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I don't know. Is there really a massive benefit? The visual explanation of the Markov chains on that web site looks elegant and simple because... it is, i.e. it

I don't know. Is there really a massive benefit? The visual explanation of the Markov chains on that web site looks elegant and simple because... it is, i.e. it's not really a contribution of the visualization, it's because DTMCs are actually easy to understand. In a lecture, the teacher can easily simulate a Markov chain on a black board ("Now we are in this state, now we have to roll a die to decide whether we will go to state X or state Y"). Same for sealf-learners: In a book, you can tell the reader to start at some state X, roll a die, etc. Honestly, I find that the Markov chain website is an example how you should NOT do it. You are replacing the active intellectual process in the head of the student by some trivial animations with scrolling texts and jumping tokens which look nice and dynamic but...what are you learning? Of course, this doesn't mean that visualizations are useless, but they should be carefully designed with some learning goal in mind. Not easy! For example, the visualization could slowly gray out states that are not visited. In that way, the student could get a feeling for concepts like recurrence etc.

dyarosla 8y ago
Totally disagree. ‘Same for self-learners: In a book, you can tell the reader to start at some state X, roll a die, etc.’ -> This requires a learner to parse a procedure correctly AND understand how it relates to the topic. This is both doubly harder on the student and doubly likely to force a mistake (either in the procedure, interpretation, or both). Learning with an approach as given in the article approximately halves the work a learner must do, and increases the likelihood that the topic is correctly interpreted. Retention with this method, however, is a whole other matter- one that does correlate with the amount of mental effort required, but how much so is a matter of debate.
jinfiesto 8y ago
I both agree and disagree. I've always found an intuitive explanation like the OP to be helpful before diving into a more rigorous study of the material. It helps contextualize the things you learn subsequently.
ryeguy_24 8y ago
See my other comment below. If you could learn the same thing at the same level with less mental effort, isn't that a good thing? If the traditional teaching approach for Markov Chains required more intellectual effort, sounds like we've been explaining it poorly, no?
activatedgeek 8y ago
I probably understand where you are coming from. But, you are may be missing the point? > The visual explanation of the Markov chains on that web site looks elegant and simple because... it is I strongly resonate with this statement. However, I disagree with the claim the "You are replacing the active intellectual process". In fact, it is the opposite - it is stimulating. Let me present an anecdote which will perhaps resonate with many people. Often times, when venturing into a new topic, one tends to read the reference texts. Let us be frank - reference texts are not beginner friendly no matter how much they claim (they are reference for a reason). To get to the meat of the story, a reader has to hold lot of context from past knowledge. This is hard and often towards reaching the actual results, the reader is already exhausted. Instead, such intuitive visualizations provide context to a new reader. The next time the reader goes back to the reference text, this "lookahead" (from the visualization) is valuable. It is easier to internalize that where in the grand scheme of things a particular topic lies. > Of course, this doesn't mean that visualizations are useless, but they should be carefully designed with some learning goal in mind. Not easy! For example, the visualization could slowly gray out states that are not visited. In that way, the student could get a feeling for concepts like recurrence etc. This I believe is nitpicking.
- thanatropism 8y ago
  Your intellect can be "activated" in the pursuit of a superficial knowledge of Markov Chains to tell your boss or remember in the future that it might help you with problems. EZ-learning stuff will help you then. Or your intellect can be "activated" in the sense that further engaging it leads you to deeper, more general knowledge. Is this website doing it? I don't believe so.
mrlala 8y ago
> but...what are you learning? You are learning that there is a very simple and elegant way to create something like a realistic weather pattern. Just like the example, if you told most people to simulate the weather with 50% R or S, nearly all would create a loop which prints out S or R with 50% probability becuase they don't know any better. This extremely simple visual example opens your mind to how easy it can be to create some way more realistic and powerful. Most basic coders who didn't know what a markov chain is could easily setup a simulation after seeing this. >You are replacing the active intellectual process in the head of the student by some trivial animations with scrolling texts That is absurd. I guess you don't like people learning, do you?
mturmon 8y ago
"For example, the visualization could slowly gray out states that are not visited. In that way, the student could get a feeling for concepts like recurrence etc." You know, this is actually a good idea. As long as you didn't set any transition matrix elements to zero, the chain will have a stationary distribution that is given by the lead eigenvector of the transition matrix. If you gave each node a score when the chain passed through it, that eigenvector would manifest as the "score" accumulated by each node over a long period of time. This is one of the cool, deep properties of the chain - and it's not "insight-free" in the same way you describe. One of my favorite examples of this is the plinko game at the Museum of Math in NYC: https://www.youtube.com/watch?v=GBu0sfzrGTY https://www.youtube.com/watch?v=GBu0sfzrGTY It's a physical manifestation of the central limit theorem, realized by a series of balls that can go either right or left in a random walk downwards. You can even adjust the bias on the left/right choice to supply drift to the random walk. The mass of balls that accumulates in the bottom is a histogram representation of the associated limiting Gaussian curve. Very cool.
florabuzzword 8y ago
I don’t think I agree, but ultimately only feel comfortable speaking for myself. I’m fairly new to programming so would be interested in hearing if someone else does this too... On a walk this afternoon (for some reason), I realized I had a visual shape in my head for most design patterns. Some of them look a lot like a knot-tying diagram, for example. I’m not sure I had realized that before. I also realized the shape representations are about as close to implementation as I would prefer to store design patterns in my mind. Beyond that, they might be limiting or, at worst, strenuous to use as guidelines. They’re surely more useful (to me) than UML or even code. But the best part is I can tell they’ve been there all along. I wasn’t trying to make them up. I was just mapping out a project while on a walk. I was pretty relaxed at the time and maybe that’s why this came up. For what they are, I was a little disappointed how long it took to parse the Elements of Reuseable OO Software book when I was just learning to code. And then when I had used the patterns and knew them, I found it a bit sad they were communicated through such rigid forms. Art actually contends with the same sort of conceptual divisions. There’s the medium which is rigid and cumbersome, the form which is more pure, critical in the abstract but medium-agnostic, and the application, being the interface or the thing out in the world. So I do agree the ability to transpose these concepts between form and implementation is what matters, but it’s the back and forth that matters, not where one begins.
throwawayjava 8y ago
This disagreement demonstrates why professional teachers are so valuable. Sometimes the material is important enough that you want to make it as easy to understand as possible. Sometimes the material is a chance to teach your students how to problem solve. Or how to teach themselves new material. Or to help them become mathematically literate (i.e., able to read a book or paper on their own without your help). A good course/curriculum does both. Some definitions are carefully explained at an intuitive level so that students can struggle with things beyond the defintion. Sometimes the definition is an opportunity to teach students how to go from a formal definition of an intuitive understanding. Or come up with extensions to the definition on their own. Or explore the implications of a definition on their own. In short, are you teaching the definition of a Markov Chain as key content knowledge, or is this being presented as an exercise in mathematical creativity and mathematical problem solving? There is no "right" answer without more context; a good course will do the former with some topics and the latter with others. So this is not a topic-level question. It's a course-level or curriculum-level question. Interestingly, misunderstanding the fundamental tension between "explain well" and "teach people how t learn for themselves" is the source of many public debates on education. E.g., common core Mathematics. Are we teaching students how to add numbers or how to problem solve? Well, ideally both... but the debates always become an either/or.

