#heuristics

that is what I did every time I was bored when I was about 7

(for who don't know what this is check this)

I calculated how many patterns of this closed circuit could have (which I failed because I soon realised there are a LOT of patterns and brute force attack won't be really effective)

Upon further research, I found out:

There are actually over 26 trillion closed Knight’s Tours on the standard 8×8 board.

26,534,728,821,064 closed tours 13,267,364,410,532 unique ones (since each closed tour can be rotated or reflected)

The rule that is used to calculate this is Warnsdorff's rule.

You’re on a square. The knight has a few options. Warnsdorff says "Look ahead. Count how many valid moves each option has. Pick the one with the least future freedom."

Why?

Because if you don’t, you’ll trap yourself later. It’s basically the knight saying “Let me first visit the squares that are hardest to reach later.”

Does it always work?

Nope.

But on an 8×8 board, starting from most squares, Warnsdorff’s Rule tends to find a complete tour. With a good tie-breaker strategy, it works almost every time.

Why does it seem to work so well?

Because the knight’s mobility varies across the board:

Corners have only 2 possible moves

Edges have 3–4

Centre can have up to 8

Warnsdorff’s Rule pushes the knight away from the highly-connected centre and into the periphery early, clearing the hard-to-reach squares while it’s still possible to get out.

Is there a formal proof of its correctness? Nope.

Warnsdorff proposed the rule in 1823, but:

There’s no general proof that it always yields a knight’s tour

It’s a heuristic, not a theorem

It just works a lot, not always

Mathematicians have studied why it often works, but they’ve also shown counterexamples where it fails. And I was able to find one too.

Let’s consider the 8×8 board, starting at sq(0, 0), the top-left corner.

If you apply Warnsdorff’s Rule naively with no tie-breaking, it fails. It gets stuck before completing the tour. The knight ends up in a dead-end after only 60-ish moves, unable to legally finish the tour.

Why does it fail? Because when multiple candidate squares have equal minimal onward moves, the rule just picks one arbitrarily.

If your tie-breaking is dumb (say, you always pick the first one in the list), you might:

Burn the escape routes early

Leave an isolated square that’s now unreachable

So even though each step looks optimal locally, the knight unknowingly walks into a trap.

The Power and Pull of Nostalgia

My first diary post this week focused on visual trends in the future. For the second, it's worth pointing out that the visuals of the past also have strong pull and influence. Trends are cyclical. Nostalgia and a yearning for the past hold great power.

Me (originally at @fierceawakening) in the previous morality-tangential discussion post:

To be sure, I've indeed never seen a "one thought too many problem" and was also unable to locate one on a short lookaround (…)

@notthedarklord42 helps out (thanks!):

I was curious, and found it easily, so, while as you say I won’t turn it into a discussion, I will cite [from the Stanford Encyclopedia of Philosophy]:

Similarly, if I need to choose between saving my drowning wife and saving a drowning stranger, it would be “one thought too many” (Williams 1981) for me to calculate the consequences of each act. I morally should save my wife straightaway without calculating utilities.

I can heartily agree with this; but then this is an argument against utilitarianism, not consequentialism. This is literally about wanting to avoid the real-world scenario, i.e. consequence, where our wife would drown! We don't want to increase the risk of this by spending too much effort on pondering about morality!

Strictly speaking even this is inexact. It's really an argument against "robot utilitarianism": the moral philosophy where you have to calculate your actions' expected utility from first principles every time. But then this is a strawman of utilitarianism. Humans do not have the ability to follow robot utilitarianism and have to rely on heuristics. Even if we did try to reduce morality to some sort of a utility function, following it heuristically instead of trying to calculate utilities on the spot will, in fact, produce the greater utility.

I do not advocate or condone abandoning heuristics! I only call for recognizing them as heuristics, not reifying them as "virtues" etc. Though it might even be useful to still continue calling them "virtues"… this is kind of what I believe virtues, as pursued by humans in the real world, should be actually thought of as: social technologies for seeking choices that would align with their values.

