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>If God exists, his benevolence is not necessarily something we can reason about, nor his omniscience, nor his omnipotence.

When we talk about God though we're talking about a Christian/Jewish/Muslim/pick your religion God. That brings its own baggage.

Sure a Christian will say God works in strange and mysterious ways but ultimately they rely on being able to reason about his benevolence and then use that as proof they are 'good' and you aren't.

So I feel this entire essay is mistargetted at atheists who may already take this pov, where it should be aimed at other religions who definitionally don't take this point of view.

>Sure a Christian will say God works in strange and mysterious ways but ultimately they rely on being able to reason about his benevolence and then use that as proof they are 'good' and you aren't.

Have you experienced this? Remind them of Mark 10:18 “Why do you call me good?” Jesus answered. “No one is good —except God alone". Remember there are many people who are clueless about Christianity including Christians sadly.

This essay is an epistemological endeavor towards logical paradoxes, and is not meant to be an advocacy on religion or atheism.
I don't think a cylinder is a circle or a square, though. It might look like one when rendered in 2D but it feels like a different thing entirely.

Now that I think about it, maybe you could also explain this idea by comparing Javascript's == and === operators.

I don't think this changes the author's ultimate point though. It reminds me of the "Blind Man and an Elephant" parable[1], although this is a nice succinct alternative.

[1]: https://en.wikipedia.org/wiki/Blind_men_and_an_elephant

Mathematicians certainly can. https://en.wikipedia.org/wiki/Taxicab_geometry#Balls:

“A topological ball is a set of points with a fixed distance, called the radius, from a point called the center. In n-dimensional Euclidean geometry, the balls are spheres. […] In n dimensions, a taxicab ball is in the shape of an n-dimensional orthoplex. In two dimensions, these are squares with sides oriented at a 45° angle to the coordinate axes.”

Such a silly treatise.

Anyone with even the most rudimentary knowledge of mathematics, the most representative of human though processes, knows that our understanding is based on axioms, assumed truths which we do challenge ourselves for.

Similarly, the object they draw in the third picture simply is not at all "the very same object": it's another 2D object or drawing that could very well be a projection of a cylinder on a 2D plane, or very well could not be.

Witness all the great Escher paintings and similar "optical" tricks that are all too easy with 2D drawings.

And anyone with a more modest understanding of Mathematics knows that it is incomplete, inconsistent, and undecidable and thus is not the end-all.

The example serves to show that a 3D object is simultaneously two different 2D objects. Very much like how waves and particle may be different concepts but things exist that are both of them at once. This is meant to be illustrative of our limited comprehension and nothing more.

And yet it's the best human mind can come up and the basis for all the scientific knowledge.

Many a 3D object can be projected in infinite ways to a 2D plane, which is not at all surprising: that "3D view" is but one of colinear projections of a cylinder just like that square or circle. None of those are isomorphic, which is not at all surprising: that square or circle or even 3D view could be a projection of any number of different objects, which does not make them the same object at all. The example chosen is a terrible one.

Basically, mathematics is a demonstration that our understanding is limited. We also do understand how incomplete it is, so there's no misunderstanding there either.

This article is demonstration of how someone can turn half-truths into seemingly something more, but not really.

Eg. I can project lemon to colour yellow, and sun to colour yellow (let's call that function ColourOf()), but that's not the basis to say that Yellow color is at the same time both a sun and a lemon: they are two distinct things which happen to have one common property in relation to the function ColourOf.

There is nothing we as humans misunderstand about that.

To take further the original example from the article, we could also construct a function/mapping/projection which maps everything to exactly one and the same dot. Would this make everything be a dot? Would this make everything be exactly the same "thing"?

Nope. In this model, a God, you, me, HN and, well, everything is a dot. But this makes it a useless system so we don't bother with it.

We know that functions can be "lossy", and there's nothing we misunderstand about it. There is even a practical application to an equivalence class of "there is a projection of any object to this shape", which is fitting something through a particularly shaped hole. But if we can pull something through an elliptical hole (like the cylinder from the example), does not make that cyllinder an ellipse.

You ask a really deep question of whether an object is limited in its definition by what can be observed about it. You see to believe the contrary i.e. object is more than what it appears. But then, how would do you distinguish when all you have is observation to reason about? How do you tell if a given purple is of a Locastae or of the Pointakr if you've never seen either of them in your entire life?

You'll perhaps say Mathematics but you yourself admit that it's only the best we can do, and inherently has its limitations.

It's not a deep question at all, which is wherein lies the fallacy.

We can and do add to our observations. Our vision is not 2D or 3D but "stereoscopic": we gain "depth" information by simply moving slightly, and we can move around a lot to get more info. Sometimes we figure out other ways to add more info, and sometimes we fully acknowledge that we can't do that and take the uncertainty as is.

This is all trivial stuff we do understand: we understand when we lack sufficient information to claim something with certainty.

Just like your example of square/circle/cylinder.

There are certainly limits to our understanding of the phenomena around us, but your examples miss the point, because they are exactly not it.