dyarosla 8y ago

Totally disagree. ‘Same for self-learners: In a book, you can tell the reader to start at some state X, roll a die, etc.’ -> This requires a learner to parse a procedure correctly AND understand how it relates to the topic. This is both doubly harder on the student and doubly likely to force a mistake (either in the procedure, interpretation, or both). Learning with an approach as given in the article approximately halves the work a learner must do, and increases the likelihood that the topic is correctly interpreted. Retention with this method, however, is a whole other matter- one that does correlate with the amount of mental effort required, but how much so is a matter of debate.

jinfiesto 8y ago

I both agree and disagree. I've always found an intuitive explanation like the OP to be helpful before diving into a more rigorous study of the material. It helps contextualize the things you learn subsequently.

ryeguy_24 8y ago

See my other comment below. If you could learn the same thing at the same level with less mental effort, isn't that a good thing? If the traditional teaching approach for Markov Chains required more intellectual effort, sounds like we've been explaining it poorly, no?

activatedgeek 8y ago

I probably understand where you are coming from. But, you are may be missing the point? > The visual explanation of the Markov chains on that web site looks elegant and simple because... it is I strongly resonate with this statement. However, I disagree with the claim the "You are replacing the active intellectual process". In fact, it is the opposite - it is stimulating. Let me present an anecdote which will perhaps resonate with many people. Often times, when venturing into a new topic, one tends to read the reference texts. Let us be frank - reference texts are not beginner friendly no matter how much they claim (they are reference for a reason). To get to the meat of the story, a reader has to hold lot of context from past knowledge. This is hard and often towards reaching the actual results, the reader is already exhausted. Instead, such intuitive visualizations provide context to a new reader. The next time the reader goes back to the reference text, this "lookahead" (from the visualization) is valuable. It is easier to internalize that where in the grand scheme of things a particular topic lies. > Of course, this doesn't mean that visualizations are useless, but they should be carefully designed with some learning goal in mind. Not easy! For example, the visualization could slowly gray out states that are not visited. In that way, the student could get a feeling for concepts like recurrence etc. This I believe is nitpicking.

