I wonder if any of my #Mathstodon acquaintances know of or have thought about the strategy of defections looked at a bit like "The Prisoner's Dilemma".
I suspect the biggest impact will be to destabilise relationships between those who are staying loyal to their party ... whether the uber loyalists are just pretending ...
Better mathematicians than me will have to weigh in (it's a low bar), but I came across this recent paper establishing a “Periodic Table” of #PrimeNumbers from 48 integer “roots" that can then be used to predict new primes: https://dx.doi.org/10.2139/ssrn.4742238
New experiments in maths, working with a statistics prof at UCL. This is a recursive fragmentation model using OpenSimplex noise as the source of the variates, allowing moving smoothly through a pseudo-random "search space”. Rotation because I like the stripey edges that form
Trying to fit π in a selfie is like squeezing into jeans post-Thanksgiving dinner—impossible! The first digit posed, but the rest? They photobombed and ran off the frame, leaving a 'pi'c that's 3.14% complete and 96.86% mystery.
Proposition: There is always scope for YouTube creators to create fresh hell for those of us who don't like flishy flash attention attractors.
Examples:
#Mathstodon#Numberphile did an audio only video but added a voice spectrum analyser flickering away as they spoke to turn it from a podcast into a "movie".
#FamilyHistory expert Connie Knox's video about "Burnt Counties" ... has a random flickering fan chart echoing what she says.
I was making salsa the other day and got to thinking about the relationship between how many cuts you make and how many pieces you end up with. It's interesting, right? If I make two cuts through a slice of tomato and the cuts are parallel, I get three pieces but if the cuts are perpendicular, I get four. Same number of cuts different outcome. What's going on? It turns out that it has to do with the dimensionality of tomatoes. 1/x #math#mathstodon
This is the thing that makes #internet a true qualitative difference in our world. Post something random, and ten minutes later it's reached someone who's an #expert or lay #enthusiast who responds.
Looking for: complex systems that defy model reduction.
The behavior of a complex system is hard to predict from its parts alone because it follows from how the parts interact.
Model reduction is a way to capture the behavior of a complex system more simply (eg to capture the magnetism of 1g of Fe2O3, you don't have to model all 1022 molecules and their interactions). My sense is that model reduction works best when you have many repeated copies.
I'm looking for some good (ideally concrete) examples of complex systems that defy model reduction. I anticipate that they will be made of heterogeneous parts.
@NicoleCRust
Weather prediction would be my best guess for 3 - it's at the root of chaos theory. My feeling is also yes on 1) and 2), but we're reaching the end of my knowledge. It would be nice to hear from someone into #chaostheory#complexitytheory or #fractals , perhaps someone from #mathstodon ?
Mastodon should support Markdown formatting. This should actually be defined as a part of ActivityPub. Beyond bold and italics, it would be great to create links to make the content easier to read. https://www.markdownguide.org#Mastodon#ActivityPub
I made a post on my (rarely used) blog thinking about my pursuit of higher mathematics and about how/where to apply for grad schools. I would love some advice from those who have pursued their love for Mathematics and it's application in other fields in grad school! I have some concerns and I feel very stuck.
WordPress-instikket ActivityPub (AP) tillater fra versjon 1.0.2 mer eller mindre alle HTML-elementer, dvs. en kan legge til MathML. Det blir da opp til AP-mottakeren, f.eks. Mastodon, om en skal fjerne disse elementene, noe de fleste pr. i dag vil gjøre.
Forslaget FEP-dc88: Formatting Mathematics forsøker å rydde opp i det ved å beskrive hvordan MathML kan tilbys, eller alternativt strippes slik at en kun står igjen med innholdet i <annotation> som ofte da vil inneholde en mer tekstlig representasjon.
Følgende er fra eksempelet i FEP-dc88:
LaTeX i <annotation>:
I have a truly marvelous proof that xn+yn≠znx^n + y^n \ne z^n which this note is too small to contain!
MathML code in posts will be replaced with a LaTeX equivalent, that the mathstodon.xyz web interface can display.
There's a PR with the code for other vanilla-ish Mastodon instances to use (I had to change the delimiters from dollars to brackets for use here): https://github.com/mastodon/mastodon/issues/26943
Question for anyone who is interested in Kolmogorov complexity: if the idea is applied recursively to some string - that is, let's say we write the the smallest program we can find to generate some larger string, and then ask what the smallest program that can generate that program is. Applied recursively, will the resulting minimum be equal to some theoretical ideal smallest program of the first step, either by definition or via some proof?