Lmst

I've noticed that #cubical tutorials introducing funExt treat it as semi-magical and I recently did the definition as an exercise and I wanted to share my thoughts. 1/

The University of Gothenburg is looking to hire a postdoc for work on
compilation of cubical type theory:

web103.reachmee.com/ext/I005/1035/job?site=7&lang=UK&validator=9b89bead79bb7258ad55c8d75228e5b7&job_id=37550

Application deadline: June 12.

#TypeTheory #Cubical #HoTT #Agda #PostDoc #Gothenburg

A cubical lightwell inside the Royal Museum of Fine Arts, Antwerp, Belgium, 2024.

Many ancient symbols, including the cube, have roots in geometry and math. It might seem a bit weird in this day and age, but at one time, math, science and religion were not considered separate pursuits. Even Sir Isaac Newton, the scientific genius most famous for his theory of gravity, had a fascination with sacred geometry. In fact, Newton poured countless hours into figuring out the exact dimension of the Temple of Solomon which, apart from the Old Testament, features prominently in the teachings of Freemasonry. And while it has not been proven conclusively, many people suspect that Sir Isaac Newton was a mason or was a member of a similar society predating Freemasonry as it was officially established in 1717. Sir Isaac Newton died in 1727.
A cube is one of many different symbols associated with sacred geometry. Since it can sit flat on the ground, a cube is associated with the earth and represents our earthly existence.

Volume and void are fundamental concepts in architecture and design, where volume refers to the three-dimensional space that an object or structure occupies, while void is the empty space surrounding or included within it. Understanding these concepts is crucial for optimizing spatial arrangements, achieving balance, and enhancing functionality and aesthetics in any design project. Mastery of volume and void enables one to create harmonious and efficient environments, making these terms essential vocabulary for architecture.

#modernarchitecture #colourphotography #colorphotography #perspective #isaacnewton #museumoffineartsantwerp #building #buildings #buildingphotography #urbanphotography #urbanexploration #architectlovers #arthistory #philosophical #modernart #exploreantwerp #antwerp #realityisanillusion #peopleinarchitecture #contemporaryarchitecture #symbolic #symbol #light #opticalillusion #illusion #volume #minimalism #minimalistarchitecture

My #blog for last week, slightly late, on cubical type theory: https://updatedscholar.blogspot.com/2023/01/discussing-cubical-type-theory.html #HoTT #cubical #TypeTheory

Screenshot from a paper, stating "The intuition is that a type in a context with n names corresponds to an n-dimensional cube", with accompanying diagrams (only up to a 2-dimensional cube, or square, sadly).

'Computing Cohomology Rings in Cubical Agda' by Thomas Lamiaux, Axel Ljungström, and Anders Mörtberg: "extends previous developments by providing the first fully mechanized definition of cohomology rings... The formalization is constructive so that it can be used to do concrete computations, and it relies on the Cubical Agda system which natively supports higher inductive types and computational univalence". #Agda #Cubical #HoTT #Cohomology

#letsroll

⚂ ⚁ ⚄ ⚄ ⚅→#grappling
⚄ ⚃ ⚁ ⚄ ⚅→#shriek
⚂ ⚃ ⚂ ⚄ ⚁→#idealness
⚁ ⚀ ⚄ ⚃ ⚄→#cubical
⚃ ⚃ ⚅ ⚁ ⚁→#pond
⚃ ⚅ ⚃ ⚁ ⚁→#rants

grappling-shriek-idealness-cubical-pond-rants

Roll your own @ https://www.eff.org/deeplinks/2016/07/new-wordlists-random-passphrases

#letsroll

⚄ ⚃ ⚁ ⚂ ⚅→#showman
⚁ ⚀ ⚄ ⚃ ⚄→#cubical
⚁ ⚄ ⚂ ⚅ ⚀→#enigmatic
⚁ ⚄ ⚄ ⚃ ⚄→#erasure
⚂ ⚅ ⚃ ⚁ ⚃→#mace
⚀ ⚂ ⚁ ⚄ ⚀→#barbell

showman-cubical-enigmatic-erasure-mace-barbell

Roll your own @ https://www.eff.org/deeplinks/2016/07/new-wordlists-random-passphrases

#letsroll

⚃ ⚀ ⚁ ⚀ ⚁→#modified
⚄ ⚁ ⚂ ⚁ ⚃→#riverboat
⚀ ⚀ ⚅ ⚃ ⚀→#angling
⚃ ⚂ ⚄ ⚅ ⚃→#parole
⚁ ⚀ ⚄ ⚃ ⚄→#cubical
⚄ ⚃ ⚄ ⚅ ⚀→#skype

modified-riverboat-angling-parole-cubical-skype

Roll your own @ https://www.eff.org/deeplinks/2016/07/new-wordlists-random-passphrases

