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The '''potato paradox''' is a mathematical calculation that results in an un-intuitive result. However it also is another name for the potato-effect, an economical paradox that was discovered in the potato-famine in Ireland in the 1840s. It describes how the law of demand in economical recessions favors cheap products which in turn become more expensive than higher quality products.<ref>Dwyer GP, Lindsay GM. Robert Giffen and the Irish potato. The American Economic Review Vol. 74, No. 1, Mar., 1984</ref>


==Description==


The paradox has been described as:<ref>http://weblog.sinteur.com/index.php/2010/08/12/the-potato-paradox/</ref>
Marie Antoinette, the ill-fated last queen of France, once declared that she wanted to be the most fashionable woman in the world.<br><br>The world is a much wider place in 2014  [http://www.pcs-systems.co.uk/Images/celinebag.aspx http://www.pcs-systems.co.uk/Images/celinebag.aspx] than it was in 1789, when cherie Marie was carted off to the Conciergerie and uncertain doom. But, with the latest round of spring/summer 2015 shows, Paris is asserting its reign across the world of la mode.<br><br>Nobody - and nowhere, it seems - does it better.<br>Why? Because Paris is [http://browse.Deviantart.com/?qh=&section=&global=1&q=bubbling bubbling] with ideas. Some we�ll want to wear - like much of Phoebe Philo�s spring C�line collection, with its ruffled and printed pastoralism and fringy-frayed craftiness. Others, we won�t, at least not so readily.<br>Rei Kawakubo�s formidable Comme des Garcons show, inspired by �blood and roses� and transforming her models into perambulating contemporary art installations drenched in single shades of riding-hood red, was aggressively, anarchically unwearable<br><br>
Front row at Paris Fashion Week spring/summer 201<br>
And who knows what will end up in shops from Jean Paul Gaultier�s show on Saturday night, his last ever ready-to-wear collection after 39 years in the game? It was a great show - staged as a beauty pageant, of mostly greatest hits. Both were bold statements<br><br>
The clothes didn�t really matter<br>
The clothes matter, enormously, at C�line. Last year the brand made record sales and while its owner Bernard Arnault�s LVMH conglomerate does not release information on their labels� individual returns, the performance was described by the group as �remarkabl<br><br>


''You have 100 [[Pound (mass)|pounds]] of Martian potatoes, which are 99 percent water by weight. You let them dehydrate until they’re 98 percent water. How much do they weigh now?''
That�s based on Phoebe Philo�s knack of nailing what women want to we<br><br>


[[The Universal Book of Mathematics]] states the problem as follows:<ref>http://www.daviddarling.info/encyclopedia/P/potato_paradox.html</ref>
It�s legendary: her latest successor at Chloe, Clare Waight Keller, is still somewhat in the shadows of Philo�s phenomenal success sto<br>.
The floaty georgette dresses, blouses and denim shorts were neat, but felt a little like left-overs from Philo�s glory years. Shoes oscillated between middling height and dead flat, which matched the mood of the show overa<br><br>


: ''Fred brings home 100 pounds of potatoes, which (being purely mathematical potatoes) consist of 99 percent water. He then leaves them outside overnight so that they consist of 98 percent water. What is their new weight? The surprising answer is 50 pounds.''
Philo is a tough act to follow - even when she�s following herself. That�s because she�s lead the march into uncharted territories - her spring/summer 2010 C�line debut, for instance, which ignited a Minimalist revival in fashi<br>.
Her spring offering was somewhat quieter, less bold and a little less fulfilli<br><br>


It is not really a paradox, but most people find the answer counter-intuitive.<ref>http://weblog.sinteur.com/index.php/2010/08/12/the-potato-paradox/</ref>
Oddly, Marie Antoinette was who I thought about when the C�line models trod out in dropped flounces splurged with florals, fluttering lappets of fabric and tattered he<br>.
Those have been seen just about everywhere: Celine took it a bit further, looping thread into a mammoth woolly fringe along the hems of skirts and slender to<br><br>


==Explanation==
They reminded me of la reine and her cohorts playing at milkmaids in her ferme orn�e. There were even a few cowbells clanging from bags, and string bel<br>.
It chimed with the folksy, Seventies feel that has been emerging across the season as a whole - swaying fraying and billowy florals underlined by flared trousers and tugged-waist jackets stiffly outlined with topstitchi<br><br>


One explanation begins by saying that initially the non-water weigh is 1 pound, which is 1% of 100 pounds. The one asks: 1 pound is 2% of how many pounds?  In order that that percentage be twice as big, the total weight must be half as big.
Philo placed her own slant on it, sure. But rather than defining, this was a refining collection, underlining stories other designers had already begun to te<br>.
 
