The successor function has no universal common name or symbol.
sqrt and log together have a rather clever construction that makes it trivial once you have derived the function, but the function certainly isn't trivial.
And in any case, puzzlers do generally exclude log to eliminate that solution.
"pi is a standard function taking no arguments and always returning the same value."
"In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. "
ugh. seriously? the point wasn't literally "how do you get to 3"; it was how do generically get further on.
The previous poster wrote (4/4)+(4/4) "etc"
As if THAT "etc" suggested it was a general extensible solution. It is not. (4+4+4)/4 is a solution for 3, but doesn't tell us how to get to 4, 5, 99, 113, 8187, or 3.148x10^32
I can write arccos(n) without explaining what arccos is, or providing a definition. You couldn't even talk about your f(x) without first defining it...
I think there is a pretty clear distinction between standard functions you DON'T have to provide definitions for because they are standard, and arbitrary functions you made up on the spot, and had to define before using.
Why would you get a prize for solving a completely different and much easier problem?
If you see SS0 in a math text book do you automatically know that its an increment? Because when I see a square root sign or a log function i don't need to look up how they have been defined in that chapter or book, because they are universally use common standard functions.
Your operation S that add's +1 is not a common mathematical operation or symbol; so its not a candidate operation for the solution.
What do you mean "etc" ?? (4/4)+(4/4) = 2; fine; that equals 2 But How do you get to 3 ? (4/4)+(4/4)+(4/4) is 6 4s.
Slashdot trying to pretend it is something intellectually interesting is what is offensive.
You posted a non-solution to the problem. I think if you are going to denigrate the video as not being intellectually interesting, you should probably at least understand the puzzle being solved.
Its 'four fours'. Not six of them, not as many as you need. Just four them. Exactly 4 of them.
sqrt has a standard mathematical symbol a 5th grader is familiar with. log is a standard mathematical function a 10th grader is familiar with. Both have dedicated buttons on a $6 calculator for high school math. This is the same reason why concat got such a rough response here; it is actually a valid operator, but its not nearly as 'common'.
I can't recall ever seeing a standard increment symbol or standard increment function in pure mathematics. Sure you could define a suitable one using any of a variety of methods, but there isn't a standard one that I am aware of. Yeah, lets of computer programming languages have one, but that isn't math, that's programming.
Answer #2:
It violates the spirit of the puzzle.
Even if INCREMENT did exist as a standard function; it would simply be immediately excluded from being used to solve the puzzle, since it renders the puzzle pointless and trivial.
The log / sqrt solution is an interesting and clever solution. Increment... is... not.
And in fact for people who actually like to play with the 4 4's problem as a puzzle today, they usually exclude log once they discover this pattern too -- precisely because it renders the puzzle pointless.
https://en.wikipedia.org/wiki/... "Typically the "log" operators are not allowed, since there is a way to trivially create any number using them."
But not suitable for Slashdot where we (should) already know this stuff, there is nothing new here.
Give it a rest.
It was really an elegant mathematical solution.
Yes its not new, but its certainly 'esoteric enough'; I certainly hadn't seen it before. I can understand the expression on the wikipedia article, but its definitely not something i'd think most people would follow; and even i would have had to study it longer than it the 5 minutes it took to watch the video to have figured out how it all worked, so I enjoyed seeing the derivation.
And if some youtuber makes a few pennies off demonstrating an elegant mathematical proof in an easy to follow and informative way... what exactly do you object to about it?
An example of something that benefits from video would be a video game walkthrough; by showing the action on-screen, the viewer will be able to see the sequence of events, both the actions of the player, and the reaction of the game engine and AIs.
That's also an example of something that is horrific on video.
If am interested in finding the secrets as I play through a game the one thing I absolutely do not want is to watch someone else play the level from start to finish, every monster shown, every cutscene revealed, every puzzle solved. Might as well not play the game now.