#letsroll

⚄ ⚃ ⚅ ⚄ ⚄→#slighted
⚃ ⚃ ⚂ ⚅ ⚃→#placate
⚁ ⚀ ⚄ ⚃ ⚄→#cubical
⚁ ⚃ ⚅ ⚀ ⚃→#educator
⚁ ⚁ ⚁ ⚀ ⚄→#dastardly
⚂ ⚁ ⚂ ⚅ ⚁→#glowing

slighted-placate-cubical-educator-dastardly-glowing

Roll your own @ https://www.eff.org/deeplinks/2016/07/new-wordlists-random-passphrases

#letsroll

⚀ ⚅ ⚅ ⚅ ⚁→#copartner
⚁ ⚃ ⚁ ⚂ ⚅→#drippy
⚄ ⚀ ⚅ ⚂ ⚅→#rethink
⚁ ⚄ ⚃ ⚂ ⚅→#entitle
⚁ ⚀ ⚅ ⚄ ⚃→#cussed
⚁ ⚀ ⚄ ⚃ ⚄→#cubical

copartner-drippy-rethink-entitle-cussed-cubical

Roll your own @ https://www.eff.org/deeplinks/2016/07/new-wordlists-random-passphrases

#letsroll

⚄ ⚀ ⚄ ⚅ ⚀→#resilient
⚁ ⚀ ⚄ ⚃ ⚄→#cubical
⚃ ⚃ ⚂ ⚁ ⚁→#pessimist
⚄ ⚀ ⚀ ⚅ ⚃→#regulator
⚀ ⚀ ⚃ ⚄ ⚂→#although
⚁ ⚅ ⚃ ⚅ ⚄→#fax

resilient-cubical-pessimist-regulator-although-fax

Roll your own @ https://www.eff.org/deeplinks/2016/07/new-wordlists-random-passphrases

#letsroll

⚁ ⚀ ⚄ ⚃ ⚄→#cubical
⚃ ⚅ ⚁ ⚄ ⚅→#quit
⚄ ⚂ ⚄ ⚃ ⚁→#sequence
⚄ ⚅ ⚄ ⚃ ⚂→#strife
⚀ ⚄ ⚁ ⚀ ⚁→#catcall
⚀ ⚄ ⚀ ⚂ ⚀→#cartel

cubical-quit-sequence-strife-catcall-cartel

Roll your own @ https://www.eff.org/deeplinks/2016/07/new-wordlists-random-passphrases

#letsroll

⚂ ⚄ ⚁ ⚂ ⚃→#judo
⚅ ⚃ ⚅ ⚀ ⚅→#unsure
⚅ ⚂ ⚂ ⚅ ⚃→#uncloak
⚁ ⚅ ⚅ ⚃ ⚄→#financial
⚁ ⚀ ⚄ ⚃ ⚄→#cubical
⚄ ⚅ ⚀ ⚀ ⚀→#squire

judo-unsure-uncloak-financial-cubical-squire

Roll your own @ https://www.eff.org/deeplinks/2016/07/new-wordlists-random-passphrases

#letsroll

⚅ ⚂ ⚁ ⚃ ⚄→#unable
⚁ ⚅ ⚃ ⚅ ⚃→#favorite
⚀ ⚁ ⚁ ⚃ ⚁→#appointee
⚃ ⚅ ⚃ ⚅ ⚄→#reason
⚃ ⚄ ⚁ ⚁ ⚅→#pregnant
⚁ ⚀ ⚄ ⚃ ⚄→#cubical

unable-favorite-appointee-reason-pregnant-cubical

Roll your own @ https://www.eff.org/deeplinks/2016/07/new-wordlists-random-passphrases

A talk by Kevin Buzzard of the Imperial College London: "Is HoTT the way to do mathematics?"

https://www.youtube.com/watch?v=q5-pykbfViA

He discusses criteria for a proof assistant to have in order to be used in formalising mathematics. Most mathematicians today assume classical logic and the axiom of choice.

#HoTT #constructive #cubical #typetheory #Agda #mathematics #formalisation

Just attended a talk by Jon Sterling on cubical type theory implementations: redtt and cooltt. Throughout the talk the speaker kept saying how all this stuff is already supported by Cubical Agda. I guess it was a good choice to choose Agda as language of preference for working with constructive type theories.

#cubical #typetheory #Agda #redtt #cooltt