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<h1 id="post-title">What is Learning</h1>
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<p><strong>Entry Question</strong>: What do we mean by “learning”?</p>
<hr />
<h1 id="why-so-long-son">Why so long, son?</h1>
<p>Based on some assumptions about my current reading speed, etc., we <a href="./Limits-on-Reading.html">saw</a> how many books I can possibly hope to study over the next 16 years.</p>
<p>The logical next question is: why does it take me so long to study a non-fiction book or a textbook?</p>
<p>If we can identify <em>exactly</em> why I’m not able to do it fast right now, then we can do something to ease those bottlenecks.</p>
<p>How will I know if I’ve got what I want from a textbook?</p>
<p>One quantitative measure is how well I do on the exam I’m studying for. This is a straightforward and reliable measure.</p>
<p>Another is to see whether I feel I “understand” the concepts after reading the textbook. How will I know if I have “understood” the concepts? Well, I should have gained <a href="./Truth-Predictive-Power.html">predictive power</a> about them. How that would feel from the inside would probably be that you can see how the system as whole works. You are able to see the equations or models governing all its behaviour. Of course, you could be wrong about how much you understand. You could be confused about the topic - you may not have much predictive power but think you do.</p>
<p>Let’s be concrete. If I’m trying to learn, say, the basic Principles of Economics, then I would want to be able to solve simple problems related to Supply and Demand, or Marginal Cost vs Average Cost, or Externalities, or something.</p>
<p>Before I studied the textbook, I was not able to solve these problems. Now I am.</p>
<h1 id="what-is-the-true-test-of-learning-a-concept-x">What is the true test of “learning” a concept X?</h1>
<p>Your <em>anticipations</em> in every relevant area should be constrained as per X.</p>
<p>So, if you’ve truly “learned” the concept gravity, not only must you be constrained to anticipate the correct answers in your physics exams, you must also expect two balls dropped from the top of the Leaning Tower of Pisa to hit the ground together.</p>
<p>If you’ve truly “learned” about evolution, you should be immensely surprised when people claim that the earth was created a few thousand years ago.</p>
<p>If you’ve truly “learned” about supply and demand, you shouldn’t be surprised to see people with rare and desired abilities make a lot of money.</p>
<p>This is what they mean by “learning to think like an economist”, or “learning to think like a scientist”, or “learning to think like a programmer”. When you study an economics textbook or lecture course, you shouldn’t just walk away with a bunch of facts and tidbits about “economics stuff”. You should walk away with the ability to see supply and demand in action around you in the real world. You should basically become an <a href="http://en.wikipedia.org/wiki/The_Undercover_Economist">Undercover Economist</a> (the awesome book that introduced me to the whole field of economics)!</p>
<p>Similarly, when you study science, you shouldn’t walk out with just some facts about gravity and the speed of light. You should be able to think about everything in terms of hypotheses and experiments.</p>
<h1 id="learning-anticipation-constraint">Learning = Anticipation Constraint?</h1>
<p>Assumption: What we learn are either hypotheses or evidence on which to update earlier hypotheses.</p>
<p>The textbook might call it a <em>theory</em> because there is an overwhelming amount of evidence to support it, but it’s a hypothesis nonetheless.</p>
<p>Yes, because the textbook is written for a human to read, it will include stuff like examples and analogies and comments and whatnot to keep the reader interested and clear in understanding. But, it’s about introducing hypotheses and predictions. It’s about getting the reader to the point where he has all the anticipation-constraints that the theory imposes.</p>
<p>So, either:</p>
<ul>
<li><p>The textbook will introduce a new hypothesis in a chapter</p>
<p>Could be one that does better than an earlier hypothesis - Einstein’s Theory of Relativity making better predictions than Newton’s Laws of Motion.</p></li>
<li><p>It might call attention to some non-obvious prediction that the hypothesis makes.</p>
<p>Some corollary that is useful somewhere</p></li>
<li><p>It might tell you about a commonly-used label for some hypothesis or prediction (like, “<em>this</em> is called Newton’s Second Law of Motion”)</p></li>
</ul>
<h1 id="research">Research</h1>
<p>What about research problems?</p>
