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Sorry another Wide Angle Lens Question-T3i indoors

It's true that our brains don't recognize distortion of a face as we get close to it, but I'm not sure that (alone) is helpful for us.
No I think your brain DOES recognize the difference. And it is very actively correcting in photos. But it simply calibrates itself to expect the proportions that "go with" the estimated distance to the subject, in the eye's typical focal length(s). This makes problems when you shoot at any focal length other than about 65mm. So when you see a picture with plenty of trees and context all around, it goes "hm, okay I must be about 10 or more feet away, because that's how far I'd be at 65mm to see all those trees around the person" but then you get the huge noses and stuff that you're only used to seeing a foot away, and the mismatch is a problem.

The brain has to resolve the conflict somehow, and the weaker of the two assumptions is the facial proportions -- because everything you look at ever reinforces the distance assumption, whereas only faces reinforce the face proportion assumptions, AND you know that people can be disfigured, etc. in real life. So it is a better guess to the brain to assume that the proportions really ARE weird on the person, not that it guessed distance incorrectly.

Thus the brain resolves the conflict not by changing its mind about distance, but by maintaining the distance assumption and instead interpreting the person as simply a weird ugly person with a big nose.

not the barrel distortion pattern I'd expect to see if I shot the same grid with a wide-angle lens.
Barrel distortion is a separate issue entirely.
BOTH barrel distortion (if/when it exists) AND simply the mathematics of perspective when near something = bigger noses. But probably 95-99% of the effect of big noses you see is from perspective, not imperfect lenses.
In other words, a 14mm lens from 6 inches away, even if it was optically perfect and crafted by the very gods themselves, would still show big noses, about as big as our lenses do.

If your nose WEREN'T big in a wide angle shot from close up, then THAT would be the evidence of a major lens distortion / flaw in your glass.

I thought I'd pretty carefully qualified my observations as things that I see when I look at portraits taken with a wide-angle lens, but clearly, I didn't take quite enough care; I'll try again.

I've seen several examples of portraits at multiple focal lengths in which the same subject was shot from wide-angle to telephoto focal lengths. Here's an example, but there are quite a few others out there:

Untitled Document

I understand that the distance to the subject has to change in order to maintain the same framing from shot to shot. I also am aware that framing in my "normal" 3D world isn't quite the same as framing in a camera, due in part to my eyes constantly darting around. As it turns out, for the purposes of this exercise, I don't care.

When I scroll to the right of the strip of images in the example above, I perceive a noticeable difference between the shot at 19mm and the shot at 350mm. Careful analysis of a sufficient number of images might show actual differences in number of pixels occupied by noses, eyes, ears, and so on from very wide focal length-framing combinations to telephoto focal length-framing combinations, but I haven't done any such analysis. Nevertheless, I perceive a difference. I have no idea if anyone else sees a difference as well, but I suspect that I'm not alone.

Now, then, just because I perceive a difference, it may or may not be important. I choose to believe it is, based on the facts that (1) some of the photos in the example above are more attractive to me than others, and (2) I've seen a number of people claiming to have isolated "beauty formulas" or other such hooey based on measurements of the human face. I'm aware that there might very well be factors other than the focal length-framing combination contributing to factor #1, but I've seen this exercise repeated a number of times, and it turns out that I typically like head shots somewhere in the 70-135mm range, and I really don't like head shots at wide focal lengths very much at all when compared to similar photos at normal to near-tele lengths. Again -- that's just me. Moving on to factor #2, I recognize that the very idea of a "beauty formula" seems subject to extreme skepticism, and I personally tend to believe that a single universal formula for beauty is probably hogwash. Despite this, I think there is an underlying hard-wiring in my brain that causes me to be more sensitive to size and proportion when I view a human face than I would, for instance, when viewing a cantaloupe. I may not always be able to tell you why I prefer (a) to (b) given any two options, but I know which one I like. My optometrist, for what it's worth, seems fond of the same technique for evaluating my optical preferences, even after measuring objective facets of my vision.

So, when I view photos, I see a difference between wide and telephoto (given similar framing), and when it comes to portraits, I prefer some over others.

Moving on to people I see in real 3D living color, I simply don't perceive the same change as they move nearer or further away. Speaking only for myself, I just don't see it. Again, I personally believe that my 3D vision accounts for at least some of this, based only on hunch and the one-eye-covered grid experiment, and again, even though "why" is of some interest to me, the mere fact that I don't perceive this effect in real life is sufficient for me for these purposes.

