Yes, I am speaking about Scott Aaronson’ post “Zork’s bloogorithm“, which comes after his excellent “Happy New Year! My response to M. I. Dyakonov” (with an outstanding and funny list of comments, a very good read).

In order to avoid any misunderstanding, here is the structure of the post. Readers may go directly to the part which is more interesting, according to personal preferences.

- Proof that Scott’s argument is counterfactual thinking, (dry, not funny)
- Steampunk and the belief in universal mathematics, (funny hopefully, but controversial)
- My innocent opinion on QC. (?)

Here is the argument which I claim is counterfactual:**Proof that Scott’s argument is counterfactual thinking.**

Let me put it this way: if we ever make contact with an advanced extraterrestrial civilization, they might have three sexes and five heads. But they, too, will have encountered the problem of factoring integers into primes. Indeed, because they’ll inhabit the same physical universe as we do, they’ll even have encountered the problem of simulating quantum physics. And therefore, putting the two together, they’ll almost certainly have discovered something like Shor’s algorithm — though they’ll call it “Zork’s bloogorithm” or whatever.

This passage can be put in the following form:

- Aliens inhabit the same physical universe as we do
- We encountered the problem of simulating quantum physics
- Therefore the aliens almost certainly have discovered something like Shor’s algorithm — though they’ll call it “Zork’s bloogorithm” or whatever.

This is counterfactual because in this world we don’t know if aliens exist, therefore we cannot make from this an argument for the fact that quantum computing is one of those ideas so strong because they are unavoidable on the path of understanding the universe. Mind you, it might be so or not, but “Zork’s bloogorithm” argument does not hold, that’s my point here.

**Steampunk and the belief in universal mathematics.**

Preceding “Zork’s bloogorithm” argument is the belief of Scott (and many others) that (boldfaces are mine):

How do I knowthat the desire for computational power isn’t just an arbitrary human quirk?Well,

the reasonI knowis that, and computation is nothing more or less than the mechanizable part of solving math problems.mathisn’t arbitrary

To this, bearing also in mind that the argument by aliens is counterfactual, I responded

By the same argument steampunk should be history, not alternative history.

Read also Vadim #47 and Scott #49 comments, which fail to notice that steampunk, as the argument by aliens of Scott, are BOTH examples of counterfactual thinking.

To this, I pretended to be an alien and responded (comment #52 still in limbo, awaiting moderation):

…let’s take the first line from the wiki page on steampunk: “Steampunk is a sub-genre of science fiction that typically features steam-powered machinery, especially in a setting inspired by industrialized Western civilization during the 19th century.”

Now, as an alien, I just extended my tonsils around the qweeky blob about hmm, let me translate with gooble: “alternative reality based fiction on the past 5^3 years greatest idea”, and it tastes, excuse me, reads, as:

“Turinkpunk is a sub-genre of science fiction that typically features computing machinery, especially in a setting inspired by industrialized Western civilization during the 20th century.”

[I localised some terms, for example 1337=industrial Western civilization and OMG=20th century]

(Funny, right?)

Besides arguing about thinking fallacies, what do YOU think, is math arbitrary, i.e. a cultural construct, or is it unavoidable? I think that it is a construct, contrary to many, for example I think that euclidean geometry is based on viral pythagorean ideas (see the posts about gnomons everywhere here and here), that curvature is a notion yet not completely understood and culturally charged, and that the Baker-Campbell-Hausdorff formula is still too much commutative, to give three examples.

**My innocent opinion on QC.**

*I* am completely outside of the QC realm but, in order to disperse any misunderstanding, here is what I think about quantum computation.

First of all I believe that the research around the idea of computation is so profound that it represents the third great advance in the history of humankind, after the ancient greek philosophers and Newton (and founding fellows of the Royal Society).

As a part of this, quantum computation is a natural thing to explore. I believe that at some point there will be constructed a device which everybody will agree to call it a quantum computer.