<p>A research problem is perhaps a class of events for which you need correct predictions. None of the current hypotheses seem to be doing well over there. They must be making no useful predictions about that event. The ones that make wrong predictions are obviously thrown out. So, solving research problems is about coming up with hypotheses to cover events for which current hypotheses don’t make useful predictions - aka come up with a hypothesis that <em>explains</em> / predicts this particular phenomenon.</p>
<p>The solution is a hypothesis that is shown to be correct. However, the difficult thing there is in plucking the correct hypothesis out of a very large space of possible hypotheses.</p>
<p>It doesn’t have to be whole new hypothesis, maybe just a modification of an earlier one or a new part to be added.</p>
<hr />
<p>Hmmm… does this mean that learning is not only about constraining your anticipations based on the facts you’ve learned? Cos that probably won’t help you too much in searching for the correct hypotheses. But a person who has learned a topic <em>well</em> should be able to contribute such solutions.</p>
<p>Ok. That seems to be about <em>research</em>. That’s about coming up with the various theories on your own. You might aspire to this level if you’re deeply interested in the subject and want to learn it exceptionally well. But, for normal high levels of learning, making predictions from the hypotheses mentioned in the textbook should do.</p>
<p>So, the first milestone to hit would be to constrain anticipations in accordance with the new concepts (i.e., hypotheses) you have learnt. A later milestone would be to understand how it is that people in this field search for the right hypotheses.</p>
<p>Also, if I’m right here, then you would be able to do research only after you have a decent “grasp of the concepts” - when you can make most of the correct predictions from the existing hypotheses. This would be so because the new hypothesis that you discover in your research would have to make correct predictions for existing events. You have to draw a curve that goes through the existing points known to the field.</p>
<p>So, you can do research (aka discover better hypotheses) only after you’ve correctly understood the relevant anticipation-constraints based on the hypotheses (note that this is non-trivial - it’s hard to see all the implications of some theory).</p>
<p>So, our first aim is to make all the correct anticipation-constraints based on the hypotheses taught in the textbook.</p>
<h1 id="normal-problem-solving">Normal Problem-Solving</h1>
<p>Hypothesis: Maybe mathy textbooks are difficult to get through because they force you to discover hypotheses not just make predictions from standard hypotheses?</p>
<p>Not sure here. But in Economics, you have a model - supply vs demand, marginal returns, etc. - and you need to solve a problem by letting your hypothesis (the model) constrain your anticipations. You’re given a word problem and you have to infer the answer using the equations you’ve learned.</p>
<p>What about math in school? Wasn’t that also about having equations and then using those equations or rules to solve problems? Like using the rules of integration to solve integration problems? Or probability theory equations to solve word problems?</p>
<p>But they were still difficult to get through. You could make mistakes anywhere. And, in any case, it took time to get through all the problems. Hmmm… maybe they weren’t difficult, just time-consuming and error-prone because you weren’t too skilled at wielding those equations.</p>
<p>So, very mathy textbooks may take more time to get through than say an economics textbook because they have more theorems and rules and stuff (aka very complex hypotheses to keep in your mind) and thus make you commit a lot more errors and take a lot more time to search for the right rules to use (in the right order).</p>
<p>So, the hypothesis is wrong.</p>
<hr />
<p>Then what is the difference between research problems and textbook problems?</p>
<p>Hypothesis: To solve a textbook problem, you have to use the rules and corollaries and other results (aka the correct hypothesis) mentioned in the textbook to make predictions about an event - i.e., come to the solution.</p>
<p>Is there any difference at all? Aren’t they just problems? Isn’t a research problem just one that hasn’t been solved yet?</p>
<p>If there is a difference between the two, what are the differing predictions?</p>
<hr />
<p>Hmmm… so maybe the textbook problems are those events for which the hypotheses taught so far in the book will (somewhat obviously) constrain anticipations - aka give you solutions if you apply them.</p>
<p>Research problems are those for which the hypotheses known so far either don’t quite so obviously constrain anticipations or don’t constrain anticipations at all. Either the solution involves a very long (or non-obvious) chain of inference from the hypotheses known or the existing hypotheses don’t make any predictions about that event at all. In the second case, you would have to search out a new hypothesis that does.</p>