I VASTLY prefer a simple list, "as you enter the subway station, first door on your left, behind the plant in the blue pot". After you kill the boss, jump down into the sewers and follow the wall to the right past the waterfall, its behind the stack of 4 boxes. That's ALL I want. Maybe links to screenshots that i can click on if I still just can't find it. Because i still want to 'find' it. And a couple sentences of description is a bit like orienteering... i have the information needed to get there without having the whole experience completely ruined by watching someone else do it from start to finish before I play.
Walkthrus also benefit from the seek and index features of text. If I played the game through and found most of the secrets, and am doing a 2nd playthrough to be completionist; and i know i am missing the '4th secret' on the 3rd level then again I can quickly jump to the list of secrets for the 3rd level, and then to the 4th secret, without clicking around trying to find it in a big long video stream.
Same with boss fights; if im having serious trouble with a fight-- e.g. after 30 minutes in a single battle the boss has only revealed its vulnerable spot to me once and I can't figure out how to trigger it... i might look up the fight. I don't want a play by play every attack it can make, every counter to the attacks, and to watch some one do it. I just want to know that I need to shoot the eggs to get it angry enough to charge, and that after it charges while its recovering if you hit it with an explosive it'll scream in rage and expose its vulnerable spot so you can damage it. That one sentence is usually ALL i want.
Did it feel good to make a post that was so indignantly self-rigteous it actually completely missed the point.
. If the concern is how it unbalances competition in online play then restrict keyboard players to play against other keyboard players, or to play against players who are willing to use a controller against a keyboard.
That would be great if you could tell which were which but this devices emulates a controller with a keyboard and mouse, giving the player that advantages of the keyboard/mouse, but exposing itself to the game as just a controller.
So even if the game adds keyboard/mouse support, separates them, and players can pick which league they play in... you will still have players with keyboards and mouse in the controller only league destroying the competition, because THOSE particular keyboards and mice users identify themselves as controllers.
1) the nesting can get pretty deep. imagine you had to do a bunch of file operations and had to check for errors after each of them. You could easily be nesting 20+ deep.
2) the nesting for the basic error checking totally obscures the logical structure of the actual code.
You can't assume the resources are allocated at the front, and unwound at the end as you might only need some resources in certain conditions. So now you've got the real program logic mixed in with the success-test nesting. And the actual flow control logic becomes invisible, lost in a mess of library call 'success test' nesting.
Full disclosure... I wrote the bug ridden sloppy pseudocode to make a point. Fisted cleaned up pretty nicely into something that essentially did what i was showing in a cleaner way.
I kind of wish he'd preserved the multiple goto labels but they weren't needed in my example, although there are cases where they would be... where you want specific error handling for certain errors. Here is some hopefully less awful pseudocode.
{
/*allocate resources */
if [allocate resources1] fails goto: errorhandler1 if [allocate resources2] fails goto: errorhandler2
/*do something */
code to do something useful with the resources result = 0 goto:cleanup
/* error handling */
errorhandling1: do something in response to 1 result = -1 goto: cleanup
errorhandling 2: do something in response to 2 result = -2 goto: cleanup
/*cleanup*/
cleanup: if resource1 is allocated free it if resource2 is allocated free it
Its not really cleaner though if you are doing a lot of operations that check for errors. You could be doing a bunch of file io, for example, and need to check for errors after pretty much every line.
Nesting 50 levels deep for success checking is not 'cleaner' and it obscures any actual conditional logic and structuring you've got.
In C in particular, which is the ONLY place I'll use goto... i might have a pattern like something like...
{ a = malloc(something) if malloc failed goto e1 b = malloc(something2) if malloc failed goto e2 c = malloc(onemorething) if malloc failed goto e3...some code... open a file... if error happened goto e3...some code... some other error happened goto e3...some code.../*cleanup*/ e3: free (a) e2: free(b) e3: return; }
The goto sequence cleanly handles the memory free. Obviously you wouldn't want to just return after the 3rd malloc failed.
My understanding is a significant percentage of Intel dies are supporting ancient x86 instructions.
Nope. You understand wrong. The ancient x86 instructions are a tiny insigificant slice of the die.
