Discover and read the best of Twitter Threads about #Topology

Most recents (8)

"I am not content with algebra, in that it yields neither the shortest proofs nor the most beautiful constructions of
geometry. Consequently, in view of this, I consider that we need yet another kind of analysis [...] which deals directly with position" - Leibniz, 1679 #topology
"On the geometry of position, which Leibniz initiated and to which only two geometers, Euler and Vandermonde, have given a feeble glance, we know and possess, after a century and a half, very little more than nothing.” - Gauss, 1833, in his note that introduced the linking number
I'm trying to learn about the beginnings of knot theory, and have gone down a fascinating rabbit hole :-) My current guide is "Classical roots of knot theory," by Józef H. Przytycki [PDF] maths.ed.ac.uk/~v1ranick/pape…
Read 3 tweets
This week at SFI: "#Complexity and the Structure of #Music: Universal Features and Evolutionary Perspectives Across Cultures", an #interdisciplinary working group assembled to explore new frameworks for understanding music. Stay tuned for highlights!

santafe.edu/events/complex…
"Every pitch class set is connected to every other pitch class set."

– @mbnUNT, co-organizer of this week's #musicology working group, presents on how to understand the #topology of #harmonic structures in music with #network diagrams (e.g. Pic 4 with #JSBach's BWV 66):
Once you represent a musical composition as a network, it is possible to examine the evolutionary dynamics of its harmonic content over time, as explained by @mbnUNT in his opening talk for this week's SFI #musicology working group.

(Ironically, this #Beethoven is #scalefree:)
Read 21 tweets
Years have fallen
Swept away
From her eyes

Creases #bear
Pain of tears
Never wailed

Tides of green
Have tsunami of
Stories veiled

Dreams stacked
As secrets in lashes
In a blink

#Topology
Of life revealed
In ebb of her eyes
#vss365
#BraveWrite
Your
Memories
Are
Like
A
#Manifold
Pages
Book
That've
Penned
As
Life
#vss365
Read 50 tweets
Daily Bookmarks to GAVNet 6/17/2020-2

greeneracresvaluenetwork.wordpress.com/2020/06/17/dai…

The Information Age Is “Weaponized” - Extra Newsfeed

extranewsfeed.com/the-informatio…

#weaponized #information
If 80% of Americans Wore Masks, COVID-19 Infections Would Plummet, New Study Says | Vanity Fair

vanityfair.com/news/2020/05/m…

#coronavirus #infections #masks
Opinion | ‘This You?’ Is Twitter’s New Meme. Here’s What It’s All About. - The New York Times

nytimes.com/2020/06/09/opi…

#accountability #meme
Read 10 tweets
Daily Bookmarks to GAVNet 6/04/2020-2

greeneracresvaluenetwork.wordpress.com/2020/06/04/dai…

Graduate Student Solves Decades-Old Conway Knot Problem | Quanta Magazine

quantamagazine.org/graduate-stude…

#topology #Knot
What We Lose When We Assume People Are Bad : NPR

npr.org/2020/05/15/857…

#people #bad #SFI
Read 12 tweets
#vss365
I started playing #guitar in college. Some of my friends back home played, so I thought I'd learn. It's been years since I kept up with it. With no job and an empty house, I had time. Plus, I could crank up my amp. Ava would have hated it. All the more reason to do it.
#vss365
Strumming a few chords or playing a riff through a loud amp usually makes me feel better. It's more of a distraction this time. My amp is a little old. Even a #ragpicker might pass on it. "If you're not going to play it, sell it," Ava nagged. Life always got in the way.
#vss365
Or I got in the way. Not even ten years ago I kept getting sick all the time. Painful stomach cramps would radiate weakness throughout my body. I learned how to wash it away like healing #rainwater. That's when I really started to figure out who I was and what I could do.
Read 857 tweets
For any subset A of a topological space X, there are no more than 14 sets that can be formed from A using the closure and complement operations. The complement of B is B' = X-B. Closure C(B) = smallest closed set containing B. (Neat problem from Kelley's General #Topology.) #math
There's a lemma that helps one show this. Letting C(A) denote the closure of A, and N(A) the complement of A, we can prove:

Lemma: for all sets A, one has the equation
CNC N CNC(A) = CNC(A).
The result follows from the semigroup with identity I generated by 2 elements N and C such that N² = I, C² = C, and CNCNCNC = CNC. Its 14 elements are:
I N C NC CN NCN CNC CNCN NCNC
NCNCN CNCNC CNCNCN NCNCNC NCNCNCN.

Should have nice matrix representation. #math
Read 4 tweets

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