When I took calculus in my
first college-degree program, the graduate-student instructor didn’t bother to
tell the class that a derivative signifies changes in the rate of acceleration.
A derivative is not the rate itself, but, rather, the change in the rate—something
much more difficult to detect empirically, as in watching an accelerating car. Formulae
were the instructor’s focus, as if they constitute ends in themselves. By the
time the climate numbers for 2025 came in, scientists could confidently say global
warming was accelerating. The rate itself may have been increasing (i.e., a
positive derivative), but attention to that by the media would have taken an
educational reform as to how calculus was being taught. We think in terms of speed
and acceleration. In this respect, we may be deficient in climate change itself
as it has been unfolding. More decades than I care to admit had passed by 2025
since I had that course in calculus; only now can I say that I have used the
math, albeit theoretically rather than via formulae.
Looking at the numbers for average
global temperature for 2023, 2024, and 2025, Robert Rohde, the chief scientist
at the Berkeley Earth Monitoring Group, said in early 2026, “The last three
years are indicative of an acceleration in the warming. They’re not consistent
with the linear trend that we’ve been observing for the 50 years before that.”[1]
A linear trend represents no acceleration, so the rate of acceleration only
became positive in 2023. Relative to the prior years, the averages for 2023,
2024, and 2025 “seemed to jump up,” said NOAA climate-monitoring chief Russ
Vose.[2]
The average for 2024 was 1.6C degrees above pre-industrial levels, hence slightly
above the internationally agreed-upon limit of 1.5C degrees, and the averages
for 2023 (1.48C above) and 2025 (1.47C above) were essentially tied so close to
1.5C that the average of the three years is above 1.5C. Even though the “leap”
from the previous years since at least 2015 instantiates an acceleration, more years
may be needed to assess whether the rate of the acceleration was increasing
(mathematics majors would know this). At the outset of 2026, the three preceding
years appeared as a plateau rather than evidence of continued acceleration, but
a plateau could exist within a trend even of a positive derivative. My point is
that we should have been more focused on changes in the rate of acceleration,
for if the rate itself was increasing, then it would not be long until the threshold
of 1.5C is surpassed and more extreme symptoms of climate change occur.
One of the weaknesses of
democracy is that such symptoms may have to be experienced and seen before electorates
treat climate-change as an important issue in voting. Human nature itself, a
product of natural selection, still prioritizes the immediate over the
long-term, especially in regard to threats. Instant gratification too is “hard-wired”
in us all, which is why we tend to vote to keep gas prices low rather than to
cut off the further manufacture of gasoline-powered cars. Whereas these contributory
drawbacks in our nature, inherited from the gradual process of natural
selection in evolution (mostly in the hunger-gatherer period of our species), have
been associated with the lack of sufficient political will in the world since
2016 at Paris to keep the average global temperature from surpassing 1.5C above
the pre-industrial level, our cognitive impairments that are also contributory
are less well-known. This is the idea.
In addition to difficulties in
conceptualizing and keeping attuned to what the derivative represents (i.e.,
change in the rate of acceleration, rather than the rate itself), our arrogance
of pride in what we think we know also holds us back from grasping the
magnitude of the human contribution to climate change. Just days before writing
this essay, a man aged 75 declared to me that climate change is “just
the natural cycles.” I don’t know whether that person had gone to college, but
I do know that he was not a scientist. So the man’s declaration itself
rang out as being out of place, given his actual level of knowledge on climate
science. Similar to how we tend to focus on acceleration rates rather than
changes in those rates, most people would be attuned to the content of the man’s
statement—that climate change is merely part of a long-term natural cycle that
will eventually reverse itself—rather than to the declaratory form of speech with
which he made the statement. It is too difficult for us to grasp changes in
rates of acceleration and focus on the presumption of entitlement that can
be detected in the way a person makes a statement, whether it is written or
verbal, and yet we tend not to realize that we have trouble with both. As one
consequence, we understate the severity of climate change.
Lest anyone needs a refresher,
“Rohde said nearly all of the warming is from human-caused emissions of
greenhouse gases. . . . Samantha Burgess, strategic climate head of the
Copernicus service, said the overwhelming culprit is clear: the burning of
coal, oil and natural gas.”[3]
Lest it be conveniently assumed that the burning has been going on somewhere in
nature away from humans, Burgess doesn’t mince words: “Climate change is
happening. It’s here. It’s impacting everyone all around the world and it’s
our fault.”[4] Climate
change is not just from a natural cycle that would be occurring even if there
were no homo sapiens species.
So, Joe the plumber, a person
let’s say who barely graduated from high school, would not only be incorrect in
declaring that climate change is just part of a natural cycle; he would
also be presumptuous in slighting the contradicting knowledge of climate
scientists, whose years of study are indeed superior to Joe’s opinion.
Like arrogance on stilts during a flood, Joe’s self-love issuing out in puffed
up “knowledge” may one day be underwater if he happens to live on a coast when
enough of the polar ice has melted to rise the level of oceans appreciably.
That Joe would likely react angrily to being corrected even though his declaration
of knowledge actually has no foundation is yet another indication of the
presumptuous that may be endemic to the human mind but seems to be more salient
in uneducated people. Formerly known in Western civilization as the sin of
pride, which Augustine and Paul set as the worse (and thus intractable) sin, treating
one’s own opinion as a fact of knowledge can be added to the list of the deficiencies
in our nature that may wind up causing the extinction of our species as the
Earth’s climate approaches a new equilibrium sooner rather than later. How
much sooner depends at least in part on whether the relevant derivative is positive.
2. Ibid.
3. Ibid.
4. Ibid. Italics added for emphasis.
