't suddenly mean we shouldn't care about controlling our own borders.
The US (and many nations for that matter) monitor, track, and protect their borders by foreigners and of a group of mathematicians cannot fathom why this may be the case amidst all-time high mistrust, spying, and academic and corporate espionage and then they should've studied harder.
But it is not just about the numbers, you are probably right that statistically, mathematicians don't have much to fear at the border, but the current administration seems to go out of its way make the US unwelcoming. All countries will protect their borders in some way but they usually don't make a show out of it like the US does.
If you go to a hotel and are greeted by a grumpy guy who asks how how you dare book a room on their property, it is a natural reaction to move to the hotel next door where the staff is hopefully more friendly.
These are just cases that make the news. There is a very real possibility of being detained, having devices confiscated, or being refused entry if you are an outspoken critic of the president.
What an utter piece of shit comment. I have had friends (research mathematicians) who were harassed at the border and you have the temerity to do the "cite your sources" shitcrap for "data" which is available with a single click of the mouse -- as the very gracious sibling comment showed, doing your work for you.
when i consider traveling to any country i don't care about statistics. i care about feeling safe. unless you can prove and guarantee that i will not be bothered when crossing the border then i'll stay away.
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