Can God create square circles?
praveshkoirala.com
praveshkoirala.com
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.
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.
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
“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.”
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.
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.
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.
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'll perhaps say Mathematics but you yourself admit that it's only the best we can do, and inherently has its limitations.
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.