http://programmer.ie/tags/vectors/ Recent content in Vectors on Programmer.ie: Modern AI programming Hugo en-us Mon, 07 Sep 2026 09:00:00 +0000 http://programmer.ie/books/embeddings-from-first-principles/01-chapter/ Mon, 07 Sep 2026 09:00:00 +0000 http://programmer.ie/books/embeddings-from-first-principles/01-chapter/ <p><em>Part I — A Vector Is Not Meaning</em></p> <h2 id="three-words-and-a-list-of-numbers">Three words and a list of numbers</h2> <p>Take three words:</p> <div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-text" data-lang="text"><span style="display:flex;"><span>cat </span></span><span style="display:flex;"><span>dog </span></span><span style="display:flex;"><span>airplane </span></span></code></pre></div><p>Turn them into numbers. Any embedding API will do it. You get three arrays, each maybe 384 or 768 or 1,536 floats long:</p> <div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-text" data-lang="text"><span style="display:flex;"><span>cat [ 0.021, -0.114, 0.062, ... ] </span></span><span style="display:flex;"><span>dog [ 0.019, -0.098, 0.071, ... ] </span></span><span style="display:flex;"><span>airplane [-0.087, 0.203, -0.041, ... ] </span></span></code></pre></div><p>Compute the angle between <code>cat</code> and <code>dog</code>. It is small. Compute the angle between <code>cat</code> and <code>airplane</code>. It is larger. Something about &ldquo;cats and dogs are both pets&rdquo; appears to have survived the trip into number-space.</p>