In today's episode of "Math #Mystifies #the #Masses," we dive into the riveting world of #probability #density #functions and #interpolation factors—because apparently, nothing screams excitement like calculating how an "entropy bulge" curves upward. 📈🤯 Spoiler alert: It's concave! Stay tuned for more edge-of-your-seat #algebraic #adventures. 🙄
https://cgad.ski/blog/entropy-of-a-mixture.html #Math #Factors #Entropy #Bulge #HackerNews #ngated
#probability
If air molecules move randomly (albeit with some Brownian motion), there iis a probability that all of the air molecules will at some point move to the corner of the room you are in and you will sufficate.
Yes, I know the fallacy.
#physics #probability
If air molecules move randomly (albeit with some Brownian motion), there iis a probability that all of the air molecules will at some point move to the corner of the room you are in and you will sufficate.
Yes, I know the fallacy.
There is a good #probability that you're not a #narcissist if you read this article: https://1testaccount.substack.com/p/no-youre-probably-not-the-narcissist #today on #substack. [Posted by Channel Management Staff].
The Probability of a Hash Collision
https://kevingal.com/blog/collisions.html
#HackerNews #Probability #Hash #Collision #Cryptography #Security #Algorithms
This is an example of amortized complexity and Strassen's "asymptotic spectra" (nice monograph by Zuiddam & Wigderson: https://www.math.ias.edu/~avi/PUBLICATIONS/WigdersonZu_Final_Draft_Oct2023.pdf)
Strassen developed this to understand the #complexity of matrix multiplication and #tensors, but it turns out to also show up in a bunch of places:
- #Entropy
- #Quantum information
- Shannon capacity of graphs
- Communication complexity https://en.wikipedia.org/wiki/Communication_complexity#Information_Complexity
- Circuit complexity (Robere & Zuiddam https://eccc.weizmann.ac.il/report/2021/035)
#math #probability #ComputationalComplexity #TCS #InformationTheory
Real coin flips are ~49-51 not 50-50 https://www.scientificamerican.com/article/scientists-destroy-illusion-that-coin-toss-flips-are-50-50/
But you can guarantee equal probability with a simple trick! Flip 2x in a row starting with the same side up.
HT->call it H
TH->call it T
HH,TT->try again
(due to von Neumann https://en.wikipedia.org/wiki/Randomness_extractor#Von_Neumann_extractor)
This leads to randomness extractors: from a given random process, what's the biggest uniform distribution you can get efficiently?
Randomness extractors give another interpretation of #entropy:
avg # bits needed to *describe* the outcome
=
# uniformly random bits you can *extract* from the outcome
#math #probability #ComputationalComplexity #TCS #InformationTheory
People ask what’s the best info to probability, by far the best short intro to probability and it is so good that even though I read it a few months back gonna read again.
https://archive.org/details/ProbabilityTheoryfirstSteps/page/n9/mode/2up
In grad school I noticed a printed message on the wall of our research lab. It was something like "distill information from the hint of implication" (bad memory).
I innocently said to an older grad student, "Yeah, that does sound like a way to commit Type-I errors" or something equivalent.
Well, that's not what the older grad student took from the sign and I got a very cold, slightly huffy response.
#statistics #probability #pvalues #typeIerror #sample #population
omg mein guter Freund zombiecalypse hat mal wieder abgeliefert: "Wieso gehen Pläne schief, erster Grund: Optimismus".
#ttrpg #pnpde #dnd #dice #statistics #success #failure #probability #maths #mathe
@androcat
It applies to all branches of science. For example statistics: there's no such thing as "letting the data speak for themselves"; they're always interpreted against a background of assumptions and prior knowledge.
I spent two weeks trying to numerically demonstrate convergence of the generalized central limit theorem for the critical case where the variance just becomes infinite. I failed! I suspect my choice of norm was a poor one.
Modeling the sum of 10^30 random variables is challenging.
https://www.skewray.com/articles/the-generalized-central-limit-theorem-for-a2-pareto-and-student-s-t
Foundations of Chebyshev and Chernoff bounds
#Probability #MarkovInequality #DataScience #Statistics #MachineLearning #Math
💁🏻♀️ ICYMI: 🎲🌀 How do mathematicians find patterns in unpredictable events? This #video explains randomness through Michel Talagrand's groundbreaking work on mathematical inequalities.
Random events follow patterns called "normal distributions". After 1,000 coin flips, getting only heads is almost impossible—randomness becomes predictable within limits.
👉 Learn more: https://zurl.co/fHXT4
🎲🌀 How do mathematicians find patterns in unpredictable events? This #video explains randomness through Michel Talagrand's groundbreaking work on mathematical inequalities.
Random events follow patterns called "normal distributions". After 1,000 coin flips, getting only heads is almost impossible—randomness becomes predictable within limits.
👉 Learn more: https://thekidshouldseethis.com/post/randomness-probability-math-talagrand
#ThisWeeksFiddler, 20250530
This week the #puzzle is: Can You Weave the Web? #geometry #trigonometry #probability (Link at the bottom.) A spider weaves a web within a unit square (i.e., a square with side length 1) in the following haphazard manner: First, the spider picks two points at random inside the square. In particular, it picks the points […]
https://stuff.ommadawn.dk/2025/06/03/thisweeksfiddler-20250530/
“You could pay as little as $0.” “Save up to $2000” may be true, but probably false without the odds.
#marketing #failure #probability
“You could pay as little as $0.” “Save up to $2000” may be true, but probably false without the odds.
@alsutton Everytime I go down that rabbit hole, I take a step back and add some context about the #MagicSkyDaddies, #ZombieJews, and other #ImaginaryFriends BILLIONS of people #Whisper their #SelfishWhispers to to bend the laws of #Physics, #Chemistry, #Biology, and #Probability to grant their #SelfishDesires and #beLIEve and will pay 10% of their earnings to. Here is some context:
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