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VIDEO: Where Algorithms Fail

My sister showed me this video a few days ago and I’d thought I’d share it with you. In it Cathy O’Neil, author of the new book ‘Weapons of Math Destruction‘, discusses the danger of algorithms, giving a few examples to illustrate her eye-opening points. O’Neil then goes on to highlight a few steps we can take, as a society, in order to overcome these pitfalls. I found this short video thoroughly interesting and hope you enjoy it as well!

“Algorithms decide who gets a loan, who gets a job interview, who gets insurance and much more — but they don’t automatically make things fair. Mathematician and data scientist Cathy O’Neil coined a term for algorithms that are secret, important and harmful: “weapons of math destruction.” Learn more about the hidden agendas behind the formulas.”

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VIDEO: Napkin Ring Problem

If you were to core a sphere (remove a cylinder from it), you are left with a shape that looks like a napkin ring. This is a “bizarre” shape, as if you have two napkin rings with the same height, they will have the same volume regardless of the size of the initial spheres that they came from. How do you prove this?

Here’s a few hints to try and solve it yourself before watching the Vsauce video below which reveals the answer:

  • There are a few variables that need to be found: the height of the napkin ring, the radius of the starting sphere and the radius of the cylinder. Using these variables you can find a volume equation.
  • You don’t need to find the volume of the whole napkin ring in one go. This is because, as the two napkin rings have to be the same height, it’s enough to show that any slice of the napkin rings has to have the same area. If every pair of slices has the same area, then the napkin rings have the same volume.

Solution:

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MATHS BITE: The Kolakoski Sequence

The Kolakoski sequence is an infinite sequence of symbols {1,2} that is its own “run-length encoding“. It is named after mathematician Willian Kolakoski who described it in 1965, but further research shows that it was first discussed by Rufus Oldenburger in 1939.

This self-describing sequence consists of blocks of single and double 1s and 2s. Each block contains digits that are different from the digit in the preceding block.

To construct the sequence, start with 1. This means that the next block is of length 1. So we require that the next block is 2, giving the sequence 1, 2. Continuing this infinitely gives us the Kolakoski sequence: 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, etc.

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VIDEO: Spiral Sculptures

John Edmark is an artist and professor at Stanford University who has used the Golden Angle to sculpt spirals. The Golden Angle is derived from the Golden Ratio: it is the smaller of the two angles created by dividing the circumference of a circle according to the golden ratio and comes out to be around 137.5°.

For more click here.

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VIDEO: Connecting the Drops

Today I thought I’d share a video that I came across the other day. Hope you enjoy!

“Bacteria and viruses hitch a ride inside droplets of all kinds—sneezes, raindrops, toilet splatter. By reviewing footage of different types of drops, applied mathematician Lydia Bourouiba records and measures where they disperse in order to better understand how diseases spread. Watch how Bourouiba designs tests—some inescapably humorous and awkward—to study infectious disease transmission.”

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VIDEO: Map of Mathematics

Today I wanted to share with you a video which I came across the other day on the Map of Mathematics.

Although many people view maths as synonymous with pain, boredom or frustration, one must appreciate its diversity and vast implications on other subjects; you may not have the background to see beauty in a particular equation, but virtually anyone can appreciate the amazing advancements humans have made from basic counting to creating full-on artificial intelligence.

While an artistic temperament is often considered the exact opposite of the kind of personality that loves complicated equations, pure mathematicians are really just a bunch of lunatics endlessly working with abstraction and beauty.

– Rhett Jones

In the video below, Dominic Walliman takes viewers through the major fields of math starting at the beginning and shows us how they inform and relate to each other. Of course many details have been left out, as to properly connect the various disciplines of math we would need a 3D web! Also, in reality, “the study of math’s foundations has yet to discover a complete and consistent set of axioms.

Hope you enjoyed the video! M x

VIDEO: Banach–Tarski Paradox

The Banach-Tarski Paradox is a theorem in geometry which states that:

“It is possible to decompose a ball into five pieces which can be reassembled by rigid motions to form two balls of the same size as the original.”

It was first stated in 1924, and is called a paradox as it contradicts basic geometric intuition.

An alternate version of this theorem tells us that:

“It is possible to take a solid ball the size of a pea, and by cutting it into a finite number of pieces, reassemble it to form a solid ball the size of the sun.”

Below is an awesome video explaining how this paradox works:

 

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