Learning Breadth-First

[Kirby]

In between thinking about evaluating points to local go positions, I ran across the following blog post:

http://arigrant.com/blog/2013/2/10/brea ... t-learning

I kind of know the guy that wrote it, but I've been going back and forth as to whether or not I agree with him. In the past, I have tended to believe the opposite of what he preaches in the post above - to get really good at something, "depth-first" learning is the way to go.

And part of me still believes that. But I found the snippet at the bottom of the page quite interesting:

"Achilles and the Tortoise" is a reference to Zeno's paradox, the idea that if there are an infinite number of locations between here and there, how can one ever get there?

I'd argue: through breadth.

Zeno's paradox is something that I've thought to be amusing, but never really thought about it in a practical sense. But I can see the connection that's being made here to learning: is "motion" possible in a "purely" depth first learning methodology?

As intrigued as I am about this idea of breadth-first learning, it seems like it would lead to someone being "a jack of all trades, master of none".

Of course, this is of little relevance to me personally, since I am not much of a "master" at anything. Still, the article got me thinking.

Any thoughts?

[jts]

Zeno's paradox seems like the wrong idea. According to Zeno's argument, it's impossible to learn to say "Konniti wa", because after saying the first half of the phrase you have to say the next quarter of the phrase, and after that you need to say the next eighth of the phrase, and in the end you need to say an infinite number of fractions of the phrase (shock! horror!) which will of course take an infinitely long amount of time. This is a very silly paradox and clearly is no more relevant to breadth-first than to depth-first approaches.

(By the way - note my artful use of "of course" above - this is key to good philosophical analysis.)

[Kirby]

Zeno's paradox seems like the wrong idea. According to Zeno's argument, it's impossible to learn to say "Konniti wa", because after saying the first half of the phrase you have to say the next quarter of the phrase, and after that you need to say the next eighth of the phrase, and in the end you need to say an infinite number of fractions of the phrase (shock! horror!) which will of course take an infinitely long amount of time. This is a very silly paradox and clearly is no more relevant to breadth-first than to depth-first approaches.

(By the way - note my artful use of "of course" above - this is key to good philosophical analysis.)

It could be the case that Zeno's paradox does not apply here, but the explanation that you provided was a more direct interpretation of the paradox than what I imagined.

In particular, I didn't imagine splitting a phrase you are trying to learn into bits and pieces. Rather, I felt of it more like saying that you would never get anywhere with a pure depth-first learning approach.

To apply this to language, if you are trying to learn Japanese, for example, and the first phrase you are encountered with is "こんにいちは", with a depth-first approach, you might see the first character: こ. Then you might ponder, "I wonder what this character is." You could look it up, perhaps. Then there are various readings. You might take a look at the angle of the strokes in creating the character. Maybe you'd think of the history.

You could investigate very deeply about various aspects of this character, こ. And you are probably learning - something. But it's not anything that will get you closer to simply saying hello to a Japanese person.

In this sense, by not being able to get to "the core" of something you are trying to learn, and getting infinitely stuck into learning more and more detailed information, I feel similarities to Zeno's paradox - you don't get anywhere.

---

But like you said, maybe this does not apply. It's just that I feel that my interpretation was not as direct as the one you illustrated, and I thought I'd share.

[daal]

Zeno's paradox ... is a very silly paradox and clearly is no more relevant to breadth-first than to depth-first approaches.

Don't know if you read the article, but your comment: "This is a very silly paradox" in a way illustrates the point that the author is making, that while a depth-first approach would struggle to contradict a false argument, possibly employing calculus, a breadth-first approach, that the argument is silly because it cannot be true, is one that could be explained to a child.

[John Fairbairn]

Since we are talking philosophical analysis, that allows me, as I've always wanted, to begin: "Twenty-eighthly..."

Breadth-first gave us Renaissance Man. Breadth-first gives us those people who can lead and manage by calling on the nerds, who have gone depth-first, whenever greater precision is needed. Greater precision does seem to require depth-first.

