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#1
Old 01-18-2012, 08:09 AM
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What does "Ten-fold" mean?

In new reports you often hear the expression "a ten-fold increase" or five-fold etc.

Take this report as an example: http://news.bbc.co.uk/1/hi/education/8605824.stm

Quote:
The results of the survey of 1,000 parents suggest around 6% of fathers, or 600,000 men, are now their child's primary carer, up from 60,000 in 2000.
I was taught by my maths teacher that ten times and ten-fold have different meanings.

Ten fold 60,000 is actually 61,440,000 not 600,000 and this is why:

When you fold something you effectively double it, think of folding a piece of paper. If you fold a piece of paper once you have 2 layers, fold it again and you have four layers and so on.

So if you "fold" 60,000 you have 120,000, fold it again and you have 240,000 and so on. After "folding" it ten times you have a figure of 61,440,000.

Please discuss :-).
#2
Old 01-18-2012, 08:18 AM
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http://merriam-webster.com/dictionary/tenfold
Quote:
1: having 10 units or members
2: being 10 times as great or as many
#3
Old 01-18-2012, 08:18 AM
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http://yourdictionary.com/tenfold
http://merriam-webster.com/dictionary/tenfold

both of these say having 10 parts or 10x as many

I don't know the origin of the phrase or your teachers interpretation but common usage goes with 10 times
#4
Old 01-18-2012, 08:19 AM
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It's nothing much to do with folding of anything - the ~fold suffix comes from old English and just means 'of (or divisible into) x many parts' - so fourfold means 'of four parts'. Manifold means 'of many parts'

The potential for misunderstanding isn't really anything to do with the term - it's just that ~fold tends to be used exclusively with 'increase', so a threefold increase is the same as a 300% increase, or in total, four times the original amount.

Last edited by Mangetout; 01-18-2012 at 08:20 AM.
#5
Old 01-18-2012, 08:19 AM
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Ten fold means ten times, so 600,000 is a tenfold increase over 60,000. What you're describing is raising something to the tenth power.
#6
Old 01-18-2012, 08:20 AM
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This is the first time I've ever run across that theory! Whenever I've seen or heard a word like "tenfold" used, it means either "ten times" or "having ten parts"; and the definitions I've managed to Google up just now agree.

I was going to say that the "-fold" suffix doesn't have anything to do with the verb "to fold," but upon checking, it looks like they have the same origin (-fold; fold), so maybe there is an etymological connection there somewhere.
#7
Old 01-18-2012, 08:24 AM
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"Fold" in this sense has nothing to do with folding paper over. Folding is equivalent to exponentiation, not multiplication. Your sum is 60,000 210, which is not an accepted definition of "increasing 60,000 tenfold".

Quote:
Originally Posted by Captain Amazing
Ten fold means ten times, so 600,000 is a tenfold increase over 60,000. What you're describing is raising something to the tenth power.
Not quite - 60,00010 would be about 6 x 1047. The OP multiplied by two to the tenth.

Last edited by Colophon; 01-18-2012 at 08:26 AM.
#8
Old 01-18-2012, 08:30 AM
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Nope, - fold (Old English - feald) as a suffix or numeric modifier just means "times" - as in fourfold (four times), or hundredfold (one hundred times).

Fold (Old English faldan or fealdan) "to bend cloth back over itself," describes the layered effect, not a doubling. There are plenty of ways to fold things without doubling.

Si
#9
Old 01-18-2012, 08:54 AM
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Quote:
Originally Posted by Featherlake View Post
I was taught by my maths teacher that ten times and ten-fold have different meanings.
I think your maths teacher was the victim of some really odd urban legend.
#10
Old 01-18-2012, 09:00 AM
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Quote:
Originally Posted by Featherlake View Post
When you fold something you effectively double it, think of folding a piece of paper. If you fold a piece of paper once you have 2 layers, fold it again and you have four layers and so on.