The CPU cores are RISC and have been for ever now. The x86 instruction set is all converted to RISC in the decoder. The decoder itself is pretty tiny part of the core, and the 'ancient obsolete instrutions' amount for a dozen or so bytes of "RISC lookup" in a table in the decoder on each core.
Cache, GPU, and the memory controller is what dominates the die of a modern i5 or i7.
Its like those old HSP modems that were terrible because of the load the signal processing put on the CPU. But around even 10 years ago even it became a non-issue, the requirements for signal processing for a 56k modem are exactly the same as they were in 1992, but the CPU is a LOT more powerful so the overhead of doing the signal processing barely registers now.
A modern i7 has around 8 million bytes of cache on die. The overhead of the old instructions for the decoder amounts to a couple hundred bytes.
Worrying about the die overhead of the obsolete instructions on a modern CPU is like deleting a half dozen old emails to save hard drive space.
If you only bet when the odds were in your favor, you would slowly bleed your stack away because the other players would immediately fold as soon as you bet.
Which is where after 120,000 hands of play, you've also optimized how often you need to bet on crappy hands. And even optimized how much you need to bet... etc.
With a little experience, simply calculating your odds is quite easy to do.
Your odds of having the best hand at the table yes. The odds of having the best hand at the table when PlayerA has done X and PlayerB has done Y... or the odds PlayerA will fold if you bet... Z... not so much. But with a few hundred thousands hands of experience you could start to nail those numbers down. So when you are playing the odds... you aren't playing the odds that you have the best hand at the table right now, this hand.
You are playing the odds of what you have to do to win overall. And that includes the odds that consistently folding on this hand will cause others to fold on hands you don't fold on. So you'd know precisely how often and how much you have have to bet on this hand to optimize your winnings on other hands where you do have the edge. etc etc.
It sounds like its just better at calculating the odds than humans are, which is not much of a feat, really. I mean... it would almost be surprising if it couldn't.
I'm not trying to diminish the significance of the research... but what is the real innovation here?
If I have a tape drive, and 7 tapes one tape labelled for each day of the week, and each day I rotate the tape.
This gives me about a week of backups. Lots of entities uses stategies like this. It is certainly a backup strategy... it has a few flaws. It's vulnerable to the building catching fire. Its vulnerable to a malicious file deletion or modification if it goes undetected for more than a week.
Likewise, have 2 scheduled rsync jobs to 2 remote sites is a backup strategy. It has some advantages over the the tape strategy above. It has some weaknesses.
A comprehensive backup strategy is incremental, goes back much longer perhaps indefinitely, has redundant offsite components etc. It might also need deletion features to go back and 'delete' things you need to delete from the backups. Lots of places don't have this. Because its a lot more expensive in terms of bandwidth and storage and dollars and maintenance time.
Having copies your data in more than one place is a backup to guard against risks to your primary copy is a backup. It may not be a good backup strategy. It may be wholly inadequate.. but you are just being overly and weirdly pedantic by suggesting that it is improper to call addtional copies of the data a 'backup'.
as for a RAID... that's where calling it a backup gets dicey because it really doesn't guard against ANYTHING except a drive failure. So calling THAT a backup is pushing it.
But even an external flash drive that you copy your files to and take home for the night is a backup. A lousy backup strategy with lots of issues. But good enough for a surprisingly large number of threat scenarios.
Give it a rest. I know full well what a back up is.
Hint: if it is not fully decoupled from the original source (as in "air gap") is not a backup.
Someone running crashplan or carbonite etc has a backup that is resilient to ransomeware, hardware failure, malicious tampering, etc. That is enough of a backup to mitigate most modern threats. It has incremental backups and versioning, and preserves deleted files. And it's not a mounted remote folder so a malicious process/user running your computer can't run amok and delete the backups. By itself, its not perfect, but its sufficient for a lot of entities.
You are probably in the league of those that think RAID5 is also a backup strategy ("sure, not always, not perfect, but in some simple cases...").
A raid5 is an availability strategy. It has an element of redundancy, and you can survive a disk failure without data loss, but it is not a backup.
