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What Exponential Means: And no... human population growth is not exponential

 
 
Reply Mon 27 Sep, 2021 04:46 am
Middle School Math.

The definition of exponential growth means "having constant growth rate".

1. This mean that for exponential growth, if the population grows 2% in 1900, then it will grow 2% in 1901, and 1902 and 1903 and 2020, and 2021. You can check to see if population growth is exponential by simply looking at the growth rate each year over time. If it isn't constant, then it isn't exponential.

2. Another way to express this is the time that it takes for a population to double. With exponential growth the time for a population to double will take the same time for any same length period over the cycle.

Consider a population doubles between 1800 and 1900. If this is exponential, than it will double for any 100 year period. It will double between 1900-2000. It will also be twice the number in 1903 than it was in 1903 and twice in 1931 then it was in 1831.

So we have two tests to see if a population is growing exponentially, and if either fails, then the growth rate is not exponential.

Hint: When we look at the data, we will find that the population growth for humans on earth isn't anywhere close to exponential. But let's agree on the definition first.
 
farmerman
 
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Reply Mon 27 Sep, 2021 05:14 am
@maxdancona,
ok, can the world pop growth hve been presented in a log/log or semi log graphs??
hightor
 
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Reply Mon 27 Sep, 2021 05:33 am
Middle School Vocabulary.

Quote:
Exponential – adjective

1. of or relating to an exponent or exponents.

2. Mathematics.
a. of or relating to the constant e.
b. (of an equation) having one or more unknown variables in one or more exponents.

3. rising or expanding at a steady, rapid rate:
a city experiencing exponential growth.
farmerman
 
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Reply Mon 27 Sep, 2021 05:33 am
@farmerman,
PS, I think you are confusing GEOMTRIC expansions v EXPONENTIAL expansions. Human pop growth, since the Late Pleistocene has been exponential not geometric.
Of this Im positive bcause we do sedimnt n prtil size analyses and the distribution curvs look sorta th same but xponentials distribute by an actual exponent whereas geometric increase by a constant.

thats out of a microbio statistics book (Prescott Harly and Klein , 2005)

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maxdancona
 
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Reply Mon 27 Sep, 2021 05:49 am
@farmerman,
farmerman wrote:

ok, can the world pop growth hve been presented in a log/log or semi log graphs??


Huh? Any data can be presented on log semi-log graphs. This has nothing to do with the topic.

Do you accept the definition of "exponential growth" or not?
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maxdancona
 
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Reply Mon 27 Sep, 2021 05:51 am
@hightor,
Ok Hightor

So if global population isnt increasing at a 'steady rate" than you will agree it isnt exponential, right?
hightor
 
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Reply Mon 27 Sep, 2021 06:01 am
@maxdancona,
Quote:

So if global population isnt increasing at a 'steady rate" than you will agree it isnt exponential, right?

What I think is immaterial. People will continue to use the word in its non-technical sense and people will differ on their definition of terms like "steady rate".
maxdancona
 
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Reply Mon 27 Sep, 2021 06:18 am
@hightor,
I am OK with your use of the word "exponential" in a "non-technical sense". I simply asking for you to offer your definition of the word, so then we can use it in consistent way.

Your hair grows constantly, each day it is a little longer than it was the day before. Would you say your hair is growing "exponentially"?

If you are going to use the word, I am only asking that you provide a consistent definition. If you can't distinguish between "exponential" growth, and any other kind of growth, than the word has no meaning.
maxdancona
 
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Reply Mon 27 Sep, 2021 07:39 am
https://ourworldindata.org/uploads/2019/06/2019-Revision-%E2%80%93-World-Population-Growth-1700-2100.png

https://ourworldindata.org/world-population-growth

This is the actual data. If population growth were exponential, the purple line (growth rate) would be horizontal (i.e. a constant value). As you can see, this is far from exponential.

The growth rate peaked around 1968, this is where the human population was growing the fastest. Since 1968, the rate at which the population growing has almost halved.
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hightor
 
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Reply Mon 27 Sep, 2021 07:49 am
@maxdancona,
https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2Fourworldindata.org%2Fuploads%2F2018%2F11%2FAnnual-World-Population-since-10-thousand-BCE-for-OWID.png&f=1&nofb=1

Malthus noted that human population grew geometrically while food production increased arithmetically. He was writing during a time when steady population growth was emerging as a phenomenon. It should be noted that the graph doesn't differentiate between growth in different continents – Malthus was describing population growth in Europe which, looking at the graph, may actually have been increasing geometrically at the time.

He also may have been describing potential population growth. Let's assume that a European woman in Malthus's time had a reproductive window of twenty years. Maybe she had ten children and maybe a half dozen of them survived to reproductive age. If all the surviving children had families of their own with similar survival rates it's easy to see how population could increase at a rapid rate. In contrast, increased agricultural production could only be accomplished incrementally. New fields and pastures would have to be developed, technology might improve, new methods could be adopted — but none of those would happen at a rate matching the rate of population growth in the example.

Quote:
If you are going to use the word, I am only asking that you provide a consistent definition.

I'm not using the word, other than to discuss its application.

Quote:
If you can't distinguish between "exponential" growth, and any other kind of growth, than the word has no meaning.

