Anima Ex Machina

Stephen Hawking asserts that while aliens almost certainly exist, humans should avoid making contact.

The original story published by BBC News can be found here.

He claims: “We only have to look at ourselves to see how intelligent life might develop into something we wouldn’t want to meet.”

Stephen Hawking recent assertion looks like an interesting time to bring up the question of intelligent life, meaning and purpose.

Let’s examine what Hawking’s argument implies, assuming that intelligent life, other than human, exists elsewhere in the universe:

1. Aliens come from an Earth-like planet.
2. The Earth has something the aliens do not.
3. The Earth has something aliens need or want.

Each point may be not necessarily independent of each other, each may be chained or added to the other. Point 2 may imply Point 1. However, Earth-like planets are likely to be quite common, as the current research on exoplanets seems to suggest. While Point 1 is chauvinistic, Point 3–the notion that Earth possesses something special– is egocentric. Concerning Point 2 again: as a sort of example, many cities on Earth are in need of potable water. Does that mean they can just go looking for it in another city?

Destructed castle on the coast way of Ireland

Originally uploaded by hzenilc.

If we think that aliens are looking for a planet with an atmosphere like ours, we are already making a very strong assumption that requires further support. To assume that their planet has the same atmosphere as ours and that they would consequently need a planet exactly like it, is to make a strong claim–and a highly implausible one at that. We may think that water is the most precious element in the universe, but it might just be lethal to an alien civilization. If it is true that we can only imagine them in the basis of the kind of life and it diversity on Earth, it is also true that we know nothing about them, if they really do exist.

If humans find life elsewhere, and if it is not related to Earth’s life, it is likely to be unrecognizable. After all we have experience of a very large range of life forms here on Earth, and we find some of them already alien enough. “Extremophiles” is the name we give to Earth species that can survive in places that would quickly kill humans and other “normal” life-forms.

As for needing a work force, it doesn’t make sense that aliens would seek it here. Humans are highly unproductive. And aliens with the technological capabilities to travel to Earth are likely to have had long experience building the kinds of machines that humans have only recently got around to building and improving. Advanced intelligent aliens most likely make extensive use of robots, if they are not some kind of cybernetic beings themselves.

Though assuming that aliens and humans are alike in their biochemical constitution may be chauvinistic and misguided, the supposition that our intelligences are similar has a more solid basis, especially since we also assume that the alien civilization in question has built spaceships, travels in space and is looking for other civilizations. According to Stephen Wolfram’s Principle of Computational Equivalence (PCE), there is a good chance that if non-trivial life forms exist they will have or develop the same degree of sophistication (e.g. intelligence) than ours. Wolfram’s PCE would also suggest that once primitive life has developed it will eventually achieve its maximal degree of sophistication, which would be the maximal possible degree of sophistication. In other words, if life is around, intelligent life is as likely as life.

We used to say that aliens are likely to be much more advanced than humans. Why so? Because the universe has a 15 billion year history. Characterizing a civilization that has been around for about 2 million years and has only begun developing technology in the last few hundred as ‘advanced’ is beyond naive, it is statistically implausible. As Carl Sagan pointed out, every intelligent civilization seems to reach a period when its own technological power is capable of destroying itself. This is the stage which human civilization reached about 70 years ago (and still is), with the invention of atomic bombs. The longevity of said aliens’ civilization means that they have managed to make good use of the resources of their host planet. Even assuming they have reached the point where they have exhausted their resources, we have to concede that they have probably been good, ecologically responsible stewards of their planet. Of course it is still possible, despite all this, that these aliens may wish to colonize a new planet in order to exploit its resources rather than simply seizing what they find and taking it away with them.

Water is one of the most common elements in the universe, or it is quiet easy to synthesize it (see the chemical recipe here). If they just need a rock revolving around a star at a distance such that life can be sustained, there are certainly many more possibilities than coming to Earth. Think about it. The human civilization is much closer to achieving the terraformation of Mars (reengineering Mars soil and atmosphere to make it Earth-life friendly), given its current and near future capabilities than traveling abroad to conquer, if not cohabit with another civilization.