Since that all seems too obvious, the next step, twenty-ninthly, is the interesting one: to what extent can breadth and depth be mixed? In go, it seems obvious to most of us some level of precision is necessary. But judging by chess, those who go for excessive depth alone fail to get to the very top (e.g. those who try to become like analytical machines). Those who add a bit of breadth by achieving some mastery of other aspects such as psychology, or who enlist the help of trainers and seconds, are those who can get to the very top. Maybe what Japanese go currently lacks is such breadth: e.g. the training aspect of the Chinese, or the team spirit and psychological mastery of the Koreans? (And maybe western go lacks both breadth and depth tout court?)

[jts]

Zeno's paradox seems like the wrong idea. According to Zeno's argument, it's impossible to learn to say "Konniti wa", because after saying the first half of the phrase you have to say the next quarter of the phrase, and after that you need to say the next eighth of the phrase, and in the end you need to say an infinite number of fractions of the phrase (shock! horror!) which will of course take an infinitely long amount of time. This is a very silly paradox and clearly is no more relevant to breadth-first than to depth-first approaches.

(By the way - note my artful use of "of course" above - this is key to good philosophical analysis.)

It could be the case that Zeno's paradox does not apply here, but the explanation that you provided was a more direct interpretation of the paradox than what I imagined.

In particular, I didn't imagine splitting a phrase you are trying to learn into bits and pieces. Rather, I felt of it more like saying that you would never get anywhere with a pure depth-first learning approach.

To apply this to language, if you are trying to learn Japanese, for example, and the first phrase you are encountered with is "こんにいちは", with a depth-first approach, you might see the first character: こ. Then you might ponder, "I wonder what this character is." You could look it up, perhaps. Then there are various readings. You might take a look at the angle of the strokes in creating the character. Maybe you'd think of the history.

You could investigate very deeply about various aspects of this character, こ. And you are probably learning - something. But it's not anything that will get you closer to simply saying hello to a Japanese person.

In this sense, by not being able to get to "the core" of something you are trying to learn, and getting infinitely stuck into learning more and more detailed information, I feel similarities to Zeno's paradox - you don't get anywhere.

---

But like you said, maybe this does not apply. It's just that I feel that my interpretation was not as direct as the one you illustrated, and I thought I'd share.

I hear what you're saying. My minor point would be that this doesn't have anything to do with Zeno's paradox - the whole point is that there is nothing paradoxical about the paradox. Zeno just didn't understand integration, so it's a bad example of "a way in which you can fail to get somewhere". (In fairness to Zeno, none of his own works survive, only summaries of the ideas he was best known for. It's possible that the paradox we now associate with his name was just a thought experiment to prime people for a more complex argument about motion.)

My bigger point is that both depth-first search and breadth-first search can fall prey to the sort of pettiness that you're talking about. You could insist on learning konniti wa by first learning the hiragana, and then the kanji that the hiragana are based on, and then the radicals that the kanji are made out of, and then the brass script pictograms that modern kanji are based on. Or you could insist on learning every phoneme exactly before saying the phrase. Or you could insist on learning every single greeting expression in the Japanese language at the same time. Or you could memorize a play in which the phrase "konniti wa" occurs. These are all ways of moving from a focus on a high priority to a focus on a low priority. I don't think that calling one type of pettiness breadth and the other depth, or one text and the other context, clarifies that much. I'm not saying that breadth-first search is actually wrong, just suggesting that no simple argument of the form "If you do X-first search, you can waste time doing low priority things" will distinguish between breadth and depth.

Daal - I don't think there's anything wrong with spelling out the problem with Zeno's paradox in mind-numbing detail to those who aren't familiar with how integration works. I'm just inclined not to be patronizing. It would have been rather pompous of me to just call the paradox silly and expect you to take it on authority. I only bought the right to call it silly by spelling out the three steps in the argument, which allows anyone who is unfamiliar with the proof to detect the problem.

[Bill Spight]

In between thinking about evaluating points to local go positions, I ran across the following blog post:

http://arigrant.com/blog/2013/2/10/brea ... t-learning

I kind of know the guy that wrote it, but I've been going back and forth as to whether or not I agree with him. In the past, I have tended to believe the opposite of what he preaches in the post above - to get really good at something, "depth-first" learning is the way to go.