thanatropism 8y ago
Your intellect can be "activated" in the pursuit of a superficial knowledge of Markov Chains to tell your boss or remember in the future that it might help you with problems. EZ-learning stuff will help you then. Or your intellect can be "activated" in the sense that further engaging it leads you to deeper, more general knowledge. Is this website doing it? I don't believe so.

mrlala 8y ago

> but...what are you learning? You are learning that there is a very simple and elegant way to create something like a realistic weather pattern. Just like the example, if you told most people to simulate the weather with 50% R or S, nearly all would create a loop which prints out S or R with 50% probability becuase they don't know any better. This extremely simple visual example opens your mind to how easy it can be to create some way more realistic and powerful. Most basic coders who didn't know what a markov chain is could easily setup a simulation after seeing this. >You are replacing the active intellectual process in the head of the student by some trivial animations with scrolling texts That is absurd. I guess you don't like people learning, do you?

mturmon 8y ago

"For example, the visualization could slowly gray out states that are not visited. In that way, the student could get a feeling for concepts like recurrence etc." You know, this is actually a good idea. As long as you didn't set any transition matrix elements to zero, the chain will have a stationary distribution that is given by the lead eigenvector of the transition matrix. If you gave each node a score when the chain passed through it, that eigenvector would manifest as the "score" accumulated by each node over a long period of time. This is one of the cool, deep properties of the chain - and it's not "insight-free" in the same way you describe. One of my favorite examples of this is the plinko game at the Museum of Math in NYC: https://www.youtube.com/watch?v=GBu0sfzrGTY https://www.youtube.com/watch?v=GBu0sfzrGTY It's a physical manifestation of the central limit theorem, realized by a series of balls that can go either right or left in a random walk downwards. You can even adjust the bias on the left/right choice to supply drift to the random walk. The mass of balls that accumulates in the bottom is a histogram representation of the associated limiting Gaussian curve. Very cool.

florabuzzword 8y ago

I don’t think I agree, but ultimately only feel comfortable speaking for myself. I’m fairly new to programming so would be interested in hearing if someone else does this too... On a walk this afternoon (for some reason), I realized I had a visual shape in my head for most design patterns. Some of them look a lot like a knot-tying diagram, for example. I’m not sure I had realized that before. I also realized the shape representations are about as close to implementation as I would prefer to store design patterns in my mind. Beyond that, they might be limiting or, at worst, strenuous to use as guidelines. They’re surely more useful (to me) than UML or even code. But the best part is I can tell they’ve been there all along. I wasn’t trying to make them up. I was just mapping out a project while on a walk. I was pretty relaxed at the time and maybe that’s why this came up. For what they are, I was a little disappointed how long it took to parse the Elements of Reuseable OO Software book when I was just learning to code. And then when I had used the patterns and knew them, I found it a bit sad they were communicated through such rigid forms. Art actually contends with the same sort of conceptual divisions. There’s the medium which is rigid and cumbersome, the form which is more pure, critical in the abstract but medium-agnostic, and the application, being the interface or the thing out in the world. So I do agree the ability to transpose these concepts between form and implementation is what matters, but it’s the back and forth that matters, not where one begins.

throwawayjava 8y ago

This disagreement demonstrates why professional teachers are so valuable. Sometimes the material is important enough that you want to make it as easy to understand as possible. Sometimes the material is a chance to teach your students how to problem solve. Or how to teach themselves new material. Or to help them become mathematically literate (i.e., able to read a book or paper on their own without your help). A good course/curriculum does both. Some definitions are carefully explained at an intuitive level so that students can struggle with things beyond the defintion. Sometimes the definition is an opportunity to teach students how to go from a formal definition of an intuitive understanding. Or come up with extensions to the definition on their own. Or explore the implications of a definition on their own. In short, are you teaching the definition of a Markov Chain as key content knowledge, or is this being presented as an exercise in mathematical creativity and mathematical problem solving? There is no "right" answer without more context; a good course will do the former with some topics and the latter with others. So this is not a topic-level question. It's a course-level or curriculum-level question. Interestingly, misunderstanding the fundamental tension between "explain well" and "teach people how t learn for themselves" is the source of many public debates on education. E.g., common core Mathematics. Are we teaching students how to add numbers or how to problem solve? Well, ideally both... but the debates always become an either/or.