A normal person would have little difficulty distinguishing its meaning by the context in which it is used. "Wow! The growth of manufactured housing in this trailer park has been exponential!"
engineer
 
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Reply Mon 27 Sep, 2021 07:53 am
@hightor,
I think exponential is correct from the mathematical sense. If the rate of change of something is a function of itself, you are going to get an exponential function when you solve for it. It the case of population growth, there are a lot of other factors in the equation as well, but there shouldn't be any argument that the rate of change of the population is a function of how many people there are. IMO what changes in this particular equation over time is the exponent. The rate of growth is also a function of time and possibly a function of population as well so you get something like:

P = Po e^(k(t)f(P)t)

Where k(t) is a function of time and could account for the advance of technology or society and f(P) is a function to account for the impact of population change (such as food or water scarcity as the population grows). If you were tracking the deer population, it would grow well until it started to use up all its resources which is where f(P) could go negative resulting in more deaths than growth. The k(t) factor would account for things like pandemics. We actually saw this in Alabama in 2020 where there were more deaths than births for the first time in over 100 years of record keeping. Also, the k(t) and f(P) functions are different in different human populations, so you are really looking at the sum of many exponentials. Still, the number of births is a function of the population so the overall form has to be exponential.
maxdancona
 
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Reply Mon 27 Sep, 2021 07:56 am
@hightor,
1. Your graph is just my graph squished. Even from your graph you can see that the growth is not exponential. You can either see how the vertical distance between the dots is smaller each time (meaning the growth rate is decreasing), or you can look at how much time it took to double.

2. Malthus was clearly wrong. We have significantly more people since Malthus was alive, and we have significantly fewer people starving now than there were in 1800.
maxdancona
 
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Reply Mon 27 Sep, 2021 08:02 am
@engineer,
Engineer's post is mathematically nonsense... Any set of continuous data can fit P = P0 e^(k(t)f(P)t).

Engineer's function is meaningless because he allows for the growth rate to change as a function of time. This means that to Engineer, any function is an exponential function. In this case the term "exponential" is meaningless.

The actual definition of the word "exponential" is a function with a constant growth rate. This means that the growth rate doesn't change each year.

That is clearly not the case.
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maxdancona
 
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Reply Mon 27 Sep, 2021 08:10 am
This thread is a perfect demonstration of how an ideological narrative can twist even basic mathematical facts.

There are two facts here.

1) Exponential growth is defined as a population with a constant growth rate.
2) The human population on the planet does not have a constant growth rate (not even close).

I don't see anyone disagreeing with either of these two points. And yet, the ideological narrative still can't let them accept that the global population is not growing exponentially.

There is a basic inability to accept simple logic that is caused by the need to fit an ideological narrative. Even engineer and Farmerman (who I would think should no better) are rejecting basic mathematics based on their politics.
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hightor
 
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Reply Mon 27 Sep, 2021 08:16 am
@maxdancona,

Quote:
Even from your graph you can see that the growth is not exponential.


Even from your graph we can see that populations has increased from 2 billion to 7.7 billion in less than one hundred years. Most people would consider that to be "steady, rapid growth".



Quote:
Malthus was clearly wrong.


I don't think so. The potential for that sort of rapid growth still exists; the fact that increased survival rates led to the option of smaller families in the developed world is the result of changed conditions. There are still places where large families are the tradition and where overpopulation and hunger are problems.
maxdancona
 
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Reply Mon 27 Sep, 2021 08:19 am
@hightor,
I think your problem is with the word "steady".

If the population increased from 2 billion to 7.7 billion in some time period. The word "steady" implies that the population increased at the same rate in the previous time period too.

That didn't happen.
maxdancona
 
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Reply Mon 27 Sep, 2021 08:23 am
Here are the facts.

1) The global population growth rate increased significantly between 1850 and 1968 (where it peaked at a rate of 2.2%).

2) Since 1968, the global population growth rate had decreased significantly and it is not at a rate of 1.05%.

Does anyone disagree with the facts?

I suppose that we can argue about whether a rate that rises and falls significantly meets the definition of "constant".
hightor
 
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Reply Mon 27 Sep, 2021 08:28 am
@maxdancona,
Quote:
The word "steady" implies that the population increased at the same rate in the previous time period too.

No, I think your problem is that you're tied to the technical definition. In everyday conversation one could simply bracket a particular time period and describe the growth during that period as being "steady". Saying "the world population increased steadily over the past century" isn't the same as saying, "the world population has grown at a steady rate over the past 12,000 years."
hightor
 
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Reply Mon 27 Sep, 2021 08:34 am
@maxdancona,
Quote:
Does anyone disagree with the facts?

Only with their interpretation. The "rate" of growth has declined but when we're talking about 8 billion people, the sheer numbers are more important than the rate. People who are worried about overpopulation aren't concerned with the decrease in the rate of growth – they are looking for a net decrease in population.
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maxdancona
 
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Reply Mon 27 Sep, 2021 08:34 am
@hightor,
Nonsense Hightor.

The number has varied drastically, from about 0.5% in 1800 wising 2.2% in 1968 and then falling to 1.05% in 2019.

By what definition is this "steady"? Just give me a definition for the word "steady" and we will go with it.

 

 
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