## August 17, 2007

After 14,000 years if the population has roughly doubled every generation, the answer would be 3.77396242 × to the 171st power, a number that I have no clue what it means. How I got to this number is that I divided 14,000 by 25 and got 560, which is the amount of times the population would double. Then I raised 2 to the 560th power and multiplied it by 1000 to get my answer.

The implications that this would have on the view of history is that the Americas were self-sufficient to an extent where life could be reproduced and maintained at a high rate. That America was disease free till 1492 and that the birth rates for healthy babies were extremely high.
For a fact we know that the number I got is ridiculously too high and that conditions were not as optimal for survival and reproduction as the numbers suggest.

The description of an unstressed population that roughly doubles every 25 years represents exponential growth (as opposed to logistical growth). Dragana has the right idea about population growth, but just to correct her number I think it is 3.77 x 10^171, which is even bigger than she suggests because you are raising TEN rather than 3.77 to a really big power, and as if that weren’t enough you then multiply the 10^171 by 3.77.

I couldn’t even comprehend this number, so to get an idea about its size, I went to Wikipedia http://en.wikipedia.org/wiki/Orders_of_magnitude_%28numbers%29 . It says there that the number of ways to arrange a 52 card deck is 52! = 8x10^67 = 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000. This number is incredibly huge, and it is only ten to the 67th power, not to the 171st! Thus, 3.77 x 10^171 is impossibly huge because, with exponential growth, the population just keeps increasing without bound. The exponential growth model does not take into account carrying capacity (maximum number of people the environment can support). Therefore, population size calculated by this model would eventually become unrealistic, but that is how we are told to treat this problem (“unstressed…with reasonable access to food”).

To show mathematically how to reach the population size, we can use the basic equation for exponential growth:

P(t) = (P“initial”)(e^(rt)), where

P“initial” represents the initial number of humans to cross the land bridge
e is the number 2.71
r represents the rate of population growth
t represents the elapsed time in years, with the land bridge representing year 0 (t=0) and today as 14000 (t=14000)
P(t) represents the population size at time t.

If we use an initial population of 1000, we know that in 25 years (t=25), the population will be 2000 (P(25)=2000). Plugging in the numbers, we can first solve for r, the rate of population growth:

2000 = 1000e^(25r)
2 = e^(25r)
ln 2 = ln [e^(25r)]
ln 2 = (25r)ln e
ln 2 = (25r)
r = (ln 2)/25 =.0277

Using this r in the equation, P(t) = 1000(e^(.0277t)), we can get
P(14000) = 1000(e^(.0277x14000)) = 3.77 x 10^171.

I think this implies that, had the Amerindians remained isolated from the Old World, they eventually would have reached a very high population density that would have meant increased rates of communication and therefore innovation. Amerindian societies had already developed superior agricultural methods, and had larger, more hygienic cities. They were working on overcoming many of the obstacles that had put them at a disadvantage compared to the Old World (many varieties of maize to deal with north/south axis; terraces to eliminate need for domesticated pack animals; having to figure out everything on their own without communicating and collaborating). I think that eventually their rate of development would have increased after overcoming these obstacles, while Europe might have stagnated without the New World. The Amerindians therefore could have eventually developed technologies that were better than those in Europe. Perhaps Amerindians, instead of Eurasians, could even have been dominant in the modern world.

The description of an unstressed population that roughly doubles every 25 years represents exponential growth (as opposed to logistical growth). Dragana has the right idea about population growth, but just to correct her number I think it is 3.77 x 10^171, which is even bigger than she suggests because you are raising TEN rather than 3.77 to a really big power, and as if that weren’t enough you then multiply the 10^171 by 3.77.

I couldn’t even comprehend this number, so to get an idea about its size, I went to Wikipedia http://en.wikipedia.org/wiki/Orders_of_magnitude_%28numbers%29 . It says there that the number of ways to arrange a 52 card deck is 52! = 8x10^67 = 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000. This number is incredibly huge, and it is only ten to the 67th power, not to the 171st! Thus, 3.77 x 10^171 is impossibly huge because, with exponential growth, the population just keeps increasing without bound. The exponential growth model does not take into account carrying capacity (maximum number of people the environment can support). Therefore, population size calculated by this model would eventually become unrealistic, but that is how we are told to treat this problem (“unstressed…with reasonable access to food”).

To show mathematically how to reach the population size, we can use the basic equation for exponential growth:

P(t) = (P“initial”)(e^(rt)), where

P“initial” represents the initial number of humans to cross the land bridge
e is the number 2.71
r represents the rate of population growth
t represents the elapsed time in years, with the land bridge representing year 0 (t=0) and today as 14000 (t=14000)
P(t) represents the population size at time t.

