Variance of Variances and Space

In summary, the conversation discusses the concept of dimensionality and its relation to time and variance. The question is raised whether a higher dimension could encompass a variance of variances, and whether time can be perceived as a dimension. One participant argues that the idea of dimension as a form of change is arbitrary and may not align with how the universe works.
  • #1
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2
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I think I'll ask it this way. Here goes...

1 point = zero dimensions.
2 points = 1, which is line; 3 points, shape; 4 minimum to have volume.

Somewhere, or rather, when, time applies, most preferably at that case in which dimensionality, quite plainly, is. My question follows a hunch that supposes a possible elegance or symmetry that's beyond me.

From 1 point to 2 we go from no dimensions to the dimension of difference.
From 2 points to 3 do we not see a difference of differences, i.e. variance? (Keep in mind that I am accounting for any change in difference here as a kind of point, as well. Time has equal application here, particularly in the establishment of dimension, itself.) If so, then would it follow that a variance of variances comes next? This is where my eyes cross.

Assuming my train of logic is still on its track (appologies. my first post.), I'll ask my final:

What then? If we can draw a comparison between variance and time (which is what I'm attempting to do), then would a variance of variances fit into one of the progressively higher dimensions? Can variance fit into space independent of time, independent of change? (or is this where we get into the concept of multiverses?)
 
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  • #2
Those are some good thoughts, but I think a problem might be that viewing any given dimension as time-like - as a form of change, as you say - is somewhat arbitrary. It works conceptually but the universe we perceive doesn't appear to work like that. I think a dimension would need to have an attribute like the http://en.wikipedia.org/wiki/Arrow_of_time" to feasibly be construed as change / time-like.
 
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What is the variance of variances?

The variance of variances is a measure of the variability in the values of different variances within a dataset. It is calculated by taking the average of the squared differences between each variance and the mean of all the variances.

Why is the variance of variances important in statistical analysis?

The variance of variances is important because it allows us to assess the variability of different variances within a dataset. This can help us understand the reliability and consistency of our data and identify any outliers or unexpected patterns.

How is the variance of variances calculated?

To calculate the variance of variances, we first take the average of all the variances in a dataset. Then, for each individual variance, we subtract the mean of all the variances and square the result. Finally, we take the average of all these squared differences to get the variance of variances.

What is the relationship between the variance of variances and sample size?

Generally, as sample size increases, the variance of variances decreases. This is because larger sample sizes tend to produce more reliable and consistent data, resulting in smaller variations between variances.

How is the variance of variances affected by outliers?

Outliers can greatly affect the variance of variances, as they can heavily influence the values of individual variances. If there are extreme outliers present, the variance of variances may be inflated, leading to inaccurate assessments of variability in the dataset.

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