From a queen of fashion, you hoped for more leadership.
An explanation via algebra is as follows.
 
The weight of water in the fresh potatoes is <math>0.99 \cdot 100</math>.
 
If <math>x</math> is the weight of water lost from the potatoes when they dehydrate then <math>0.98(100 - x)</math> is the weight of water in the dehdrated potatoes.  Therefore
 
 
: <math>0.99 \cdot 100 - 0.98(100 - x) = x</math>
 
 
Expanding brackets and simplifying
 
 
: <math>99 - (98 - 0.98x) = x</math>
 
: <math>99 - 98 + 0.98x = x</math>
 
: <math>1 + 0.98x = x</math>
 
 
Subtracting the smaller <math>x</math> term from each side
 
 
: <math>1 + 0.98x - 0.98x = x - 0.98x</math>
 
: <math>1 = 0.02x</math>
 
 
And solving
 
 
: <math>1 / 0.02 = 0.02x / 0.02</math>
 
 
Which gives the lost water as
 
 
: <math>50 = x</math>
 
 
And the dehydrated weight of the potatoes as
 
 
: <math>100 - x = 100 - 50 = 50 </math>
 
== See also ==
* [[List of paradoxes]]
 
==References==
{{reflist}}
 
==External links==
* {{MathWorld|id=PotatoParadox|title=Potato Paradox}}
 
{{math-stub}}
 
[[Category:Mathematics paradoxes]]

Latest revision as of 14:20, 25 November 2014


Marie Antoinette, the ill-fated last queen of France, once declared that she wanted to be the most fashionable woman in the world.

The world is a much wider place in 2014 http://www.pcs-systems.co.uk/Images/celinebag.aspx than it was in 1789, when cherie Marie was carted off to the Conciergerie and uncertain doom. But, with the latest round of spring/summer 2015 shows, Paris is asserting its reign across the world of la mode.

Nobody - and nowhere, it seems - does it better.
Why? Because Paris is bubbling with ideas. Some we�ll want to wear - like much of Phoebe Philo�s spring C�line collection, with its ruffled and printed pastoralism and fringy-frayed craftiness. Others, we won�t, at least not so readily.
Rei Kawakubo�s formidable Comme des Garcons show, inspired by �blood and roses� and transforming her models into perambulating contemporary art installations drenched in single shades of riding-hood red, was aggressively, anarchically unwearable

Front row at Paris Fashion Week spring/summer 201
And who knows what will end up in shops from Jean Paul Gaultier�s show on Saturday night, his last ever ready-to-wear collection after 39 years in the game? It was a great show - staged as a beauty pageant, of mostly greatest hits. Both were bold statements

The clothes didn�t really matter
The clothes matter, enormously, at C�line. Last year the brand made record sales and while its owner Bernard Arnault�s LVMH conglomerate does not release information on their labels� individual returns, the performance was described by the group as �remarkabl

That�s based on Phoebe Philo�s knack of nailing what women want to we

It�s legendary: her latest successor at Chloe, Clare Waight Keller, is still somewhat in the shadows of Philo�s phenomenal success sto
. The floaty georgette dresses, blouses and denim shorts were neat, but felt a little like left-overs from Philo�s glory years. Shoes oscillated between middling height and dead flat, which matched the mood of the show overa

Philo is a tough act to follow - even when she�s following herself. That�s because she�s lead the march into uncharted territories - her spring/summer 2010 C�line debut, for instance, which ignited a Minimalist revival in fashi
. Her spring offering was somewhat quieter, less bold and a little less fulfilli

Oddly, Marie Antoinette was who I thought about when the C�line models trod out in dropped flounces splurged with florals, fluttering lappets of fabric and tattered he
. Those have been seen just about everywhere: Celine took it a bit further, looping thread into a mammoth woolly fringe along the hems of skirts and slender to

They reminded me of la reine and her cohorts playing at milkmaids in her ferme orn�e. There were even a few cowbells clanging from bags, and string bel
. It chimed with the folksy, Seventies feel that has been emerging across the season as a whole - swaying fraying and billowy florals underlined by flared trousers and tugged-waist jackets stiffly outlined with topstitchi

Philo placed her own slant on it, sure. But rather than defining, this was a refining collection, underlining stories other designers had already begun to te
. From a queen of fashion, you hoped for more leadership.

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