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@@ -16,8 +16,8 @@
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<body>
@@ -87,7 +87,7 @@
<p><img src="https://direct-img.link/nervous+sweating+aim+fps+meme" alt="Nervous aim meme"></p>
<h2>Step 1: DPI is a distance threshold</h2>
<p>DPI means counts per inch. So the physical distance needed to generate one count is:</p>
<p>$$<br>d = \frac{25.4\text{ mm}}{\text{DPI}}<br>$$</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>d</mi><mo>=</mo><mfrac><mrow><mn>25.4</mn><mtext> mm</mtext></mrow><mtext>DPI</mtext></mfrac></mrow><annotation encoding="application/x-tex">d = \frac{25.4\text{ mm}}{\text{DPI}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">DPI</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">25.4</span><span class="mord text"><span class="mord"> mm</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>
<p>That gives:</p>
<table>
<thead>
@@ -128,7 +128,7 @@
<p>Everyone has physiological tremor. Not pathology. Normal human motor noise. It gets worse with adrenaline, caffeine, fatigue, clutch pressure, cold hands, and overgripping.</p>
<p>A reasonable working range for fingertip/grip micro-tremor is roughly <strong>0.05–0.3 mm</strong>, depending on the person and the moment. The low end is calm aim. The high end is “why is my crosshair auditioning for a seizure?”</p>
<p>Counts produced by tremor are approximately:</p>
<p>$$<br>\text{counts} = \text{tremor amplitude} \times \text{DPI}<br>$$</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mtext>counts</mtext><mo>=</mo><mtext>tremor amplitude</mtext><mo>×</mo><mtext>DPI</mtext></mrow><annotation encoding="application/x-tex">\text{counts} = \text{tremor amplitude} \times \text{DPI}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6151em;"></span><span class="mord text"><span class="mord">counts</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">tremor amplitude</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord text"><span class="mord">DPI</span></span></span></span></span></span>
<p>If your calm tremor amplitude is around <strong>0.05 mm</strong>, then:</p>
<ul>
<li><strong>400 DPI</strong> → about <strong>1.0 count</strong></li>
@@ -147,11 +147,11 @@
<h2>Step 3: the suspicious part</h2>
<p>Here is the part that made the theory feel less like a vibe and more like a trapdoor.</p>
<p>Solve for the DPI where a given tremor amplitude crosses roughly one count:</p>
<p>$$<br>\text{DPI}_{\text{tremor}} \approx \frac{25.4}{\text{tremor amplitude in mm}}<br>$$</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mtext>DPI</mtext><mtext>tremor</mtext></msub><mo>≈</mo><mfrac><mn>25.4</mn><mtext>tremor amplitude in mm</mtext></mfrac></mrow><annotation encoding="application/x-tex">\text{DPI}_{\text{tremor}} \approx \frac{25.4}{\text{tremor amplitude in mm}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord text"><span class="mord">DPI</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">tremor</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2019em;vertical-align:-0.8804em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">tremor amplitude in mm</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">25.4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>
<p>For a <strong>0.06 mm</strong> micro-tremor:</p>
<p>$$<br>25.4 / 0.06 \approx 423\text{ DPI}<br>$$</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>25.4</mn><mi mathvariant="normal">/</mi><mn>0.06</mn><mo>≈</mo><mn>423</mn><mtext> DPI</mtext></mrow><annotation encoding="application/x-tex">25.4 / 0.06 \approx 423\text{ DPI}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">25.4/0.06</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">423</span><span class="mord text"><span class="mord"> DPI</span></span></span></span></span></span>
<p>For a <strong>0.05 mm</strong> micro-tremor:</p>
<p>$$<br>25.4 / 0.05 \approx 508\text{ DPI}<br>$$</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>25.4</mn><mi mathvariant="normal">/</mi><mn>0.05</mn><mo>≈</mo><mn>508</mn><mtext> DPI</mtext></mrow><annotation encoding="application/x-tex">25.4 / 0.05 \approx 508\text{ DPI}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">25.4/0.05</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">508</span><span class="mord text"><span class="mord"> DPI</span></span></span></span></span></span>
<p>That bracket — <strong>~423 to ~508 DPI</strong> — is uncomfortably close to the proposed <strong>450–500</strong> band.</p>
<p>That was the moment the theory stopped sounding like numerology. We did not pick 450–550 first and reverse-engineer a justification. The tremor math independently landed on almost the same neighborhood. <strong>Suspiciously close.</strong> Close enough that the sweet spot hypothesis deserved to be treated as a real model, not preference folklore.</p>
<p><img src="https://direct-img.link/galaxy+brain+realization+meme" alt="Galaxy brain realization"></p>
@@ -160,7 +160,7 @@
<p><img src="/assets/dpi-latency-d_t7aS0h.webp" alt="Mouse sensor latency chart"></p>
<p>The chart shows the expected pattern: extremely low DPI is bad. At <strong>100 DPI</strong>, end-to-end latency is enormous. At <strong>400 DPI</strong>, latency is still clearly worse than the higher-DPI entries. From <strong>800 to 3200 DPI</strong>, latency improves.</p>
<p>A reasonable fitted curve for the usable 400–1600 region is approximately:</p>
<p>$$<br>L \approx 17.2 + \frac{4640}{\text{DPI}}\text{ ms}<br>$$</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>L</mi><mo>≈</mo><mn>17.2</mn><mo>+</mo><mfrac><mn>4640</mn><mtext>DPI</mtext></mfrac><mtext> ms</mtext></mrow><annotation encoding="application/x-tex">L \approx 17.2 + \frac{4640}{\text{DPI}}\text{ ms}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">L</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">17.2</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord text"><span class="mord">DPI</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4640</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord text"><span class="mord"> ms</span></span></span></span></span></span>
<p>Estimated from that model:</p>
<table>
<thead>