SHOCKING: Libertarian will support right-wing judicial nominee crammed down your throat

[Emily Lake]

Actually, orthogonal doesn't mean no overlap. The two lines intersect at a point. It simply means that they move in completely different directions. The most common usage of orthogonal refers to the axes in cartesian coordinates, which are at right angles to one another.

Orthogonal in statistics means no correlation whatsoever - which means no overlap.

I can see that interpretation, but the measurement of correlation between two variables are still based on two axes at right angles to one another. The correlation is more or less the slope of the linear regression fit between the two variables - A change of 1 in variable A results in a change of ~x in variable B. Loose analogy, of course, but reasonable. Independence of those two variables results in the plots of value-pairs aggregating to the origin... and looking at it from the perspective of either variable results in the plot of the other variable being a line at right angles to the plot of the the first variable.

ETA: Wikipedia

Statistics, econometrics, and economics

When performing statistical analysis, independent variables that affect a particular dependent variable are said to be orthogonal if they are uncorrelated,[13] since the covariance forms an inner product. In this case the same results are obtained for the effect of any of the independent variables upon the dependent variable, regardless of whether one models the effects of the variables individually with simple regression or simultaneously with multiple regression. If correlation is present, the factors are not orthogonal and different results are obtained by the two methods. This usage arises from the fact that if centered by subtracting the expected value (the mean), uncorrelated variables are orthogonal in the geometric sense discussed above, both as observed data (i.e., vectors) and as random variables (i.e., density functions). One econometric formalism that is alternative to the maximum likelihood framework, the Generalized Method of Moments, relies on orthogonality conditions. In particular, the Ordinary Least Squares estimator may be easily derived from an orthogonality condition between the explanatory variables and model residuals.

 

[laughing dog]

I can see that interpretation, but the measurement of correlation between two variables are still based on two axes at right angles to one another. ...

Your own quoted material says

If correlation is present, the factors are not orthogonal

, so, orthogonality means no correlation which means no logical overlap.

 

[Emily Lake]

I can see that interpretation, but the measurement of correlation between two variables are still based on two axes at right angles to one another. ...

Your own quoted material says

If correlation is present, the factors are not orthogonal

, so, orthogonality means no correlation which means no logical overlap.

True - there's no logical overlap, but they're still geometrically perpendicular. Uncorrelated variables are geometrically orthogonal (at right angles, perpendicular) as both vectors and density functions.

I'm revising this. I don't think it's true to say that there's no logic overlap. There's no relational overlap. For example, green trees and green candies have a logical overlap in that they're both green. But there's no relational overlap, since the degree and extent and shade of green in trees has no relationship to the degree/extent/shade of green in candies, and a change in the greenness of trees won't change the greenness of candy in any way.

Two variables being orthogonal in a statistical sense still means that they're at right angles to one another in the geometric sense.


Circling back to the context of this discussion... authoritarian/libertarian and left/right are orthogonal in the geometric sense. It might be true-ish to say that "Big L" libertarians, as a political party tend to fall in the libertarian-right quadrant. But I don't think it's true to say that of "little l" libertarianism as a philosophical concept. There are plenty of people who fall in the libertarian-left quadrant too.

 

[laughing dog]

...beep boop...

No one cares about robotic pedantry.

 

[Emily Lake]

...beep boop...

No one cares about robotic pedantry.

You say that... but you seemed to care enough to continue the discussion for a good while. At least until you fell back on implied insult, I suppose.

 

[laughing dog]

...beep boop...

No one cares about robotic pedantry.

You say that... but you seemed to care enough to continue the discussion for a good while. At least until you fell back on implied insult, I suppose.

I did until it sunk to robotic pedantry.

 

[Jarhyn]

Do Libertarians believe that some have a right to dictate over others?

A natural right?

That is the failing of libertarianism. It has this remarkably naive idea that people can be trusted if left to their own devices. It ignores about 230 years of history in our nation that led us to this point. The bank panics, depressions, violence, work place deaths, discrimination.

It is a fundamentalist religion.

The worship of unfettered capitalism for the sake of unfettered capitalism.

The hell with people.

Ayn Rand didn't like other people very much.

Thus her philosophy based on an unwavering focus on the self.

Capitalism with it's focus on the self to the point of allowing dictatorship was perfect for her mentality.

Hell, my own philosophy contains an unwavering focus on self, too, but I've looked at what real self interest is shaped like enough to realize that supporting the good, rights, and wellbeing of all the other people is synonymous with serving self. Ayn is just a myopic idiot.