If we use an initial population of 1000, we know that in 25 years (t=25), the population will be 2000 (P(25)=2000). Plugging in the numbers, we can first solve for r, the rate of population growth:

2000 = 1000e^(25r)
2 = e^(25r)
ln 2 = ln [e^(25r)]
ln 2 = (25r)ln e
ln 2 = (25r)
r = (ln 2)/25 =.0277

Using this r in the equation, P(t) = 1000(e^(.0277t)), we can get
P(14000) = 1000(e^(.0277x14000)) = 3.77 x 10^171.

I think this implies that, had the Amerindians remained isolated from the Old World, they eventually would have reached a very high population density that would have meant increased rates of communication and therefore innovation. Amerindian societies had already developed superior agricultural methods, and had larger, more hygienic cities. They were working on overcoming many of the obstacles that had put them at a disadvantage compared to the Old World (many varieties of maize to deal with north/south axis; terraces to eliminate need for domesticated pack animals; having to figure out everything on their own without communicating and collaborating). I think that eventually their rate of development would have increased after overcoming these obstacles, while Europe might have stagnated without the New World. The Amerindians therefore could have eventually developed technologies that were better than those in Europe. Perhaps Amerindians, instead of Eurasians, could even have been dominant in the modern world.

I do not see anything wrong with Lauren's calculation of the Amerindian population figure to be 3.77 x 10^171, assuming optimal living conditions. The implication of this gargantuan number is that the Armerindians could have had a very large population on the Americas for thousands of years and could have had the opportunity to innovate and influence Eurasia. There were many materials and goods explorers brought back to Europe from America so Europe was influenced from outside, but disease killed many of the native American people so they were not capable of getting technology from Europe. Europeans reaped the benefits of Amerindians' innovation, but Amerindians were not able to do the same to the extent that Europe did.

According to the article, the population of the Amerindians had doubled every generation. This could have led to an amazing development if their population had remained undisturbed due to the Europeans. The Amerindians had different technology than that of Europe and may have been able to innovate something different than what has led up to the technology today. We may never know. However, with that huge of a population (3.77396242*10^171), I also believe that this could have led to their demise as well. If they were able to communicate and reach the Europeans, they would have contracted the diseases from the Europeans regardless of their population size and this could have killed many of them as well. Thus, we cannot say that the Amerindians would have been successful if it weren't for the disturbance from Europe. The Amerindians might have found a way to reach the Europeans first and lead themselves to their own demise. All we can do is wonder at the alternatives of what might and could have happened.

I also see no fault with the conclusion that the population, if doubling every 25 years, would reach a total population of 3.774*10^171. The magnitude of this number is astounding, however it is unlikely that the Ameroindian population was unstressed, since any population moving into newly discovered territory encounter hardships while trying to acclimate to new climates, topography etc. This calculation once again brings into question the Eurocentric view of North America before 1492 that is perpetuated in some classrooms today. If the population of North America was indeed that large, there are two consequences. First it proves that mere population is not the key to technological development, as new technologies have to be applicable in outlying areas from where they were developed which was simply not possible in Pre-Columbian North America. Also, this large of a population would be even more susceptible to the plagues from Europe as biological pathogens spread much more rapidly in areas of high population density.

I tried to plug in the numbers into my scientific calculator which resulted in an overflow error, so assuming that the Amerindian population really lived unstressed for 14000 years, and that Dragana’s first calculation is correct, I am also assuming that the Amerindian population would reach 3.774*10^171. Many people point out the very reasonable and true point that populations realistically tend to face some amount of disturbances such as disease, starvation or natural disasters. This was my first thought based on historical knowledge as well as the fact that the hypothetical population does not even fit into my calculator. However, another point that crossed my mind is the comparison between the Amerindian populations today that have survived after the arrival of Europeans to the New World in comparison to the hypothetical population that we have created. It is poignant to think about the past hardships of the Amerindian population as well as the current sparse population today, however to compare the current population to the hypothetical population and relate them to the readings last week, the numbers are truly appalling.

I used a simple calculation without the necessity of using e or natural logs (following Dragana's method from the 1st post):
given that the population doubles every 25 years (for simplicity let's just call it a generation) and that there were 14000 years since, so that means that within the 14000 years, there were 560 generations.
so, 1000x2^560 = 3.77396*10^171, or put crudely, it's approximately 377 plus 169 0's after it, which is an extremely large number.
So just for fun, the area of North America is approx. 24490000 sq. km., and the area of South America is 17840000 sq. km., with the total area being approx. 42330000 sq. km., which is equivalent to 4.233*10^17 sq. cm. Now assuming that the incipient Amerindian population remained unstressed and allowed to grow at a constant rate, then the current American continents would be so overcrowded that there will be around 8.91557*10^153 people in every single square centimeter!!!
Of course, it would be impossible for the population to grow at a constant rate of 100% every 25 years, given the natural and physical limitations of the environment and their own social structures. At a certain point, the resources would be depleted, land would run out, food sources will be insufficient to support to population, and overcrowding would lead to migration elsewhere. And of course, as history has demonstrated, the introduction of a foreign population (or the conquest by a foreign population) has greatly reduced the native Amerindian population as well, with the introduction of germs and annihilation in warfare due to the European's far superior technology.
However, the notion that the Amerindian population was able to double their population every 25 years prior to 1492 indicates that they have relative no natural enemies. They were able to live in peace in isolation from the rest of the world and were able to sustain their lifestyles by utilizing all that nature has to offer. There was low birth mortality rate and life expectancy in general was quite high. There were likely no constant grand-scale warfares as those in Europe, but does not suggest that there were none at all. In short, they were sheltered by the geographical barriers of the 2 oceans from foreign influence, and were thus able to live long and unstressed lives.

