This is the 52nd week note!
I’ve made it to a year1 of week notes.
I love writing them.
They’re my favourite part of having a website.
I think that this year has been the most regular streak of blogging that I’ve ever had in ~20 years of blogging.
They’re so low friction.
I’ve got a nifty bash alias hugo-week-notes that pulls up the current one, so
they’re always “at hand” and I can quickly add to them.
On Saturday mornings, we tend to have waffles for breakfast. This weekend, I got downstairs a little bit after the waffles were ready and Mabel was eating her cinnamon waffle with some ketchup. A bit unusual but she thought it was delicious.
A small mountain of Esperanto books arrived from UEA.
This week, I only read the first volume of Historio de La Lingvo Esperanto. It originally came out in 1923. Why is that interesting? See: 100 Year Old Books in Esperanto. Moreover, Historio is from the pen of Edmond Privat, who was an powerful force in the early Esperanto world. He co-organized the first Universala Kongreso in 1905. I’m excited to read the second volume which deals with the period after 1900.
The MAT D92 project has taken an interesting turn. We have a second small paper in the works. It’s highly confidential top secret stuff related to string figures. Hopefully, I’ll be able to share some information soon.
While pondering the piece about Growing Linearly Independent Sets, I realized that the context we were working in was so simple and down to Earth that we might not need the dimension bound theorem. A bit of thinking about it revealed that for vector spaces with a finite number of elements: the pigeonhole principle implies the dimension bound theorem. A nice little TIL moment.
Consider a finite vector space $V = \mathbb{F}_p^d$ over a finite field $\mathbb{F}_p$. Fix a set of vectors $S = \{v_1, \dots, v_n\}$. We want to argue: if $n > d$ then $S$ is linearly dependent. Consider the function $L : \mathbb{F}_p^n \to V$ defined by \[ L(c_1, \dots, c_n) = c_1v_1 + \dots + c_nv_n. \] If $n > d$ then $|\mathbb{F}_p^n| = p^n > p^d = |V|$. Therefore, by the pigeonhole principle, $L$ is not injective. We get some $(a_1, \dots, a_n) \neq (b_1, \dots, b_n)$ such that: \[ a_1v_1 + \dots + a_nv_n = b_1v_1 + \dots + b_nv_n. \] It follows that: \[ (a_1 - b_1)v_1 + (a_2 - b_2)v_2 + \dots + (a_n - b_n)v_n = 0. \] We want to show that this is a non-trivial linear combination of the vectors $v_i$. To do so, we need to show that there is a non-zero coefficient somewhere on the left-hand side. And there must be some non-zero coefficient $a_i - b_i$ because $(a_1, \dots, a_n) \neq (b_1, \dots, b_n)$.
We’re in Week 11 of 12 and the end of semester is approaching quickly. In my beloved MAT A02: The Magic of Numbers, we covered the symmetries of frieze patterns. We followed this lovely article pretty closely.
Belcastro, Sarah-Marie, and Thomas C. Hull. “Classifying frieze patterns without using groups.” The College Mathematics Journal 33.2 (2002): 93-98.
DOI: https://doi.org/10.1080/07468342.2002.11921925
– Classical Greek Friezes from ElaKwasniewski of Shutterstock (#95391073).
My courses are getting pretty close to the end. I’m saddened that MAT B42 got hit with a few snow days and a holiday closure. We’re way behind on the material and won’t get to the cool theorem at the end of the course.
I finally decided to undertake the Great Note-Blog Merger.
Nevermind.
I decided not to do this merger.
I don’t want to break any links or pester people by changing my RSS2 setup. (Cool URIs don’t change.)
Two years ago, I pondered for ages whether to make a blog as a separate entity from the notes part of this website. Eventually, I did and I somewhat regret the decision. It is sometimes tricky decide where posts should go. Moreover, I often have to check both groupings for something that I’ve written. This is a bit silly. I wish that I’d just posted everything in notes and done the categorization via tags
It’s a perfect game full stop, but especially for those seeking to rekindle their creativity, or simply to sit down and create with friends.
The chronology doesn’t work out for reasons that I don’t quite understand: Week Note 1 happened on February 14th of 2025. I must have slow played a few week notes. ↩︎
Hello, to the three or four people who read this via RSS! ↩︎
Published: Mar 28, 2026 @ 19:00.
Last Modified: Mar 25, 2026 @ 16:15.
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