Somebody please explain the importance/use of Abundant Numbers
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What use are primes? It's not until your start looking at some really complex stuff like cryptography that prime numbers become useful rather than just "oh wow, cool!" - but we teach kids about them! So why not teach Abundance? They are a simple enough concept, that's kinda cool to think about and it gets you thinking (and practicing) division, addition, and logic (to an extent). I haven't knowingly used a prime number since I was introduced to them at school - but every time I go shopping, every site I visit: they are there hiding in the background! I have no idea if Abundance has a "real world" use - but if it does, then it's probably hidden away in common sight! :laugh:
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
Ironically you mention the most hidden in plain sight one: time. Hours, minutes, seconds, months all use Abundant numbers. The imperial system makes extensive use of them. The idea of using them is there are more divisors, so you can split into more different sized items. For example 12 can be divided into 2, 3, 4 or 6 but 10 can only be divided into 2 and 5.
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Slacker007 wrote:
3 decide at the last minute to use the restroom
You're obviously not from the UK. :laugh: The toilets on the stations tend to be owned by Network Rail, and the regional operators save money by not renting them, so they're permanently closed. And even if you're lucky, and happen to be at one of the large stations where they are open, you need to make sure you have the correct change to pay to get in. Toilets on the trains - on the vanishingly few trains that have them - tend to be permanently out of order. As a result, very few people ever use them, so the PHBs use that to justify saving money on newer trains by not including toilets at all. Basically, if you're planning to travel by train in the UK, make sure you take an empty bottle with you, since they don't even provide a "toilet-replacement bucket service".
"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer
When you're a man, the whole world is your restroom. That's probably why those stations are always so dirty, because these people are learning abundant numbers :sigh:
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Ironically you mention the most hidden in plain sight one: time. Hours, minutes, seconds, months all use Abundant numbers. The imperial system makes extensive use of them. The idea of using them is there are more divisors, so you can split into more different sized items. For example 12 can be divided into 2, 3, 4 or 6 but 10 can only be divided into 2 and 5.
The only reason we use base10 is that we have ten fingers. (Well except for the French and Danes amongst others, no not the number of fingers, but they both partially use base20 in their spoken language) The Babylonians appreciated abundant numbers and used base60 instead of base10, or the Sexagesimal system, this is where we got our minutes and seconds from. I don't know why they decided to divide a day into twelve hours instead though. :doh:
Wrong is evil and must be defeated. - Jeff Ello
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The only reason we use base10 is that we have ten fingers. (Well except for the French and Danes amongst others, no not the number of fingers, but they both partially use base20 in their spoken language) The Babylonians appreciated abundant numbers and used base60 instead of base10, or the Sexagesimal system, this is where we got our minutes and seconds from. I don't know why they decided to divide a day into twelve hours instead though. :doh:
Wrong is evil and must be defeated. - Jeff Ello
Jörgen Andersson wrote:
The only reason we use base10 is that we have ten fingers.
That's why the French use base 20 - they take their socks off to count ... :laugh:
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
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Jörgen Andersson wrote:
The only reason we use base10 is that we have ten fingers.
That's why the French use base 20 - they take their socks off to count ... :laugh:
"I have no idea what I did, but I'm taking full credit for it." - ThisOldTony "Common sense is so rare these days, it should be classified as a super power" - Random T-shirt AntiTwitter: @DalekDave is now a follower!
Yup, that's it. Many years ago I recieved a book (actually two tomes) from my brother, "Histoire universelle des chiffres". Luckily a translated version since my French is utterly weak. An amazing book, but a heavy read that I still haven't finished. :sigh: The first chapters explains probable origins for different bases we have been using throughout history. Base12 (very common in imperial measures) used the fingerjoints on one hand, excluding the thumb. Add the thumbs and use both hands and you can count the days of a month.
Wrong is evil and must be defeated. - Jeff Ello
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Slacker007 wrote:
3 decide at the last minute to use the restroom
You're obviously not from the UK. :laugh: The toilets on the stations tend to be owned by Network Rail, and the regional operators save money by not renting them, so they're permanently closed. And even if you're lucky, and happen to be at one of the large stations where they are open, you need to make sure you have the correct change to pay to get in. Toilets on the trains - on the vanishingly few trains that have them - tend to be permanently out of order. As a result, very few people ever use them, so the PHBs use that to justify saving money on newer trains by not including toilets at all. Basically, if you're planning to travel by train in the UK, make sure you take an empty bottle with you, since they don't even provide a "toilet-replacement bucket service".
"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer
A few years ago I went by train from Manchester airport to Leeds, it was a weird experience that now got an explanation. :sigh:
Wrong is evil and must be defeated. - Jeff Ello
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Slacker007 wrote:
3 decide at the last minute to use the restroom
You're obviously not from the UK. :laugh: The toilets on the stations tend to be owned by Network Rail, and the regional operators save money by not renting them, so they're permanently closed. And even if you're lucky, and happen to be at one of the large stations where they are open, you need to make sure you have the correct change to pay to get in. Toilets on the trains - on the vanishingly few trains that have them - tend to be permanently out of order. As a result, very few people ever use them, so the PHBs use that to justify saving money on newer trains by not including toilets at all. Basically, if you're planning to travel by train in the UK, make sure you take an empty bottle with you, since they don't even provide a "toilet-replacement bucket service".