I approached this question in the way that Lauren did, but my calculator registered an overflow when I tried to solve for 1000e^(.027X14,000). I will use Lauren’s answer of 3.77x10^171 people as my answer because her strategy is identical to mine, and I would like to thank her for posting her solution.

The magnitude of this number is enormous, and roughly 5x10^161 greater than the current world population. Thus, speculation about the human history of the Americas between ca. 12000 BC and 1492 certainly must address the factors that limited population growth.

First, there are inherent limits to population growth that result from things such as supply of natural resources and predators. Upon arrival, the fist settlers did not even know how to cultivate and utilize the land most efficiently so this alone would restrict population growth. Given its vastness and geographical diversity, the continent was settled as many distinct groups in distinct regions, rather than one giant land. As the original population was divided and different areas of the continent explored, several groups must have suffered loss of human life, and some may have been completely eradicated. Also, limited resources in these geographical areas must have restricted population. Finally, it is possible that undocumented epidemics that the early Americans we not immune to constrained the population.

I approached this problem with an HP12C financial calculator, thinking of it as a future value if today's value is 1000. Using a present value of 1000, an annual interest rate of 72/25 (using the rule of 72 - not 70 like the text book suggests) and number of years of 13492 with no payment; my calculator thought about it and then decided the future number was too big for its display. Then, thinking about it logically, I decided that the doubling of the population every 25 years seemed not to make sense, especially when you get past a few million without access to iron tools and (modern) agriculture. The number however, is big enough to think that there were many more people here than the older text books imply, and the American continent was more populated by civilizations that were able to feed, house, govern, trade and tax than orginally thought.

I agree with Lauren's calculation of [3.77396242*10^171] as the number of American Indians there would be today (assuming the unstressed & constant growth of the population). Although this would never have happened in reality, even if they were to be left alone, just the idea that their population size could have grown so large is interesting and reminiscent of the Indian numbers debate in Mann's article, "1491." America was not an unoccupied, vast space of land; there were cities and complex civilizations inhabiting its space and the way history happened to wipe out such large numbers through foreign disease is a deeply sad matter. We can't know for sure what would have happened if they had survived or what happened in the past before foreigners set foot on their land. It's just not as simple as historians once believed it to be.

I used the same method that Dragana used and came up with the same answer that Lauren had. 14,000yrs/25yrs= 560; (2^560) x (1000) = (3.7739 x 10^168) x (1000) = 3.7739x 10^171. This number is way too high to be supported by the earth’s limited resources and illustrates that fact that exponential population growth will be slowed by numerous factors including diseases, limited resources, or other natural disasters. Since the population was nowhere near this in 1492, from 12000 B.C. to 1492 Amerindians could have been facing similar problems with diseases, shaping nature, disasters, and possibly war that Eurasians dealt with for 14,000 years as well.

I thought it would be interesting to compare the current population of ‘American Indians’ and the theoretical amount. Currently, U.S. records indicate that there are approximately 2.5 million, or 2.5 x 10^6. If my math is correct, this means that there is one current living ‘American Indian’ for approximately every 1.5 x 10^165 ‘theoretical American Indians’ at Columbus’ time, and that doesn't account for the additional theorectial growth in the past 500 years since Columbus arrived.

I also got 3.77*10^171 using the same methodology as the previous posters. This figure is obviously unrealistic, given limited food and resource supplies and a number of other health and environmental factors. I even think it would have been difficult for the original population of 1000 people to double in 25 years, given the short life expectancy rates, high infant mortality rates, and high rates of death during childbirth that must have prevailed back then. The implied growth given in the prompt would meant there would have been 2.88*10^165 (I assumed 13492 years, rather than 14000 years, to get this) natives in the Americas by the time Columbus sailed over in 1492, all before European diseases were introduced!

Nonetheless, the implications of this exercise are that Native Americans could have existed in significantly larger populations throughout the Americas than history texts cite, and that they lived may have lived healthier and more peaceful lives than the Europeans.

I did the same thing Lauren and Delara did and I came up with the answer 3.77*10^171 too.

Now, I think this is very interesting. So, if everything had worked out correctly, there would be a whole lot more people on Earth right now. However, currently today, there's only about 6 billion people. That is only 6*10^9, which is way less that 3.77*10^171. So what factors could have affected the number so dramatically?

