[suxs]

What you are describing is a steady growth which is not exponential as you called it in your first post. A big difference there.

No, you are mistaken.

I quote from studiousguy.com

Exponential growth is a pattern of data that shows a sharp increase over time. The graph of exponentially growing data is generally plotted on a logarithmic scale. There are a number of domains that make use of the concept of exponential growth for research and growth purposes such as biology, finance, mathematics, economics, business, management, etc.

The concept of exponential growth can be best understood by observing the growth of the human population. According to the recent survey conducted in the year 2019, the world’s population had reached 7,673,533,974, and it is growing exponentially at a fast rate.

Following is a similar definition per Stanford University:

Human population growth is one of the most famous examples of exponential growth because of its archetypical curve. We often refer to the graph of human population growth as a “J-curve” because of the letter that so closely resembles its shape. The gradual increase in slope suddenly gives way to a sharp increase that looks nearly vertical at first glance, and a J-curve is born. Human population growth provides a textbook definition due to its J-curve graph shape representing classical exponential growth, or a growth pattern where the growth of a population proportionately increases the rate of expansion as well. As a population grows larger, it will start to grow more quickly as well.

[suxs]

Many thanks:

The Club of Rome prognostications gets updated.
https://medium.com/the-bad-influence/we ... 71887ae009

[vtsnowedin]

What you are describing is a steady growth which is not exponential as you called it in your first post. A big difference there.

No, you are mistaken.

No I am not mistaken. While human population was growing exponentially post WW2 it has now changed. The quotes you post are either dated or from people not paying attention.

[Tanada]

https://www.worldometers.info/world-population/

[vtsnowedin]

https://www.worldometers.info/world-population/

Try this one. The blue line is not an exponential J curve.
https://www.macrotrends.net/countries/W ... rowth-rate

[Pops]

I'm no math guy but exponential growth is just a description of growth that is a function of the size of the group - the bigger the group, the bigger the growth at a given rate. As long as it is a positive growth "rate" acting on the whole group it is exponential by definition.

20% growth per period on a population of 100 is 120 at the end of the first period, but 144 at the end of the second period— absolute growth of 24 vs 20 because the group is bigger in the second period. Just like compound interest. Even a rate of .1% acting on the total is exponential, because it is constantly increasing the total it is acting on.

Good news is nothing says the rate will stay the same, and, if the rate goes negative (like payments on a mortgage), exponential decay can reduce the population —just like payments eventually reduce the principle faster and faster.

But births are only half the story. We're way better than we were but even if the birth rate were cut in half from here —or death rates doubled— we'd still be growing exponentially. According to this deaths are 7.5% per 1,000 and births are 17.5/m so still growing at 10% per 1,000 or 1%/yr total.

The population in general is getting older so the death rate for the population overall will naturally rise, so there is that
.

[vtsnowedin]

I'm no math guy but exponential growth is just a description of growth that is a function of the size of the group - the bigger the group, the bigger the growth at a given rate. As long as it is a positive growth "rate" acting on the whole group it is exponential by definition.
.

I am a bit of a math guy or was in my younger years and I have been a bit picky here. A truly exponential growth curve has a constant rate of growth or doubling time. All I am saying is that our rate of growth is declining so is no longer exponential. Yes the total is increasing and will for decades unless something drastic and unexpected happens but it is over dramatic and inaccurate to call it exponential.

[theluckycountry]

https://www.worldometers.info/world-population/

Try this one. The blue line is not an exponential J curve.
https://www.macrotrends.net/countries/W ... rowth-rate

And the infection point is right around 2007~8, the peak of conventional oil production.

[theluckycountry]

I am a bit of a math guy or was in my younger years and I have been a bit picky here... All I am saying is that our rate of growth is declining so is no longer exponential.

I'd suggest it's still exponential, just in decline
https://image2.slideserve.com/5320910/slide3-l.jpg

[AdamB]

I am a bit of a math guy or was in my younger years and I have been a bit picky here... All I am saying is that our rate of growth is declining so is no longer exponential.

I'd suggest it's still exponential, just in decline
https://image2.slideserve.com/5320910/slide3-l.jpg

I'd suggest you don't know what an exponential is any more than you can properly use your 2 wheeled hardware. VT described it correctly in words as your graph describes the equations, and just because something is in decline doesn't mean it is an exponential decline. Now run along, don't you have some banana's to be bending?

[Pops]

All I am saying is that our rate of growth is declining so is no longer exponential

OK, the rate of growth is declining. Why not just stop there?

