Pwrong

On June 12, 2017 a research team studying the complex networks involved in information processing, revealed that the processes involved in the creation of neural structures are built on multiverse-like structures. Using algebraic topology, they “zoomed” into the neural networks of the brain, finding hidden structures of the neurons. When they are presented with a stimulus, groups of neurons form a clique, each individual neuron connecting via a specific configuration, forming a precise geometric object. And the more neurons clique, the higher the dimensions.

The left shows a digital copy of a part of the neocortex, the most evolved part of the brain. On the right is a representation of the structures with different dimensions. The black hole in the middle symbolizes a complex of multi-dimensional spaces, or cavities.BLUE BRAIN PROJECT

“The appearance of high-dimensional cavities when the brain is processing information means that the neurons in the network react to stimuli in an extremely organized manner.

It is as if the brain reacts to a stimulus by building then razing a tower of multi-dimensional blocks, starting with rods (1D), then planks (2D), then cubes (3D), and then more complex geometries with 4D, 5D, etc. The progression of activity through the brain resembles a multi-dimensional sandcastle that materializes out of the sand and then disintegrates”

- Ran Levi. of the researchers

Exemplification of a  clique formed by five pyramidal cells (A), with zoom into the somata of the clique in (A) and representation of their connectivity as a directed graph. (B3).

“We found a world that we had never imagined. There are tens of millions of these objects even in a small speck of the brain, up through seven dimensions. In some networks, we even found structures with up to eleven dimensions.”

Having trouble picturing those 11 dimensions, aren’t you?

@pwrong: Dear Mr Xenophon, your fellow team members would like to know how you’ll be voting. Dear Mr Xenophon, we think the parliament is hung so who are you promoting?

Me: Malcolm or Bill? We know it’s lose-lose with Malcolm or Bill But if you had to choose

@pwrong: Well I’ll be damned, well I’ll be damned, Xenophon’s on your side

“They gathered and began the sandwalk, gliding over the surface in a broken rhythm that would disturb no maker.”

“They fell into the disjointed rhythm of movement across this broken land." 

https://twitter.com/PureRomance/status/700792377674493952

Still a pyramid scheme though. Most of their distributors lose money. People shouldn’t host or go to their parties, or any other party following their model. 

Since the source of gravitational force is mass and the strength of such a force gets exponentially weaker with distance from the center of this mass it can be reasoned that as you travel from the center of the Earth’s mass, you would get exponentially lighter.

And yet you don’t.

The Earth is therefore round (I.e. your distance from the center of Earth’s mass doesn’t change much from any single location on Earth’s surface).

…but by all means don’t take my word for it. Mathematically prove it to yourself:

Force = Mass • Acceleration

Force of Gravity = (Gravitational constant • Mass1 • Mass2)/ distance between the two masses^2

Lets shorten that to:

F=ma

F=GmM/r^2

Now combine the two equations (since both are equations to derive a force, this is mathematically allowed):

ma=GmM/r^2

Since we’re only approximating, and G (the gravitational constant) is an extremely small number, we can discard it as this will simplify the example for you without changing the approximation by much.

Therefore:

ma=mM/r^2

Obviously we can divide ma by m on both sides of the equation leaving:

a=M/r^2

You getting nervous?

Multiply r^2 on both sides to get:

ar^2=M

Divide by a:

r^2=M/a

Take the square root of both sides:

r=√(M/a)

Again, M is the mass of the Earth and a is the rate of acceleration towards it due to gravity (9.8 m/s^2 fyi). Both numbers are always the same. If they weren’t then at certain places and certain times you’d be able to moonwalk across the surface of the Earth.

As you can see I have just literally mathematically proven that the radius of the Earth is constant in all directions.

I.e. it’s a sphere.

But if you do assume that, gravity on a disk-shaped planet would be interesting and very different from a globe. You're right that the strength would be depend on where you are, but the direction would change as well. As you get further from the centre, you're pulled back towards it, so it would feel like you're walking uphill. It would look flat but feel like living inside a bowl.

There's a couple of minor errors in your proof: 1. 1/r^2 is not exponentially decreasing.

Terms like nullspace and eigenvalues will be confusing until you learn how how they work geometrically. Then it'll all fall into place.

All right! So:

I was commissioned to illustrate how a given everywhere-continuous but nowhere-differentiable function fails to be differentiable.

So I made this one up! It’s basically a sum of functions f at the top there.

You don’t have to know anything about debating. You don’t have to have a lucid and sound defense of your stances. You don’t have to know how to engage and provide counterpoints to others who are challenging your point of view. You don’t have to have the slightest idea of what you’re talking about…….Just remember these phrases and you’ll always win:

-”to each his own”

-”I’m on my own journey”

-”you’re not better than me”

-”live and let live”

-”I believe in freedom” (People really, really, LOVE that word)

-”It’s my choice” (Choice is another crowd pleaser)

You have instructions written down. You don’t need them, but you check them anyway. Somehow they’re different from what you remember. Have they changed since you tucked the paper in your pocket? 

You realize that you’ve lost your train of thought. You can’t remember what you were thinking before. There is only your present thought, now a loop of panic at your lost memory. 

You stop in the middle of a room. Why are you here? Which room did you come from? You leave the room and remember what you were going to do. You walk back into the room. Why are you here? 

You bring up an inside joke with a friend. They look at you blankly. They do not remember this joke. But you were there when I made it, you argue. They were not. They are not the friend you are thinking of. You realize it was your other friend, from work instead of high school, with blond hair instead of brown, tall instead of short. You do not know how these two friends are so similar in your mind. 

You refer to every experience as happening “the other day.” Was it three years ago or yesterday? You try to remember context clues. Time is not real. 

Someone asks you for an important piece of information. You have not thought about it since you saved it on your computer, labelled very clearly. You search through your files. It is not there. You find it days later by accident, labelled with a cryptic set of codes. You don’t know why you would label it this way. No one else uses this computer but you. 

You are running late. You are always running late. 

You have lost something. You check everywhere. You check everywhere again. Someone tells you to think of when you last had it. You don’t tell them that is the problem. 

You watch a movie for the first time. Half way through, the scenes become familiar and you remember how it ends. Frustrated, you watch a movie you know you've seen three times before. You don't remember this character, who is he?