Eternal life — Dyson vs. Krauss

I’ve been mean­ing to post this for a while, but kept putting it off because I antic­i­pated it being a rather long post. Sev­eral months ago I attended a lec­ture given by Lawrence Krauss at the CUPC. He gave us an overview of a “debate” he had with Free­man Dyson about whether or not life could exist for­ever. Keep in mind, this is not an argu­ment for the like­li­ness of eter­nal life, it’s just sim­ply address­ing the pos­si­bil­ity of it. In physics, the ques­tions about whether or not some­thing is even remotely phys­i­cally pos­si­ble are, many times, the most fun! And the ideas Krauss shared with us that orig­i­nated from his back-and-forth with Dyson were so fun and inter­est­ing that I thought I’d take a stab at repro­duc­ing an overview of it all here. Keep in mind, I will be glaz­ing over all of the math­e­mat­ics and so if you want a more in depth look at the deriva­tions of these results you should prob­a­bly check out the orig­i­nal papers (here is Dyson’s; here is Krauss’s). They are enjoy­able to read if you have a physics back­ground (and maybe even if you don’t). So here it goes. Dyson vs. Krauss. But before we begin this face­off, we need to buckle down and tend to a ques­tion that is beg­ging to be answered:

…what do we mean by “life”?

Firstly, I must men­tion that we are not talk­ing about eter­nal life for a sin­gle being. This debate was focused on eter­nal life for, say, a civ­i­liza­tion albeit one that may evolve. Sec­ondly, liv­ing things come in many shapes and forms, some of which we may not yet be aware of. It seems unrea­son­able to make the assump­tion that all forms of life are like those on earth; car­bon based, depen­dent on water to sur­vive, etc. In any case, Dyson and Krauss are both physi­cists and so for the pur­poses of their debate they were more con­cerned with the physics of “life” than its biol­ogy. Let me put it like this: we are not really con­cerned with the bio­log­i­cal processes that lead to the thought “I think there­fore I am”, we are sim­ply con­cerned with the exis­tence of the thought itself to define “life”. In other words, by “life” we really mean con­scious­ness, or more sim­ply, com­pu­ta­tion. Con­scious­ness seems to have a lot to do with the fir­ing of neu­rons which go about pro­cess­ing infor­ma­tion much like a com­puter (or per­haps a quan­tum com­puter). Whether or not con­scious­ness is really akin to some kind of com­puter pro­gram is a whole new debate in itself (per­haps some neu­ro­sci­en­tist read­ers can com­ment on this). Despite this, com­pu­ta­tion must at least have a lot to do with con­scious­ness and so surely by inves­ti­gat­ing the eter­nal exis­tence of com­pu­ta­tion we won’t be doing too badly.

So, what restricts us from run­ning a com­puter pro­gram for all time? Well, the first bar­rier is: energy. Hope­fully you are famil­iar with the fact that the uni­verse is expand­ing. Not only is it expand­ing, it is expand­ing at an accel­er­ated rate. It turns out that this puts a con­straint on the amount of energy any civ­i­liza­tion can har­vest to keep them alive (com­put­ing). With a finite amount of energy avail­able one might give up at this point and declare that life, which requires energy to sus­tain itself, can’t exist for an infi­nite amount of time. Dyson, how­ever, was still opti­mistic. He real­ized that liv­ing things are less con­cerned with phys­i­cal time and are more con­cerned with, what he calls, sub­jec­tive time. Liv­ing things mea­sure time by the num­ber of thoughts they have, so if a civ­i­liza­tion can have an infi­nite num­ber of thoughts using only a finite amount of energy, one could say that they have achieved eter­nal life. This sub­jec­tive time depends on the tem­per­a­ture at which the entity oper­ates. So if we assume that the civ­i­liza­tion has the abil­ity to change its tem­per­a­ture at whim, at first glance it seems like the civ­i­liza­tion can have an infi­nite num­ber of thoughts (live for an infi­nite sub­jec­tive time) if it keeps decreas­ing its tem­per­a­ture for all time (get­ting closer and closer to absolute zero, but never exactly zero). That strat­egy (again, at first glance) will allow an infi­nite num­ber of thoughts using only a finite amount of energy.