The time to double the population at 1% is a mere 70 years, that's just one lifetime. It surprises me that even here where we've been talking about compounding for coming on 2 decades the ramifications are still not clear. It is the nature of the system that makes it act exponentially at whatever rate not the rate itself.

My point is there is no arbitrary cutoff that makes proportional growth or decline no longer proportional. Whatever the rate is at any particular time, it's always acting on the whole. The whole is growing today at about 1% rate, that means next year there will be 101% as many people, and whatever the rate at that time, it will act on the new total. That's what makes it exponential, not the rate, not some unspecified big-sounding number, not the hockey stick, but the compounding.

Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself.

https://en.wikipedia.org/wiki/Exponential_growth

In mathematics, a quantity that grows exponentially is one that grows at a rate proportional to its size. This does not mean merely that for any exponentially growing quantity, the larger the quantity gets, the faster it grows. It implies that the relationship between the size of the dependent variable and its rate of growth is governed by a strict law, of the simplest kind: direct proportion.
...The phrase exponential growth is often used in nontechnical contexts to mean merely surprisingly fast growth. In a strictly mathematical sense, though, exponential growth has a precise meaning which does not necessarily mean that growth will happen quickly. In fact, a population can grow exponentially but at a very slow absolute rate (as when money in a bank account earns a very low interest rate, for instance),

https://academickids.com/encyclopedia/i ... ial_growth

In a linear function, the rate of change is constant. In an exponential function the rate of change is proportional

https://www.austincc.edu/agladish/Preca ... rowth.html

But importantly, as lucky said, exponentials also work in the negative.

The implication is since any population change rate other than zero is exponential, as soon as the rate consistently falls below zero, decline will be exponential as well. Although as I mentioned earlier, birth rate must halve or death rate double before that can happen. (17.5 & 7.5 per thousand respectively I think it was)

Unless our chart turns into a logistics curve bumping against carrying capacity like most other living things seem to do. Personally I think that ship has sailed because we've been so good at exploiting nature. So exponential decay, likely far below our original carrying capacity it is.

.

[jedrider]

My wife has a thing about pain that she fears that the most.

I think she would prefer an impulse or step function.

Exponentials are just wannabe impulse functions!

[theluckycountry]

Nature has the habit of coming into the equation from time to time too, plagues, tsunamis, I imagine a Campi Flegrei eruption would have a good effect on population. But the most common one is famine. The way we are handling agriculture I'd put my money on that. I wonder how much of Putin's push into the Ukraine has to do with it being the bread basket of Europe.

https://www.osw.waw.pl/en/publikacje/os ... sket-world
https://www.academia.edu/36021664/Starv ... t_Genocide

[Pops]

I wonder how much of Putin's push into the Ukraine has to do with it being the bread basket of Europe.

Russia May Have Passed Peak Oil Output – Government
Russia’s oil production is unlikely to recover to pre-coronavirus levels, according to a government strategy document cited by Kommersant.
April 12, 2021

Russian oil production might never recover to pre-coronavirus levels, the country’s Energy Ministry has forecast, according to the Kommersant business paper.

In a strategy document outlining prospects for Russia’s critical oil and gas industry, the government said its “base case” — or most likely — scenario, is that Russia’s oil production will never again hit the record levels recorded in 2019.

In the last full year before the pandemic, Russia produced 560 million tons of oil — equivalent to 11.3 million barrels a day. But output dropped for the first time in more than a decade in 2020 as Russia agreed significant production cuts with Saudi Arabia and other members of the OPEC cartel in a bid to support oil prices at the start of the pandemic — pushing production down 9% to 10.3 million barrels per day.

https://www.themoscowtimes.com/2021/04/ ... ent-a73558

Not that I trust the Moscow Times any more than Fox but gotta put it out there

[vtsnowedin]

Not that I trust the Moscow Times any more than Fox but gotta put it out there

Fair enough. I do try to read anything from any source with a grain (or ten) of salt applied.

[theluckycountry]

Sort of on topic, found this on our local ABC site. Now as a preface, this is as mainstream a news outlet as you can get and was rabidly Anti-Trump, as was all Australian media. They haven't had much to say about your current president, because there isn't much to be said is there, but certainly nothing negative or negative about the USA. Now today, this.


With the war in Ukraine, US resolve is crucial — and yet we can see the sunset on the American century
https://www.abc.net.au/news/2022-02-27/ ... /100859774

In 1991, the United States stood unchallenged. The Cold War was over. The Berlin Wall had come down two years before and now the red flag of the Soviet Union had been lowered for the last time in Moscow. Francis Fukuyama, the American political scientist, hubristically pronounced this moment "the end of history". This would be a triumph of liberal democracy and usher in a new era of democracy worldwide...

