Archive for the Science & Math Category

Coin Flipping Odds

Posted in Science & Math, Uncategorized with tags , , , , , , on February 2, 2016 by Drogo

Essay on Coin Flip Probability

by Tom Over-Being and Drogo Empedocles

Basically the odds of a coin toss in your favor are 1/2 right? 50/50 in other words, 50% of the time tails, 50% heads. It’s a function of how many times you toss the coin then, represented as (1/2) ^ x Where x is number of tosses. In the case of 6 coin tosses then it would be (1/2)^6 which works out to be 0.015625 or 1/64.

It is easy to understand that each time you flip a coin you are re-setting the odds. The previous result means nothing. So the fact that the chances of getting the same result over and over is not 50/50 is the weird part; as referenced in ‘Rosencrantz & Guildenstern Are Dead’ by Tomm Stoppard (Video clip). Each toss is supposed to be 50/50, but the odds of 6 results ending up one way is not the same math, and this may seem odd.

Tom O – “say I have a d4 (pyramid dice), It’s (1/4) if I toss it once, it’s (1/4)^1; if I toss it twice, and want to get “3” both times, the odds are (1/4)^2. Now with the dice the only thing that changes is the fraction coins are (1/2) dice are (1/6). Or another way of looking at it is say you have to make the best of 3 tosses. That’s the most equitable way to randomly make a decision if you don’t want to flip just once right? Well each time you toss that coin the odds of getting heads is 1/2.. You could also solve the problem by throwing 3 coins at once too right? Well that means you’ve run those odds (1/2) by themselves 3 times (1/2)^3 the exact same thing as tossing the same coin 3 times too.”

The odds of getting heads 6 times in a row are not 50/50, like in the Democratic Iowa Caucus of 2016 (‘lucky’ Hillary) that used coin flips in the ‘democratic’ process rather than votes; the odds of getting heads 6 times in row are 1-to-64 !!!

6 heads in a row = 1 / 64

12 heads in a row = 1 / 4096

24 heads in a row = 1 / 16.87million

Khan Academy – Probability & Statistics

Other Probability Math links: Calulator / Coin Flip Pyramid Stat Basics

Matrix

Posted in Science & Math with tags , , on October 12, 2014 by Drogo

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You may have heard the term ‘matrix’ from Doctor Who and the film series called ‘The Matrix’. Some of us even remember matrices from school. Anyone fascinated with organizing will immediately appreciate the idea of a matrix intuitively, even if we cannot spend time on a holodeck like in Star Trek.

A Matrix is a rectangular array of numbers symbols arranged in rows and columns. The individual items in a matrix are called its elements or entries. Matrices are found in most scientific fields, including many branches of physics. Matrices are used to study physical phenomena, such as the motion of rigid bodies. In computer graphics, matrix applications are used to project a 3-dimensional image onto a 2-dimensional screen. Statistical matrices (Stochastic) comprise probability sets; as used in internet search algorithms. Matrix calculus generates classical derivatives and exponentials to higher dimensions. Finding efficient algorithms for matrix computations is part of the expanding field of numeric analysis.

Matrices chart the fabric of physical reality, and create artificial worlds of the imagination as well. Whether we are escaping or investigating, we often use matrix technology in our daily lives. The complex concept of matrix is akin to what Sartre called ‘the simulation of the simulacra’ in post-modern philosophy.