Just yesterday, I was musing to a (younger) research visitor, "I hope that within my lifetime we will still see another breakthrough on the bounds for R(3,k)"...
https://arxiv.org/abs/2505.13371
I am excited to see what developments follow on from here!
(Also that old adage: just as soon as you publish a survey (https://arxiv.org/abs/2501.03379) it is out of date.)
#math #mathematics #combinatorics #ExtremalCombinatorics #graphtheory #probability
Bayes: Your calculations can only be as reliable as your priors and everyone always has priors. So it pays to be humble.
AI Techbros: I'm a total Bayes guy and that's why I know without a shadow of a doubt that AGI will be here in 2 years. Don't believe me? Debate me. Now!
🤩 what a gem 💎 from @geogebra. Probability distributions app:
https://www.geogebra.org/classic#probability
#probability #iteachmath #visualization
#ThisWeeksFiddler, 20250509
This week the #puzzle is: Can You Sweep the Series? #probability Let p represent the probability the Celtics win any given game in the [best-of-seven] series. You should assume that p is constant (which means there’s no home-court advantage) and that games are independent. For certain values of p, the likeliest outcome is indeed that […]
https://stuff.ommadawn.dk/2025/05/13/thisweeksfiddler-20250509/
Averaging a bunch of Pareto distributions together approaches a normal distribution, because of the central limit theorem. But how does the speed depend on the slope of the power-law tail?
If nothing else, at least there are a lot of wild plots.
(Just finished writing my laudatio speech.)
Eoin Hurley will defend his PhD on Wednesday.
#combinatorics #graphtheory #ExtremalCombinatorics #probability #algorithms #math
Sugihara monoids, RM3, infinite valued logic, and probability ...
Infinite-Valued Relevance Logic as a Probability Structure
Here’s a conceptual leap: if truth values form a bounded poset (e.g. real unit interval [0,1]), and conjunction, disjunction, and implication are operations preserving some form of ordering or residuation, you can begin to think of logic as probabilistic entailment.
Now, if we make the truth values correspond to probabilities (or credences), then:
A⇒B is strongest when the truth value of A is less than or equal to that of B.
This mimics conditional probability: P(B∣A) is highest when A almost implies B.
In fact, some researchers have developed algebraic models of conditional probability using residuated lattices or MV-algebras (multi-valued algebras from Łukasiewicz logic), and relevance logic’s demand for resource sensitivity fits naturally with context-sensitive probability assignments.
You can think of A⇒B not as a function of static truth values, but as "the degree to which A supports B," akin to Bayesian support.
How hard is it to teach clinicians #probability?
After a 2-hour e-learning course clinicians felt more confident and did better on multiple choice questions, but didn't improve their #risk calculations (n > 200).
The cackling villain gesticulates wildly and pronounces, "You must flip this coin and take a step to the right for heads and to the left for tails. Somewhere is a pit that leads to the caldera of the FIERY VOLCANO OF INFINITE DEATH!" With much trepidation, you begin flipping the coin and stepping accordingly. Suddenly, you find nothing below your right foot! The villain gloats, "If only you had some way to unflip that coin!"
If we multiply two irrational numbers together, like root-2 times root-2, we can get an integer. So, in the same way, we should be able to toss half a coin twice to get a whole coin toss, right? Right?
#probability #statistics #MathHumor
https://www.skewray.com/articles/what-happens-when-someone-tosses-half-a-coin-mayhem
What's a better predictor of med. students' accuracy in #diagnosis?
- #Motivation to become a researcher
- #Math ability
Among 128 students of #medicine, #numeracy was *much* more predictive of scores on medical cases involving #probability.
We #Whisper our #SelfishWhispers to our #ImaginaryFriends to bend the laws of #Physics #Chemistry #Biology and #Probability to grant our #SelfishDesires. In #ZombieJew's name we #Whisper. #Amen
People were less averse to #risk (d = 0.4) when making #prenatalTesting decisions in their SECOND #language — even when they seemed to understand the relevant information.
https://doi.org/10.1002/bdm.70016
#parenting #cogSci #medicine #genetics #edu #probability #stats #linguistics #econ
TIL: independence is a (much) stronger property than unrelatedness. It is definitely in the embarrassing category that I only discovered this after many years of using probability theory. But glad I did.
Averaging a bunch of symmetric beta distributions together approaches a normal distribution as 1/N. But how does this depend on the distribution parameters?
https://www.skewray.com/articles/central-limit-theorem-speed-of-convergence-of-the-beta-distribution
The central limit theorem states that a sum of independent identically-distributed random variables with finite variance will ultimately converge to a normal distribution. But how fast? Is the convergence so slow that theorem is useless for real data?
https://www.skewray.com/articles/speed-of-convergence-for-the-central-limit-theorem
How can #language impact #risk perception?
#CIA's Sherman Kent famously attempted to standardize "words of estimative #probability" (1964): https://philpapers.org/rec/KENWOE
Milczarski et al. find many WEPs seem commensurable across #English and #Polish: https://doi.org/10.1017/jdm.2025.3
#probability : appearance of reality or truth
- French: Probabilité
- German: die Wahrscheinlichkeit
- Italian: probabilità
- Portuguese: probabilidade
- Spanish: probabilidad
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As NHL playoffs approach, how odds, math and probability collide on picking a Stanley Cup favourite
"The Eastern Conference, just like the Western Conference, I think is wide open right now," said one hockey handicapper.
#hockey #sports #probability #math #NHL #NHLPlayoffs
https://globalnews.ca/news/11133455/nhl-playoffs-odds-math-stanley-cup-favourites/
As NHL playoffs approach, how odds, math and probability collide on picking a Stanley Cup favourite
"The Eastern Conference, just like the Western Conference, I think is wide open right now," said one hockey handicapper.
#hockey #sports #probability #math #NHL #NHLPlayoffs
https://globalnews.ca/news/11133455/nhl-playoffs-odds-math-stanley-cup-favourites/