So if you "fold" 60,000 you have 120,000, fold it again and you have 240,000 and so on. After "folding" it ten times you have a figure of 61,440,000.
I would assume that the mere fact most people can not quickly and easily perform this calculation in their head would make it unlikely this interpretation is preferable to a simple "times".
#11
Old 01-18-2012, 09:02 AM
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On re-reading, I see I misread the nature of the disagreement (I thought it was a contest between 10 times and 'increase by ten times itself' - the latter of which may mean 11 times).

However, the definition of the ~fold suffix stands. Sounds like your maths teacher had his own special, non-standard definition.
#12
Old 01-18-2012, 09:15 AM
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Thanks for the replies, I know the general consensus if that ten-fold means ten times and five-fold means five times etc.

There does seem to be a bit of confusion about the term, here for example: http://blurtit.com/q577324.html

I am slowly being convinced that my maths teacher was incorrect, but I will wait for a little longer, it's like being told that Einsteins' theory or relativity is wrong .

Also, why don't people just use the term "ten times"?
#13
Old 01-18-2012, 09:21 AM
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I think your teacher was overthinking it. I have never heard that interpretation.
#14
Old 01-18-2012, 09:37 AM
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Quote:
Originally Posted by Featherlake View Post
Also, why don't people just use the term "ten times"?
Because using "tenfold" as an adjective conveys the idea very economically and fluidly. The word works perfectly well for this. Getting the same thought across with the phrase "ten times" offers no improvement, and would either be awkward and confusing or require a whole lot more words.
#15
Old 01-18-2012, 09:50 AM
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Quote:
Originally Posted by Gary T View Post
Because using "tenfold" as an adjective conveys the idea very economically and fluidly. The word works perfectly well for this. Getting the same thought across with the phrase "ten times" offers no improvement, and would either be awkward and confusing or require a whole lot more words.
Another possible reason is that, in some contexts, "ten times" could be ambiguous: does it mean "ten times as much" or "ten separate occurences"?
#16
Old 01-18-2012, 09:55 AM
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Middle English Dictionary for tenfold.
#17
Old 01-18-2012, 11:21 AM
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Quote:
Originally Posted by Thudlow Boink View Post
Another possible reason is that, in some contexts, "ten times" could be ambiguous: does it mean "ten times as much" or "ten separate occurences"?
Yes, that would be the "confusing" part. And to clarify it takes a lot more verbiage.
#18
Old 01-18-2012, 11:47 AM
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Quote:
Originally Posted by Featherlake View Post
There does seem to be a bit of confusion about the term, here for example: http://blurtit.com/q577324.html
You're going to trust random internet posters, rather than the dictionary and hundreds of years of usage?

It's NOT like being told Einstein theory of relativity was wrong.

It's like being told Einstein's theory of relativity really dealt with how his relatives were spread over Germany (hence relativity). If your teacher told you that, they'd be wrong. Same case here. The explanation is wrong - not the term or theory.

As I mentioned in another thread, some math teachers (and I imagine teachers, in general) do often give just plain bad information to students. They're not infallible.

Last edited by Great Antibob; 01-18-2012 at 11:48 AM.
#19
Old 01-18-2012, 01:12 PM
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Quote:
Originally Posted by Featherlake View Post
There does seem to be a bit of confusion about the term...
So far the confusion seems to lie with that poster, your math teacher, and you. I think it's safe to say that the other 99.9+% of the world, including every actual authority on the matter, is not confused.
#20
Old 01-18-2012, 01:53 PM
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I've encountered something like the OP's usage occasionally, for instance, in cosmological inflation, one often speaks of '60 e-foldings', meaning an increase by e60. So what the OP wants could be framed as 'ten two-foldings', and if the two is understood, I could see abbreviating that as 'tenfold'. But if I encountered 'tenfold' in the wild, I'd assume it to mean 'by a factor of 10'.
#21
Old 01-18-2012, 01:54 PM
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Quote:
Originally Posted by Featherlake View Post
Thanks for the replies, I know the general consensus if that ten-fold means ten times and five-fold means five times etc.
Well, it's a bit more than "the general consensus." It's more like "every use on record except one website and you."

