Waste Heat, part III: Climbing Kardashev’s Scale

In my last entry I discussed Kardashev’s scale of civilizations and Dyson’s insight into a completely general method of detecting distant alien civilizations.  I gave a talk on all of this last Friday and before the talk Eric Feigelson mentioned to me that Nikolai Kardashev is alive and active:  in fact he is currently the deputy director of the Russian Space Research Institute at the Russian Academy of Sciences at age 80.


 Freeman Dyson, too, is an active scientist at 88 at the Institute for Advanced Study at Princeton.  I heard Dr. Dyson speak when I was a graduate student at Berkeley (on the “garbage bag” theory of the origin of the cell, if I recall) and I may get to meet him in person next week in Philadelphia.

The next scientist in my tale left us far too early.  Carl Sagan took Kardashev’s scale and extended it to include fractional numbers by noting that the fraction of all sunlight that strikes the Earth is (very) roughly the inverse of the number of stars in the Galaxy.  That is, 

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This allowed him to redefine Kardashev’s scale slightly by defining:
Sagan extension II
On this scale, a civilization with energy supply of 10 billion MegaWatts (which is roughly 5% of the total incident sunlight on the Earth) would have K=1.  Humanity’s current energy supply is about 10 million MegaWatts, or K=0.7, and if we collected and used all of the incident energy on the Earth we would have K=1.12.   
A civilization that collected and used almost all of the radiant energy of a star like the Sun (4 x 1020 MW) would have K=2.06, and one with 100 billion solar luminosities of energy supply would have K=3.16, roughly consistent with Kardashev’s scale.
It is interesting to note that humanity’s energy supply has doubled in the last 30 years.  At this exponentially increasing pace, we will achieve K=1 in 300 years, and have an energy supply equal to the incident sunlight on Earth in 400 years.  At this point, we will have doubled the Earth’s pre-industrial mid-infrared waste heat signature.  In fact, this will be a new form of global warming that has nothing to do with greenhouse gasses:  just by using energy for our own needs we will significantly warm the planet with the waste heat from our computers and electric cars and phones.  
This gives a sense of how quickly we are approaching our Malthusian limits on energy:  unless we start colonizing space, we will hit hard energy limits in just a few human lifetimes.  As I wrote before; every other Malthusian limit, from food supply to fresh water to material, we can, in principle, overcome with technology and energy expenditure, but energy itself will eventually limit us, and unless we want to seriously heat the Earth we’re going to have to move to space to find the energy and waste-heat emission surfaces to keep expanding our economic activity.  Given how poorly coordinated most of our energy use is (even when we know it’s heating the planet, we continue to burn more and more fossil fuel), it seems very typical of our species that some fraction of our population will always be looking for new sources of energy. Viewed this way, the question is not whether we will ever be able to build a Dyson sphere;  the question is why it isn’t inevitable!  


I like to generalize the Kardashev scale the way that Zubrin did in 2000 (in his book Entering Space, I think), not by the actual energy use, but by the extent of a civilization.  A planet-wide species (like ours) would be a “K1”, or civilization of the first Kardashev type.  A solar-system-wide civilization would be a “K2”, and this would include everything from a thriving moon colony to a full-on Dyson sphere.  A “K3” civilization would have colonies between the stars.
I should note that the transitions between these types will actually be very quick, cosmologically speaking.  Consider a space-faring civilization that can colonize nearby stars in ships that travel at “only” 0.1% the speed of light (our fastest spacecraft travel at about 1/10 this speed).  Even if they stop for 1,000 years at each star before launching ships to colonize the next nearest stars, they will still spread to the entire galaxy in 100 million years, which is 1/100 of the age of the Milky Way.  In other words, if you watched a galaxy in time-lapse from its formation to the present day in a movie 1 minute long, it would go from having a single K2 civilization to having a K3 civilization in under 1 second.  
So if we scan the heavens for galaxies with aliens, we should not expect to find many that have only a few aliens:  they should have either no K2’s, or a K3.  Interestingly, we can apply the same logic to the Milky Way:  if there are aliens in the Milky Way, it is very unlikely that we would have come of age in an era where they were in transition between K2 and K3.  Either the Galaxy is filled with spacefaring aliens, or we are the first.  So we should either expect the galaxy to be filled with Dyson spheres, or totally empty of spacefaring life.  This makes a null detection of Dyson spheres very interesting! (This is also a rephrasing of the so-called Fermi paradox).
OK, practical numbers for Dyson spheres will have to wait for another entry.  Next time, I’ll look at the problem of extinction and perhaps why aliens might not have any waste heat to detect.
[Image credits: Carl Sagan from Wikipedia, “Trantor from Space” by Slawek Wojtowicz]

7 thoughts on “Waste Heat, part III: Climbing Kardashev’s Scale

  1. Dan

    Here’s a 4th option for Marshall Perrin.


    There is a powerful theory, which I agree with, that human history is driven by a combination of greed and fear.

    Technical advances are not made to benefit humanity, they are made to kill or for financial gain, often both. Samuel Colt and his repeating revolvers lead in part to the mass production of precision assemblies with interchangeable parts, without which no modern machine could function. Railways were built because those involved saw a quick profit – some got rich, most lost their shirts. Was ever thus.

    Humanity is not going to stay on earth if there is a profit to be had from leaving it behind. With trillions of dollars worth of minerals on just one asteroid, the one organisation that cracks the problem will become fabulously wealthy very quickly. Elon Musk is well aware of this, hence his interest.

  2. Jason T Wright

    Hi, Alan! Thanks for posting. That’s a very insightful question.

