thanks

this is a really cool idea! Do you have any links to posts/videos that further describe, analyse, etc this trick?

Not that I know of…

Yes, He is legendary which is why i reference this page despite it being rarely updated.

yeah. I think his website is extremely old and hasn’t been updated in the last decade or so. Despite this I linked to it because he is a legend in this field and so i think this is still the definitive reference.

As far as i understand, part of the story as to why dodecahedron and the cube fall short is due their non-triangular faces.

Did the article switch the dodecahedron and icosahedron? It specified that the icosahedron is optimal for 12 points and the dodecahedron for 20 which seems backwards to me.

I believe it is right. However, I often get these two intuitively mixed up because:

Icosahedron: 12 points, 20 faces (and 30 edges)

Dodecahedron: 20 points, 12 faces (and 30 edges)

Hmm, that explains it.

Although the rejection method easily generalises, for higher dimensions say d>8, it becomes extremely inefficient and so may become unduly slow.

Yes, that's right.

I haven't verified it but suspect that you might be able to improve on this by generating the coordinates in order, constantly decreasing the range to ensure that the point falls within the sphere. Then, to ensure spherical symmetry, you randomly shuffle the points at the end.

For those interested in this problem, a while back I wrote a blog post listing all the well-known ways of correctly generating random points on the surface (or inside) of a d-dimensional sphere. It includes all the frequently used ones as well as some lesser know elegant methods.

http://extremelearning.com.au/how-to-generate-uniformly-rand...

I think this definition of "data intuition is a resilience to misleading data and analyses" is an elegant attempt to describe a notoriously fuzzy concept. Well done to author on this one. As a trained teacher, I believe this is one of those soft skills (or aspects of tacit knowledge) that is notoriously difficult to teach or train someone.

I often say to people that the difference between an average person and an expert is that an expert knows which shortcuts/compromises you can make that will only have a small effect on the outcome, and which shortcuts will come back and to shoot you in the foot (and thus should be avoided from the outset). I like that the author's concept of data intuition neatly covers this scenario.

One might say that the author's definition is a negative definition, inasmuch as it is the ability to identify/avoid mistakes, but I think an equally important component of data intuition is the (positive) ability to identify implicit strengths and insights within the data (or data processes) that is presented.

I believe this skill is also very closely related to the ability in identifying which paths of data/statistical/scientific exploration are more likely to produce results than others. And as other commenters have said, this in turn is related to the ability of 'second-order thinking'. That is, connecting the dots where the there is no obvious or explicit connection.

As the saying goes, "sophistication is subtle".

preferably OP or moderators should add (2018) to the end of this title.

Like many others in this thread have said, it is often worth remembering the proverb: "Comparison is the thief of joy."

There is another thread on the front page right now dedicated to comparing (salaries). The Democratic Party platform is based on comparison. Maybe they should both come with a warning about possible loss of joy.

Once the joy is gone, stopping comparisons doesn’t really bring it back unfortunately. And comparisons only hurt in a few individualized things. Everywhere else they show the path of incremental progress and long term strategy.