First, naturally, there are limits to the human population. According to Thomas Malthus, diseases and other issues start occurring when the population gets to large. Sure, there are lots of controversy over his arguments, but in some ways it does make sense because nature must have some ways of controlling itself. Malthus believes that we need to avoid overpopulation now or else we will reach a point that we will dramatically use up our resources at an exponential rate that we will reach human extinction. Now, I also do believe his claims could be overexaggerated, but there could also be some truths to his argument.

Now lets relate this back to what factors we should take into consideration from 12000 BC and 1492. During this time, humans were definitely affected by diseases. Diseases and viruses come and go as some die off and some become more resilient. So for instance, when the Europeans came to America, the natives were greatly affected by smallpox and other diseases. This certainly lowered the population by quite a bit.

Other factors to consider are wars. Hundred of thousands of people die during wars. This is important because this can also significantly lower the number of people on Earth. Moreover, technology wasn't at its best in the old ages. People did not know how to utilize their resources; hence, there may not be enough food for everyone. We almost take it for granted these days that we can just buy food at the supermarket. People did not get to do this in the early days. If they can find food during their hunt, they will starve.

Also, in the 12000BC, land was still connected in some ways, instead of now. This means that people got to collaborate more and work together. However, as the land started to separate more, the geographies of the continents change and so did the resources. This can cause lots of humans to die, for some may not get use to the changes in nature; hence, survival of the fittest.

Now, the most important key to all this is that all the factors above and more all limit population growth. This snowballs down to another factor. With less humans surviving than the "expected number," the population growth doesn't grow as exponentially high as it would have had. Hence, we have a significant less number than 3.77*10^171

As shown before, assuming population doubles every 25 years and leaving out continuous growth to make things easier for myself, the result would be 1000*2^(14000/25), which is an incomprehensibly large number. Of course, because of population limitations such as weather, food, water, habitable land, war, and disease, the carrying capacity of the Americas is heavily reduced. Because the human population between 12000 BC and 1492 AD was not nearly as large as this figure, one can deduce the forces of economics had manifested themselves prior to the invasion of the Europeans. If nature were a supplier of living necessities and mankind were a demander, the respective curves of each respective party would dictate where the population was at the time.

If a population doubles every 25 years, then the population of 1000 Native Americans that migrated to North America 14,000 years ago would have doubled in population a total of 14,000/25 times which is equal to 560 times. Using the Malthusian growth model, or the simple exponential growth model to estimate the hypothetically resulting population today, we would calculate 1000*(2^560). This turns out to be a very big number that is drastically different from the Native American population today. According to Mann in his article "1491," the population of people inhabiting the Americas actually exceeded that of Europe. Mann's estimate of 90-112 million Native Americans rapidly died out with the spread of small pox, typhus,and influenza brought over from Europe by its explorers. The pigs that De Soto and his men brought caused a catastrophe even more deadlier than the Black Plague as the pigs spread their microbes to the wildlife of the Americas, contaminating the environment. Although many possess the notion that the Amerindians were uncivilized and barbaric prior to the arrival of the Europeans, Mann hypothesizes that they were actually in the process of transforming Cahokia into Terra Preta, turning sterile soils fertile and rich with microorganisms, making the land more hospitable to the thriving of their populations. Perhaps the Amerindian way of life before the arrival of European explorers was very advanced, contrary to prior misconceptions.

The calculation required to determine the number Indians that would be here today can be done by dividing 14000 by 25, which yields 560. This implies that the population doubled 560 times in the duration of time. The total population of Indians can be found by multiplying 1000 by 2 to the 560th power. This number is incredibly large. I think it is unrealistic because this number is based on several unreasonable assumptions. The population is assumed to be unstressed with constant access to food. This is highly unlikely since the more people there are, the competition among humans for food will be greater. Also there are times of famine and epidemics, which will cause the death rates to fluctuate. A couple implications can be made from this result. First, I agree with the fact that larger denser population will spread disease faster; which could explain the accelerated death rates of Amerindians upon the arrival of Europeans. Another implication is that, if the population is able to reach that size (bigger than Europe), then the Americas can be viewed as a land with abundant resources that many countries will try to claim as their own. The result reflects what actually happened when the European powers came to the Americas.

Implications: None. The figure is obviously unrealistic. The population was stuck in a Malthusian trap up until the point at which the Europeans landed. In other words, the Americas were in fact not sparsely populated, but populated as dense as technology at that time would allow. 14,000 years minus (1492-present) is still 13,500 years. I doubt the Native Americans would ever have achieved the "critical mass" of people to reach the point at which they would have escaped the Malthusian trap. This is a society that hadn't invented the wheel and I really don't like how Native Americans have become so romanticized in higher learning, especially California higher learning. The number is really pointless and meant to make people feel collectively guilty for something no one alive today should bear responsibility for.

