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

The idea that humanity is facing a "senescence" phase is also ridiculous.

The population growth rate has been falling sharply since 1968. The reasons for this are not "decline in resources". The reasons are that women are choosing to have fewer children. This is because...

1) Poverty has been decreasing across the globe. This leads to smaller family sizes as there are more options given to potential parents.

2) Family planning education and resources are now available to the world.

3) Sharply declining child mortality and increasing education opportunities for women globally have lead to cultural changes in expected family sizes.

I can say that the basic expasions in "exponential anything" involve an xponent .
When I asked you before about graphing ither log, smi log, or cartsian, you said that we can plot anything in any form. Thats where you get it confused. We dont use log plots until E NEED EM. When you must plot expansions where the y axis presents itself in terms of billion from starting as unit numbers allows us to plot so the y axis can ven fit on a graph.
Where youre getting it wrong is mere definition an im not gonna bother playing magister if you ven refuse to think it out.

As to what we call these units, doesnt mn that they all must occur. Left to a fixed base of resources, the growth and senescence curves will occur

Such curves are seen in biology all the time, the flattening out and senescence phases relates to the "carrying capacity" of an environment and "critical mass" of the population so that growth , or at last sustainable populations can be maintained.
You dont think humans shot every last passenger pigeon do you? All we did was to assist the extant population to dip below a critical breeding mass. Nature took care of the rest. Most all life displays these rates until something external arrives to clip it.

Your phenomenal trust in our abilities fails to recognize the roles that war, starvation an disease play.
I agree that e are probably no longr in an xponential growth rate but not sinc the industrial revolution. You also seem to ignore critical time periods and the planets population as a whole.



Ill not waste any more time, youre simply incorrct an youve got your mind stubbornly set on confusing arithmetic v exponential. If we plot xponential growth (or reaction time), on a semi log scale, it forms a srait line (That IS what the population expansion of humanity has been).

I wont b casting insults, that seems to be your forte. I wish your daughters math skills well.

Farmerman is being ridiculous.

1) Exponential growth is defined by population growth with a constant growth rate.

2) Human population growth does not have a constant growth rate. The growth rate has varied wildly over the past several hundred years.

Farmerman can't even clearly state which of these two things he disagrees with. It is simple... if there is no constant growth rate, than the population is not exponential. This really is middle school mathematics.

Why is it necessary to preface a response with these prejudicial setup lines? I think any of the three or four people reading this discussion can determine the seriousness of posts for themselves by reading and assessing the arguments on their own. There's no need to make it personal.

It is frustrating when someone who purports to have a scientific background makes absurdly incorrect statements about basic mathematics, and then doubles down with mumbo jumbo when corrected.

I don't think either you or Farmerman can complain about "making things personal". I am sincere when I say that having to argue about middle-school mathematics is absurd.

There are any number of middle-school level videos on this topic. Yes, I find the need to do this frustrating.

Hightor, I do want to point out that I am not arguing with your posts on this thread. They are mathematically correct (you have purported to find a linear function in the past 30 years, and I think the data is close to linear for this time range).

You are stating that it the population growth is "too high". This is an opinion, and in some respects I agree with you. Things would certainly be better if the population growth were slower right now.

On the other hand, the population growth continues to fall (which is good) and most experts predict that the population will stop growing in the foreseeable future and level off at about 10.5 billion. Maybe that is still "too high", that I won't argue.

Fine.


I've complained about your tendency to engage in personal criticism before. It sets a combative tone right from the start, and simply provokes a hostile response.

Sure, you're having a discussion/argument with someone and sometimes online debates can be exasperating, for any number of reasons. But why start off a reply with an insulting comment about another member instead of just saying, "In this case I believe you have mistaken function x for variable y"? People normally don't appreciate being told that they're being "silly", "absurd", or "ridiculous" when they are engaged in a discussion and have put some effort into trying to address an issue of mutual interest. Leave it for other readers to determine the quality of a reply or the reasonableness of a response. A more objective, less personally-insulting, answer would promote better discussions. You like to don the mantle of science-hood, but petty insults have no place in a science-based rejoinder.

1. There are reasonable arguments that I think are wrong. Then there are ridiculous arguments. I want to make that distinction clear.

2. There are people here (friends of your I think) who say "Max is a White Supremacist". That is a personal attack. I don't take it personally when someone tells me that one of my arguments is ridiculous. As a matter of fact, that seems like a rather reasonable statement, I may disagree... but I can get along just fine with someone who criticizes my arguments.

The people who call me a fascist are crossing a line, even with me. When this happens, I restate my points clearly (which seems to really piss them off).

