[barmar]

 TimG, on 2013-April-11, 06:31, said:

Let's compare "two times fewer" with "four times fewer". It seems to me that the difference between these two statements is "two times", that is "four times fewer" is "twice as many" as "two times fewer". But, look at this in an absolute sense: suppose we start with 100 and compare "two time fewer", which is 50 fewer; and "four times fewer" which is 75 fewer. 75 is not twice as many as 50.

But why would you look at it in an absolute sense? "N times fewer" means "1/Nth as many". So 4 times fewer is half as much as 2 times fewer, and 25 is half of 50.

Language is not always consistent. N times fewer is not interpreted the same way as N% fewer.

Why don't people say "1/370th as many"? Fractions seem more confusing. Logically there's no difference, but the brain isn't logical. It works by association, and fractions are associated with harder problems than integers.

[billw55]

Agree with Ken that realtors are some of the most deliberately deceitful businesspeople out there, right up with car salesmen and carnival barkers.

[Vampyr]

 barmar, on 2013-April-11, 06:48, said:

But why would you look at it in an absolute sense? "N times fewer" means "1/Nth as many". So 4 times fewer is half as much as 2 times fewer, and 25 is half of 50.

Language is not always consistent. N times fewer is not interpreted the same way as N% fewer.

Native English speakers had until recently not adopted this usage, but they have picked it up from non-native speakers. It's a shame, because x times fewer, x times cheaper etc is very inelegant.

[Trinidad]

 billw55, on 2013-April-11, 07:17, said:

Agree with Ken that realtors are some of the most deliberately deceitful businesspeople out there, right up with car salesmen and carnival barkers.

Maybe so, but sometimes they are outright silly.

The house that we bought several years ago (and currently live in happily) was described by the agent as "conveniently located near important outgoing highways".

Keep in mind that I am living in The Netherlands, one of the more densely populated countries on this planet, when I am telling you that the only road that is somewhat near goes to the next village of less than 3000 people. There, you can take a ferry and when you drive an additional 20 km (or about 1/7th of the width of the entire country) you get to one of the main freeways.

Alternatively, you can drive through town, all the way to the opposite side (takes about 10-20 minutes) and get on the freeway. Our house is about as far from "important outgoing highways" as possible.

And I think you will figure that out when you come to see the house before you buy it.

Rik

[gwnn]

Poor old Sir Isaac Newton, misled by some foreigners!

http://www.volokh.co...253897118.shtml

BTW is 'three times smaller' also confusing? Or 'three times cheaper'?

[barmar]

I wonder if there's an XKCD about this. It seems like the kind of thing he'd pick up on. I tried searching for "times less" but didn't see anything likely.

[GreenMan]

"times fewer" is an idiomatic expression that has taken root and is widely recognized, so whatever "logic" you can bring to bear against it will just bounce off like a tennis ball off a brick wall.

It's certainly more elegant than "one-three-hundred-seventieth as much".

[barmar]

 GreenMan, on 2013-April-11, 08:43, said:

It's certainly more elegant than "one-three-hundred-seventieth as much".

My theory is that most people find fractions with a denominator more than the typical number of slices in a pizza difficult to handle. Maybe because when we learn fractions in grade school, pies and pizzas are the common means of demonstrating them.

I think fear of fractions is also the reason percentages were invented. They allow common fractions to be spoken of in terms of whole numbers. While 9% may mean "nine one-hundredths", we don't actually hear the denominator so it doesn't triger the association with fractions.

[TimG]

 gwnn, on 2013-April-11, 08:27, said:

BTW is 'three times smaller' also confusing? Or 'three times cheaper'?

I find those annoying as well.

I would prefer "three times as big" to "three times bigger". The former, I think, is clearly 300%; the latter could be intended as 300% or 400%.

[GreenMan]

Percentages were invented (perhaps as far back as Ancient Rome, per Wikipedia) because they're easier to work with than fractions, especially for businesses, which have an economic interest in efficiency. They became standard in textbooks starting in the Middle Ages.

[Vampyr]

 gwnn, on 2013-April-11, 08:27, said:

Poor old Sir Isaac Newton, misled by some foreigners!

Well, I was not talking about mathematicians, and was also describing a course of events that I have seen in my lifetime -- which does not overlap Newton's!

[gwnn]

 Vampyr, on 2013-April-11, 10:46, said:

Well, I was not talking about mathematicians, and was also describing a course of events that I have seen in my lifetime -- which does not overlap Newton's!

I thought you were describing something that had never occurred until recently and I found some native English-speakers who have done it and not just recently.

A quick Google books search has revealed results from each decade in the past five, as well as each century since Newton. So it has been around for at least five hundred years, most likely without interruption. Of course you can say that by 'adopt' you just meant that a certain number of people use it, fair enough (I cannot prove you right or wrong on that), but do we have to blame it on the non-native speakers?