Re: barrel distortion, the "barrel distortion pattern" I mentioned (I checked to make sure that I really referred to it as a "pattern", and I did) was meant to describe my perception of distortion, whether through perspective or through lens distortion. On the off chance you're not familiar with the pattern, this is what I'm talking about:

$240px-Barrel_distortion.webp

Forgive my earlier lack of precision re: the pattern. In any event, I stand these observations: when I move a grid close to my eyes, I perceive very little distortion. When I move a person close to my eyes, I perceive very little distortion. When I see a portrait shot up close at a wide focal length, it usually looks pretty odd to me.

I understand there's no proximity-induced subject shape-shifting going on as the focal length of my lens varies, and while I've got a passing interest in understanding how my brain's RAW processing works (again, this is a metaphor), my intent was mainly to support Ron.I've found that an uncorrected 2D representation of a portrait shot at close range using a wide-angle lens doesn't really seem to have the same proportions I perceived through my squishy-eyeball-lenses prior to mashing them up against the viewfinder.

Normally, I'd let that pass as "distortion" in a context like this (Ron, I knew what you meant).
 
Okay, so several things here:
1)
You cannot just ignore the fact that your eyes dart around. This is probably important to what's going on to some degree. The darting causes you to perceive a wide view of the world, despite your eyes not actually being all that wide angle. It is similar to the "Brenizer Method" of using a crop camera to look more like medium format by snapping a bunch of photos panning back and forth. It causes images from real world vision to appear different than photographs and might have a good deal to do with why you perceive the two differently (if you actually do. See next point for possible corrections to the experiment)
2)
The link you provided in your post is NOT what you should be comparing your real life experience to. You can't dramatically change the focal length of your eye, so you shouldn't be comparing to a series of images that use different focal lengths. You should be comparing to a constant focal length at different distances. Also, are you going off random memories from general life? Or did you actually sit there and look at a friend for this express purpose, moving in and out? What you want to do is:

a) Grab a friend close to your height, have them stand still, and put a few yardsticks on the floor in front of them.
b) Grab a 65mm or similar lens, and with ONLY that lens, take photos at let's say 15 feet, 10 feet, 7, 5, 3, 2, 1.
c) Stand yourself at 15 vs 10, 7, 5, 3, 2, 1, and look with your eyeballs.
d) compare results, keeping in mind the point #3 below
^
If you want to simulate lenslike conditions, then force your eyes not to dart as you do it. if you want to simulate eye-like conditions, then take composite photos with your 65 "darting" around by about the same angles and stitch them in post processing. The first method is probably simpler and easier, though.

Moving on to people I see in real 3D living color, I simply don't perceive the same change as they move nearer or further away. Speaking only for myself, I just don't see it. Again, I personally believe that my 3D vision accounts for at least some of this, based only on hunch and the one-eye-covered grid experiment, and again, even though "why" is of some interest to me, the mere fact that I don't perceive this effect in real life is sufficient for me for these purposes.
3)
The grid you posted as "either due to distortion or perspective" -- This is incorrect! Perspective and distortion do different things. The grid you posted is what you get with distortion only. What you get from perspective close up in a distortion-free lens is different. It looks like this (straight lines still, but still nose in the middle uses up more of the sensor than the ears on the sides):
$cos_grid.webp

This is rendered, not photographed -- I.e. it is what a mathematically perfect wide angle lens up close would see if made by the camera designing god of Nikon-os himself.

If you were looking for curved lines, then no wonder you didn't perceive them, because you shouldn't be getting them very strongly with your eyeball or your lens (a little bit due to imperfections, but it's not the main effect). You SHOULD still be seeing the nose and eyes as getting bigger compared to the ears, though, despite grids still being straight. So make sure you're looking for the right thing!
 
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Oh also to complicate things further, usually when you look at people in the world, they aren't standing perfectly still and staring straight at you as you also stand perfectly still!

They tend to move and shift their heads a lot, or you walk past them, etc. And so the nearest point of their head to you is constantly changing. When they look to the side, suddenly perspective will actually make their ear bigger than their nose, not vice versa. And your brain stitches these moments together. That's cheating!

When you're VERY close, even just moving your head around (not just your eyeballs) changes where your eyes are and can result in a more equalized perception of nose and ears, to a significant extent!


So when comparing the two experimentally you must
NOT move your head side to side,
NOT change your height compared to the subject,
NOT stray from your perfect ruler line, and as mentioned before probably
NOT try to dart your eyes at all.

Oh and close one eye, because your camera doesn't have stereo vision
 

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