tag:blogger.com,1999:blog-8436330762136344379.post9198386304339066994..comments2018-09-20T08:08:24.946-04:00Comments on Metadata: Master your toolsMurathttp://www.blogger.com/profile/07842046940394980130noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-8436330762136344379.post-60526363672367809332018-04-22T23:22:19.667-04:002018-04-22T23:22:19.667-04:00In the process of tutoring classmates on mathemati...In the process of tutoring classmates on mathematics and computer science in my university, I've found that there is one tool I am constantly reminded of because I need to guide my classmates to use it: substitution.<br /><br />Substitution is the basic technique in proof construction and algebra. Years of programming and proof writing has made substituting variables a second nature for me, but witnessing the difficulty which my classmates have with the problems always intrigues me into attempts to better explain this principle. I believe I have been inspired by lambda algebra to develop such an intuition about substitution after all the experience, but lambda algebra is not taught to them so I cannot really use it to explain. Too many mistakes made in algebra comes from hacks taught to shortcut substitution. On the other hand, basic algebra laws are underutilized because substituting the name of a variable can totally throw off one's understanding of the properties of the variable. It also has implication in proofs. For example, when a universal instantiation is performed to instantiate a variable from the same set as the universal quantifier, failure to relate the instantiated variable and the universal quantifier is very common, and I've given up explaining the full formality of it.<br /><br />In computer science, parameter substitution is the necessary skill for writing abstractions such as functions. I was first led to lambda algebra by Haskell. But in the process of tutoring, I've found classmates struggling to keep track of variables and parameters as data flows from the scope of one function to another. A common mistake is to refer to a value passed into a function not by the parameter name declared in the function signature, but by the name of the variable passed in as the parameter. This is quite similar to the above failure of distinguishing an instance and the universal quantifier in proof writing.<br />YuFan Louhttps://www.blogger.com/profile/06338553350463365218noreply@blogger.comtag:blogger.com,1999:blog-8436330762136344379.post-59582376126162163702018-03-29T16:13:40.273-04:002018-03-29T16:13:40.273-04:00And SHU-HA-RI principle https://en.wikipedia.org/w...And SHU-HA-RI principle https://en.wikipedia.org/wiki/ShuhariNikitanoreply@blogger.comtag:blogger.com,1999:blog-8436330762136344379.post-70393765919368573552018-03-28T14:41:58.295-04:002018-03-28T14:41:58.295-04:00Hi Murat,
Just thought you might be interested t...Hi Murat, <br /><br />Just thought you might be interested to know (in case you didn't already). The 'three levels of learning' you write about map quite well onto the three levels of understanding that amateur Buddhist mediators are taught. For them it goes:<br /><br />1. Belief. Having been told something and believing it to be true. Essentially dogmatic.<br />2. Intellectual understanding. Knowing why your belief is true. Being able to express the reasons for it's correctness.<br />3. Experiential understanding. Having experienced the truth of your belief first hand. Better than 2) because no doubt can possibly exist.<br /><br />In case you didn't know, I thought you might like to see that your idea is backed up by ancient teaching. :)<br />Alex Parmentierhttps://www.blogger.com/profile/01015565886407394020noreply@blogger.com