"These people looked deep within my soul and assigned me a number based on the order in which I joined." - Homer
Richard Deeming wrote:
Toilets on the trains
And when they are available, (apart from being awash with assorted bodily fluids) they have electronic doors with no physical lock, and the sliding door opens very wide (to be "accessible") so you spend your time in there in terror of the door randomly and unstoppably opening and exposing your attempts to avoid other people's wee/poo/sick/etc to the entire carriage. (Though these days a large proportion of trains are running almost empty anyway, and I suspect a proportion of the remaining passengers don't even bother looking for the toilet).
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The children of a relative in the UK are being taught Abundant Numbers and mum is having a tough time keeping up. The theories are almost 2000 years old. I understand how to work out the various (numerous) derivatives but what worldly purpose do they serve?? I have lived many years without requiring any abundance (other than a paycheck) It seems almost as crazy as the Common Core Math they teach here in the USA. Anyway, I would like to understand the importance/use of Abundant Numbers.
Live long and prosper
My first impression is that it might be useful when ordering, cutting and building with lumber; 8, 12, and 16 (foot) lengths seem most common. Watch 2 people build the same fence and see how much is left over; the one with more scrap is "less abundant".
It was only in wine that he laid down no limit for himself, but he did not allow himself to be confused by it. ― Confucian Analects: Rules of Confucius about his food
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The only reason we use base10 is that we have ten fingers. (Well except for the French and Danes amongst others, no not the number of fingers, but they both partially use base20 in their spoken language) The Babylonians appreciated abundant numbers and used base60 instead of base10, or the Sexagesimal system, this is where we got our minutes and seconds from. I don't know why they decided to divide a day into twelve hours instead though. :doh:
Wrong is evil and must be defeated. - Jeff Ello
Jörgen Andersson wrote:
The only reason we use base10 is that we have ten fingers.
I've heard this stated many times but is there any evidence for it? As we only have unique symbols for the numbers 0 to 9, might it not have been invented by a nine fingered person? (Insert your preferred locale for in-breeding jokes here) - which just happens to work out better for us to do arithmetic. I've always found it interesting that our system of writing uses a different approach to the way our fingers work. If I want to give someone the sign for ten I'll hold up all ten fingers but to write it down, I have to use a second symbol ("1") followed by an arguably redundant zero, when it could have been "0A" - if we borrow from hex. Of course, if you used e.g. "A" to represent the number after 9, then you hit all sorts of interesting questions related to zeroes e.g. should it be written "1A" or "20"?
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Ironically you mention the most hidden in plain sight one: time. Hours, minutes, seconds, months all use Abundant numbers. The imperial system makes extensive use of them. The idea of using them is there are more divisors, so you can split into more different sized items. For example 12 can be divided into 2, 3, 4 or 6 but 10 can only be divided into 2 and 5.
That isn't a function of those being abundant it's a function of them being highly composite
KeithBarrow.net[^] - It might not be very good, but at least it is free!
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Assuming there are 10 people in a train, and 15 of them go out in a train station, 5 must go in at the next station for the train to arrive empty. Oh nevermind, I read abusing numbers.
Is the train perfectly frictionless, and the people perfectly spherical? Asking for a physics friend.
KeithBarrow.net[^] - It might not be very good, but at least it is free!
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Is the train perfectly frictionless, and the people perfectly spherical? Asking for a physics friend.
KeithBarrow.net[^] - It might not be very good, but at least it is free!
Of course, and it travels at the speed of light.
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The children of a relative in the UK are being taught Abundant Numbers and mum is having a tough time keeping up. The theories are almost 2000 years old. I understand how to work out the various (numerous) derivatives but what worldly purpose do they serve?? I have lived many years without requiring any abundance (other than a paycheck) It seems almost as crazy as the Common Core Math they teach here in the USA. Anyway, I would like to understand the importance/use of Abundant Numbers.
Live long and prosper
CoolTeddyBear wrote:
I understand how to work out the various (numerous) derivatives but what worldly purpose do they serve??
In all honesty I think the main "worldly purpose" was for Michael Gove (who re-jigged the curriculum some time ago) to claim to Conservative Party members that he'd introduced a more traditional/stricter curriculum. Home schooling under lockdown has starkly revealed how bad the curriculum has become, much more wrote learning than in my day, but without the added depth previous generations seem to have been exposed to (if the past exam papers I looked at in my teens were anything to go by). My 6 year old's English work spent weeks categorising words into weirdly fine (and largely useless) groups - by all means make sure there are words to change how often a verb happens (or even adverbs generally) but what use is being able to split them down into adverb types at that age? Answer - it looks like proper education to a certain group of people.
