If infinity can be further divided in mathematics, then my question is significant for machine learning and understanding of learning. What is the closest point from unlearnability to learnability?.
Interesting question, and a creative approach to try solving it.
However, I think it would be more fruitful if you take your (understood) questions: "How can we teach the unteachable?" and "When (and why) do we get unteachable students?" and invert them: "At what stage does a person become unteachable?" and "Why did they become unteachable?". Then you can invert your answers to answer your (understood) questions. "At what stage and how was the damage done?" and "How to undo the damage that was done?" Sorry about my long sentence.
https://books.google.com.hk/books?id=Dg4Ww6cr8Y4C&pg=PA257&lpg=PA257&dq=unlearnability&source=bl&ots=M6V9jBD629&sig=pielOOkXcnYpoul4KjCDzi77iDk&hl=zh-TW&sa=X&ved=0ahUKEwilu7ONi9rVAhWMoJQKHbS5BMo4ChDoAQgZMAA#v=onepage&q=unlearnability&f=false
Dear Ian,
Thank you for your erudite comments, you are right, very interesting. I have thought it from a teaching learning perspective. I summarize yours and mine as follows
For teachers: Please answer the following
How can we teach the unteachable? The research topic of paper is Teach the unteachable.
When (and why) do we get unteachable students? and "At what stage does a person become unteachable?" and "Why did they become unteachable?".
For students and others,
How can we learn the unlearnable. The research topic of paper is Learn (learning) the unlearnable
When must we learn the unlearnable?
how can we change the unlearnable to learnable.
I have developed the latter three questions for for some time, the paper entitles Learn (learning) the unlearnable, which will be submitted for publication.
Dear Michael, thank you very much for your help with the reference. My summary for it is below
Solomon Marcus (1998) Contextual Grammars, Learning Process and the Kolmogorov-Chaitin Metaphor Preliminary Considerations, Report 213, Fachbreich der Informatik, Hamburg University, which has been published in the book of Word and Language Everywhere (known on 16 August 17), Marcus discusses unlearnability and its degree in terms of contextual grammars. However, our topic aims to focus on unlearnability in machine learning and education, please see my summary above here.
From learner's perspective, unlearnability degree of Marcus (1998) is meaningful, this will be decided by fuzzy logic, for example, using fuzzy logic, if the unlearnability degree of X approaches 1, then the learner does not learn X any more, if the unlearnability degree of X approaches 0, then the leaner likes to learn X.
Different from Markus (1998), we define unlearnability degree of X is in [0, 1] based on fuzzy logic.
Prof. Dr. Zhaohao Sun
2017-8-16
In my article on unlearnability, I have also classified unlearnability using classic set theory including set operations, For example, if x is not learnable by all the persons in the world in the past and now, then an average learner does not learn x any more. Therefore, unlearnability is with respect to individual, community, a country and the world, past and now and future. For example, if x is not learnable by all the persons and machines in the world by 2050, then the absolute majority of the people alive and machines have no interest in learning x any more. This kind of unlearnability is hard one. Currently machine learning has no interest in learning hard unlearnability. Machine learning only likes to learn what can be learnable and has commercial value if it has.
Prof. Dr Zhaohao Sun
2018-8-23
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