Parth G | The Most Powerful Tool Based Entirely On Randomness @ParthGChannel | Uploaded 2 years ago | Updated 11 hours ago
We see the effects of randomness all around us on a day to day basis. In this video well be discussing a couple of different techniques that scientists use to understand randomness, as well as how we can harness its power. Basically, we'll study the mathematics of randomness.
The branch of science and math that deals with such randomness is known as "stochastics". The kind of randomness we'll focus on is the kind where we can't predict the result of an experiment or measurement before we make it, but crucially we do know the probability of each possible result before we make the measurement, and this does not change over time. An example is tossing a coin. A fair coin has a 50% chance of landing on either heads or tails and this does not change regardless of the results of any previous coin flips.
We understand the difference between perceived randomness and true randomness. A coin toss is perceived to be random because we don't have any way to collect all the data we would need to predict the outcome of a coin toss. A quantum measurement is considered truly random because it relies on the collapse of the wave function.
We'll take a look at a random walk model, which works on the principle that a particle is allowed to move a fixed distance every unit time, but in varying (random) directions. In 1D, the particle can move either up or down (for example), in 2D along any direction on a flat surface, and in 3D along any direction at all.
We can use a spinner to model the "randomness" in the random walk. The direction that the spinner lands on, will determine which direction the particle moves for a given unit of time. The spinner can be spun repeatedly to model multiple steps in the random walk. The spinner has the kind of randomness we described at the beginning of this description.
The random walk model can be used to describe real life systems, such as particles undergoing Brownian motion. This involves particles jiggling around rather than staying still, due to collisions with smaller particles that are too small to be visible.
We can model randomness using a random number generator (RNG). We can get it to generate random numbers between 0 and 1, using a uniform distribution. This simple technique can be used to model both discrete and continuous systems, as well as uniform and non-uniform probability systems.
We see how to use the RNG numbers to model the random walk, by multiplying the random numbers by 360 to give the angle at which the particle moves for each time step. We also see how the RNG numbers can be used to model an unfair die, by assigning ranges between 0 and 1 to each possible die result based on the unfairness of the die.
At the moment RNGs aren't truly / perfectly random, but maybe one day they will be! And they are the key to harnessing the power of randomness.
Thanks for watching, please do check out my socials here:
Instagram - @parthvlogs
Patreon - patreon.com/parthg
Music Chanel - Parth G's Shenanigans
Merch - https://parth-gs-merch-stand.creator-spring.com/
Here are some affiliate links for things I use! I make a small commission if you make a purchase through these links.
Introduction to Elementary Particles (Griffiths) - the book used in this video: https://amzn.to/3I3ld71
Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
My Camera: https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
Microphone (Fifine): https://amzn.to/2OwyWvt
Gorillapod: https://amzn.to/3wQ0L2Q
Videos linked in cards:
1) youtu.be/Is_QH3evpXw
2) youtu.be/fBR5HQ-Ja10
Brownian Motion: https://en.wikipedia.org/wiki/Brownian_motion
Timestamps:
0:00 - The Randomness Around Us
0:49 - What Do We Mean by Randomness?
2:38 - True vs. Perceived Randomness
4:27 - The Random Walk Model
6:24 - Brownian Motion: a Real Life Random Walk
9:50 - Random Number Generator: Modelling Reality
13:42 - The Problems with an RNG
We see the effects of randomness all around us on a day to day basis. In this video well be discussing a couple of different techniques that scientists use to understand randomness, as well as how we can harness its power. Basically, we'll study the mathematics of randomness.
The branch of science and math that deals with such randomness is known as "stochastics". The kind of randomness we'll focus on is the kind where we can't predict the result of an experiment or measurement before we make it, but crucially we do know the probability of each possible result before we make the measurement, and this does not change over time. An example is tossing a coin. A fair coin has a 50% chance of landing on either heads or tails and this does not change regardless of the results of any previous coin flips.
We understand the difference between perceived randomness and true randomness. A coin toss is perceived to be random because we don't have any way to collect all the data we would need to predict the outcome of a coin toss. A quantum measurement is considered truly random because it relies on the collapse of the wave function.
We'll take a look at a random walk model, which works on the principle that a particle is allowed to move a fixed distance every unit time, but in varying (random) directions. In 1D, the particle can move either up or down (for example), in 2D along any direction on a flat surface, and in 3D along any direction at all.
We can use a spinner to model the "randomness" in the random walk. The direction that the spinner lands on, will determine which direction the particle moves for a given unit of time. The spinner can be spun repeatedly to model multiple steps in the random walk. The spinner has the kind of randomness we described at the beginning of this description.
The random walk model can be used to describe real life systems, such as particles undergoing Brownian motion. This involves particles jiggling around rather than staying still, due to collisions with smaller particles that are too small to be visible.
We can model randomness using a random number generator (RNG). We can get it to generate random numbers between 0 and 1, using a uniform distribution. This simple technique can be used to model both discrete and continuous systems, as well as uniform and non-uniform probability systems.
We see how to use the RNG numbers to model the random walk, by multiplying the random numbers by 360 to give the angle at which the particle moves for each time step. We also see how the RNG numbers can be used to model an unfair die, by assigning ranges between 0 and 1 to each possible die result based on the unfairness of the die.
At the moment RNGs aren't truly / perfectly random, but maybe one day they will be! And they are the key to harnessing the power of randomness.
Thanks for watching, please do check out my socials here:
Instagram - @parthvlogs
Patreon - patreon.com/parthg
Music Chanel - Parth G's Shenanigans
Merch - https://parth-gs-merch-stand.creator-spring.com/
Here are some affiliate links for things I use! I make a small commission if you make a purchase through these links.
Introduction to Elementary Particles (Griffiths) - the book used in this video: https://amzn.to/3I3ld71
Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
My Camera: https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
Microphone (Fifine): https://amzn.to/2OwyWvt
Gorillapod: https://amzn.to/3wQ0L2Q
Videos linked in cards:
1) youtu.be/Is_QH3evpXw
2) youtu.be/fBR5HQ-Ja10
Brownian Motion: https://en.wikipedia.org/wiki/Brownian_motion
Timestamps:
0:00 - The Randomness Around Us
0:49 - What Do We Mean by Randomness?
2:38 - True vs. Perceived Randomness
4:27 - The Random Walk Model
6:24 - Brownian Motion: a Real Life Random Walk
9:50 - Random Number Generator: Modelling Reality
13:42 - The Problems with an RNG