But, being an optimistic person, I don’t believe that the Turing machine is the last great idea in the history of humankind (hence the comparison which I made between steampunk and those arguments for QC, by saying that steam engines were the greatest idea of the industrial revolution, but not last great idea, so let’s not assume now that QC is the last great idea).

Arguments that there is life after computation are to be found in the life sciences, where mysteries abound and computation-based ideas are ineffective. Available mathematics seems ineffective as well, in stark contradiction with the well known old opinion on “The unreasonable effectiveness of Mathematics in the Natural Sciences“.

This is not meaning as an appeal to use magic instead mathematics, but is only a sign that many more new mathematics (and computation) ideas await us in the future, to be discovered.

It would be counterfactual, if it were the case that we know aliens don’t exist. But the previous sentence might itself be counterfactual, since aliens might very well exist. It’s just a prediction by Scott (which will be verified of falsified the day we meet the aliens ^^), and I must say, I completely agree with him. And even if it were the case that his hypothesis is counterfactual (note that this sentence IS counterfactual ;)), that still by itself doesn’t invalidate his reasoning. Thought experiments have their value, after all.

Thanks for stressing the point of ineffectiveness of mathematics, particularly when it comes to life. I completely agree that math is still strongly culturally bound and by no means universal. Referring to the inevitable 😉 Wittgenstein we could say that, since logic is necessarily transcendent, math is always bound to cultural limits, even if we once will understand that there many sorts of math, just depending on the initial belief set (called self-evidence, axioms or whatsoever)

I do not agree however with your point that math is something that is being discovered. Precisely due to necessary to instantiate (any kind of) logic and this instantiation is dependent on the Form of Life, the interesting part of math is always sth that is invented.

Regarding your optimism about QC: again with Wittgenstein, QC-supporters do not understand that the basic setup of quantum worlds is not compatible with the central axiom of contemporary math, that is identifiability and atomism. It is a different game. Trying to use QC to solve math problems is like trying to play “journey to Jerusalem” on a chess board (or vice versa).

In math and Turing-computing we find identifiability and atomism, i.e. ultimately a representation of causality, in the quantum world we are faced with the need for decoherence, uncertainty principle, coupled states, particle/wave dualism and micro-reversibility, that is i.o.w., a representation of information. (in much more detail: http://theputnamprogram.wordpress.com/2011/10/20/information-causality/ and http://theputnamprogram.wordpress.com/2011/10/28/non-turing-computing/)

Maybe, there are tasks or problems where we once could meaningfully apply QC, but these tasks have not been found yet. Certainly, however, we will never be able to use QC to get “results”, to get sth calculated, since any result, even intermediate ones, are already again part of the identifiability game. So I would say that the probability for meaningfulness of QC is rather low.

I would rather predict the convergence of quantum-based systems, non-turing-computing and the development of machine-based episteme, i.e. true understanding. Yet, that’s nothing that could not be simulated on digital computers. Such, there is no principal difference, it is just one of speed (which is nonetheless an important difference).

cheers

Re: “ineffectiveness of mathematics”, this is a view hold by Gromov, for example, as far as I understand at least. More specifically, the mathematics needed for understanding big data is not yet invented, be it about how a big protein unfolds, about how a cell or about how our vision system works. This is not meaning that mathematics will be ineffective forever, but it means that probably we need a new frame. To make a comparison, it is like physics before Newton and Leibniz. Without differential calculus, it is just a vast collection of particular data. As many people remark, we know all about the fundamental principles (or almost, there is always a possibility of something new to appear), but this is not sufficient for understading the behaviour of even moderately large systems made by parts which function according to said principles (for example a protein).

Re: QC, I am not qualified enough to have opinions to share, others than it looks fascinating to try to understand, model and experiment.

Re:computation in general, I am barely more competent, but in some sense this is mathematics combined with models of nature, which falls within my experience. From this experience I find very hard to believe that the “extended Church-Turing thesis” makes even sense as a formulation, although the Church-Turing thesis looks as strong as possible.

To close with an example of mine of counterfactual thinking, who knows, maybe if Turing would have lived more, he would have formulated a “living Turing machine”. But that’s not proof of anything.