<story><title>Notation as a Tool of Thought (1979) [pdf]</title><url>https://www.eecg.utoronto.ca/~jzhu/csc326/readings/iverson.pdf</url></story><parent_chain></parent_chain><comment><author>abainbridge</author><text>I think this is a fascinating subject that touches on how human general purpose intelligence works. I&amp;#x27;ve spent decades working with C like languages and by now I find them hugely helpful thinking tools.&lt;p&gt;I did some optimization work on a bilinear bitmap upscaler recently [1]. There were times in the middle of that work where I felt like I was sitting watching someone else do it for me. Not physically watching, but more like a part of my brain was doing it automatically. The amount of state in scope at once is too big to fit into my working memory (maybe I&amp;#x27;m weak at this), so the work has to be symbolic manipulation. It feels like there are patterns in the symbol manipulation that my brain can do with minimal effort. Somehow the result is that I can write (hopefully) correct code that is beyond my ability to comprehend without the notation. The fact that I don&amp;#x27;t understand how I understand it contributes to the feeling that someone else wrote it for me.&lt;p&gt;The problem I have looking at APL is that it doesn&amp;#x27;t look like it would help with this kind of work. The examples in the paper are all mathematical and abstract. I&amp;#x27;d like to see some real-world practical examples, where performance matters, IO is fiddly and memory layout is part of the API. And instead of the problem domain being &amp;quot;differentiating a polynomial&amp;quot;, I&amp;#x27;d rather it was decoding the Huffman data out of a JPEG, or implementing a video game&amp;#x27;s collision detection system. My feeling is that C like notations are better for that type of thing. Maybe that isn&amp;#x27;t what APL is supposed to be good at. However, the paper starts by saying APL is needed because maths notation is not universal.&lt;p&gt;[1] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;stackoverflow.com&amp;#x2F;a&amp;#x2F;69633678&amp;#x2F;66088&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;stackoverflow.com&amp;#x2F;a&amp;#x2F;69633678&amp;#x2F;66088&lt;/a&gt;</text></comment>
<story><title>Notation as a Tool of Thought (1979) [pdf]</title><url>https://www.eecg.utoronto.ca/~jzhu/csc326/readings/iverson.pdf</url></story><parent_chain></parent_chain><comment><author>narush</author><text>Cool paper - thanks for posting! I love the typesetting of the math in these old papers - I have no idea how it was done, but it&amp;#x27;s ~good vibes~ for me.&lt;p&gt;If you&amp;#x27;re interested in reading a more recent take on notation, check out this post [1] by Terence Tao on MathOverflow. It&amp;#x27;s pretty cool, and a shorter read than this PDF - if you&amp;#x27;re in a rush.&lt;p&gt;While I&amp;#x27;m posting overflow questions I like, check out this gem [2] on parsing HTML with a regex.&lt;p&gt;[1] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;mathoverflow.net&amp;#x2F;questions&amp;#x2F;366070&amp;#x2F;what-are-the-benefits-of-writing-vector-inner-products-as-langle-u-v-rangle&amp;#x2F;366118#366118&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;mathoverflow.net&amp;#x2F;questions&amp;#x2F;366070&amp;#x2F;what-are-the-benef...&lt;/a&gt;&lt;p&gt;[2] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;stackoverflow.com&amp;#x2F;questions&amp;#x2F;1732348&amp;#x2F;regex-match-open-tags-except-xhtml-self-contained-tags&amp;#x2F;1732454&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;stackoverflow.com&amp;#x2F;questions&amp;#x2F;1732348&amp;#x2F;regex-match-open...&lt;/a&gt;</text></comment>