Now, from a practical standpoint, the notion that we could hide away in a corner of the universe is nonsense, to say the least, if we are not somehow already hidden due to the size of the universe itself. The Earth has been broadcasting to space since radio signals were invented. Messages have been kept symbolical on purpose. So in the worst case scenario, assuming Hawking is right and our signals are likely to be picked up by an alien civilization willing to take us on, hiding is just rubbish because we can’t. As Seth Shostak says, the first thing to do would be to shut down the BBC, NBC, CBS and the radars at all airports. Not unless we install a kind of Dyson sphere around the Earth or stop broadcasting altogether. Now, the only way to make sense out of Hawking particular comment in this regard, is taking into consideration time scales. If it is true that Earth has been broadcasting to the space during the last 50 or more years, it is also true that someday in the future it may reach a technological state that allows it to avoid, purposely or not, doing so. So it may be the case that civilizations decide to hide themselves after a short period of broadcasting history.

The advice to hide from aliens implies of course that they are destructive, or that the contact between our civilizations may be destructive, and this brings us back to the question of their longevity. If they were indeed destructive they would have annihilated themselves. As Hawking does right, consider the human case.

But if Hawking is right, we would probably have nothing to be scared of. If an alien civilization wants us dead we will either barely notice it when that happens or that won’t ever happen if it hasn’t happened already. The chances of a destructive civilization to exist seem lower than the chances of a pacific civilization to extend their existence time period in the universe history. The former would have likely already destroyed itself while the latter may have better chances. Caution would not hurt though. We ought to keep an eye on ourselves and how we develop, and that means using our resources more intelligently and not necessarily manufacturing more bombs. But being scared definitely says much more about us than anyone else because we simply know nothing about them, nor we can pretend to know what are their intentions, if any.

But of course in the matter of encounters between civilizations in space, every possibility is time-scale dependent. Imagine for an instant that two alien civilizations are at war. We would certainly be well advised to keep away from the conflict. We may be justified in thinking that if we were in the way when either of the parties ran short of resources to prosecute their war, they would most likely help themselves to anything we had that could be of use. But think a little further. The odds of encountering two civilizations actually engaged in warfare are rather small.

Civilizations making war would either annihilate each other, or if they don’t, then one party would end up achieving hegemonic status. It would seem logical that periods of peace are much longer than periods of war. In the first place civilizations that contemplate war must be both smart enough and hostile enough, and reaching these thresholds of achievement and antagonism takes time–peacetime.

As Hawking claims, many of the life forms in the universe are probably just microbes, but unlike Hawking I believe that if civilizations do exist they’d have little time to make war, even assuming they wanted to. Once again, one has only to think of the Earth to reach this conclusion. If the Cold War had not remained cold, we either wouldn’t be here or else we’d all now be ruled by a single country–as has been pretty much the case (despite there being no actual war) over the last few decades, with the emergence of a current single superpower (with a partial sharing of the global power, and other powers emerging). But when superpowers emerge these days, they are more interested in keeping the peace because they have reached a stage where they depend on each other, chiefly because trade and commerce have become globalized. It turns out that the human world has become much more cooperative than we might have expected. But this is not by chance; it seems to be a common path. Not that one can be absolutely certain, though. Only by witnessing other civilizations could we safely make generalizations. And yet logic dictates that the opposite path–the path of belligerence–would be unlikely.

What I think is that if civilizations were to find each other they are more likely to be interested in each other’s culture and knowledge, than in each other’s natural resources–either because natural resources can be found in many places, or even created by civilizations that are sufficiently advanced, or else because they are simply not needed, curiosity about the universe being the sole motive behind exploration. Which would mean that civilizations would preserve ‘alien’ civilizations to enrich themselves, just as anthropologists and ethnologists do on Earth. To make my point in terms of Hawking, aliens are more likely to be like modern scientists than like the barbaric Europeans who colonized the Americas.

To wrap up, and with all due respect for Hawking and his technical work, let me quote Philip Ball’s article ( Stephen Hawking’s grand theory of what? The National September 17. 2010 6:30AM GMT)

…why is Hawking awarded such a special place in that debate, given his evident lack of sophistication? The answer is surely that Hawking’s “disembodied mind” is tailor-made for guru status.

The lack of correspondence between the abstract and the physical world seems sometimes to suggest that there are profound incompatibilities between what can be thought and what actually happens in the real world. One can ask, for example, how often one faces undecidable problems. However, the question of undecidability has been considered to be better formulated (and understood) in computational terms because it is closer to our physical mechanical reality (through the concept of computation developed by Turing): Whether a computing machine enters a certain configuration is, in general, an undecidable question (called the Halting problem). In other words, no machine can predict whether another machine will halt (under the assumption of Church’s thesis –aka Church-Turing thesis).

