Expected utility | Decision-making paradoxes
In philosophy, Pascal's mugging is a thought-experiment demonstrating a problem in expected utility maximization. A rational agent should choose actions whose outcomes, when weighed by their probability, have higher utility. But some very unlikely outcomes may have very great utilities, and these utilities can grow faster than the probability diminishes. Hence the agent should focus more on vastly improbable cases with implausibly high rewards; this leads first to counter-intuitive choices, and then to incoherence as the utility of every choice becomes unbounded. The name refers to Pascal's Wager, but unlike the wager, it does not require infinite rewards. This sidesteps many objections to the Pascal's Wager dilemma that are based on the nature of infinity. (Wikipedia).
Is AI Safety a Pascal's Mugging?
An event that's very unlikely is still worth thinking about, if the consequences are big enough. What's the limit though? Do we have to devote all of our resources to any outcome that might give infinite payoffs, even if it seems basically impossible? Does the case for AI Safety rely on t
From playlist Best Of
Sum of Entries Pascal's Triangle: https://youtu.be/gxFl1fGn_kg Gaussian Diamond: https://youtu.be/8P0nvUjUZJU Today we take a look at another gem! We be talkign about a diamond fraction in the form of Pascal's Triangle! :) The Solution involves Floors and is pretty spicy overall! =D Enjoy
From playlist Number Theory
The amazing secrets of Pascal's Triangle!
Pascal's Triangle is packed full of hidden patterns and sequences, some of which I talk about in this video, hope you enjoy! Correction: At 1:06, the first exponent is supposed to be 0. Image credit: Beojan Stanislaus, https://en.wikipedia.org/wiki/Sierpiński_triangle#/media/File:Sierp
From playlist Summer of Math Exposition Youtube Videos
Mathsplanations: 5 Reasons to like Pascal's Triangle
This video lists 5 cool facts about Pascal's Triangle, including how to build it and what the number are counting and how they can be useful. The numbers in Pascal's Triangle are called binomial coefficients or nCk. For a more in-depth videos about Pascal's Triangle, check out my other ch
From playlist Mathsplanations
Pascal's Triangle & its Sum of Entries of Each Row [Binomial Theorem, Generating Polynomial]
Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://papaflammy.myteespring.co/ https://www.amazon.com/shop/flammablemaths https://shop.spreadshirt.de/papaflammy Become a Member of the Flammily! :0 https://www.youtub
From playlist Number Theory
Fluids at Rest: Crash Course Physics #14
This episode is sponsored by Audible. Try Audible: http://audible.com/crashcourse Get Your Crash Course Physics Mug here: http://store.dftba.com/products/crashcourse-physics-mug In this episode of Crash Course Physics, Shini is very excited to start talking about Fluids. You see, she's a
From playlist Physics
Discrete Math: 03. Combinatorial Proof on Pascal's Triangle
There is a straightforward way to build Pascal's Triangle by defining the value of a term to be the the sum of the adjacent two entries in the row above it. We also know that Pascal's Triangle contains the binomial coefficients nCk. In this video I provide a combinatorial proof to show w
From playlist Discrete Math part-1
Blaise Pascal 1623-1662 Famous mathematician, scientist, inventor, theologian, and author. Together with Fermat, started modern probabilty theory, a whole new branch of mathematics. Questions supplied by wvannoni http://www.youtube.com/user/wvannoni Le Guardian http://leguardien.wordp
From playlist My Maths Videos
This is a recreation of a short clip from a long form video showing six different ways to construct the Sierpinski triangle: https://youtu.be/IZHiBJGcrqI In this short, we shade odd entries of the Halayuda/Pascal triangle to obtain the Sierpinski triangle. Can you explain why this works?
From playlist Fractals
Temperature: Crash Course Physics #20
Welcome to the new Crash Course Physics Studio! This episode of Crash Course Physics is sponsored by Audible.com. You can go to http://audible.com/crashcourse to get a 30 day trial and help us out as well! Get Your Crash Course Physics Mug here: https://store.dftba.com/products/crashcour
From playlist Physics
National 5 Physics Live: Electricity and energy part 2
National 5 Physics 'Electricity and energy' unit - in this live session, I go over the second half of the National 5 Physics 'Electricity and energy' unit. Topics covered - kinetic and potential energy, conservation of energy, heat and the gas laws. ---------------------------------------
From playlist National 5 LIVE lessons
What's on Your Mind: Series 3 - A Sam Howison Special
Take a mathematician with an endless curiosity about the world around him & the capacity of his subject to interpret it, & you have Series 3 of our #WhatsonYourMind films: a Sam Howison special featuring geometry, flying spiders &, of course, introducing Professor Pointyhead. Cast in orde
From playlist What's on Your Mind - 60 seconds inside the mind of an Oxford Mathematician
Pascal's Triangle and the Binomial Coefficients
Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Pascal's Triangle and the Binomial Coefficients. In this video I show how one can use Pascal's Triangle to quickly compute the binomial coefficients! I do no
From playlist All Videos - Part 8
Adam Savage's Favorite Things of 2020!
Oculus Quest 2: https://amzn.to/32F2YBL Elite Headstrap: https://amzn.to/35KNBtk Cubism: https://www.cubism-vr.com/ Silicone Grips for controllers: https://amzn.to/3kTJqiU AMVR Earbuds: https://amzn.to/3q3vPcC Ultra-thin hook and loop fasteners: https://www.etsy.com/ie/listing/722493801/ul
From playlist Inside Adam's Cave
AQA June 2018 AS Level Maths Paper 1 Walkthrough Q4: Binomial Expansion
Welcome to my walkthrough of the AQA AS Level Maths 2018 paper 1, which comprises of core mathematics and mechanics! These are the first set of real papers for the new 2017 specification AS Level Maths and so they are the best way to revise for your AS Level Maths 2019 exams, as well as t
From playlist AQA June 2018 AS Level Maths Paper 1 Walkthrough
The Rich Have Their Own Ethics: Effective Altruism & the Crypto Crash (ft. F1nn5ter)
Get Nebula cheaper with this link: https://go.nebula.tv/philosophytube Watch "The Prince: https://nebula.tv/videos/philosophytube-the-prince" Support the show! - https://www.patreon.com/PhilosophyTube When crypto company FTX crashed, it posed big questions for the Effective Altruism movem
From playlist The Main Show
PUSHING A GAUSSIAN TO THE LIMIT
Integrating a gaussian is everyones favorite party trick. But it can be used to describe something else. Link to gaussian integral: https://www.youtube.com/watch?v=mcar5MDMd_A Link to my Skype Tutoring site: dotsontutoring.simplybook.me or email dotsontutoring@gmail.com if you have ques
From playlist Math/Derivation Videos
Atmospheric Polar Warming at Mars - Tamara McDunn (SETI Talks)
SETI Talks archive: http://seti.org/talks This talk will cover two active areas of research in the field of martian atmospheric dynamics. The first is polar warming, a temperature enhancement over mid-to-high latitudes that results in a reversed (poleward) meridional temperature gradient.
From playlist Mars Atmosphere Playlist
Discrete Math: 02. Rowsums of Pascal's Triangle
The rowsums of Pascal's Triangle are always powers of 2. Here I provide a combinatorial proof of this fact. The proof involves a very useful technique involving sequences of 0's and 1's. I describe the technique using a small example before moving to the general proof. --An introduction
From playlist Discrete Math part-1