Exponential growth gets away from you even when you allow for resources that are vastly beyond what we now have access to. At an annual growth rate of 1%, star

Exponential growth gets away from you even when you allow for resources that are vastly beyond what we now have access to. At an annual growth rate of 1%, starting from the present population in 3400 years the amount of mass we need for human bodies is equal to the combined mass of the Earth and the Moon. In another 600 years and the mass we need for humans equals the mass of Jupiter. From there it is only 700 years until we need the mass of the entire solar system, including the Sun, for human bodies. From then it is about 2000 more years before we need the mass of the entire Milky Way galaxy, which is problematic because unless we have FTL travel we won't have been able to use any resources that are farther than 6700 light years from Earth, which is only a small fraction of the Milky Way. Another 5600 years (about 12300 years from now) we need the mass of the observable universe. Without FTL after about 12000 years at 1% annual growth the amount of space we could theoretically have access to (a sphere of radius 12000 light years around the Earth) does not have enough space to hold everybody. The volume of that sphere divided by the population would fall below 0.006 m^3, which is about how much volume a human body takes up. (And we can't actually pack people that densely because we are not actually a shape that packs well). How about energy, rather than mass or space? If our energy needs grow by 1% per year in about 9300 years our annual energy consumption will be equal to the total energy of the Milky Way. By "total energy of the Milky Way" I mean what we could get if all of it were converted to energy (E=mc^2). In 12000 years we'd need the energy of the entire freaking observable universe.