Rudolf Winestock @winestock@qoto.org

Computers are like onions. Everything is layers built on layers, and every layer makes you cry. #sysadmin

Ton Marar's 'A ludic journey into geometric topology' "is an excellent introduction to geometry and topology, for people who do not know much about these subjects", says Athanase Papadopoulos's review https://zbmath.org/1507.55001.
"This book constitutes a very interesting reading for any advanced high-school pupil and for non-mathematicians. It should be also useful for university undergraduates. Geometers and topologists will also find it pleasant to skim, because of the historical remarks, the questions and relations that the author establishes between geometry and topology and topics of everyday life."

Our PiDP-8/i running TSS/8 have been moved to a new location.

Can you MASTER the PiDP-8/i?

Visit https://tss8.sdf.org for full details on the challenges.

#retrocomputing #code #challenge #study #learning

#PhysicsFactlet
"Anderson localization" is a weird phenomenon that is not well known even among Physicists, but has the habit of popping up essentially everywhere.
So here is an introductory thread 🧵

The idea of "localization" originally came about as an explanation (by P.W. Anderson, hence the name) of why the spins in certain materials did not relax as fast as expected. What Anderson realized was that when you have a wave (in this case a quantum mechanical wavefunction) that propagates in a random system, interference can play a major role, and potentially impede propagation completely.
The original paper (and, frankly, most of the literature on the subject) is pretty impenetrable, but thankfully Anderson localization can happen any time we have a wave and a random medium, doesn't matter what kind of wave, so we can try to look at a simple system.

Let's start VERY simple with the simple pendulum, and let's make it even simpler by assuming the oscillations are small, and thus we only have to deal with an harmonic oscillator. The pendulum has a natural frequency (i.e. the frequency at which it will naturally oscillate if you just let it go), which will depend on its length and the gravity acceleration pulling it down: ω₀= √(g/L). If you take a bunch of such pendula, they will all oscillate with the same natural frequency.
Let's complicate the problem a bit and add a (elastic) coupling between the pendula. The system in its entirety now will have a number of natural frequencies equal to the number of pendula, resulting in a complex motion that is the superposition of the oscillations at all those different frequencies.
1/

I’ll be honest: even as a practicing computer scientist, last year, if you had asked me which Star Trek technology was least likely to emerge in my lifetime, I might have ranked AI as less likely than even Warp Drive.

Logic Syllabus
• https://inquiryintoinquiry.com/logic-syllabus/

Logical Concepts
• https://oeis.org/wiki/Logic_Syllabus#Logical_concepts

Ampheck • https://oeis.org/wiki/Ampheck
Boolean Domain • https://oeis.org/wiki/Boolean_domain
Boolean Function • https://oeis.org/wiki/Boolean_function
Boolean-Valued Function • https://oeis.org/wiki/Boolean-valued_function
Differential Logic • https://oeis.org/wiki/Differential_logic
Logical Graph • https://oeis.org/wiki/Logical_Graphs
Minimal Negation Operator • https://oeis.org/wiki/Minimal_negation_operator
Multigrade Operator • https://oeis.org/wiki/Multigrade_operator
Parametric Operator • https://oeis.org/wiki/Parametric_operator
Peirce's Law • https://oeis.org/wiki/Peirce%27s_law
Propositional Calculus • https://oeis.org/wiki/Propositional_calculus
Sole Sufficient Operator • https://oeis.org/wiki/Sole_sufficient_operator
Truth Table • https://oeis.org/wiki/Truth_table
Universe of Discourse • https://oeis.org/wiki/Universe_of_discourse
Zeroth Order Logic • https://oeis.org/wiki/Zeroth_order_logic

#Ampheck #BooleanDomain #BooleanFunction #BooleanValuedFunction #DifferentialLogic
#LogicalGraph #MinimalNegationOperator #MultigradeOperator #ParametricOperator
#PeircesLaw #PropositionalCalculus #SoleSufficientOperator #TruthTable
#UniverseOfDiscourse #ZerothOrderLogic

Good ol' Tom looking out for us.

Computer peripheral advertising has really lost its way since the 80s

The worst thing that ever happened in software engineering was when Kirk asked Scotty how long something would take and Scotty said thirty minutes and Kirk said you’ve got five and Scotty got it done in five and impressionable children watched this and grew up to become managers.

#Processing #CreativeCoding #Procedural #Generative #PerfectLoop #Art #Math #Mathstodon

Conway's Game of Life automaton simulated by another, in turn simulated by another, in turn ... ad infinitum:
#Automaton

https://oimo.io/works/life/

Quite a few people have been connecting to our new Systems Concepts SC40 PDP-10

Here is an image gallery of what it looks like on the inside:

https://twenex.org/sc40/

The SC40 kept the 36bit computing market alive through the 1990s into the 2000s. Services like CompuServe and Tymnet relied on them.

If you're interested in an account, check out https://twenex.org for access to our XKL Toad-2 which will also get you an account on the SC40.

#retrocomputing #pdp10 #hacking

Tamar Ziegler and I have just uploaded a short #NumberTheory paper to the #arXiv titled "infinite partial sumsets in the primes". https://arxiv.org/abs/2301.10303 The main result is that there exist two increasing sequences \(a_1 < a_2 < \dots \) and \(b_1 < b_2 < \dots\) such that a_i+b_j is prime for all i<j. The argument uses the Maynard sieve and an intersectivity lemma of Bergelson. I discuss this result further on my blog at https://terrytao.wordpress.com/2023/01/26/infinite-partial-sumsets-in-the-primes/

I'm going to give a couple of talks about the 'tenfold way' in early February. One is in Nicohl Furey's seminar Algebra, Particles, and Quantum Theory on February 6, available online:

https://researchseminars.org/seminar/AlgebraParticlesFoundations

The tenfold way is a beautiful piece of math that originated in condensed matter physics. I want to understand it better before I give my talks!

(1/n)

@robin One more thought:

PDFs keep eating our lunch in the "web documents" space, since browsers don't have an ePub option in the "Save As" menu.

I recall there is a long and winding history underpinning all of this, but saving pages as ePubs ought to be at least an option, if not the norm.

Perhaps Mathstodon can be a place to note some folklore #MathTricks that are useful but too trifling to devote an entire paper to. Here's one (that I recalled on browsing MathOverflow https://mathoverflow.net/questions/435728): If one is trying to prove a Hilbert space identity or inequality which is invariant under a unitary group action, one can often reduce "for free" to the irreducible components of that group action. (1/2)

Memes can efficiently (and memorably) convey mathematical relationships; for instance, in https://mathstodon.xyz/@tejotaefe/109410012839349418 the "spiderman pointing" meme conveys "the following are equivalent". As another example, one could imagine the enclosed "Spongebob" meme being used to describe a toy result, a weak version of a theorem, and a strong version of a theorem respectively. Would readers like to contribute further examples? I could see myself using one in a talk one day (with attribution, ofc).