<p>As an undergraduate student, I was a bit mystified by the occurrence of the notion of entropy (from physics) into theoretical computer science (at the time, for the description of the optimal compression of a text with <span class="math-container">$n_i$</span> occurrences (summing to <span class="math-container">$n=\sum_{i\in[1..k]}n_i$</span>) of each symbol <span class="math-container">$i\in[1..k]$</span> by <a href="https://www.scribd.com/doc/20852918/Huffman-1952-Minimum-Redundancy-Codes" rel="nofollow noreferrer">prefix free codes</a>, such as the one described by <a href="https://en.wikipedia.org/wiki/David_A._Huffman" rel="nofollow noreferrer">David A. Huffman</a>) and its (at the time to me) occult definition: <span class="math-container">$${\cal H}(n_1,\ldots,n_k) = \sum_{i\in[1..k]} \frac{n_i}{n} \log_2\frac{n}{n_i}.$$</span> Since then, I have learned to respect its potency and adequacy in measuring the (des)equilibrium of probability and frequency distributions, and I have used it to measure the spaced used by <a href="https://doi.org/10.1016/j.tcs.2012.08.010" rel="nofollow noreferrer">compressed data structures</a>, the time used by <a href="https://doi.org/10.1145/1328911.1328915" rel="nofollow noreferrer">adaptive algorithms</a> (in internal and <a href="https://doi.org/10.1016/j.jda.2015.11.001" rel="nofollow noreferrer">external memory</a>), sometimes in <a href="https://doi.org/10.3390/a13010012" rel="nofollow noreferrer">convoluted ways</a>, and even in <a href="https://doi.org/10.1145/3046673" rel="nofollow noreferrer">instance optimality results</a>.</p>
<p><a href="https://i.sstatic.net/F0ae3.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/F0ae3.jpg" alt="Entropy Formula in Theoretical Computer Science" /></a></p>
<p>In 2013, for a colleague's birthday anniversary, I drew quickly a feminine character holding an equation often used in our research, one of the definition of the entropy of a vector of integers. At the time I wrote on my <a href="https://jyby.blogspot.com/2013/08/tnt-and-entropy.html" rel="nofollow noreferrer">blog</a> &quot;<em>I hope that he will hang it in his office so that it helps his students to memorize it!</em>&quot;, and a few years later, a PhD student admitted that he searched on the web for the blog post to find back the formula :).</p>
<p>The definition of the entropy that I used in this drawing, <span class="math-container">$$n{\cal H}(n_1,\ldots,n_k) = n\log_2 n - \sum_{i\in[1..k]} n_i \log_2 n_i,$$</span> is a bit atypical (one typically normalizes both sides of the equation by <span class="math-container">$n$</span>, and combines the two <span class="math-container">$\log$</span> terms into one, maybe so that to make it closer to the definition used by statistical physicists). I like this formulation better because it highlights the terms measuring the imbalance of the distribution, and give an intuition into the various analysis which lead to such a formula.</p>
<p>Feel free to use either the formula itself or the drawing: I would be honored! (Do let me know if you do!)</p>

CC BY-SA 4.0
2022-11-21T10:49:41.807Z
2022-11-23T14:02:03.373Z
2022-11-23T14:02:03.373Z
J.y B.y
<p>I've always found <a href="https://www.nationalgeographic.com/science/article/y-combinator" rel="nofollow noreferrer">this tattoo</a> pretty daring. Would work on a hoodie.</p>

CC BY-SA 4.0
2022-11-24T00:56:01.660Z
This answer could be much improved if it included more than just a link.
Amazon Dies In Darkness
CC BY-SA 4.0
2022-11-20T17:47:59.883Z
2022-11-20T17:47:59.883Z
Martin Berger
<p>I have to design a hoodie for my computer science batch, and I want it to be related to Theoretical computer science. I don't want to slap on some text with HTML-like angle brackets, but actually want something cool + nerdy that only people with some basic knowledge of CS might understand. I would be grateful, if you could give some suggestion, resources for ideas, or links to similar products.
Thank you.</p>

<soft-question>
Resources for hoodie design related to theoretical CS
Mr.HiggsBoson
# Resources for hoodie design related to theoretical CS

(Asked by: username_0 on 2022-11-20)

I have to design a hoodie for my computer science batch, and I want it to be related to Theoretical computer science. I don't want to slap on some text with HTML-like angle brackets, but actually want something cool + nerdy that only people with some basic knowledge of CS might understand. I would be grateful, if you could give some suggestion, resources for ideas, or links to similar products.
Thank you.

**Tags:** soft-question

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## 2 answers

### Answer by username_1 on 2022-11-21. Score: 2

As an undergraduate student, I was a bit mystified by the occurrence of the notion of entropy (from physics) into theoretical computer science (at the time, for the description of the optimal compression of a text with $n\_i$ occurrences (summing to $n=\sum\_{i\in[1..k]}n\_i$) of each symbol $i\in[1..k]$ by [prefix free codes](https://www.scribd.com/doc/20852918/Huffman-1952-Minimum-Redundancy-Codes), such as the one described by [David A. Huffman](https://en.wikipedia.org/wiki/David_A._Huffman)) and its (at the time to me) occult definition: $${\cal H}(n\_1,\ldots,n\_k) = \sum\_{i\in[1..k]} \frac{n\_i}{n} \log\_2\frac{n}{n\_i}.$$ Since then, I have learned to respect its potency and adequacy in measuring the (des)equilibrium of probability and frequency distributions, and I have used it to measure the spaced used by [compressed data structures](https://doi.org/10.1016/j.tcs.2012.08.010), the time used by [adaptive algorithms](https://doi.org/10.1145/1328911.1328915) (in internal and [external memory](https://doi.org/10.1016/j.jda.2015.11.001)), sometimes in [convoluted ways](https://doi.org/10.3390/a13010012), and even in [instance optimality results](https://doi.org/10.1145/3046673).

[![Entropy Formula in Theoretical Computer Science](https://i.sstatic.net/F0ae3.jpg)](https://i.sstatic.net/F0ae3.jpg)

In 2013, for a colleague's birthday anniversary, I drew quickly a feminine character holding an equation often used in our research, one of the definition of the entropy of a vector of integers. At the time I wrote on my [blog](https://jyby.blogspot.com/2013/08/tnt-and-entropy.html) "*I hope that he will hang it in his office so that it helps his students to memorize it!*", and a few years later, a PhD student admitted that he searched on the web for the blog post to find back the formula :).

The definition of the entropy that I used in this drawing, $$n{\cal H}(n\_1,\ldots,n\_k) = n\log\_2 n - \sum\_{i\in[1..k]} n\_i \log\_2 n\_i,$$ is a bit atypical (one typically normalizes both sides of the equation by $n$, and combines the two $\log$ terms into one, maybe so that to make it closer to the definition used by statistical physicists). I like this formulation better because it highlights the terms measuring the imbalance of the distribution, and give an intuition into the various analysis which lead to such a formula.

Feel free to use either the formula itself or the drawing: I would be honored! (Do let me know if you do!)


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### Answer by username_2 on 2022-11-20. Score: 2

I've always found [this tattoo](https://www.nationalgeographic.com/science/article/y-combinator) pretty daring. Would work on a hoodie.

> **Comments:**
> **username_3**: This answer could be much improved if it included more than just a link.  

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