If a Soviet astronomer named Nikolai Kardashev and an American physicist named Michio Kaku are correct, then interstellar travel, 400 yottawatts of energy, and a terrible space-crunch lie in humanity's next millennium.
I just came across an interesting concept called the Kardashev scale. Using a simple formula, it defines how advanced a civilization is based on its energy consumption on a scale of three possible values. These values are demarcated as Types I, II and III.
Conceived by Soviet astronomer Nikolai Kardashev in 1964, and given a formula by Carl Sagan in 1973, the scale places the human civilization as in 2008 at 0.717, and about 100-200 years away from attaining Type I status according to an extrapolation by physicist Michio Kaku.
According to Kardashev, and later, Guillermo Lemarchand, a Type I civilization consumes between 10E16 and 10E17 watts, a Type II, about 4E26 watts, and a Type III, about 4E37 watts. Ergo, successive stages involve a hike in 10 orders of magnitude and then 11 orders of magnitude, respectively.
These are exponentially massive jumps, as Kaku's estimation of few thousand years and a million years as the consecutive attainment periods evince.
What's really interesting about these definitions is that, on Earth, humans are hardly the civilization to keep an eye out for. In 2008, humans consumed about 15 terawatts while photosynthesis, the primary biotic source of energy on the planet, produced about 1,800 terawatts of energy, with single-celled microalgae being the most efficient among the producers.
That places nature at 0.9 on the Kardashev scale.
Not that this comes as any kind of a surprise, but we are underdeveloped in our own environment. Forget extra-terrestrial intelligentsia: Diseases should be the stuff of Asimov-esque or Clarke-esque science fiction! That we imagine we are ready to confront alien military technology and so scream high-energy radio signals into space in the hope of pinging another civilization is laughable.
Another interesting aspect comes to light if we addressed the human biosphere as one system - conserving energy and momentum all the time and everywhere - then a Type 0.717 civilization like ours must consume and expel 15 terawatts. All that power cannot accumulate and then disappear from our ergonomic accounts. All units must have a contraentry. So, as a formula:
Consumed energy = Expelled energy
There are different ways of expelling this energy. As a simple example, consider the running of a car: every second, some amount of petrol and electrical energy from the battery goes into keep the car moving at some speed. This energy is lost in transmission, combustion, air-conditioning, overcoming friction, etc.
Similarly, at the moment, a planet of 7 billion humans consumes and expels 15 terawatts.
Consider if we were a Type III civilization, however. We'd have to consume and expel about 4E37 watts, which is about the entire luminosity of the Milky Way galaxy (100-400 billion stars). This means that, if each human body consumed and expelled about 100 watts, i.e. the basal metabolic rate, then Earth would have to harbor... 400 million trillion quadrillion humans.
Obviously, the world is not enough.
One would imagine that as we progressed, we'd consume and expel energy at higher efficiencies. As a result, fewer machines would be needed to convert energy into useful energy. So, with the same quantity of resources, we'd be able to produce more machines as time passes. Consequently, the rate at which we consume energy will grow exponentially, i.e. accelerate.
In fact, even as a Type II civilization, we'd need space for more than a quadrillion humans. Thus, somewhere between the Type I and Type II statuses, we'd have to figure out interstellar travel or simply go the Douglas Adams way and ship off all our telephone sanitizers into a random direction in space.
Footnote: If you're able to track down a reliable ballpark of how much of the Earth's surface area is occupied by humans, then you'll be able to calculate the Kardashev-scale's counterpart in occupation-space scaling.