Orthogonal

[Rover_KE]

How many of you know and use the word orthogonal?

I ask because in another forum a teacher replying to a question about it said that the man in the street is well aware that it means. . . [a much commoner synonym].

Well this man in this street feels ignorant and undereducated and wonders if he's the only one who's never heard of it before.

Please don't mention the meaning here until a few people have had the chance to think about it.

Thank you.

Rover

 

[5jj]

Well this man in this street feels ignorant and undereducated and wonders if he's the only one who's never heard of it before.

No. We are two.

 

[SoothingDave]

It's not a common word outside of math/science. I've heard it, but I'm an engineer.

The man on the street has a hard time placing the Civil War in the proper century or naming the vice president. He hardly knows mathematical terms.

 

[Tdol]

It would depend on which man was in the street at the time. ;-)

 

[bhaisahab]

I'd never heard/seen it before either.

 

[Raymott]

It would depend on which man was in the street at the time. ;-)

... and most likely which street he was in/on.

I know the word from computer studies, but I've forgotten what it means exactly.

 

[birdeen's call]

I used to use the word often. Orthogonality is a crucial notion in mathematics.

 

[Hedwig]

I know the word but I've got several friend who are architects.

Hedwig
Woman in the street.
Not a street woman.

 

[emsr2d2]

Another woman in the street here but I don't have any architect friends and I've never heard of it.

The person who asserted that we would all know it must indeed live on a very unusual street.

 

[Rover_KE]

I used to use the word often. Orthogonality is a crucial notion in mathematics.

Thanks for your input, BC.

Is orthogonal a better word to use than perpendicular in certain cases?

Rover

 

[birdeen's call]

Is orthogonal a better word to use than perpendicular in certain cases?

Yes. The word "perpendicular" is used exclusively in geometry. The concept of perpendicularity (or orthogonality) has been generalized outside geometry, and in those generalized contexts, we use the word "orthogonal" (although we do use it in geometry too). It's typical for mathematicians to take a familiar notion and generalize it in abstract ways without changing its name. The generalized orthogonality bears only a slight resemblance to geometric perpendicularity, but contains it as a special case.

 

[Drear Pooson]

Perpendicular really only makes sense when you're considering lines and shapes in two and three dimensions. Orthogonality extends the idea into space of higher dimensions.

In answer to the original question, I doubt I'd ever heard the word before I took any higher level math classes. I wouldn't expect anyone to know the the word unless they had a specific reason to, and I wouldn't use the word in daily use as a synonym to perpendicular (although it wouldn't be wrong).

 

[birdeen's call]

Perpendicular really only makes sense when you're considering lines and shapes in two and three dimensions. Orthogonality extends the idea into space of higher dimensions.

Right, but "orthogonal" will also be used for two- and three-dimensional objects (and, trivially, zero- and one-dimensional) when there is a reason for that. It's the general name for the concept that arises in linear algebra, regardless of dimension. But, as the name "linear algebra" suggests, it's more of an algebraic concept than a geometric one.

 

[Hedwig]

Perpendicular really only makes sense when you're considering lines and shapes in two and three dimensions. Orthogonality extends the idea into space of higher dimensions.

More than three dimensions in space?! You scientific fellows make me dizzy! :-o

 

[birdeen's call]

More than three dimensions in space?! You scientific fellows make me dizzy! :-o

Some smart scientific fellows who are interested in physics claim that the universe has as many as eleven dimensions. Mathematicians are not bothered by the reality so much, so they use infinite dimensional spaces freely.

 

[Hedwig]

Oh, yes. I was introduced to the concept by Terry Pratchett's Discworld novels, as he often mentions the multiverse and multiple dimensions. I did a little (just a little) research and tried my best to understand. It's really too much for a simple brain like mine. :-?

 

[birdeen's call]

The string theories, to which I was referring, are too much for many brains, including mine. :-(