The US talks a tough game; it rallies allies, hits back with sanctions, moves its troops around the world — but it won't fight. President Joe Biden said as much. He will not put American lives on the line to defend the sovereignty of democratic Ukraine. That's an invitation to Vladimir Putin. Xi Jinping would be wondering if the US will spill blood for Taiwan. The last they saw of the US military it was retreating from Afghanistan, and after 20 years the Taliban was claiming victory.

The question now is, what happened to America? How did the world go from the unipolar moment to the end of the American order?
-------------------------------------------------------------------------------------------------------------------------------

It's almost like they want to undermine the nation's faith in the US as an ally?

[vtsnowedin]

The question now is, what happened to America? How did the world go from the unipolar moment to the end of the American order?
-------------------------------------------------------------------------------------------------------------------------------

Don't you worry, if push comes to shove the Ukrainian resistance to the Russians will look like amateur hour compared to Red state America believing "gun control" means a steady aim and a slow squeeze on the trigger.
Sorry about the Blue coastal states they are going to take it even harder then they already are.

[AdamB]

Sort of on topic, found this on our local ABC site. Now as a preface, this is as mainstream a news outlet as you can get and was rabidly Anti-Trump, as was all Australian media.

With the war in Ukraine, US resolve is crucial — and yet we can see the sunset on the American century
https://www.abc.net.au/news/2022-02-27/ ... /100859774

Wow. Sounds pretty bad. Until you compare it to folks who consider it an accomplishment to bend bananas I suppose. The 20th was certainly the American century. 20% of the 21st has been written to date, and I've got my money on the world's biggest economy, the world's largest oil and gas producer, the world's largest LNG exporter, world's largest agricultural exporter, I mean really, but we do hang our heads over how silly our political leadership is sometimes.

So who cares what residents and the press from mining colonies think. Now run along and bend some bananas like a good drone and we promise that we'll sell you those submarines you don't have the brains to do for yourselves, and after maybe a decade of training some of the smarter banana benders or aborigines might be able to clear harbor without beaching the things!

[Pops]

The question now is, what happened to America? How did the world go from the unipolar moment to the end of the American order?
-------------------------------------------------------------------------------------------------------------------------------

It's almost like they want to undermine the nation's faith in the US as an ally?

So a little on topic. America was founded as an extractive colony, a business venture with a side of religious cult. It's what we still are even though the extraction is getting thin. Our government was founded with the express intent of: A, keeping the slave economy viable and B, keeping the mob at bay. Jefferson said democracy is mob rule where 51% take away the rights of the minority. The founders were in favor of minority rule — not the 49%, the 1%. Rockefeller himself couldn't have dreamed up a more efficient extractive economy.

The one saving grace is we were from the start an ownership society, because land was so plentiful it had little value, it was used as a lure and payment. I have ancestors who came here (early on) as indentured servants who were paid in property at the end of their contract. In contrast to the conquests in S. America where a few conquistadores were sent to enslave the natives, we killed the natives and enslaved or at least indentured the colonists.

So fast forward to the world wars, the US had a large business class who were able to see the profit in wartime manufacturing and a naive population still willing to sacrifice on principle. Actually wwii was more of a expanded works administration program to be honest. Regardless, we threw every bit of our then massive resource and manufacturing base at making money, oh, I mean bailing out the allies.

That was a nice feather in our cap, (even though it took the British until 2000-something to pay their portion of the tab). The Marshall plan was great PR too. It not coincidentally bought the demise of trade barriers and opened the way for that same US business class to move in right behind the tanks and invent the American Supranational Corporation. Salute!

The US started as a a religious cult fronted slave based extractive colony and wound up an undemocratic corporate empire still convinced of their grace under god to do whatever the hell we like.

What's not to love?
.

[AdamB]

The US started as a a religious cult fronted slave based extractive colony and wound up an undemocratic corporate empire still convinced of their grace under god to do whatever the hell we like.
What's not to love?
.

Good thing our model isn't much different than many others, although until the industrial age came along it was far more about extracting labor from the peons in favor of a single ruler, the hierarchy pyramid was quite pointy at the top. But if our religious convictions and slightly different extraction model looks like it worked better than just about anyone else's, it could be because the top of our pyramid is flattened, spreading the advantage of our system to a wider population. But at the end of the day. if you are part of a species of scumbags, 'tis better to have the best business model for your particular tribe of scumbags.