NationStates Jolt Archive

Connes's idea was to extend the relation between geometric space and its commutative algebra of Cartesian coordinates, such as latitude and longitude, to a geometry based on noncommutative algebras. In commutative algebra, the product is independent of the order of the factors: 3 x 5 = 5 x 3. But some operations are noncommutative. Take, for example, a stunt plane that can aggressively roll (rotate over the longitudinal axis) and pitch (rotate over an axis parallel to the wings). Assume a pilot receives radio instructions to roll over 90 degrees and then to pitch over 90 degrees toward the underside of the plane. Everything will be fine if the pilot follows the commands in that order. But if the order is inverted, the plane will take a nosedive. Operations with Cartesian coordinates in space are commutative, but rotations over three dimensions are not.

Discuss. :)

Ok, I know it's in English.....

Discuss. :)
Isn't that how shit works now?

*is confused*

:confused:

*wanders off*

This is why pilots don't need to know algebra.

Ok, I know it's in English.....

Liar.

Please don't DEAT me.

Discuss. :)

So what? Nothing I didn't already know.

And I've also logged countless hours on flight sims. That's rudimentary knowledge there, pal. If you do that during a dogfight, you're F-U-C-K-E-D.

Is this English?

Discuss. :)
Rotational effects aren't commutative in two dimensions either. You can't make the comparison between two- and three-dimensional mathematics and use apples and oranges to show how one doesn't follow. The correct response would be, "Well, duh."

This is why pilots don't need to know algebra.

Well not true, we need to know some Algebra.

So what? Nothing I didn't already know.

And I've also logged countless hours on flight sims. That's rudimentary knowledge there, pal. If you do that during a dogfight, you're F-U-C-K-E-D.
Don't miss the forest for the trees. This is about the math. Using the plane was just an example. The point is that this guy has figured out how the geometry of space can create Bosian particles, a hole in the standard model that has needed to be filled.

So what? Nothing I didn't already know.

And I've also logged countless hours on flight sims. That's rudimentary knowledge there, pal. If you do that during a dogfight, you're F-U-C-K-E-D.
I still don't see what commutativity has to do with a stunt plane. Flying a stunt plane is not at all like multiplying 3 by 5 in any order you want.


Also, isn't the cartesian coordinate system 2d? And aren't planes 3d?

Nevermind, i'm going over there
:confused:

Is this why the RAF beat the Luffewaffa in WW2?

It seems to me rather self explanatory. The way a plane works you can roll it one way first, then flip it over... but if you flip it first, it will crash. This has to do with the way a plane is built.

However, if you are talking about pure numbers, you can manipulate them in many different ways and it all comes out the same. This had to do with the fact that numbers are not subject to G forces, friction, centrifugal forces, etc.

Use, instead, as your example, a ball. If thrown in such a way that first it rotates forward, then rolls to the left, will it end up in the same place as if it first rolled left, then rotated forward? Unlike the plane, a ball can take both stresses equally, but would the final trajectory be the same if it got the same push each time but in a different order?

For the record, I don't actually know the answer... let me know if you find out.

It seems to me rather self explanatory. The way a plane works you can roll it one way first, then flip it over... but if you flip it first, it will crash. This has to do with the way a plane is built.

However, if you are talking about pure numbers, you can manipulate them in many different ways and it all comes out the same. This had to do with the fact that numbers are not subject to G forces, friction, centrifugal forces, etc.

Use, instead, as your example, a ball. If thrown in such a way that first it rotates forward, then rolls to the left, will it end up in the same place as if it first rolled left, then rotated forward? Unlike the plane, a ball can take both stresses equally, but would the final trajectory be the same if it got the same push each time but in a different order?

For the record, I don't actually know the answer... let me know if you find out.

Answer?



There's a question?
:confused: X 100000000

If PsychoticDan is flying a two dimensional plane over Bosian airspace and the Serbs attempt to shoot him down with particles, would it be possible to make a noncommutative roll whilst pitching evasively?