[kenberg]

 billw55, on 2013-April-11, 07:17, said:

Agree with Ken that realtors are some of the most deliberately deceitful businesspeople out there, right up with car salesmen and carnival barkers.

The house we bought a few years back advertised passive solar heating. As near as I can tell, this means that it has windows.

[barmar]

 GreenMan, on 2013-April-11, 10:39, said:

Percentages were invented (perhaps as far back as Ancient Rome, per Wikipedia) because they're easier to work with than fractions, especially for businesses, which have an economic interest in efficiency. They became standard in textbooks starting in the Middle Ages.

It doesn't say that Rome used percentages, it says that it was common to use fractions whose denominators were 100. It's not clear how they make business more efficient -- when you do the calculations, you have to convert into decimals or fractions. They just change the way some numbers are presented in text -- you say "12% annual interest" instead of "interest is 0.012 x principle".

My related pet peeve: real estate tax rates in Massachusetts are specified per $1,000. Why not per 100, so they can just use percentages? I wonder if some anti-tax lobby had them do this, since it makes the taxes look larger if they have to say $13.61 instead of 1.361%.

[gwnn]

I hate different brackets for the same function, i.e. {5+6*[5-4/(5+2)]} or something. [] should be reserved for the arguments of functionals (ok and another bunch of stuff of course) and {} should be reserved for sets (and another bunch of stuff of course). Using them like this is just confusing. You can draw bigger round brackets if you like. And yes I know that it's kind of standard and probably Isaac Newton also used them that way.

[kenberg]

 gwnn, on 2013-April-13, 03:36, said:

I hate different brackets for the same function, i.e. {5+6*[5-4/(5+2)]} or something. [] should be reserved for the arguments of functionals (ok and another bunch of stuff of course) and {} should be reserved for sets (and another bunch of stuff of course). Using them like this is just confusing. You can draw bigger round brackets if you like. And yes I know that it's kind of standard and probably Isaac Newton also used them that way.

When I took algebra in 1952 we were given a priority list: w[v+x(y+z)] was right, w(v+x[y+z]) was wrong. After [ ] came { }. I associate this with Movietone newsreels at the theater and Patti Page singing How Much Is That Doggie in the Window.

[gwnn]

That's also what I learned in the 90's but then my Computer Science teacher made me realise how strange a convention it is

[GreenMan]

 barmar, on 2013-April-12, 11:14, said:

It doesn't say that Rome used percentages, it says that it was common to use fractions whose denominators were 100. It's not clear how they make business more efficient -- when you do the calculations, you have to convert into decimals or fractions. They just change the way some numbers are presented in text -- you say "12% annual interest" instead of "interest is 0.012 x principle".

If you were using fractions, as you were suggesting earlier, the last would be "interest is 3/25 of principal" which requires more calculations (one each for the numerator and denominator) than starting with decimal numbers. And if the interest rate had more significant figures you could end up with fractions with 5 or more digits in either field. I don't think "fear of fractions" explains any reluctance to work with them on that scale.

[kenberg]

 barmar, on 2013-April-12, 11:14, said:

My related pet peeve: real estate tax rates in Massachusetts are specified per $1,000. Why not per 100, so they can just use percentages? I wonder if some anti-tax lobby had them do this, since it makes the taxes look larger if they have to say $13.61 instead of 1.361%.

Just as a guess, I would say that it is because prices are often phrased in terms of thousands. If the tax is $13.61 per thousand and the property is valued at three hundred thousand dollars, presumably just about everyone understands that the tax is calculated by multiplying $13.61 by three hundred. For some reason there are a lot of people who have a mental collapse when percentages are mentioned, even some who in other respects appear to be quite capable. If you tell them the tax is 1.361% of the valuation they will have to call someone in for a translation.

I don't understand why this happens, but I have seen it and I bet you have seen it. I think I mentioned a while back that at the Y I was in an exercise and weight loss program, and we got weekly reports of our weight loss as a percentage of our initial weight. A man was given the task of calculating these numbers, I would bet because it was thought to be too difficult for women. I don't know if it was too difficult for the women but it definitely was too difficult for him.

[Mbodell]

 gwnn, on 2013-April-13, 03:36, said:

I hate different brackets for the same function, i.e. {5+6*[5-4/(5+2)]} or something. [] should be reserved for the arguments of functionals (ok and another bunch of stuff of course) and {} should be reserved for sets (and another bunch of stuff of course). Using them like this is just confusing. You can draw bigger round brackets if you like. And yes I know that it's kind of standard and probably Isaac Newton also used them that way.

Wow, I've literally never heard of that before in any math notation. Having coded a bit in lisp I'm completely fine with lots of nested ().