Sounds to me like a classic case of "false etymology," where people try to imagine how a word or phrase came to be and they supply something that sounds logical ("Hey, if you fold it ten times...") without actually knowing the real origin of the word or term. False etymologies usually sound plausible and thus tend to get some traction in people's minds.
#22
Old 01-18-2012, 03:08 PM
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Anyway, if you want to double the size of something ten times, that would be ten-unfold. Furthermore, it's nigh impossible to fold a piece of paper in half more than seven or eight times, so as well as being just plain wrong, this etymology doesn't even make sense, and is impossible.
#23
Old 01-18-2012, 03:19 PM
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Quote:
Originally Posted by Sailboat View Post
Well, it's a bit more than "the general consensus." It's more like "every use on record except one website and you."
I wouldn't be surprised if it's more than that. Unless his math teacher wrote that entry in that site, it has some traction.
#24
Old 01-18-2012, 03:49 PM
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Quote:
I've encountered something like the OP's usage occasionally, for instance, in cosmological inflation, one often speaks of '60 e-foldings', meaning an increase by e60.
Which is still the same usage as everyone else in this thread is saying. One e-folding is an increase by a factor of e, not by a factor of 2e. And "60 e-foldings" is not the same thing as a "(60*e)-folding".
#25
Old 01-18-2012, 06:18 PM
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Quote:
Originally Posted by Mangetout
Furthermore, it's nigh impossible to fold a piece of paper in half more than seven or eight times...
The myth was that it's impossible to fold a piece of paper more than seven times, but the Mythbusters were able to take a football field-sized piece of paper and fold it eleven times, albeit with the help of a steamroller and forklift, into about the size of a twin mattress.

As long as we're on the subject of tens, the one that bugs the crap out of me is when the TV news people say something was decimated, when they really mean it was ruined or destroyed. Decimation shouldn't be all that bad - originally, it's just a reduction by 10%, but the dumbing-down of everything has changed it to now mean complete ruin.
#26
Old 01-18-2012, 06:52 PM
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Quote:
Originally Posted by gotpasswords View Post
The myth was that it's impossible to fold a piece of paper more than seven times, but the Mythbusters were able to take a football field-sized piece of paper and fold it eleven times, albeit with the help of a steamroller and forklift, into about the size of a twin mattress.
That's why I said nigh impossible. Certainly not easy enough for this etymology to work properly.
#27
Old 01-18-2012, 07:17 PM
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There was also a high-schooler (link will work tomorrow) who used her own muscle power to fold a piece of paper 12 times. It's not a matter of strength; it's just a matter of the length-to-thickness ratio of the paper (the student, Britney Gallivan, used unrolled toilet paper).
#28
Old 01-18-2012, 11:47 PM
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Quote:
Originally Posted by Featherlake View Post
I am slowly being convinced that my maths teacher was incorrect
Your teacher was either (1) a crackpot, at least on this one issue, or (2) yanking your chain, or (3) free-associating and letting the word "ten-fold" lead to an observation on what would happen if you actually folded something ten times, and you mistakenly thought he was giving a serious definition of the word "tenfold."
#29
Old 01-19-2012, 07:14 AM
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Actually I was taught that tenfold (or twofold or hundredfold) meant doubled ten (or two or onehundred) times as well. Due to the large difference between multiplying something 10 times and doubling something ten times, I always took it to mean multiplied (whether used correctly or not) and just never used the phrase myself.
#30
Old 01-19-2012, 08:02 AM
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I think the fact that there is a term 'hundredfold' demonstrates that it can't reasonably mean 100 doubling operations. There can't be very many everyday contexts in which it's useful to talk about something increasing by a factor of 2100.
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