Answer?



There's a question?
:confused: X 100000000

LOL.. yes, actually, there is...

Discuss. :)
It makes perfect sense if you look at it from the geothermal psyconytheis point of view.

Quite simple.

If PsychoticDan is flying a two dimensional plane over Bosian airspace and the Serbs attempt to shoot him down with particles, would it be possible to make a noncommutative roll whilst pitching evasively?
Sure, but the particles would still hit him. Then 2d matter and 3d matter would react in an unknown way. I predict annihilation.

It makes perfect sense if you look at it from the geothermal psyconytheis point of view.

Quite simple.
Ruffy is so smart :fluffle:

If PsychoticDan is flying a two dimensional plane over Bosian airspace and the Serbs attempt to shoot him down with particles, would it be possible to make a noncommutative roll whilst pitching evasively?

No, but if he were flying through a kitchen, and they attempted to shoot him down with duck sauce, he might be able to make a spring roll...

If PsychoticDan is flying a two dimensional plane over Bosian airspace and the Serbs attempt to shoot him down with particles, would it be possible to make a noncommutative roll whilst pitching evasively?
Are these fecal particles or roach particles?

Ruffy is so smart :fluffle:
Ruffy is so bullshit. :p

Ruffy is so bullshit. :p
Nooooooooooooooo
*faith in mankind goes bye bye*
*not womankind though*

Nooooooooooooooo
*faith in mankind goes bye bye*
*not womankind though*

In other news, Women have decided to go back into the Kitchen, and the men are once again breadwinner of the family. :p

Nooooooooooooooo
*faith in mankind goes bye bye*
*not womankind though*
*checks Ifreann's name off list*

Don't miss the forest for the trees. This is about the math. Using the plane was just an example. The point is that this guy has figured out how the geometry of space can create Bosian particles, a hole in the standard model that has needed to be filled.

I know it's about the math. I was just saying what I wanted to say, because hey, I like aircraft. :p

And it was pretty obvious anyway, really. I mean, two and three dimensional planes are very different things.

I mean, two and three dimensional planes are very different things.
They fly differently.

Not enough info. What you say makes sense as far as the need for sequential description of motion, but you speak nothing of the proposed solution. I'm not going to research it.

In other news, Women have decided to go back into the Kitchen, and the men are once again breadwinner of the family. :p


Oh, not good. I just burnt my house down trying to boil toast...

I disagree with the airplane thing. It's a bad example because the author not consistent with the axis of rotation, rather is varying it with the orientation of the aircraft body. In fact I'm going to say that rotation in 3-d is commutative. (Set of all 3-1 vectors whose entries are real). So :p .

With the rest of it, I'm not sure what you are getting at.

Not enough info. What you say makes sense as far as the need for sequential description of motion, but you speak nothing of the proposed solution. I'm not going to research it.

If you want to have a 3d model of reality including motion then it must be a 4d model that includes time. simple really.

I disagree with the airplane thing. It's a bad example because the author not consistent with the axis of rotation, rather is varying it with the orientation of the aircraft body. In fact I'm going to say that rotation in 3-d is commutative. (Set of all 3-1 vectors whose entries are real). So :p .

With the rest of it, I'm not sure what you are getting at.

Agreed, itwould most likely be commutative if the space shuttle did these acrobatics in orbit outside of the influence of gravity and the friction of airflow.

If you want to have a 3d model of reality including motion then it must be a 4d model that includes time. simple really.
Best I've read so far. And I work in 4d.

I understood that perfectly. It's simple, clear, and quite frankly, obvious.

If you want to have a 3d model of reality including motion then it must be a 4d model that includes time. simple really.
I'm a degreed engineer, with the dangerous minor in experimental psychology... Describing partical motion is simple, really. However, describing the motion of a body with multiple axes of rotations is not so simple, really.