KeithBarrow.net[^] - It might not be very good, but at least it is free!
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Jörgen Andersson wrote:
The only reason we use base10 is that we have ten fingers.
I've heard this stated many times but is there any evidence for it? As we only have unique symbols for the numbers 0 to 9, might it not have been invented by a nine fingered person? (Insert your preferred locale for in-breeding jokes here) - which just happens to work out better for us to do arithmetic. I've always found it interesting that our system of writing uses a different approach to the way our fingers work. If I want to give someone the sign for ten I'll hold up all ten fingers but to write it down, I have to use a second symbol ("1") followed by an arguably redundant zero, when it could have been "0A" - if we borrow from hex. Of course, if you used e.g. "A" to represent the number after 9, then you hit all sorts of interesting questions related to zeroes e.g. should it be written "1A" or "20"?
No proofs but plenty of evidence. :) 1) The word for digit comes from the latin word for finger. B) The roman symbol for 5 is a V which symbolizes a hand, and the symbol for 10 is an X which is two hands. Interestingly the exeption that the Babylonian sexagesimal system would be, also has symbols for 1-9 and 10-50 and then a new symbol for 60. There are obviously plenty of exeptions, but the main reason for using base10 is that we have a built in calculator in our hands. Can recommend reading the book The Universal History of Numbers: From Prehistory to the Invention of the Computer[^] by Georges Ifrah if you're interested.
Wrong is evil and must be defeated. - Jeff Ello
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No proofs but plenty of evidence. :) 1) The word for digit comes from the latin word for finger. B) The roman symbol for 5 is a V which symbolizes a hand, and the symbol for 10 is an X which is two hands. Interestingly the exeption that the Babylonian sexagesimal system would be, also has symbols for 1-9 and 10-50 and then a new symbol for 60. There are obviously plenty of exeptions, but the main reason for using base10 is that we have a built in calculator in our hands. Can recommend reading the book The Universal History of Numbers: From Prehistory to the Invention of the Computer[^] by Georges Ifrah if you're interested.
Wrong is evil and must be defeated. - Jeff Ello
Interesting. Did you happen to see the episode of QI where they claimed that Roman numerals were only very rarely used by the Romans and their popularity is MUCH more recent encouraged by the BBC and others to make dates less readable? I know nothing of this so merely repeating their claim (they allege it was a BBC policy so that repeated programmes were harder to spot if the date was flashed up quickly in Roman numerals!)
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Interesting. Did you happen to see the episode of QI where they claimed that Roman numerals were only very rarely used by the Romans and their popularity is MUCH more recent encouraged by the BBC and others to make dates less readable? I know nothing of this so merely repeating their claim (they allege it was a BBC policy so that repeated programmes were harder to spot if the date was flashed up quickly in Roman numerals!)
No, I didn't see it, but if that's the case, what did they use instead? As far as I understand, roman numerals were pushed away by arabic numerals around 900 AD. I know they have found Roman Abacuses (Or Abacii? What is the plural actually?) several times that was obviously built according to the roman system. But that doesn't rule out anything. As so often there could be different system in use in different social layers.
Wrong is evil and must be defeated. - Jeff Ello
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No, I didn't see it, but if that's the case, what did they use instead? As far as I understand, roman numerals were pushed away by arabic numerals around 900 AD. I know they have found Roman Abacuses (Or Abacii? What is the plural actually?) several times that was obviously built according to the roman system. But that doesn't rule out anything. As so often there could be different system in use in different social layers.
Wrong is evil and must be defeated. - Jeff Ello
Sorry, only had it on as "background" and wasn't paying proper attention. They also said that e.g. four might just as often be written a IIII or IV, similarly VIIII for nine. Both systems were popular.
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Sorry, only had it on as "background" and wasn't paying proper attention. They also said that e.g. four might just as often be written a IIII or IV, similarly VIIII for nine. Both systems were popular.
Ok, makes sense.
Wrong is evil and must be defeated. - Jeff Ello
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The only reason we use base10 is that we have ten fingers. (Well except for the French and Danes amongst others, no not the number of fingers, but they both partially use base20 in their spoken language) The Babylonians appreciated abundant numbers and used base60 instead of base10, or the Sexagesimal system, this is where we got our minutes and seconds from. I don't know why they decided to divide a day into twelve hours instead though. :doh:
Wrong is evil and must be defeated. - Jeff Ello
Jörgen Andersson wrote:
I don't know why they decided to divide a day into twelve hours instead though
Huh, and I thought a day was 24 hours .. Oh well :)
Live long and prosper
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A few years ago I went by train from Manchester airport to Leeds, it was a weird experience that now got an explanation. :sigh:
Wrong is evil and must be defeated. - Jeff Ello
Jörgen Andersson wrote:
it was a weird experience that now got an explanation
according to wikipedia "An abundant number which is not a semiperfect number is called a weird number" perhaps that also applies to experiences :) I am bemused by quasiperfect numbers... "An abundant number with abundance 1 is called a quasiperfect number, although none have yet been found"
Live long and prosper