If a population can double its size in 25 years, in 14000 years, the population should have doubled 560 times. I agree with the work written above (thanks to those who already wrote it out!) that says the original population of 1000 people should have grown to 1000* 2^560 people today if it remained unstressed. Because this number seems too large for the Amerindian population that existed between 12000 BC and 1492, it provides proof that the population was stressed (famine, disease, war, etc) if in fact it could double itself in 25 years.

After speaking to my roommates about this question, I figured two ways to do the problem that both gave the same answer. The first way was similar to all the answers above 3.77*10^171. The second method used was to use Excel and put 1000 in cell A1. In A2, I put the following "=2*A1". I copied and pasted this formula all the way into cell A561 and got 3.8*10^171. This number is so big, I don't even know how to say it.

Basically, this tells us that humans in America did not even come close to duplicating this growth patterns. This kind of reproduction seems to be impossible to achieve. This doubling of every 25 years, ignores the limitations that that environment, land, war, disease, and food production places on reproduction.

The answer as confirmed in previous posts is 1000*2^(14000/25). This would be a very large population, which we know due to limited resources would be impossible. We know that the assumption that the Ameridian population would have remained unstressed could never be true, however; this question does open eyes to the fact that Ameridian population was probably larger than was once believed. If this is true then many more Ameridians were killed by foreign disease, settler advancement, etc. than was once thought, which makes this part of history that much more depressing.

I agree with the previous posts that if the incipient Amerindian population had remained unstressed, the population today would be extremely large. However, the number computed based on pure math may be far too large. Population growth is restricted by various factors such as resources and the natural environment. But we can conclude from the calculation that the population will grow exponentially over the course of history without the historical culture genocide of the Amerindians. If this population becomes unstressed, history would unfold differently with them dominating this “new world” and eventually communicating with the old world through trade and their culture would spread across the globe. Larger population could imply more brainpower, thus innovations would come about. The largely computed number also brings us to awareness that European colonization of the Amerindian does not prove them to be superior and more intelligent. However, this whole assumption of unstressed population is much too ideal.

hmmm....
14,000/25=560
(2^560)(1000)=3.774*10^171 American Indians!

Obviously, factors kept the population from growing, such as disease, war, and perhaps overpopulation, along with other factors that the Indians experienced since moving to a new continent. At the time 12000 BC and 1492 AD, such a population in the Americas would be nearly impossible to survive. The fact that the actual number of American Indians that were around at that time was significantly less than the possible count, along with huge decrease in population due to invasion, enslavement, and lack of remedies to fight off European diseases makes me feel sorry for the American Indians and their suffering.

As Lauren Tombari shown us her very detailed calculations in her comment, I feel I must agree that there would be 3.77 x 10^171 American Indians today if the incipient Amerindian population had remained unstressed.

The implications of this to history as we know it? This huge population can only be possible if we lived in a perfect world where nothing occurs by chance. It is highly unlikely that any group of people have ever lived unstressed unless you count Adam and Eve and their life in the Garden of Eden. Things rarely go exactly as planned, and everyone faces hardships. The humans who first made it to America could hardly live an unstressed life. They arrive in a new land were they are forced to adapt to survive. They had to adjust to the weather, find food, choose a location, set up institutions, etc. Then there are the conquests that will occur whether the American Indians have a large population size or not. Would the conquerors win? That may be something we'll never discover as there are pros and cons for both sides. However, the arrival of Europeans will still bring diseases, destroying much of the population. Still this huge population will definitely make discovering technologies easier and lead to a greater technological advancement with the American Indians. But as people make advancement, all these ugly emotions of greed, jealousy, and hatred will appear and eventually causing wars and leading to the population demise.

So the overall impact of this finding to history is all speculation. But it is fun to think about.

In order to calculate the American Indian population in the past 14000 years, assuming the population was not effected by European settlers, we divide 14,000 by 25 which gives us the number of periods for which the population will double. Then calculate 2^560 and multiply by 1000 to give the approximation 3.77 x 10^171. Bottom line, this number exceeds any estimates before the 1960s which was believed to be between 10 - 15 mm prior to European settlement in 1942. The implications of this number insight questions attempting to discover the technology and social development of the American Indians before the arrival of European settlers. In addition, this number raises questions on how American Indians decreased substantially in population. Some theories of causal factors include sickness, displacement from homes or massacre. In summary, there is still much to be learned and discovered in the history of the Americas. After all, pyramids do not just appear out of the blue . . .

To solve the problem I divided 14,000 by 25, which equals 560. This means that the Amerindian population would have doubled 560 times. Then I started to look at the pattern of how the population number was changing: 1,000...2,000...4,000 etc. and simplified that to 2^560 and because I simplified it you would have to then multiply that huge number by 1,000. The fact that this number is so enormous emphasizes how much the arrival of Columbus changed the entire course of the world. Today the percentage of indigenous people in the USA is less than one percent. It also calls for a re-evaluation of the rather low estimations that many scholars have made in reference to the Amerindian population before Columbus arrived. Such an enormous number implies a human catastrophe that cannot compare with the number of lives lost in both world wars. It is also frusterating to reflect upon how much of the history of the Amerindians was either glossed over or completely ignored in grade school.