<h1 id="what-does-learning-mean">What does learning mean?</h1>
<p>What happens when we “learn something” or “have an insight”? Can we make that process more efficient somehow?</p>
<p>“Having an insight” means either thinking of a prediction made by your hypothesis that you hadn’t thought of earlier or thinking of a new hypothesis that makes the correct predictions for the evidence you have.</p>
<p>Learning something means learning of a new hypothesis that makes correct and useful predictions about interesting events.</p>
<p>Normal problem-solving is about making predictions (aka anticipation constraints) using the hypotheses given in the textbook.</p>
<p>Research problem-solving is about making predictions not made so far using known hypotheses.</p>
<p>Researching a new theory is about coming up with a hypothesis that allows you to make predictions (aka solve) a class of problems. Here, you would have to generate several hypotheses (maybe using your intuition) and updating on all the evidence you have.</p>
<p>Note: You could be confused about the research problem. In which case, you would neither be able to solve it using existing hypotheses nor generate new hypotheses.</p>
<hr />
<p>Note, though, that the human brain doesn’t work like an ideal inference engine. It can’t handle long chains of inference at one go. It has to cache intermediate results along the way or you’ll get lost.</p>
<p>So, learning is not just about learning the absolute fundamentals of a topic and saying that you will infer everything else from those building blocks. Not happening so easily. You need to either learn or discover some intermediate concepts - stuff that makes it easier for your limited brain to solve problems in the moment.</p>
<p>Learning = Make all the correct predictions based on the hypothesis and the intermediate results you have learnt</p>
<p>Also, don’t be <a href>confused</a> about any of the concepts. Keep yourself honest by actually testing out your Learning.</p>
<h1 id="past-knowledge">Past Knowledge</h1>
<p>How does Learning interact with past knowledge?</p>
<p>A person X who has prior knowledge of some subject will pick up a new topic faster than a stronger Y to the area, right?</p>
<p>Why is that?</p>
<ul>
<li><p>X could have the fundamentals in place and find it easy to place the intermediate or new hypotheses taught here.</p></li>
<li><p>For Y, the intermediate result might be floating. He won’t know of the fundamentals that necessarily imply the result.</p></li>
<li><p>So, Y won’t be able to make other predictions; for example, those that combine the new result and some earlier results.</p></li>
<li><p>X might have the other result more available in his memory and thus be able to make inferences faster.</p>
<p>The brain works by association and would have strengthened the new result for free because it is linked with known memories.</p>
<p>He might understand the new result’s position better and be able to make direct inferences from it faster because it is clearer in his mind.</p></li>
</ul>
<p>In other words, it pays to associate with existing memories. Leverage your brain’s mechanisms.</p>
<h1 id="learning-from-textbooks">Learning from Textbooks</h1>
<p>What does all the above theory say about learning from textbooks?</p>
<p>It says that the textbook is trying to tell you about:</p>
<ul>
<li><p>Problems</p>
<p>Classes of Events about which you need to make predictions</p>
<p>Maybe give concrete examples</p></li>
<li><p><strong>Facts</strong> about events.</p>
<p>Known outcomes for events. i.e., the evidence we have collected.</p>
<p>The correct hypotheses would have to explain all of this.</p></li>
<li><p>Labels for the facts, events, and hypotheses.</p></li>
<li><p>Solutions</p>
<p>The best hypotheses that people in the field have come up with.</p></li>
<li><p>Intermediate results</p>
<p>Various intermediate results so that you don’t have too difficult an inference chain from your hypothesis to the prediction about some event.</p>
<p>Or maybe even techniques for solving problems.</p></li>
<li><p>Worked-out problems</p>
<p>Events for which they show you how their hypothesis can be used to make predictions.</p></li>
<li><p>Exercise problems</p>
<p>So that you can deepen your grasp of the hypotheses and intermediate results and use them well</p></li>
<li><p>Make the results easy to absorb</p>
<p>Link the current results with earlier knowledge so that they become strong memories and can let you make fast inferences.</p>
<p>Build up the hypotheses slowly by giving motivating problems? Give a simpler hypothesis first so that they can understand it fully, and then move on to more complex cases.</p>