The "my dog ate my homework aka I mistakenly deleted a file can you recover it?" has *always* been the number one cause of checking out a restore,
damn! all our boxes are infected by a virus
The massive majority of all virus infections prior to the recent rise of ransomware shoveled ads at the interactive user, or turned the system into part of a botnet or both, or exfiltrated passwords and banking information. Only a tiny fraction of a percent ever trashed the users data files... because until ransomware there wasn't any money in that. So the data files tended to be ok, and rsync was fine.
our main server has BSOD'ed, let's reinstall and recover from backups"
The rsync to remote sites works fine for this scenario too.
This may not be quite as evil as you think. Norton's plugin are installed by way of the installer under elevated privileges; because of this they're owned by "SYSTEM" (iirc) so regular users and even administrtor's can't remove them.
It's not so much that they are trying to be douches as being a side effect of how they got installed. And, there is an argument to be made that you don't want it to be possible for a random user or user-space process to be able to remove your antivirus plugins at will.
That said I completely agree that Norton is a boat anchor of a product you throw onto computers to stop them from working properly in order to punish users you don't like. BOFH style.
On the upside it renders the computer so unusable, that its unlikely to get infected by viruses by virtue of the users avoiding touching it.
Slashdot Mirror
The successor function has no universal common name or symbol.
sqrt and log together have a rather clever construction that makes it trivial once you have derived the function, but the function certainly isn't trivial.
And in any case, puzzlers do generally exclude log to eliminate that solution.
Sure its basic, but its not a common or standard or universally understood by a particular symbol.
S(n) could be a LOT of things, even lots of common things.
I guess that depends what you intend 'etc' to represent but only you know that...
"pi is a standard function taking no arguments and always returning the same value."
"In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. "
https://en.wikipedia.org/wiki/...
If it has no inputs, its not a function. The word you are looking for is 'constant'.
ugh. seriously? the point wasn't literally "how do you get to 3"; it was how do generically get further on.
The previous poster wrote
(4/4)+(4/4) "etc"
As if THAT "etc" suggested it was a general extensible solution. It is not. (4+4+4)/4 is a solution for 3, but doesn't tell us how to get to 4, 5, 99, 113, 8187, or 3.148x10^32
I think you overstate the distinction.
I can write arccos(n) without explaining what arccos is, or providing a definition. You couldn't even talk about your f(x) without first defining it...
I think there is a pretty clear distinction between standard functions you DON'T have to provide definitions for because they are standard, and arbitrary functions you made up on the spot, and had to define before using.
Where is my prize? (What a stupid video.)
Why would you get a prize for solving a completely different and much easier problem?
If you see SS0 in a math text book do you automatically know that its an increment? Because when I see a square root sign or a log function i don't need to look up how they have been defined in that chapter or book, because they are universally use common standard functions.
Your operation S that add's +1 is not a common mathematical operation or symbol; so its not a candidate operation for the solution.
(4/4)+(4/4) etc
What do you mean "etc" ??
(4/4)+(4/4) = 2; fine; that equals 2
But How do you get to 3 ?
(4/4)+(4/4)+(4/4) is 6 4s.
Slashdot trying to pretend it is something intellectually interesting is what is offensive.
You posted a non-solution to the problem. I think if you are going to denigrate the video as not being intellectually interesting, you should probably at least understand the puzzle being solved.
Its 'four fours'. Not six of them, not as many as you need. Just four them. Exactly 4 of them.
If we can use any functions such as arbitrary number of SQRT in combination with LOG
Answer #1:
Increment isn't a 'common standard function or operator in math'
sqare root is here: https://en.wikipedia.org/wiki/...
log is here: https://en.wikipedia.org/wiki/...
Both articles start out "In mathematics..."
Where is 'increment'??
sqrt has a standard mathematical symbol a 5th grader is familiar with. log is a standard mathematical function a 10th grader is familiar with. Both have dedicated buttons on a $6 calculator for high school math. This is the same reason why concat got such a rough response here; it is actually a valid operator, but its not nearly as 'common'.