An interesting example of the gap between what the abstract theory says and what can be empirically ascertained was recently suggested by Klaus Sutner from Carnegie Mellon. He rightly points out that if no concrete instance is known of a machine with an intermediate Turing degree, and consonant with Wolfram’s Principle of Computational Equivalence, is because intermediate degrees are artificial constructions that do not necessarily correspond to anything in the real physical world.

In David Deutsch‘s words physics is at the bottom of everything and therefore everything relies on physics (ultimately on quantum physics according to Deutsch himself). This is true for the core objects of study and practices in math: proofs, and in computer science: computer programs. At the end, that they are and how they are, is only possible by what it is feasible in the physical world. As if sometimes it were forgotten that mathematics and computation also follow in practice the same laws of physics than everything else.

Sutner defines what he calls “physics-like” computation and concludes that machines with intermediate Turing degrees are artificial constructions unlikely to exist. According to Sutner, in practice machines seem to follow a zero-one law: either they are as computationally powerful as a machine at the bottom of the computational power hierarchy (what Wolfram empirically calls “trivial behavior”) or they are at the level of the first Turing degree (i.e. capable of universal computation). This seems to imply, by the way, that what Wolfram identifies as machines of  equivalent sophistication cannot be other but capable of universal computation, strengthening the principle itself (although one has to assume also Church’s thesis, otherwise PCE could be referring to a higher sophistication).

So is PCE a conflation of Church’s thesis?

No. Church’s thesis could be wrong and PCE be still true, since by the negation of Church’s thesis the upper limit of the feasible computational power would just be shifted further, and even if it turns out that the hypothesis of a Turing universe is false, PCE could be still true disregarding whether the universe is of a digital nature or not since it would refer then to the non-Turing limit as the one holding the maximal sophistication (not that I think that C-T is false though).

Is PCE tantamount to the Church thesis in the provable sense?

Wolfram’s PCE would be still falsifiable if the distribution of the intermediate degrees is proven to be larger than what informally PCE suggests. However, so far that hasn’t been the case and there are nice examples supporting PCE suggesting that very simple and small non-trivial programs can easily reach universal computation. Such as recent (weak) small universal Turing machines discovered by Neary and Woods and particularly the smallest TM proven universal by Alex Smith (a 2-state 3-color machine that Wolfram conjectured in his NKS book). However PCE could be as hard to prove or disprove as the Church thesis is. Unlike Church’s thesis PCE could not be disproved by exhibiting a single negative case but proving that the distribution of machines is different to what PCE suggests. A positive proof however may require an infinite verification of cases which is evidently non-mechanically feasible (and only negating Church’s thesis itself one would be able to verify all the infinite number of cases).

I see PCE acting below the curve while Church’s thesis acting from above determining a computational limit (known as the Turing limit).

PCE and Church's thesis (C-T) diagram

Alex Smith has recently been able to prove that a Turing machine conjectured to be capable of universal computation by Wolfram was actually universal (Wolfram 2,3 Turing machine Research Prize).

Part of the challenge was to find an encoding not doing by itself the universal computation that would make the Turing machine universal. Smith succeeded providing an encoding providing a background that while nonperiodic is sufficiently regular to be generated by infinite word written on the tape can be generated by a ?-automaton (not itself universal).

This relaxation of the tape content has been regular in the cellular automaton world, but also in the field of what is called weak-universality with the only difference that the Turing machines are allowed to start with other than blank tapes (blank tapes are periodic tapes with period 1).

An objection might be that such a coupled system could turn a nonuniversal machine into a universal one, but Smith showed that his encoding was capable of restarting the computation itself, something that coupled systems usually are not capable of. In other words, the preparation of the tape in Smith’s case is done in advance and the ?-automaton do not longer interact in any further time, while to have nonuniversal machines to become universal usually requires an automaton intervening at every step (or every certain steps) of a computation.

One may also be surprised by the need of an ?-automaton for infinite strings. But the difference to the traditional blank tape is subtle. Think of how machines operate in the real world. Machines do not run on blank tapes, they usually do so over memory (the cache, RAM or a HD) with all kind of information (that is considered garbage if it is not instantiated by a running program). You may think that this garbage is not infinite, but it is not so a blank tape for a Turing machine, so instead of thinking of providing a Turing machine with blank tape as need it, one can think of providing the Turing machine with a non-blank tape. Now, what is on the tape in the case of Smith is not exactly “garbage” because it plays a role in “helping” the Turing machine to perform its computation, in a kind of support on which the Turing machine that is capable of universal computation actually achieves the computation with the help of a defined background (that doesn’t mean that the machine cannot perform universal with other backgrounds) yet the background is not powerful enough to perform the hardest part of the computation. In the physical world, if processes are seen as computations, computations are performed on a support, on the background of the physical world. So these kinds of relaxation may be closer to actual physical situations than abstract situations in which a blank tape for a computation is assumed or required.

