Buying a scratch card feels harmless.
But if every ticket guarantees a negative expected value…
are you paying for hope, not opportunity?
https://www.emberhart.com/may-the-odds-never-be-in-your-favor-probabilities-of-winning-christmas-scratch-cards/
#Probability #EmberhartJourney #PositiveParenting #KindnessRocks#ExpectedValue #FinancialThinking #MathMatters
May the Odds Never Be in Your Favor: Probabilities of Winning Christmas Scratch Cards - Emberhart

The Odds of Winning Christmas Scratch Cards: A Lesson in Probabilities. Explore the real probabilities behind winning with Christmas scratch cards. Discover how the odds work, and learn why playing the lottery may not be the best investment, even during the holidays.

Emberhart
Biases & Rain 2/10
📉 Poor intuition about ratios: even if you know 7 is more likely than 11, you might underestimate how much. 7 is actually 3x more common.
#MathMatters #Ratios #HiddenPatterns #Emberhart

Assistance has 1/x power: the less you make, the more each dollar matters.
Recipients amplify it with creativity.
Screening wastes resources when the goal is impact.
Universality shifts policy from moralism to efficacy.

#UBI #Nomodynamy #FreeWillInAction #MathMatters

After years working in tech, I'm convinced that AI safety requires mathematical rigor, not just ethics committees. The formal verification of neural networks isn't optional—it's essential if we want AI systems whose behavior we can truly understand and predict. #AI #MathMatters

West Virginia University is trying to drop its maths graduate program (i.e. no longer offer MS or PhD in mathematics), and to cut the number of maths academics by about 37%.

https://provost.wvu.edu/files/d/62ea2c4f-99bd-431d-9e97-7199271fecab/preliminary-recommendation-mathematical-and-data-sciences.pdf

"📢 Sad News: WVU recommends ending Math graduate programs (MS & PhD). This means that there will potentially be no PhD math program in WV. A puzzling move for a land-grant institution! #MathMatters #WVU #EducationMatters"
https://twitter.com/wvumath/status/1689823117684752385

"Mathematics and Data Sciences: Discontinue MS Mathematics, PhD Mathematics. Approval for intent to plan for MS Applied Mathematics/Data Sciences program. Eliminate 18 of 49 faculty.

This is consistent with earlier reports."
https://twitter.com/AnonymousF59605/status/1690077384282607616?s=20

via Reddit's r/math

How imaginary numbers describe the fundamental shape of nature | Aeon Essays

These odd values were long dismissed as bookkeeping. Now physicists are proving that they describe the hidden shape of nature

Aeon

@[email protected] it might help to go the other way, take an even distribution on a disk, and measure the angles and radii

#mathmatters

https://stats.stackexchange.com/a/481544

Generating random points uniformly on a disk

I have to randomly generate 1000 points over a unit disk such that are uniformly distributed on this disk. Now, for that, I select a radius $r$ and angular orientation $\alpha$ such that the radius...

Cross Validated

"It's crazy to think that quaternions, an abstract mathematical tool discovered by William Rowan Hamilton in 1843, would be so perfectly suited to solve hard problems in the world of 3D character animation more than a hundred years later. The story of how he discovered quaternions is also beautiful."

#animation #quaternions #MathMatters

https://diegomacario.github.io/Animation-Magic/public/index.html

Beware the universal structural instability at particular fractal dimensions that can change fundamental properties!

What happens here? It's like a phase transition, a universal instability point. So my next question was, do graphs have fractal dimensions, like social graphs or network graphs, and yes, of course they do...

#mathmatters #fractaldimensions #nanoparticles #networks #complexity #chaos #surprise

https://pubs.rsc.org/en/content/articlelanding/2022/CP/D1CP04709D

The universal relationship between sample dimensions and cooperative phenomena: effects of fractal dimension on the electronic properties of high-TC cuprate observed using electron spin resonance

As demonstrated by the unique electronic properties of nanostructured materials, which are qualitatively different from the bulk properties of the same materials, there should be a general relationship between the dimensions of the sample structures and the physical/chemical properties. However, it is demand