Geometric population growth is not a theory. It is well observed in many species, including our own.
"Since evolving about 200,000 years ago, our species has proliferated and spread over the Earth. Beginning in 1650, the slow population increases of our species exponentially increased. New technologies for hunting and farming have enabled this expansion. It took 1800 years to reach a total population of 1 billion, but only 130 years to reach 2 billion, and a mere 45 years to reach 4 billion."

M.J. Farabee, Population Ecology,
For those who want to plot the J curve on a graph, here's some historical information:

Year      Population in billions
0         0.30
1000      0.31
1250      0.40
1500      0.50
1750      0.79
1800      0.98
1850      1.26
1900      1.65
1910      1.75
1920      1.86
1930      2.07
1940      2.30
1950      2.52
1960      3.02
1970      3.70
1980      4.44
1990      5.27
1999      5.98
2000      6.06

It was observed also in reindeer on St. Matthew Island in the middle of this century.
"Transgressing the carrying capacity for one period lowers the carrying capacity thereafter, perhaps starting a downward spiral toward zero. David Klein's classic study of the reindeer on St. Matthew Island illustrates the point.26 In 1944 a population of 29 animals was moved to the island, without the corrective feedback (negative feedback) of such predators as wolves and human hunters. In 19 years the population swelled to 6,000 and then "crashed" in 3 years to a total of 41 females and one male, all in miserable condition. Klein estimates that the primeval carrying capacity of the island was about 5 deer per square kilometer. At the population peak there were 18 per square kilometer. After the crash there were only 0.126 animals per square kilometer and even this was probably too many once the island was largely denuded of lichens. Recovery of lichens under zero population conditions takes decades; with a continuing resident population of reindeer it may never occur. Transgressing the carrying capacity of St. Matthew Island reduced its carrying capacity by at least 97.5 percent. It is facts like these -- repeated over and over again in game management experience -- that justify the ecolate game manager in viewing carrying capacity as partaking of the sacred. I do not think it is going too far to assert and defend the sanctity of the carry capacity."

Garrett Hardin, An Ecolate View of the Human Predicament,, with more information available at
Exponential growth has also been demonstrated in just about every 10th grade biology class in the last twenty years, by using a small dish, and a tiny sample of yeast. Not that yeast is alone in this--many of those same classrooms likely did the same with fruit fly populations. Even viruses have exponential growth patterns (; a rare disease will slowly increase in occurrence until its growth explodes.

As shown, geometric growth can and does occur, and as in the case of the reindeer on St. Matthew Island, geometric growth of a population can and does occur when the growth pattern of the food is not geometric; the result of geometric growth is that the population will strip its environment of its natural resources until the environment is no longer able to maintain that population. The carrying capacity of that population will then have been reduced, and a dieoff will occur. Geometric growth does occur, and it has its consequences.

Population density is not the only factor in determining whether or not overpopulation is a problem. Though India has a lower population density and is currently somewhat able to sustain its population, it has a much higher growth rate than that of Europe. As stated above, Italy and Germany both have or have very nearly zero population growth. India has the highest level of population growth of any country and within ten years will surpass China as the most populated country in the world. To say that it is unjustifiable for a world population to talk about world population problems is ridiculous. Overpopulation is a serious problem, and it does affect everyone, as the cumulative effects of six billion people affect all six billion people.

Regarding fitting the population of the world into Texas:
"If you divided the world's 6 billion humans into Texas's 261,914 square miles, each person could claim .028 acres of land. It is obvious, however, that the land in Texas, (or even the land in North America for that matter), would not be able to sustain these people. Resource experts say a minimum of 0.17 acres of arable land is needed to sustain a person on a largely vegetarian diet without the intense use of fertilizers and pest controls.

An estimated 253 million people currently live in countries with scarce arable land --which have on average no more than 0.17 acres available per person -- and this population is expected to at least triple by 2025 if current trends continue. Only 11 percent of the Earth consists of arable land, and that area is rapidly diminishing due to erosion, salinization and a decline in the practice of fallowing land."
In addition:
"If just the present world population of 5.8 billion people were to live at current North American ecological standards (say 4.5 ha/person), a reasonable first approximation of the total productive land requirement would be 26 billion ha (assuming present technology). However, there are only just over 13 billion ha of land on Earth, of which only 8.8 billion are ecologically productive cropland, pasture, or forest (1.5 ha/person). In short, we would need an additional two planet Earths to accommodate the increased ecological load of people alive today. If the population were to stabilize at between 10 and 11 billion sometime in the next century, five additional Earths would be needed, all else being equal -- and this just to maintain the present rate of ecological decline (Rees & Wackernagel, 1994).

"While this may seem to be an astonishing result, empirical evidence suggests that five phantom planets is, in fact, a considerable underestimate (keep in mind that our footprint estimates are conservative). Global and regional-scale ecological change in the form of atmospheric change, ozone depletion, soil loss, ground water depletion, deforestation, fisheries collapse, loss of biodiversity, etc., is accelerating. This is direct evidence that aggregate consumption exceeds natural income in certain critical categories and that the carrying capacity of this one Earth is being steadily eroded. We should remember Liebigs "Law of the Minimum" in this context. The productivity and ultimately the survival of any complex system dependent on numerous essential inputs or sinks is limited by that single variable in least supply. In short, the ecological footprint of the present world population/ economy already exceeds the total productive area (or ecological space) available on Earth."