So, is this strat­egy really pos­si­ble? Well, in answer­ing this ques­tion we come to the next road­block: heat dis­si­pa­tion. Com­pu­ta­tion gen­er­ates heat (there’s a rea­son your com­puter gets warm when you turn it on). Liv­ing things will also gen­er­ate heat. Even if we ignore all of the heat gen­er­ated from famil­iar bio­log­i­cal func­tions and only focus on the heat gen­er­ated from think­ing, we still have a min­i­mum rate for heat pro­duc­tion of a liv­ing entity. This heat has to be radi­ated away at a rate greater or equal to the rate at which the heat is pro­duced, or the entity will “die” (there’s a rea­son your computer’s CPU needs a fan). Dyson con­sid­ered this and deduced that the best way to get rid of waste heat would be through elec­tro­mag­netic radi­a­tion. How­ever, going through the math he deduced that the rate of radi­a­tion of waste heat this way would depend on the tem­per­a­ture and the num­ber of elec­trons of which the entity was made. And if the life form kept reduc­ing its tem­per­a­ture in this way, there would even­tu­ally be a time when it could not radi­ate its heat fast enough with only a finite num­ber of elec­trons. So, this couldn’t work. Did Dyson give up?

Nope.

Think about this: what if you really really wanted to go about run­ning a com­pu­ta­tion on your lap­top but your fan couldn’t cool it off quickly enough. What would you do? What Dyson would prob­a­bly do, is run the com­pu­ta­tion for a while, put the com­puter into sleep mode, let it cool off, wake it up, con­tinue the com­pu­ta­tion and then repeat this until the com­pu­ta­tion was done! That’s exactly what he sug­gested a civ­i­liza­tion might try to do to live for­ever; namely peri­od­i­cally hiber­nate in order to get rid of the excess waste heat! The civ­i­liza­tion could con­tin­u­ally lower its tem­per­a­ture (decrease its metab­o­lism) and peri­od­i­cally hiber­nate for longer and longer in order to have an infi­nite num­ber of thoughts using a finite amount of energy.

A nice strat­egy… but this is where Krauss stepped in and poked a lot of holes in this argu­ment. The first caveat comes from the neces­sity for some kind of alarm clock to wake up the civ­i­liza­tion from its hiber­na­tion. Any alarm clock is inevitably going to be per­form­ing some kind of com­pu­ta­tion in order to cal­cu­late when it should “ring” and tell the life forms to wake up and smell the cof­fee. This alarm clock is sub­ject to the same laws of physics as the life forms them­selves and, as such, will even­tu­ally use up all energy reserves by the same argu­ments as above (since a hiber­nat­ing alarm clock would defeat the purpose).

The sec­ond caveat comes from the fact that we are liv­ing in a uni­verse which is expand­ing at an accel­er­ated rate. It turns out that a uni­verse with that prop­erty will be per­me­ated by back­ground ther­mal radi­a­tion (anal­o­gous to Hawk­ing radi­a­tion) which means a lower cut­off for tem­per­a­ture. In short, in a uni­verse under­go­ing accel­er­ated expan­sion there is a min­i­mum tem­per­a­ture, which means that Dyson’s strat­egy of con­tin­u­ally reduc­ing a civilization’s tem­per­a­ture won’t work.

Now, you may have heard a bit about quan­tum com­put­ers and be think­ing: “… but quan­tum com­pu­ta­tion doesn’t nec­es­sar­ily require any energy. You can, in prin­ci­pal, do as many com­pu­ta­tions as you like with­out gen­er­at­ing heat as long as you don’t mea­sure the result”. If you did think of that, great! How­ever, as Krauss pointed out, you’ll nec­es­sar­ily have to radi­ate heat if you want to do any eras­ing in order to pre­pare for a new com­pu­ta­tion. If you had an infi­nite amount of mem­ory stor­age avail­able you could ignore that point, but any civilization’s mem­ory stor­age is lim­ited by the num­ber of par­ti­cles it has access to, which is (as with the case of energy) lim­ited in sup­ply. Krauss sums up this point well.

Thus any civ­i­liza­tion can have only a finite total mem­ory avail­able, and reset­ting reg­is­ters is there­fore essen­tial for any organ­ism inter­act­ing with its envi­ron­ment, or ini­ti­at­ing new cal­cu­la­tions. While an exis­tence, even nir­vana, might be pos­si­ble with­out this, we do not believe it is sen­si­ble to define this as life.

So right now it looks as though life (as some form of com­pu­ta­tion), by its very nature, must end. Mor­tal­ity is a neces­sity of life. I am actu­ally fond of this wist­ful result. I find it gives life more mean­ing and makes it more pre­cious… but that’s just me. What do you think?