I can't recall ever seeing a standard increment symbol or standard increment function in pure mathematics. Sure you could define a suitable one using any of a variety of methods, but there isn't a standard one that I am aware of. Yeah, lets of computer programming languages have one, but that isn't math, that's programming.
Answer #2:
It violates the spirit of the puzzle.
Even if INCREMENT did exist as a standard function; it would simply be immediately excluded from being used to solve the puzzle, since it renders the puzzle pointless and trivial.
The log / sqrt solution is an interesting and clever solution. Increment ... is ... not.
And in fact for people who actually like to play with the 4 4's problem as a puzzle today, they usually exclude log once they discover this pattern too -- precisely because it renders the puzzle pointless.
https://en.wikipedia.org/wiki/...
"Typically the "log" operators are not allowed, since there is a way to trivially create any number using them."
But not suitable for Slashdot where we (should) already know this stuff, there is nothing new here.
Give it a rest.
It was really an elegant mathematical solution.
Yes its not new, but its certainly 'esoteric enough'; I certainly hadn't seen it before. I can understand the expression on the wikipedia article, but its definitely not something i'd think most people would follow; and even i would have had to study it longer than it the 5 minutes it took to watch the video to have figured out how it all worked, so I enjoyed seeing the derivation.
And if some youtuber makes a few pennies off demonstrating an elegant mathematical proof in an easy to follow and informative way... what exactly do you object to about it?
An example of something that benefits from video would be a video game walkthrough; by showing the action on-screen, the viewer will be able to see the sequence of events, both the actions of the player, and the reaction of the game engine and AIs.
That's also an example of something that is horrific on video.
If am interested in finding the secrets as I play through a game the one thing I absolutely do not want is to watch someone else play the level from start to finish, every monster shown, every cutscene revealed, every puzzle solved. Might as well not play the game now.
I VASTLY prefer a simple list, "as you enter the subway station, first door on your left, behind the plant in the blue pot". After you kill the boss, jump down into the sewers and follow the wall to the right past the waterfall, its behind the stack of 4 boxes. That's ALL I want. Maybe links to screenshots that i can click on if I still just can't find it. Because i still want to 'find' it. And a couple sentences of description is a bit like orienteering... i have the information needed to get there without having the whole experience completely ruined by watching someone else do it from start to finish before I play.
Walkthrus also benefit from the seek and index features of text.
If I played the game through and found most of the secrets, and am doing a 2nd playthrough to be completionist; and i know i am missing the '4th secret' on the 3rd level then again I can quickly jump to the list of secrets for the 3rd level, and then to the 4th secret, without clicking around trying to find it in a big long video stream.
Same with boss fights; if im having serious trouble with a fight-- e.g. after 30 minutes in a single battle the boss has only revealed its vulnerable spot to me once and I can't figure out how to trigger it... i might look up the fight. I don't want a play by play every attack it can make, every counter to the attacks, and to watch some one do it. I just want to know that I need to shoot the eggs to get it angry enough to charge, and that after it charges while its recovering if you hit it with an explosive it'll scream in rage and expose its vulnerable spot so you can damage it. That one sentence is usually ALL i want.
The video is actually worth watching.
They don't need concatenation; and can get any whole number from
log
sqrt symbol
division
the sqrt symbol is the 'trick' to it all; since it can be applied an infinite number of times to a single expression.
Did it feel good to make a post that was so indignantly self-rigteous it actually completely missed the point.
. If the concern is how it unbalances competition in online play then restrict keyboard players to play against other keyboard players, or to play against players who are willing to use a controller against a keyboard.
That would be great if you could tell which were which but this devices emulates a controller with a keyboard and mouse, giving the player that advantages of the keyboard/mouse, but exposing itself to the game as just a controller.
So even if the game adds keyboard/mouse support, separates them, and players can pick which league they play in ... you will still have players with keyboards and mouse in the controller only league destroying the competition, because THOSE particular keyboards and mice users identify themselves as controllers.
