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‎content/posts/julia-poem/index.md‎

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title: "Poem 14. \"Julia\""
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category: personal
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date: 2025-12-30
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---
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n/a
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2025-12-30
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{{< highlight text "linenos=true,linenostart=1" >}}
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{{< /highlight >}}
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2026-01-07
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{{< highlight text "linenos=true,linenostart=1" >}}
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rivers of ice, pillars of glass,
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like water, light runs through crystal;
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thoughts travel inside your forehead:
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in my mind, to think is now to reason
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the precious movements of your will:
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across the earth
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glacial penmanship,
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beautiful writing
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springs of magma, columns of light,
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deep in those channels, molten flows;
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warm blood filters through your dermis:
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on my chest, to feel is now to witness
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waves of sun washing over your skin:
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across the earth
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volcanic flows,
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solar embrace
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{{< /highlight >}}
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2026-01-12
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{{< highlight text "linenos=true,linenostart=1" >}}
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turbulent flames over the water,
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soothing stillness hugs me fixed-
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come evening, you dress me
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in ever more radiant skin,
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now warm evermore:
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of all the earthly pillars built from rock,
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infinite is the throne in which we now lay;
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high
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waterfall of light, one endless flow,
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it washes through insufficient hands:
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always insufficient
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yet now complete
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and forever more:
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we phosphoresce in our presence,
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glowing evermore:
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everything shines over the water-
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set ablaze and held calmly still:
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{{< /highlight >}}
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‎content/posts/tensors-signals-kernels/index.md‎

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### Dimensionality
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I begin by considering infinite-dimensional vector spaces. I demonstrate how the definition of span can a be relaxed to allow the coordinate-based treatement of vector spaces of dimensions with different (infinite) cardinalities, and what the notion of a basis becomes under these relaxations. This leads us to Banach and Hilbert spaces while being a digestible way to ramp-up for the following sections.
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I begin by considering infinite-dimensional vector spaces. I demonstrate how the definition of span can be relaxed to allow the coordinate-based treatement of vector spaces of dimensions with different (infinite) cardinalities, and what the notion of a basis becomes under these relaxations. This points us to Banach and Hilbert spaces, while providing a digestible way to ramp up for the following sections.
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### Tensor Spaces
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I organize the semantics behind matrices, vectors, and linear maps. After introducing some preliminary concepts not usually covered in a first course in linear algebra (e.g. canonical isomorphisms), I provide an abstract introduction to tensors and tensor spaces, showing how they are "many things at once" up to (quite practical) isomorphism. After the abstract introduction, I share notation standards for coordinate-based and coordinate-free tensor algebra paired with real-world examples from differential geometry and deep learning.
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{{% hint title="2.1. Note" %}}
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The logical procedures and syntax conventions of this section are shown to be valid for Hilbert spaces and tensor products thereof, although there are other infinite-dimensional cases where they also apply. But it would be too difficult to structure these nuances in a complete way, and they would not enjoy much overlap with subsequent topics regardless.
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The logical procedures and syntax conventions of this section are shown to be valid for Hilbert spaces and tensor products thereof. However, there are other infinite-dimensional cases where they also apply. But it would be too difficult to structure these nuances (that lie beyond Hilbert spaces) in a complete way, and they would not enjoy much overlap with subsequent sections regardless. So I leave them unexplored, as they would not clearly contribute to conceptual unification.
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{{% /hint %}}
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VX = np.einsum('ij,jt->it', V, X) # values
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result = np.einsum('is,st->it', VX, weights)
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‎public/notes/index.xml‎

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‎public/poem-14.-julia/index.html‎

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<div>
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<time>December 30, 2025</time>
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</header><p>n/a</p>
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</header><p>2025-12-30</p>
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<pre tabindex="0" class="chroma"><code><span class="lnt"> 1
@@ -95,6 +95,88 @@ <h1>Poem 14. &#34;Julia&#34;</h1>
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</span></span><span class="line"><span class="cl">an original gift of your goodness</span></span></code></pre></td></tr></table>
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</div>
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<p>2026-01-07</p>
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<pre tabindex="0" class="chroma"><code class="language-text" data-lang="text"><span class="line"><span class="cl">rivers of ice, pillars of glass,
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</span></span><span class="line"><span class="cl">like water, light runs through crystal;
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</span></span><span class="line"><span class="cl">thoughts travel inside your forehead:
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</span></span><span class="line"><span class="cl">in my mind, to think is now to reason
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</span></span><span class="line"><span class="cl">the precious movements of your will:
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</span></span><span class="line"><span class="cl">across the earth
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</span></span><span class="line"><span class="cl"> glacial penmanship,
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</span></span><span class="line"><span class="cl"> beautiful writing
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</span></span><span class="line"><span class="cl">
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</span></span><span class="line"><span class="cl">springs of magma, columns of light,
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</span></span><span class="line"><span class="cl">deep in those channels, molten flows;
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</span></span><span class="line"><span class="cl">warm blood filters through your dermis:
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</span></span><span class="line"><span class="cl">on my chest, to feel is now to witness
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</span></span><span class="line"><span class="cl">waves of sun washing over your skin:
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</span></span><span class="line"><span class="cl">across the earth
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</span></span><span class="line"><span class="cl"> volcanic flows,
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</span></span><span class="line"><span class="cl"> solar embrace</span></span></code></pre></td></tr></table>
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</div>
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</div>
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<p>2026-01-12</p>
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<pre tabindex="0" class="chroma"><code class="language-text" data-lang="text"><span class="line"><span class="cl">turbulent flames over the water,
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</span></span><span class="line"><span class="cl">soothing stillness hugs me fixed-
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</span></span><span class="line"><span class="cl">come evening, you dress me
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</span></span><span class="line"><span class="cl">in ever more radiant skin,
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</span></span><span class="line"><span class="cl"> now warm evermore:
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</span></span><span class="line"><span class="cl">of all the earthly pillars built from rock,
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</span></span><span class="line"><span class="cl">infinite is the throne in which we now lay;
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</span></span><span class="line"><span class="cl"> high
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</span></span><span class="line"><span class="cl">waterfall of light, one endless flow,
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</span></span><span class="line"><span class="cl">it washes through insufficient hands:
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</span></span><span class="line"><span class="cl"> always insufficient
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</span></span><span class="line"><span class="cl"> yet now complete
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</span></span><span class="line"><span class="cl"> and forever more:
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</span></span><span class="line"><span class="cl">we phosphoresce in our presence,
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</span></span><span class="line"><span class="cl"> glowing evermore:
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</span></span><span class="line"><span class="cl">everything shines over the water-
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</span></span><span class="line"><span class="cl">set ablaze and held calmly still:</span></span></code></pre></td></tr></table>
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</div>
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</div>
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