I really dont know where youve drawn that from but exponentil growth is graphed log log as a strait line
YOU ARE CLEARLY TALKING"A GEOMETRIC" GROWTH RATE> , xponential is where the increase rate increases. (Thats how its defined in biology, geophysics, and applied nuclear sciences(like isotope dating, and critical mass energy)

Im not wrong about this, youve missed the mid level of measuring. OF course theres a constancy of multipliers but " log growth " has an EXPONENT that increases.

Im not arguing this, Im letting you know where youre incorrect. Ive never "claimed" a scientific background, Im trained and experienced as one.

Farmerman,

First, you are making this definition up. Here is one of millions of sources that say that exponential growth is a constant growth rate. http://www2.gcc.edu/dept/math/faculty/BancroftED/buscalc/chapter1/section1-7.php#:~:text=An%20exponential%20growth%20or%20decay%20function%20is%20a,f%20%28x%29%20%3D%20a%20%281%20%2B%20r%29%20x

Second, even by your own made up definition, your claim is we have had an "increasing growth rate" until 1980 is simply wrong. We had declines in the 1950's, and have been on a downward trend in growth since 1968.

If you are going to make up your own definitions... you should at least try to have your made up definitions match the claims you are trying to support.

I spent some time trying to find conclusive data if human growth was exponential for any significant part of human history. I think the answer is no.

First of all, humans have always faced events that reduced population. The Black Death wiped out 25 million people, surely this is reduction. Humans have always faced things that negatively impacted population growth; widescale famine, wars, diseases, migratory pressures have all been a part of history. Not only that, but societies have always constantly changed... and family sizes have varied widely as societal norms change.

For exponential growth to occur you need to have a consistently large birth rate and a steady mortality rate. I am not sure that this has ever happened. Over most of human history growth rates were small (birth rates were high and mortality was high). But even then the fluctuated to higher and lower and sometimes net population declined.

I did find mathematical papers that suggest that in the best of times (when there is a high birth rate, abundant resources, and no war or disease) population growth is quadratic rather than exponential. I found this surprising, I like when learn something new.

The idea is that in times of abundance and peace, a human population is bounded by geography. Humans live on what to them is a 2 dimensional surface, and area is a quadratic function. Historically humans have self regulated to limit themselves to a population density (this was changed with urbanization).

There are plenty of articles on this behind paywalls, this explanation is free.

https://medium.com/@FreisinnigeZtg/is-quadratic-growth-a-general-phenomenon-fab7d799a1e1

yawn, Dont quad expansion defined bcause they are only set to a limit function?? we dont us quad (f) bwcause in nature, limits are only en in rtrospct and Mathematically, quad functions are SET limits

That makes no sense.

I suppose a populational limit could be defined wrt to "Carrying capacity", otherwise it always goes through the four stages I mentioned previously.

I think your entire arguments are more semantic than fact based, so I will leave you for a planned weekend at the shore during "Shoulder season"

Try not to explode

Why does it matter? If it's just to settle an argument, fine, but why is it important if it's linear, geometric, exponential, or quadratic?

I think we're making too big an issue over the rate of population growth, trying to find a formula or mathematical constant which will describe it accurately when in reality growth is subject to all sorts of external factors, like plagues, war, and rising living standards.

I believe the real lesson is simply that growth is potentially self-limiting if it outstrips the resources needed to sustain that rate of growth.



Or, as Aristotle noted in 350 BCE, "...in the generality of states, if every person be left free to have as many children as he pleases, the necessary consequences must be poverty..."

Hightor,

Outside of the political discussion... the mathematics is interesting to me on their own. I suppose my post functions both as a political point and as ruminations of a math nerd.

Our conversation over several threads is about politics versus mathematics. My point is that facts are facts and that political ideology shouldn't change your understanding of the facts.

A fact is something that is testable. If you claim something is a fact, you should tell me what evidence would prove your claim wrong. Any factual claim that I make comes with this assumption (and you can ask me).

1. It is a fact that population growth has not been exponential since 1700. The data is readily available and this is simple to prove mathematically (in fact your analysis did just that).

2. I didn't find enough data to determine if population growth was exponential before 1700. I strongly suspect that it wasn't (and things like the Black Death make it pretty unlikely). However I won't state that this is a fact; let's call it a strong suspicion.

3. The questions about what the population should be, or the measures we should take to reduce the population are opinions. I would be happy to have this discussion.

Hightor,

I hope you accept that birth rates have been falling pretty steadily in the past 300 years, and that now they are at historical lows.

How low should we expect is a matter of opinion I guess. The UN has experts predict global population in the future. I just checked the latest report; the "middle growth" prediction shows fairly low linear growth in the next couple of centuries. The "low growth" prediction shows stabilization.

I believe strongly that we should be investing a lot of money into the development of Sub-Saharan Africa and other developing regions. This will increase education and prosperity and is the best way to reduce population growth. Unfortunately development does mean more carbon emissions, but real life comes with trade-offs.