Thanks madamswer, pretty much as I expected. Sorry, I should...

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LJsilver

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07/01/20

19:06

Post #: 42270181
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Originally posted by madamswer ↑

"I haven’t followed the whole thread, but your comment on the reduction of the rate of increase caught my eye.
If this is the case, then the function of co2 v time will have negative concavity, thus there are two possibilities."

Ah, at last.

Some application of differential calculus on HotCopper ...it is not often the resident geeks on HotCopper get to debate the change in the sign of the second derivative of the function describing carbon emissions in India (!)

"Either it will be heading for a point of inflection or it’s heading for a maximum."

As you may well know, the mathematical description of such sorts of physical phenomena is given by the function:

Y = a(X)^3 + b(X)^2 + cX +k

in this particular case, where:

Y is the level of emissions
X is time and
a < 0
b, c > 0
k = 0

The graph-of-best-fit when it comes to Indian emissions data shows that the country has already moved out of the "concave-up" (i.e.. positive concavity) range of the function (the point of inflection - represented by the blue hatched circle in the schematic below - was passed sometime around 2014/15), and is somewhere in the "concave-down" (i.e., negative concavity) range - as you rightly surmised.

View attachment 1921618

So, to answer your question: based on the physical nature of the data series in question, along with observed precedent, the function is fortunately not heading towards another point of inflection (to be followed by acceleration), but along a path of continued deceleration towards a maximum.

So the good news is that, while the second derivative has turned negative for India, the first derivative is still very much a positive value, and is certainly likely to remain that way for at least the next decade-and-a-half, probably the next two decades and possibly longer.

.

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Thanks madamswer, pretty much as I expected.

Sorry, I should have clarified my statement on the POI. My curiosity was if there was going to be a Horizontal Point of Inflection, at the place in your graph that shows a maximum. (Take f(x)=x^3 at x=o, for example).

That would change the shape of the graph completely, although I suspect it’s not likely the case.
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