100 quadrillion, trillion, billion Amerindians would be on this continent had the original population of 1,000 doubled every twenty five years for 14,000 years. The number is astronomical. There is no way that the resources on the continent, nor the entire world, could feed that many mouths. That supplemented with disease, infection, war, drought, famine, flood, and meteorites must have kept the population down to realistic numbers. Assuming there were 100 quadrillion, trillion, Amerindians by the 1400s, wouldn't they have surpassed the technological advances of their counterparts in Eurasia since they had more minds, more thinkers? Perhaps the Amerindian societies were not fragmented enough or were too fragmented to encourage the proper blend of competition and collaboration. In any event, there were great civiliztions here with huge urban centers (Aztecs, Mayans, Incas) which rivaled Eurasian centers in size and sophistication. It is possible that the number of Amerindians living on the continent when Columbus bumped into the new world was 100, even 200 million. The number exercise only enlarges the scale of the genocide that was committed, it does not really change the implications. Miss Howell makes a good point above that the genocide of amerindians isn't really talked about too much in grade school, the effective loss of the Amerindians is a little too daunting and close to home for us to bear.

To solve this, I divided 14,000 by 25 which is 560. The population for each year would double each year for 560 years. The first year is 1,000 x 2^0. The second year the population would double to 1000 x 2^1 which equals 2000. This pattern will continue for 560 years, so from the 159th interval of 25 years to the 160th interval the equation will be 1000 x 2^159, which is 1000 x 7.30750819 × 10^47, which an extremely large number, more simply, 1 x 7.30750819 × 10^50. Realistically, this is not that case, as I do not even know what 10^50 is even called, and the earth today has approximately 6 x 7^8 inhabitants according to [http://www.ibiblio.org/lunarbin/worldpop]. Had the trend continued, we MIGHT have seen an Amerindian population of this caliber, but even that is uncertain. The Europeans had brought new diseases in the late 1400's which wiped out a large population as well as genocide, but could we really know what the amerindians fate had been had Europeans had not settled? The mortality rate was much higher 600 years ago. How would survival adjust to changes in climate and topographies due to migration? I think the large population number would fit had American Indians been completely isolated and continually growing in a constant climate, but even American Indians migrated and such conditions are not reasonable.

Had there been no environmental stress (already an impossibility), the American Indian population would have reached 3.77 x 10^171, or a very large number. Even in Eurasia, where the population was much higher than the Americas, there was sufficient environmental stress to prevent this kind of limitless exponential growth. The fact that the American Indian population isn't even nearly as large as this theoretical number or as large as the Eurasian population shows that there was a very large amount of environmental stress as humans slowly moved across the Americas. The Americas are not a very human-friendly environment, with few domesticable animals and plants (such as corn) that took thousands of years to successfully domesticate. I think this shows the truly formidable environment that American Indians were up against and helps explain why they were unable to form the great civilizations and technological advancements often seen in Eurasia. While the Eurasians were innovating technology and building empires, many of the American Indians were struggling against a hostile environment just to stay alive.

If the incipient Amerindian population had remained unstressed, there would be about 3.77 x 10^171, which is an extremely large number.

Like many other people have said, this is quite the unrealistic number because there is only so much space and resources in the Americas and it would not even be possible for the country to sustain such a large number of inhabitants. Human history has always been plagued with disease, warfare, and other factors and therefore, the population can not grow at such a rate. I also think that the planet wouldn't let a population grow so much because it is so taxing on its resources and people would die as kind of a check in the world.

Doing this calculation was interesting because I never really thought of how many people could have been is the population had been unstressed for so long.

I too got 3.774*10^171 using the equation 1000*2^560. When the Europeans reached the Americas, there were far less Amerindians than this number indicates. Therefore, we can only assume that the Amerindian population was as large as the environment (weather conditions, natural disasters, warfare, etc.) would allow. Looking just at the numbers, it seems that there were significant factors that hindered the population growth, and these factors may explain why the Amerindians were technologically lagging behind the Europeans.

I, of course, got the same answer as previous posters: 3.77 x 10^171. Seeing as there are definitely not that many people here now, it makes me think about Malthus and his theories on population control. Perhaps it was natural disaster that brought the population down, or the limits on food production, among other things of course. This doesn't say anything about whether it's good or not that the population didn't grow this exponentially, but it's just something to think about. It makes me think about how crazily overpopulated the world could become if left unstressed, which is a little scary. It makes humans seem like rodents or weeds that just reproduce like crazy.

I, of course, got the same answer as previous posters: 3.77 x 10^171. Seeing as there are definitely not that many people here now, it makes me think about Malthus and his theories on population control. Perhaps it was natural disaster that brought the population down, or the limits on food production, among other things of course. This doesn't say anything about whether it's good or not that the population didn't grow this exponentially, but it's just something to think about. It makes me think about how crazily overpopulated the world could become if left unstressed, which is a little scary. It makes humans seem like rodents or weeds that just reproduce like crazy.