<p>Hmmm.. there’s this whole thing of “intuition”. What’s that? Somehow, it’s considered better to teach things so that they line up with students’ intuitions.</p>
<p>Follow much of the Brain Rules for fast learning (emotional touch, exciting, etc.).</p>
<p>Make them <em>succinct</em> and easy to remember. This is very important. Vast swathes of information are not helpful.</p></li>
<li><p>Spice</p>
<p>Stuff to keep you motivated - a graph or picture, a bit of humour, or some anecdote, etc.</p></li>
</ul>
<p>Note that even non-fiction general books should do more or less the same thing. Go a bit lighter on the practice problems and heavier on the spice.</p>
<h1 id="whats-the-big-deal">What’s the big deal?</h1>
<p>How are all these ideas about learning different from our usual notions?</p>
<p>How is this new theory different from even <em>my own</em> beliefs about learning earlier?</p>
<p>More to the point, what <em>new predictions</em> can I make after knowing this so-called “theory” of learning?</p>
<p>Well, the first thing is that people general won’t constrain their anticipation about subjects outside of their original context (exams or labs). The main surprising insight for me was: Learning is Anticipation-Constraint. If you have learned something, you should be able to make correct predictions about it in all areas that it governs. Your thinking about that field should be in line with the hypothesis (aka the main theory) you just learned.</p>
<p>Also, I think people (including me) don’t realize what the true rationale behind learning is. I think most people and I are <em>confused</em> about what we are supposed to do with the stuff in a textbook.</p>
<p>Sure, I mean, we all know that we want to “understand” the concepts and get good marks in the exam. But what does “understand” mean? How will you know if you’re doing well (apart from waiting for your exam results)? How can you improve on it if you don’t know how to judge it?</p>
<p>It’s ok to have the wrong idea about learning. You can still correct yourself quickly enough. But, when you’re confused, you have no hope. You won’t get better no matter how much evidence you get that your current learning process sucks.</p>
<h1 id="how-did-he-do-it-hes-a-genius">How did he do it?! He’s a Genius!</h1>
<p>The most dangerous consequence of being confused about the learning process is that you start seeing high performance as magical. There! <em>That</em> is the main problem I want to correct. We know that confusion makes you think of the subject as <em>inherently mysterious</em> and <em>unknowable</em>.</p>
<p>So, when you’re confused about how learning works, you start thinking that only those high-flying geniuses over there can do it. You don’t have to be a complete dumbass for this. Even if you perform at high levels, you can still look at people performing much higher and think that they’ve got something you’ve not. It’s not that they haven’t got. They have. The point is you have <em>no clue</em> what it is.</p>
<p>Waving your hands and saying “high intelligence” doesn’t help. It doesn’t pay any rent on its own. You need to be un-confused about the difference between them and you. You should be able to see the causal structure behind performance. You should be able to say, they are better than me <em>because</em> they are doing more of this and they have more of this skill and so on. It could be genetic (taller people will generally jump higher than you), it could be some skill they acquired, whatever. But you need to know <em>what</em> it is they’ve got going right.</p>
<p>You may even decide that you can’t keep up with them, maybe because the skill will take too much time to master and you have other commitments. But you have to know. You have to know that if you did X, Y, and Z, your performance would go up by this much. If you decide to improve your performance, you should have a pretty good idea of what to do.</p>
<p>Why can’t we achieve stuff comparable to what Einstein or von Neumann or whoever did? I’m not saying we <em>can</em> do what they did. Maybe the biggest limiting factor is some genetic component, maybe IQ or the size of your working memory or something. But the problem is that it seems completely mysterious to us. Something, something, something, and <a href="http://lesswrong.com/lw/ix/say_not_complexity/">then a miracle occurs</a>… and then he comes up with general relativity.</p>
<p>That is the main aim of this fledgling theory. I want to become un-confused about learning.</p>
<p>If I can start to see the causes behind high performance in learning, then I can do something about it. I can work hard to improve the necessary skills. I can eliminate all unnecessary crap from my learning process and do <em>only</em> those things that give me increased performance. Think about that - I’m pretty sure I do tons of things while studying that give me no Impact. Won’t it be useful to know that what you’re doing actually works?</p>