Also, don't take just my word for it, as a mere consequentialist-but-not-utilitarian. Here's notable local Actual Self-Described Utilitarian blogger @theunitofcaring making the same point about the folly of robot utilitarianism already in a post from 2015:

A very naive utilitarian might say 'ah, the utilitarian thing to do is to speed every time except when you’ll get caught, whereas those deontologists will tell you to never speed’. Except I don’t know which times I’ll get caught, and as long as there’s a substantial risk of it, the actual utilitarian thing to do is to compare the risk of getting caught to the benefits and come up with a rule to follow consistently. If 'speed whenever I feel like I can get away with it’ turns out to do worse than 'don’t speed’, DON’T SPEED. (…) If following the rule every time results in better outcomes than following the rule sometimes, then the utilitarian thing to do is to always follow the rule.

A bit further towards the source, this is likewise spelled out also by Notable Utilitarianist Demagogue Eliezer Yudkowsky; e.g. in When Not To Use Probabilities from 2008. Noted, indeed, also for already embracing the terminology of virtues despite his rejection of virtue ethics the philosophy.

Maybe there are actually people who do try to follow robot utilitarianism, necessitating posts like these. I don't think they're setting the general tone of consequentialist moral philosophy, though. Certainly they're not the typical brand I ever run into… though of course, most of these are people downstream of Yudkowsky anyway.

(On which topic, I suspect that variations of his "Virtue of Perfectionism" are a decent part of what people who think there is a pressing need to counter Robot Utilitarianism are actually running into. It is indeed a virtue that I for one would reject as stated. As per the thread that started off this discussion, in a world of too much knowledge to learn it all, we are constantly required to be content with answers that are almost right. Pretty often the most we might have time for is the knowledge how and where an answer that is more correct might be found but not its actual possession.)

–––

Also it's kind of ironic that my core argument against either deontology or virtue ethics is likewise that they prescribe way too much effort on pondering about morality — which is to say, on the morality of things that don't actually bottom out to any real-world consequences. Other people are free to believe that thoughtcrimes are real and worrisome if they so desire; but in a civil society of freedom of opinion and religion, I reject this idea and refuse to be bludgeoned into entertaining it by appeals to authority. You have to actually make an argument for why I should care.

Honestly, i don’t remember the last time i had to stay focused for so many hours XD However we had the chance to get several breaks during the day which helped a lot (thanks Nevan!)

Despite the ongoing situation (covid-19) I decided to attend the lesson directly in the Campus; here I was able to meet in person other 2 classmates and honestly, going was the best choice! We were able to interact and helping each other even during the lesson and without interrupting others. I was really glad to see I was not the only one going, although, even if I would have been alone, I saw that it is easy to socialise with other members of the Campus, there is a very nice atmosphere there!

Already in the first day, we faced some challenges and worked in teams to analyse different aspects, for example: - taking in consideration the “Double Diamond” model, we had to try to identify differences between the meaning of divergent and convergent in respect of the Design Thinking process. - choosing a website, and from it analysing the Strong and the Weak points in relation to the 10 Heuristic Principles. All this under the pressure of a time limit, which sometimes was definitely not enough; however, managing time will be something very essential to learn.

Overall I can say it was definitely a positive experience, and since we already got the first project to deliver by the end of this week, I am really curious to see how me and my mates will manage the time and the anxiety by delivering a good project under a specific deadline. Let’s see...

Whenever I hear about what is arguably the best way to read manga online that supports the manga industry in North America, I usually get one answer - Viz’s Shonen Jump app. The app is promoted by almost all manga industry/press/bloggers/podcasters in the West as THE option to read manga legally.

The Shonen Jump app has almost every series from the Japanese version of Jump along with a few other Jump titles published in other Jump-related magazines. They come out the same release day as the magazines do in Japan. You get all of this for about $2 a month.

It’s an amazing deal and yet I’m somewhat concerned about Shonen Jump being treated as the answer to satisfy one’s digital manga needs.