# Tire theory

Discussion in 'Free Thoughts' started by arfa brane, Jun 20, 2018.

1. ### arfa branecall me arfValued Senior Member

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A lot of tires are directional these days--they rotate in a direction fixed by the tread pattern.

You may find yourself behind the wheel of a large automobile.
And you may say to yourself, "Directional tires go on the left or the right, I can't put a left tire on the right or a right tire on the left."
And you may say to yourself, "But it doesn't matter if I swap front and back."
And you may ask yourself, "Is that an equivalence relation?
If it is I can quotient my tire-space and say modulo front-equivalent-to-back, I have two ways to locate directional tires, one of which is the right way, and one of which is the wrong way."
And you may say to yourself, "That has to be a Boolean algebra of tire orientations."

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3. ### DaveC426913Valued Senior Member

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Letting the days go by.

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5. ### Michael 345New year. PRESENT is 69 years oldValued Senior Member

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And the wheels on the bus go round and round
Round and round
Round and round
And the wheels on the bus go round and round
Round and round

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7. ### iceauraValued Senior Member

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Rotations in 3D space are described as a group, mathematically, via quaternions.
https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation

Have fun.
I once lived in a town that harbored an engineering firm known for developing robotic arms used in nuclear reactors to handle dangerous stuff in the hot areas - according to rumor, the history of these arms included an early control setup that used ordinary vectors (rather than quaternions) with complicated limits and special codes to handle the range of motion when rotating the arm, and there was a bug. The bug was discovered in testing, when a command to rotate slightly around around the base joint was interpreted by the arm as a command to instantly occupy a position 180 degrees away - the resulting very rapid and full power swing supposedly killed one of the supervisors. I never verified the story, but I have seen some of the wild behavior in machinery that using vectors to control rotations can generate.

I've been puzzled ever since by the omission of quaternions from the standard undergrad mathematics curricula in engineering schools. Maybe things have changed - it's been a while, and coding for games and visual displays (involving rotations) has moved into the mainstream. Anybody know?

Last edited: Jun 22, 2018
8. ### James RJust this guy, you know?Staff Member

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32,302
Same as it ever was.

9. ### gamelordRegistered Senior Member

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673
I am trying to understand quaternions watching this video.

I have got to 11:07 and understood everything. But the part I do not understand is right around 11:07.
At 11:07 he says ijk=-1.
But then he says, iijk=-i. He does not explain how he came to this reasoning.
Because earlier he said that ii=ijk. Therefore it does not follow that the sign would be flipped, since it is indicated that an even amount retains the sign and is no different than the sign of an odd amount. Also, in my mind, imaginary numbers are simply the mirror image of regular numbers.

It is not enough for me to simply memorize and repeat the quaternion code itself. I must truly and deeply understand the mathematics behind it for my soul to be filled.

10. ### gamelordRegistered Senior Member

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673
Going to have to stop you right there. A tires rotation is based on the cylindrical shape of the object. Once it is affixed to an axle, it smoothly rotates on the axle. It's rotation is not "fixed" by the tread pattern, and the tread pattern only has nominal influence on the rotation of the tire.

Going to have to stop you again. I have never personally removed the tires of a large vehicle. But I have removed the tires of a lego car, and if a tire is on the left, you simply unplug it, rotate it 180 degrees, and put it on the right. I am fairly sure that tires of large vehicles are the same, and if they are not, then should be made to be so.

In any case, the song you are alluding to, is this.

The song is relating to the nature of Consciousness, immortality, reincarnation, need, and empathy, in the general sense of one soul to travel through various persons on Earth, at least that is my interpretation.

11. ### arfa branecall me arfValued Senior Member

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Directional tires are designed to rotate in one direction. Non-directional tires aren't. It's pretty simple--your directional tires won't perform like they should if they're mounted the wrong way. In that case, as you state, the tires are rotated 180°, so the direction (the tire is designed to rotate in) is inverted.

But there's nothing stopping anyone from doing that, at least until they have an accident.
Actually the song is based on a radio preacher's broadcast. Brian Eno and David Byrne heard it while driving somewhere and then wrote a song together.

Last edited: Jun 25, 2018
12. ### Michael 345New year. PRESENT is 69 years oldValued Senior Member

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If you are about The Wheels on the Bus I know it as a childrens sing along from a Australian Broadcasting Corporation childs program called Play School

It might have been imported from the British Broadcasting Corporation from a similar program

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13. ### arfa branecall me arfValued Senior Member

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Fascinating. Just. Fascinating.

14. ### river

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11,805
You rotate tires for balanced wear .