# Imaginary Number

Members

11

## Posts posted by Imaginary Number

### Hairy Ball Theorem

To clear this up, lets say that I have a furry sphere with all the hairs combed in the same direction, almost all, will I have a vector that looks like (0)

(0)

Actually would the same rules apply to "four vectors?"

### The Flat Earth Society!

The flat earth society still exists? Now that is a shame.

Incredible.

Wonderful!

### Isn't energy actually a vector?

Energy has always been defined as a scalar quantity since it measures magnitude but, of course has no direction. (E.g. temperature)

And as we know vectors have magnitude and direction. (E.g: Velocity)

However, there are 4 dimensions. Our three spacial dimensions and then the fourth: Time. Now as I understand it, everything in the universe is travelling through the fourth dimension at lightspeed. So while energy has no typical direction it has a forwards direction in time. So energy in one place, 3 seconds later, will have traveled forwards (4 dimensionally) by "3 seconds"

So isn't energy technically a vector?

### Can any event occur that has no cause?

Does causation have a cause?

"causation" is not a proper noun. It is incorrect to use it in the way you have, which is why it is nonsense.

Another example would be "What is bluer than blue?"

Anything "bluer" would obviously just be blue.

### Hairy Ball Theorem

Look up vector bundles.

In this context we mean no non-zero globally defined vectors.

In other words, there does not exist an everywhere non-zero tangent vector field on even dimensional spheres. That is at some point(s) on the sphere the vector field will vanish.

So if I am understanding you correctly: There has to be somewhere on the sphere where one of the vectors is zero. Is that right?

I know that a vector is magnitude AND direction, so is the magnitude zero and the direction also zero?

### Can any event occur that has no cause?

What is the difference between something that has no cause and something which has a cause that cannot be known?

One of them has a cause while the other does not.

### Hairy Ball Theorem

Take a look at Wiki.

It states that there are no non-vanishing continuous vector fields on n-spheres for n even. It is a consequence of the tangent bundle of even dimensional spheres are non-trivial. It has no non-zero global sections.

If you try to comb a "hairy ball" you will always get a tuft.

What do you mean by "non-zero global sections?"

What are they?

### Can any event occur that has no cause?

Yes & No.

Spontaneous things can happen out of the blue, but they wouldn't happen if the thing from which they were spontaneously emmitted, didn't exist. So if a radioactive substance didn't exist then neither would any following emmisions.

### Hairy Ball Theorem

I've heard of this mathematical theorem but could someone explain it to me, in very, very short words and simple sentences?

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