Listen, I have never said that 2 + 2 does not equal 5. All I want is for the team to show their workings and provide me with their computer code, intermediate results and original values of 2 so that I can check their maths.

Some people say that if the original values of 2 are not correct, the final answer may be even more than 5. I say that we need to investigate 2, because if the answer is more than 5 we really need to know that.

If I were a politician, I would listen to the scientists and take decisions based on 2 + 2 = 5

]]>1. Mauna Loa, what makes this site ‘an ideal’ for average CO2 indication? I seem to remember seeing [en passant] that it wasn’t such a good indicator.

2. Is it so that high CO2 levels exist in certain areas of high forestation?

Thanks

StuartG

I think that the conversation also included something along the following lines:

VS: 2+2=4

Bart: 2+2+4?

VS: Yes, 2+2=4

Bart: You cannot have a result that violates the 2d law of thermodynamics!!

Nature: We have agreed to publish your comment, but space restrictions dictate that it can only be 4 character in length. Please edit. ]]>

He’s not adding them.

]]>Trev: I say, GeoffS, wasn’t that “complex numbers”? “Compound”, “complex” – it’s all so confusing.

]]>It was a legitimate attempt to show how the addition of two fuzzy number twos creates a situation where the degree of belief in an answer of 5 can become almost as high as 4.

So here is the comment again expanded to show how different fuzzy number two definitions with increasing variances (or S.D.) increases the Degree of Belief in the “wrong” answer (3 or 5). The degree of belief in the “right” answer (4) of course, is always 100%.

This dichotomy in which uncertainty propagates (increases) by applying an arithmetic operator while at the same time, the likelihood of an “off-correct” answer increases, may have led Mann to misunderstand that his answer is less certain not more.

A failure to accept the inherent variances in measured inputs to a model may lead one to accept an increasing degree of belief as evidence of a better answer when in fact what has happened is the distribution of “possible” answers (any of which might be true) has actually widened.

1. Allow fuzzy(2) to range from 1.5 to 2.5 Equivalent to an S.D. of ~0.167

So fuzzy(2) + fuzzy(2) = 4 ranging from 3 to 5

In this case, fuzzy(2) + fuzzy(2) = 5 has a degree of belief of 0.0% and a S.D. of 0.33

2. Allow fuzzy(2) to range from 1.25 to 2.75 Equivalent to an S.D. of ~0.25

So fuzzy(2) + fuzzy(2) = 4 ranging from 2.5 to 5.5

In this case, fuzzy(2) + fuzzy(2) = 5 has a degree of belief of 33.3% and a S.D. of 0.50

3. Allow fuzzy(2) to range from 1.0 to 3.0 Equivalent to an S.D. of ~0.33

So fuzzy(2) + fuzzy(2) = 4 ranging from 2 to 6

In this case, fuzzy(2) + fuzzy(2) = 5 has a degree of belief of 50.0% and a S.D. of 0.67

4. Allow fuzzy(2) to range from 0.5 to 3.5 Equivalent to an S.D. of ~0.50

So fuzzy(2) + fuzzy(2) = 4 ranging from 1 to 7

In this case, fuzzy(2) + fuzzy(2) = 5 has a degree of belief of 66.7% and a S.D. of 1.00

5. Allow fuzzy(2) to range from 0.0 to 4.0 Equivalent to an S.D. of ~0.67

So fuzzy(2) + fuzzy(2) = 4 ranging from 0 to 8

In this case, fuzzy(2) + fuzzy(2) = 5 has a degree of belief of 75.0% and a S.D. of 1.33

6. Allow fuzzy(2) to range from -1.0 to 5.0 Equivalent to an S.D. of ~1.00

So fuzzy(2) + fuzzy(2) = 4 ranging from -2.0 to 10.0

In this case, fuzzy(2) + fuzzy(2) = 5 has a degree of belief of 82.5% and a S.D. of 2.0

7. Allow fuzzy(2) to range from -2.0 to 6.0 Equivalent to an S.D. of ~1.33

So fuzzy(2) + fuzzy(2) = 4 ranging from -4.0 to 12.0

In this case, fuzzy(2) + fuzzy(2) = 5 has a degree of belief of 88.9% and a S.D. of 2.67

8. Allow fuzzy(2) to range from -3.0 to 7.0 Equivalent to an S.D. of ~1.67

So fuzzy(2) + fuzzy(2) = 4 ranging from -6.0 to 14.0

In this case, fuzzy(2) + fuzzy(2) = 5 has a degree of belief of 90.0% and a S.D. of 3.33

9. Allow fuzzy(2) to range from -4.0 to 8.0 Equivalent to an S.D. of ~2.00

So fuzzy(2) + fuzzy(2) = 4 ranging from -8.0 to 16.0

In this case, fuzzy(2) + fuzzy(2) = 5 has a degree of belief of 91.6% and a S.D. of 4.00

In summary:

Input Output of 5

S.D. DoB S.D.

0.167 0.0 0.33

0.250 33.3 0.50

0.333 50.0 0.67

0.500 66.7 1.00

0.677 75.0 1.33

1.000 82.5 2.00

1.333 88.9 2.67

1.666 90.0 3.33

2.000 91.6 4.00