<p>Once we know what is really going on behind the scenes, we can enlist all kinds of tools and resources to help us amplify our performance. We can use computer programs to help us out with several parts of the process. We can optimize our writings to contain those things that will increase learning and cut out all the crap.</p>
<h1 id="the-proof-of-the-pudding">The Proof of the Pudding</h1>
<p>I’m making some pretty bold claims here. I’m claiming that we can improve our learning efficiency like hell. I’m also claiming that I have a hypothesis for a way to do that.</p>
<p>What is the best test of that?</p>
<p>Go and make it happen. Go learn some stuff incredibly fast (or, at least, much faster than usual).</p>
<p>All the theorizing will be useless if I don’t have a practical process that produces results at the end of it.</p>
<p>(to be continued)</p>
<hr />
<h1 id="appendix-testing-my-theory">Appendix: Testing my theory</h1>
<p>Notes on the chapter Obsessions from the book “What you can change and what you can’t” by Thalaivar Martin Seligman.</p>
<p>Let’s see what each paragraph does. I want to test whether my Learning Hypothesis predicts everything he is doing. If he does something important that the hypothesis doesn’t account for, then it is wrong. I need to replace it with a hypothesis that does explain the stuff.</p>
<ul>
<li><p>Jingle Channel - Evoke some past concept that you weren’t aware of. Or is this an event?</p>
<p>Event: What thoughts will you think subconsciously?</p>
<p>Some hypotheses that can explain the outcomes of that event - friend humming can change the music on your channel.</p></li>
<li><p><strong>Facts</strong> about events. Aka known evidence. The correct hypotheses would have to explain all of this.</p>
<p>Hard to change the channel</p>
<p>Earlier, Bible and other stuff was on the channel</p></li>
<li><p>Facts and labels</p>
<p>When thoughts about loss and hopelessness are dominant and recurrent -> person is “depressed”. The thoughts are “ruminations” or “automatic thoughts”</p></li>
<li><p>Humour. Keep me interested. (Motivation)</p></li>
<li><p>Event: Do I need clinical help? Hypothesis: Checklist of problems.</p></li>
<li><p>Label about a school of psychiatry - “biological psychiatrists”.</p></li>
<li><p>Event: How can OCD be cured? Hypothesis: OCD is a brain disease.</p></li>
<li><p>Evidence for the above Hypothesis (Wait, where’s the alternative hypothesis?!!!). He is trying to show us what our belief-level for that hypothesis should be.</p></li>
<li><p>Strong evidence against some hypothesis (Psychoanalysis and CBT don’t appear to give results on OCD)</p></li>
<li><p>Decent evidence about some hypothesis: Efficacy and side-effects of Anaframil for OCD.</p></li>
<li><p>Behavioural Hypothesis: People who are not good at distracting themselves or dismissing thoughts are most prone to OCD.</p></li>
<li><p>Evidence: This theory “fits” the subjective OCD experience very well.</p></li>
<li><p>Evidence from studies (aka scientific evidence)</p></li>
<li><p>Treatment table - intermediate results</p>
<p>Results or techniques in a succinct format so that you can easily hold it in your head.</p></li>
<li><p>Direct Philosophy - Direct Anticipation Constraint - That we have a jingle channel is a fact we cannot change. Accept it.</p>
<p>Event: Should you refuse to accept that you have a hard-to-change jingle channel?</p>
<p>Predicted Outcome: No. Accept it.</p>
<p>More precisely, if you resist it, you will come to harm. If you accept it, you will not harm yourself and will even have a chance to get better.</p>
<p>So, Event: Which action will be more beneficial? Refusing to accept it or Accepting it?</p>
<p>Predicted Outcome: Accepting it.</p></li>
</ul>
<p>The chapter contained problems (the events we care about - here, regarding OCD), evidence about what we’ve seen so far, labels for the different phenomena, different hypotheses for what causes OCD, and finally anticipation-constraints (predictions) about the different events.</p>
<p>One thing I had not predicted was the compression of information. At the end, Martin gave a table listing out his recommendations for the various therapies, summarizing his advice succinctly so that we can hold it in our head easily. Succinctness matters a lot. Have added this to my list of things that textbooks give us.</p>
<div class="info">Created: November 22, 2014</div>
<div class="info">Last modified: August 6, 2015</div>
<div class="info">Status: finished</div>
<div class="info"><b>Tags</b>: learning, anticipation constraint</div>
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