sunsettommy
01-23-2006, 09:27 AM
From John Brignells NUMBERS WATCH,
Linearity
Snip:
What are the consequences of incorrectly assuming linearity?
A good example of a serious error arising from a mistaken assumption of linearity is the so-called “Hockey stick (http://news.bbc.co.uk/1/hi/sci/tech/3569604.stm)” curve. This was adopted by the UN IPCC, resulting in potentially devastating economic consequences. The mathematical method employed by the authors was “principal component analysis (http://www.cis.hut.fi/~jhollmen/dippa/node30.html)”, which is a form of linear algebra applied to statistical data.
One of the main sources of data for this exercise was plant growth (tree rings).
It is easy to demonstrate that plant growth is a non-linear process. Plants require for growth nutriment, light, warmth and moisture. Consider just the last two of these. In the middle range of variables, increases in warmth and moisture both increase growth rates. However, at the extremes, this is not true. If it is very cold, then more moisture will impede growth, while if it is very dry, more heat will also reduce it. Thus plant growth is not only non-linear, it is not even monotonic, which implies a gross non-linearity and excludes the use of linear algebra.
The results of this analysis were used by the IPCC for the basis of a claim that phenomena such as the Little Ice Age and the Mediaeval Warm period never actually happened, despite the copious evidence to the contrary from history, art, archaeology, entomology etc. The error was compounded by arrogant dismissal of criticisms, attempts to prevent their publication and refusal to make public the computer programmes involved, but that is another story (http://www.climateaudit.org/index.php?). It is curious that a prolonged and intricate argument has followed, when all that needs to be said is that the method used was not valid.
(Red and black bolding,my emphasis)
15/01/06
http://www.numberwatch.co.uk/linearity.htm
The first part of the link covers what is linear and also gave two examples of what is additive and homogenus.
I wonder what Bob Arctor will say about this?
Linearity
Snip:
What are the consequences of incorrectly assuming linearity?
A good example of a serious error arising from a mistaken assumption of linearity is the so-called “Hockey stick (http://news.bbc.co.uk/1/hi/sci/tech/3569604.stm)” curve. This was adopted by the UN IPCC, resulting in potentially devastating economic consequences. The mathematical method employed by the authors was “principal component analysis (http://www.cis.hut.fi/~jhollmen/dippa/node30.html)”, which is a form of linear algebra applied to statistical data.
One of the main sources of data for this exercise was plant growth (tree rings).
It is easy to demonstrate that plant growth is a non-linear process. Plants require for growth nutriment, light, warmth and moisture. Consider just the last two of these. In the middle range of variables, increases in warmth and moisture both increase growth rates. However, at the extremes, this is not true. If it is very cold, then more moisture will impede growth, while if it is very dry, more heat will also reduce it. Thus plant growth is not only non-linear, it is not even monotonic, which implies a gross non-linearity and excludes the use of linear algebra.
The results of this analysis were used by the IPCC for the basis of a claim that phenomena such as the Little Ice Age and the Mediaeval Warm period never actually happened, despite the copious evidence to the contrary from history, art, archaeology, entomology etc. The error was compounded by arrogant dismissal of criticisms, attempts to prevent their publication and refusal to make public the computer programmes involved, but that is another story (http://www.climateaudit.org/index.php?). It is curious that a prolonged and intricate argument has followed, when all that needs to be said is that the method used was not valid.
(Red and black bolding,my emphasis)
15/01/06
http://www.numberwatch.co.uk/linearity.htm
The first part of the link covers what is linear and also gave two examples of what is additive and homogenus.
I wonder what Bob Arctor will say about this?