‘And Lo! It is our own’: The Normal Curve

What we observe is not Nature in itself but Nature exposed to our method of questioning’ noted Werner Heisenberg [who was very familiar with the old Gaussian Curve].

Arthur Eddington

‘Something unknown is doing we don’t know what. We have found that where Science has progressed the farthest, the Mind has but regained from Nature that which Mind put into Nature.

We have found a strange footprint on the shores of the unknown. We have devised profound theories..to account for its origins.

At last we have succeeded in reconstructing the creature that made the footprints. And Lo! It is our own.’

You know, there’s been this flip question floating around for a few centuries as to whether Mathematics measures a Real World.

Or is it just us painting with a palette limited to the colors we can see [like the visible .30 % of the Electromagnetic Spectrum]. And then claiming we’ve caught the ghost in our picture.

Sort of like the Nobel Committee limiting the Literature Prize to a Writer writing in a language it can read [about 5 out of around 7,000].

Same thing here. Most of the testing talked about in the previous post is grounded on the perfectly symmetric Gaussian Curve [the ‘Normal Distribution’: see the Diagram].

It is arguably the most widely used tool in Applied Mathematics. Various theorems prove that all things sampled in sufficiently large quantities converge to the Gaussian Curve.

If you are taking a daily pill for blood-pressure, a vaccine for Covid, you can be certain than somewhere in the process of being approved, the Gaussian Curve had to stamp its approval.

The Curve is conceived on a binary platform and mounted on the critical assumption [among others] of ‘Independent, Separate Observations’, a fairly dodgy idea but embraced in the Scientific community as perfectly realistic and sensible.

Is this the way Nature really curves? Or is this the only way Nature knows to curve given how how we’ve rigged the rules, given how we think?

Is this Grandma being nice to her adorable grandson before he throws another fit?

I won’t get into the entrails of this issue. But if you are curious, it revolves around the notion of ‘Independent and Separate’, the claim to samples of ‘Independent Observations’ that underlies all of this theory.

It is nearly impossible to find two events that are perfectly uncorrelated in Nature. But would you like the privilege of being uniquely ‘Independent’? Give yourself a grant of immovable ‘Being’. You will show a correlation with all things as Zero.