And part of me still believes that. But I found the snippet at the bottom of the page quite interesting:

"Achilles and the Tortoise" is a reference to Zeno's paradox, the idea that if there are an infinite number of locations between here and there, how can one ever get there?

I'd argue: through breadth.

Zeno's paradox is something that I've thought to be amusing, but never really thought about it in a practical sense. But I can see the connection that's being made here to learning: is "motion" possible in a "purely" depth first learning methodology?

As intrigued as I am about this idea of breadth-first learning, it seems like it would lead to someone being "a jack of all trades, master of none".

Of course, this is of little relevance to me personally, since I am not much of a "master" at anything. Still, the article got me thinking.

Any thoughts?

You are not sure if you agree with the guy, I do not understand him. Maybe he is using search as a metaphor for the specialist-generalist distinction, I dunno.

His suggestion that breadth resolves the Achilles and the tortoise paradox only raises questions for me.

As far as go is concerned, go is solvable by depth first search. We're waiting.

[emeraldemon]

http://xkcd.com/761/

[Phoenix]

I'm currently in the process of grooming a beginner into a mid-SDK.

(It's going along really well, too)

Of course, you have to adapt to people's strengths and learning styles.

Originally, I had a 'set' course that I thought to teach by. I would introduce basic shapes, moves and techniques. Then move up to concepts in practical form. Generalized concepts. Go theory. Up and up. Actually, Go theory 101 is as far as I've got.

Turns out I've decided to chunk down from the very top instead. I'm introducing him to the idea of the direction of play, assuming influence, thickness, patient play, indirect approaches to goals, etc, organically. What I mean by 'organically' is that I'm gently getting him to play like a stronger player before he has learned the individual 'building blocks'.

I'm using 'good play' (relatively of course) as a launching pad to introduce him to Go concepts (aji, miai, furikawari, etc). Since these are (mostly) things you have to study through play, I gave him resources such as tsumego and tesuji problems, which he has learned to enjoy already, in order to give him the basis on which to figure out how to get from stones to result using these concepts.

I've also decided to get him to learn some joseki. He's a patterns guy, learned both main variations of the 3-3 invasion on the first try and clearly delineates between the straight 3-3 and the hoshi approach-pincer-invasion joseki. He learned two different refutations to the hane in that last one and has learned to identify (and counter) basic hamete.

I'm throwing at lot at him, but the idea here is that while I'm keeping the exercises within his strength range (and special aptitudes), he's getting very strong in a ludicrously small amount of time by learning top-down. There are clear gaps, and will be for a while, in the form of simple patterns of play, but his studies will bring him to those. At that point, he will know why he is playing them, and when.

That's the theory, anyway. So far it's working very, very well.

[Monadology]

I hear what you're saying. My minor point would be that this doesn't have anything to do with Zeno's paradox - the whole point is that there is nothing paradoxical about the paradox. Zeno just didn't understand integration, so it's a bad example of "a way in which you can fail to get somewhere". (In fairness to Zeno, none of his own works survive, only summaries of the ideas he was best known for. It's possible that the paradox we now associate with his name was just a thought experiment to prime people for a more complex argument about motion.)

In all fairness, Zeno had other 'paradoxes' and its questionable whether or not calculus successfully addresses even the one in question.

The risk of the breadth approach is of that someone has to do depth first for it to be at all possible for a surface-level analysis to even be accurate to the original topic. It is, therefore, dependent on taking much prior work for granted both practically and theoretically (since only through depth does one gain the capacity to question). Furthermore, in some areas more depth is required to really get a grasp on the basic concepts in the first place.

[marvin]

I like the artice very much and I agree with it(mostly). I belive it is important to have 'knowledge' from different areas to gain intuition.
Intuition ->idea ->theory-> then you make an experiment if possible.
Example: 2010 Nobel Prize http://en.wikipedia.org/wiki/Graphene