Dividing 14000 years by the 25 years it takes to double yields 560 doubling periods. If the original population of 1000 doubled 560 times, there would be 3.77*10^171 (1000 * 2^560) people today. This is a highly unrealistic number because it does not take into account the limitations of resources and competition for those resources, hence the term "unstressed".
Compare this number to a very rough approximation of the current population of the Americas at 1 billion people (higher than most estimates). If we divide the number from our previous calculation by 1 billion, we get 3.77*10^162. This number represents the number of people our calculation predicts should exist for each person in the Americas today. Furthermore, if we convert the approximate area of the Americas, 42,330,000 square kilometers (from Wikipedia), to square inches we get approximately 6.56*10^16 square inches, still of much smaller magnitude than our calculated population. This demonstrates that the spatial limitations of the Americas would have curbed population growth before it came anywhere near the predicted number.

If for 14,000 years the Amerindian population would've remained unstressed and allowed to double in size about every 25 years it would've doubled 14,000/25 = 560 times, 560 generations would've occurred. If the population started with 1,000 people, and the population had been allowed to grow unstressed we today have a population of 1,000 x 2^560 American Indians. I'm sorry about the exponential form, my calculator thought the number was too large to display.

The large number above (1,00 x 2^560) implies a population far larger than the population of the Americas today. This would indicate that our perception of human history of the Americas between 12000 BC and 1492 as being relatively stress free is erroneous. Aside from the conflict and disease that the colonists brought upon the new world which ended many, many Amerindian lives, there had to be more conflict or stress that prevented the Amerindian population from spreading at exponential rates before the colonists even arrived. Perhaps the Amerindians were raided by diseases at different times throughout their history?

After performing the calculation—I trusted everyone else’s calculations but I thought it would be an interesting exercise—I too got an answer of 3.77 * 10^171. I guess the first thing that this figure tells us is that the Amerindian population was not unstressed. Moving across a North-South land mass with different climates, lengths of day, and vegetation with no domesticable animals would provide more than enough stress to limit the growth of the Amerindian population. That being said, the number still suggests that a massive population inhabited the New World before European conquest, refuting the notion that colonists settled an “empty continent.” It is hard to fathom the immense cultural losses that resulted from the disappearance of whole civilizations (composed of millions of members) in a matter of decades.

The Amerindian population would have been doubled 560 times (14000/25) eliciting an equation exactly this-given perfect living conditions. 3.77 X 10^171(1000 X 2^560). The implication that this number develops is the fact that living conditions at this time were far from even satisfactory. The Amerindians were plagued with diseases, malnutrition, war and an 'infrastructure' lacking the bare necessities. The number representing the population should be exponentially smaller. Even today, we could not use this irrational formula to calculate population because even our extremely advanced society is stressed by a plethora of factors.

There are 560 25-year periods in 14,000 years, meaning that the population of American Indians would have (theoretically) been equal to 1000 x 2^560. However, this enormous number is obviously not possible, and the assumption that the American Indians could grow at this rate and remain unstressed is clearly impossible. The total land mass of the Americas would not even be enough to hold this many people. So obviously a more realistic number would have to take into account the fact that at some point the size of the country would become an issue to population growth (lack of food resources, etc.). Larger and denser population also spread disease faster, and would probably make it more likely for revolts and wars to occur.
Nevertheless, the Americas are a large land mass and if the Amerindians had remained relatively unstressed for a longer period of time, there would clearly be a very large number of them around today.

The question seems to suggest an answer of 14000/25 = 560 doubling periods. 1000*2^560, even without calculating it out, is unrealistic. The Americas have a S.A. of 16340000 sq miles. The highest population density urban center in the world is the Maldives in Male, with a population density of 124,338 people/sq mi. Assuming a realistic average of 1/100th of this density spread over all of the Americas, the maximum population, by today's standards, is about 20 billion. Probably the Amerindian population would have reached a series of growth plateaus dictated by the advent of new technologies (Large-farm agriculture, long-distance transport, public sanitation, etc), with the highest current one being no more than an order of magnitude larger than 20 billion, and probably significantly smaller.

The population of the Amerindians had doubled every generation. In the very beginning there had only 1000 people. If doubling the population every 25 years, the calculation would be (3.77396242*10^171).

I think this implies that Amerindians have a very high population and reproducing rates, and their innovation influenced Eurasia. Amerindians had better technology innovation than European. However, I think the number of population is incredibly large and unrealistic. Disease kills people faster especially in the denser population. Population growth is also limited by natural resources and many other reasons

I got 3.77x10^171 for the number. I did this by dividing 14000 by 25 and got 560 (meaning the times it doubled) and then I raised 2 to the 560 and then multiplied by 1000.

Of course this number is way too high to possibly be correct.