The discussion opened up by Wolfram’s work and motivated by Smith’s answer has generated a fruitful and renovated discussion of universality and complexity of small Turing machines. This is why I think this research s relevant to modern computer science, and not only as an amusing mathematical puzzle:

• New techniques for proving universality are found (Alex Smith’s novel approach for unbounded computations from arbitrary lengths and non-periodic initial configurations).
• New universal models of computation have been discovered (cyclic tag- systems, bi-tag systems).
• Such research provides a better understanding of universality,  its limits, its  underlying principles and its necessary and sufficient conditions.
• It is a base for actually building universal devices when only a few elements can be used, e.g. in nanotechnology or molecular computation.
• Simple/small machines may be more easily/effectively embedded in other systems.
• The old discovery/invention duality question comes to the fore: It sheds light on how simple universality is, how frequently it occurs, whether  it is engineered or not, whether  one builds universal computation or finds it in the universe.
• It could shed light on the relative feasibility of  universal Turing machines based on different tape configurations (e.g. blank characters, repetitive words, non-repetitive with computationally simple backgrounds) as actual physical systems.  At present it is not at all clear why one ought to  favor blank characters over other possible real-world backgrounds, such as “noise.”
• Questions of size and complexity  arise: It would be interesting, for instance, to find out whether there is a polynomial (or exponential) trade-off between program size and and the concept of simulating a process.
• Some questions  on algorithmic complexity arise: Will the encoding always be more complex if the machine is simpler? All theorems in algorithmic information theory depend on additive constants, which depend on the sizes of typical universal Turing machines. What is the impact of different generalizations of universality on algorithmic complexity and what is the role of  encoding in such a measure?
• Some questions arise on the relation between several variants of universality definitions: Is there an effective and efficient encoding for each non-periodic encoding preserving universality? If so, how does this impact their complexity? Is there a non-periodic encoding with blank characters for each periodic blank word encoding, and what would the impact of such  an encoding be on the size/complexity of the Turing machine in question?

The field is active and still an important area of research. Several computer science conferences include talks on small computational systems such as Computability in Europe (CiE) and Machines, Computations and Universality (MCU) included such talks this year, focusing in particular on reversible cellular automata and universal Turing machines.

Here are some references from the small Turing machine community:

[1] Manfred Kudlek. Small deterministic Turing machines. Theoretical Computer Science, 168(2):241-255, November 1996.
[2] Manfred Kudlek and Yurii Rogozhin. A universal Turing machine with 3 states and 9 symbols. In Werner Kuich, Grzegorz Rozenberg, and Arto Salomaa, editors, Developments in Language Theory (DLT) 2001, vol. 2295 of LNCS, pp. 311-318, Vienna, May 2002. Springer.
[3] Maurice Margenstern and Liudmila Pavlotskaya. On the optimal number of instructions for universality of Turing machines connected with a finite automaton. International Journal of Algebra and Computation, 13(2):133-202, April 2003.
[4] Claudio Baiocchi. Three small universal Turing machines. In Maurice Margenstern and Yurii Rogozhin, editors, Machines, Computations, and Universality (MCU), volume 2055 of LNCS, pp. 1-10, Chisinau Moldavia, May 2001. Springer.
[5] Turlough Neary and Damien Woods. Four small universal Turing machines. Machines, Computations, and Universality (MCU), volume 4664 of LNCS, pp. 242-254, Orleans, France, September 2007. Springer.
[6] Yurii Rogozhin. Small universal Turing machines. Theoretical Computer Science, 168(2):215-240, November 1996.
[7] Shigeru Watanabe. 5-symbol 8-state and 5-symbol 6-state universal Turing machines. Journal of the ACM, 8(4):476-483, October 1961.
[8] Shigeru Watanabe. 4-symbol 5-state universal Turing machines. Journal of Information Processing Society of Japan, 13(9):588-592, 1972.
[9] Stephen Wolfram. A New Kind of Science. Wolfram Media, 2002.