The thing I don't like about that pattern is that
1) the nesting can get pretty deep. imagine you had to do a bunch of file operations and had to check for errors after each of them. You could easily be nesting 20+ deep.
2) the nesting for the basic error checking totally obscures the logical structure of the actual code.
You can't assume the resources are allocated at the front, and unwound at the end as you might only need some resources in certain conditions. So now you've got the real program logic mixed in with the success-test nesting. And the actual flow control logic becomes invisible, lost in a mess of library call 'success test' nesting.
taking alignment into account (ie: 8)
Full disclosure... I wrote the bug ridden sloppy pseudocode to make a point. Fisted cleaned up pretty nicely into something that essentially did what i was showing in a cleaner way.
I kind of wish he'd preserved the multiple goto labels but they weren't needed in my example, although there are cases where they would be... where you want specific error handling for certain errors. Here is some hopefully less awful pseudocode.
{
/*allocate resources */
if [allocate resources1] fails goto: errorhandler1
if [allocate resources2] fails goto: errorhandler2
/*do something */
code to do something useful with the resources
result = 0
goto:cleanup
/* error handling */
errorhandling1:
do something in response to 1
result = -1
goto: cleanup
errorhandling 2:
do something in response to 2
result = -2
goto: cleanup
/*cleanup*/
cleanup:
if resource1 is allocated free it
if resource2 is allocated free it
return result;
}
Its not really cleaner though if you are doing a lot of operations that check for errors. You could be doing a bunch of file io, for example, and need to check for errors after pretty much every line.
Nesting 50 levels deep for success checking is not 'cleaner' and it obscures any actual conditional logic and structuring you've got.
lol. on the upside it won't compile so no one will ever suffer them. :p
The point is that you have several mallocs to deal with, and more than one error condition (not just failing the malloc itself).
So if you make 3 mallocs, and then there is an error opening the file... you still have to free all 3 mallocs.
the use of 3 if(x) free(x) instead of multiple goto labels is fine, but you still need goto to get to the cleanup block from the various error points.
How is goto return better than just return?
In C in particular, which is the ONLY place I'll use goto... i might have a pattern like something like...
{
a = malloc(something)
if malloc failed goto e1
b = malloc(something2)
if malloc failed goto e2
c = malloc(onemorething)
if malloc failed goto e3
open a file... if error happened goto e3
some other error happened goto e3
e3:
free (a)
e2:
free(b)
e3:
return;
}
The goto sequence cleanly handles the memory free. Obviously you wouldn't want to just return after the 3rd malloc failed.
My understanding is a significant percentage of Intel dies are supporting ancient x86 instructions.
Nope. You understand wrong. The ancient x86 instructions are a tiny insigificant slice of the die.
The CPU cores are RISC and have been for ever now. The x86 instruction set is all converted to RISC in the decoder. The decoder itself is pretty tiny part of the core, and the 'ancient obsolete instrutions' amount for a dozen or so bytes of "RISC lookup" in a table in the decoder on each core.
Cache, GPU, and the memory controller is what dominates the die of a modern i5 or i7.
Its like those old HSP modems that were terrible because of the load the signal processing put on the CPU. But around even 10 years ago even it became a non-issue, the requirements for signal processing for a 56k modem are exactly the same as they were in 1992, but the CPU is a LOT more powerful so the overhead of doing the signal processing barely registers now.
A modern i7 has around 8 million bytes of cache on die. The overhead of the old instructions for the decoder amounts to a couple hundred bytes.
Worrying about the die overhead of the obsolete instructions on a modern CPU is like deleting a half dozen old emails to save hard drive space.
If you only bet when the odds were in your favor, you would slowly bleed your stack away because the other players would immediately fold as soon as you bet.
Which is where after 120,000 hands of play, you've also optimized how often you need to bet on crappy hands. And even optimized how much you need to bet... etc.
With a little experience, simply calculating your odds is quite easy to do.