This would be assuming that the Amerindians would be able self-sustainable from the resources of the Americas. However, to flourish at this rate is improbable. Also, this would assume that the Amerindians could retain high birth rates and steer clear of diseases. This would especially be very difficult because it's been proven that high density population provide a breeding grounds for diseases since there would be a high contact rate with animals.

This provides implications because popular opinion has always been that the Amerindians lived in small groups and that there were not a hugh population of them. However, with this information it could present the idea that there were large and complex civilizations for hundreds of years.

As previous posts have stated, the calculations dont really give a realistic figure of the population of American Indians that would be here today. However, it gives us an idea of how history unfolded before the colonists came to America. It tells us that there must have been a large amount of stress on the population, possibly due to resources or conflict. It also gives us an idea of how many American Indians there were before the colonists came to America, since even a tiny fraction of 3.77x 10^171 is a very large number, suggesting that the impact of the settlers on American Indians was pretty catastrophic when you consider the number of American Indians there are today.

Apparently the number of Amerindians that would have survived "stress free" at that doubling rate over 14,000 years or so we would end up with something like 3.77x10^171. This number is interesting in our little discussion, but it is hard to draw much conclusion from it in regard to the time period of 12000 BC to 1492. If this simple model were even close to reality, it would clearly mean that the population was much larger than ever really realized. But if you factor in that they would need land mass to support such a large number of people with when discovered had the most "primitive tools" ( No wheel and no metals). They would have needed the innovation of some form of technology along with greater unity. If I recall the natives developed dozens to hundreds of different languages, tribes, etc. It is also noticed in history that large groups of people tend to clash, especially if there was a language barrier, restriction of innovation, or any other hinder to their specific situation. So if they were able to surpass wars, diseases, famine, etc., it's very possible that their population should have been much larger in numbers. However, I'm a realist and in my very brief and extremely minimal research done on this topic, I would say that it looks like the numbers weren't that big. The U.S. is at 300 billion over 200 plus years not accounting for net migration and everything, so I guess it's still possible.

I also got 3.77*10^171. The implications of this number is that there could have been a huge population in America if they were left unstressed. However, the world would not be able to support that many people and eventually the population would have reached America's maximum carrying capacity. This implies that the Amerindians could have had a huge population before Columbus came to America which eventually led to a lot of stress factors released into the environment (ex: smallpox).

After a number of calculations, I also received the highly unrealistic figure of 3.774x10^17. This figure assumes that under “stress-less” living conditions, Amerindians could flourish, overcoming disease and achieving high birth rates. Like previous posts have stated, this extremely high figure highlights for historians a clearer indication of the disastrous impact settlers, as they brought disease and heightened limitations on the available amount of natural resources.

After a number of calculations, I also received the highly unrealistic figure of 3.774x10^17. This figure assumes that under “stress-less” living conditions, Amerindians could flourish, overcoming disease and achieving high birth rates. Like previous posts have stated, this extremely high figure highlights for historians a clearer indication of the disastrous impact settlers, as they brought disease and heightened limitations on the available amount of natural resources.

The calculations performed by my classmates above are correct. But do these calculations necessary infer that without European conquest of the new world, Native Americans would have instead flourished into an invincible civilization? Not at all.

The hypothetical population numbers provide a flawed conclusion. If we take into account Diamond’s article, the lack of Native American success against the Europeans not only stems from alien diseases or inhuman treatment that accompanied mere European arrival. Instead, the natural environment (north-south axis instead of an east-west axis) dictates the mass development of agricultural and the availability of animals for domestication, factors upon which a grand civilization depends. An increase in population numbers will fail to change these factors.

the question has too many variables. The term unstressed needs to be better defined because disease could have stricken the colony. I agree with Yufei about Diamonds article and European arrival. Hypothetically speaking, there will be population growth, people will leave and eventually they will run out of land and migrate, so the actual number is really hard to count for.

I'd guess there would be closer to 500 million or so now, if unaffected by European exploration, i think it would depend on the level of technology native americans achieved though. I think at low levels of technology, population growth would be very little and probably not much greater than in the 10,000 years of history before. However, one small industrialization boom can cause exponential growth that could have led to well over 100s of millions in population.

If doubling every 25 years, the unstressed Amerindian population would reach a ridiculously huge number of 3.774*10^171. However, its seems as though this is an unrealistic and unachievable number even though it is an unstressed population. In order to support such a population, it would require an agriculturally and technologically advanced infrastructure, which was absent in the Americas between ca. 12000 BC and 1492.

If the population were to double every 25 years, the population would be about 3.774*10^171. I got this number by dividing 14000 by 25 to get the number of times the population would double, and got 560. Therefore, 2^560*1000 (size of population)= 3.774*10^171. This would imply that the Amerindians were able to maintain a constant rate of growth. However, this number is extremely large and improbable. It is unlikely that the Amerindians were able maintain growth while overcoming any hardships they suffered. For example, harsh weather conditions, sicknesses and diseases, and conflicts with the Europeans.

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