    Aye, there’s the rub. Dust can look a lot like what we’re looking for, as can certain kinds of giant starts (AGB stars, in particular). Indeed, this is what has stymied previous Dyson sphere searches. I’m getting ahead of myself, but dust has many photometric and spectroscopic characteristics that distinguish it. Dr. Matt Povich on our team is an expert in identifying these sorts of very red objects in the data sets we’re using, and we can further weed them out with follow up observations.

    So the tricky part isn’t finding “red” things, it’s finding red things that don’t look like all of the other red things out there. I’ll get into all of this more in future posts.

  3. Alan MacRobert

    Jason, we need an explanation of how an artificial Dyson sphere could be told from a star naturally enveloped in a dust cloud at the same radius. These are common!


    Alan MacRobert
    Senior Editor
    Sky & Telescope
    macrobert AT SkyandTelescope.com

  4. Jason T Wright

    Hi, Marshall! Thanks for posting.

    I think there are two, linked questions: why do we seem to be alone?, and what will become of us?

    For why we appear to be alone:

    My personal bias is towards option 1) (we are the first) but there is also the option that is that we don’t see the Galactic super-civilization for any of various reasons, yet (one variant here is the Berserker “immune system” that periodically comes along and scrubs particularly virulent strains of life that threaten to climb out of their petri dishes (e.g., us!)).

    For what will become of us:

    If option 1), then we will go as you predict unless an unfortunate extinction event gets us before we can grow large enough to avoid them all (nearby supernova, massive cataclysmic climate change, war, solar event, etc.). Once we’ve colonized a few other stars, though, there’s almost no stopping us, even intentionally, unless you’ve got Berserkers (see above).

    I really don’t buy that advanced civilizations inevitably destroy themselves or else inevitably level out with population growth. That might be true for SOME species, but it only takes one on an exponential growth path to populate a Galaxy. I file this under the same sort of reasoning as Dr. Donald Kessler uses (no, not that one).

  5. Marshall Perrin

    So, given your conclusions here and the apparent absence of any K3s in our local environment, where does that leave us? I see three main possible paths this could play out in the long term future of humanity:

    Case 1: “We are the Vorlons”. For various reasons deterministic and stochastic, we are the first species to develop in the local group with the capability for and interest in spaceflight. By the year 100,000,000 AD, our descendants rule the galaxy in some kind of glittering star-spanning empire or republic. By that point, civilization is essentially indestructable. Our ultimate progeny, huddled around trillion-year-old M dwarfs, wave goodbye to the distant galaxies as cosmic acceleration carries them away and the universe settles into the long chill at the end of time.

    Case 2: “Next stop, Planet of the Apes”. Hold on to your hats, ’cause here comes the apocalypse. We do ourselves in through some combination of resource overexploitation, nuclear war, genetic engineering of superplagues, and/or turning our planet into a seething gob of nanotechnological grey goo. In fact, such tragic outcomes are the inevitable result of technological civilizations: every time the universe produces a technological species, the evolutionary forces that have shaped that species have invariably given them enough negative baggage, bad instincts, and lousy senses of long term self preservation that all species always end up toasting themselves before they get to the stars. Whoops.

    Case 3: “Steady state, status quo”. Global population peaks at around 9 billion in 2050, but then the demographic transition really kicks in. One child policies and the free choices of educated and empowered women everywhere reduce global birth rate to just around, or maybe a bit under, the 2.1 kids/family replenishment rate. Population settles back down maybe a couple billion lower in the long term, and simmers along in a fairly steady state. Green energy costs drop with economies of scale and Moore’s Law. The world heats up for a while, there are some localized resource wars, but the year 4000 AD finds a global population of maybe five billion in the midst of readapting back to a cooler planet as the worst impacts of global warming fade away. Meanwhile the space race puttered along much as it has the last 40 years, with no transcendent progress. Launch costs stay painfully high, humans walk on Mars around 2100, and briefly Europa and Titan in the 2300s, but there’s no compelling reason to send people rather than telepresence robots, most people think it’s cold and boring anyway, and Einstein laid down the law that no one could ever reach any exoplanets within their own lifetimes. Nobody but a handful of nerds cares that much when space programs all just gradually fade away. As the millennia spin along, people spend their time making art, enjoying the fruits of thousands of years of culture, and going on far greater adventures in immersive virtual reality cosmoses than can ever be achieved in the frustratingly limited real one.

    So… whence humanity? I can’t decide which of these I think is most likely…

  6. Jason T Wright

    Hi Dave! Thanks for posting!

    Yes, Mamajek and I had a brief back and forth about this on the FaceBook thing. I agree with your analysis. If most of our power is fossil or nuclear it’s pure extra heating, but if it’s all from solar (or any other renewable, like wind, hydro, tide, or what have you) then we’re just using energy that would have dissipated as heat, anyway. As you note, though, there is a secondary effect as we collect light that would have reflected back into space, and there’s enough of that to cause a real global warming problem.

  7. Dave Spiegel

    Very interesting series, Jason!

    Just one quick addendum —
    It’s certainly true that if we keep getting power by converting chemical and/or nuclear energy to waste heat, we’ll soon start to warm our planet significantly and probably catastrophically. But if we get our energy from the Sun, there’s no real serious global warming effect from using more energy, right? Worst-case scenario, it’s like lowering our albedo from 0.3 to (at minimum) 0. I don’t pretend that this would come without cost — it’s a ~50% increase in heating rate, roughly equivalent to moving the Earth to a 0.82-AU orbit, which would be pretty devastating.  But we could get a lot of energy from solar power without significantly altering the Earth’s albedo at all.

    Looking forward to the next installment in the series….

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