Your odds of having the best hand at the table yes. The odds of having the best hand at the table when PlayerA has done X and PlayerB has done Y... or the odds PlayerA will fold if you bet... Z... not so much. But with a few hundred thousands hands of experience you could start to nail those numbers down. So when you are playing the odds... you aren't playing the odds that you have the best hand at the table right now, this hand.
You are playing the odds of what you have to do to win overall. And that includes the odds that consistently folding on this hand will cause others to fold on hands you don't fold on. So you'd know precisely how often and how much you have have to bet on this hand to optimize your winnings on other hands where you do have the edge. etc etc.
It sounds like its just better at calculating the odds than humans are, which is not much of a feat, really. I mean... it would almost be surprising if it couldn't.
I'm not trying to diminish the significance of the research... but what is the real innovation here?
If I have a tape drive, and 7 tapes one tape labelled for each day of the week, and each day I rotate the tape.
This gives me about a week of backups. Lots of entities uses stategies like this. It is certainly a backup strategy... it has a few flaws. It's vulnerable to the building catching fire. Its vulnerable to a malicious file deletion or modification if it goes undetected for more than a week.
Likewise, have 2 scheduled rsync jobs to 2 remote sites is a backup strategy. It has some advantages over the the tape strategy above. It has some weaknesses.
A comprehensive backup strategy is incremental, goes back much longer perhaps indefinitely, has redundant offsite components etc. It might also need deletion features to go back and 'delete' things you need to delete from the backups. Lots of places don't have this. Because its a lot more expensive in terms of bandwidth and storage and dollars and maintenance time.
Having copies your data in more than one place is a backup to guard against risks to your primary copy is a backup. It may not be a good backup strategy. It may be wholly inadequate.. but you are just being overly and weirdly pedantic by suggesting that it is improper to call addtional copies of the data a 'backup'.
as for a RAID... that's where calling it a backup gets dicey because it really doesn't guard against ANYTHING except a drive failure. So calling THAT a backup is pushing it.
But even an external flash drive that you copy your files to and take home for the night is a backup. A lousy backup strategy with lots of issues. But good enough for a surprisingly large number of threat scenarios.
You don't understand what a back up is.
Give it a rest. I know full well what a back up is.
Hint: if it is not fully decoupled from the original source (as in "air gap") is not a backup.
Someone running crashplan or carbonite etc has a backup that is resilient to ransomeware, hardware failure, malicious tampering, etc. That is enough of a backup to mitigate most modern threats. It has incremental backups and versioning, and preserves deleted files. And it's not a mounted remote folder so a malicious process/user running your computer can't run amok and delete the backups. By itself, its not perfect, but its sufficient for a lot of entities.
You are probably in the league of those that think RAID5 is also a backup strategy ("sure, not always, not perfect, but in some simple cases...").
A raid5 is an availability strategy. It has an element of redundancy, and you can survive a disk failure without data loss, but it is not a backup.
The "my dog ate my homework aka I mistakenly deleted a file can you recover it?" has *always* been the number one cause of checking out a restore,
damn! all our boxes are infected by a virus
The massive majority of all virus infections prior to the recent rise of ransomware shoveled ads at the interactive user, or turned the system into part of a botnet or both, or exfiltrated passwords and banking information. Only a tiny fraction of a percent ever trashed the users data files... because until ransomware there wasn't any money in that. So the data files tended to be ok, and rsync was fine.
our main server has BSOD'ed, let's reinstall and recover from backups"
The rsync to remote sites works fine for this scenario too.
and doesn't allow you to remove it.
This may not be quite as evil as you think. Norton's plugin are installed by way of the installer under elevated privileges; because of this they're owned by "SYSTEM" (iirc) so regular users and even administrtor's can't remove them.
It's not so much that they are trying to be douches as being a side effect of how they got installed. And, there is an argument to be made that you don't want it to be possible for a random user or user-space process to be able to remove your antivirus plugins at will.
That said I completely agree that Norton is a boat anchor of a product you throw onto computers to stop them from working properly in order to punish users you don't like. BOFH style.
On the upside it renders the computer so unusable, that its unlikely to get infected by viruses by virtue of the users avoiding touching it.