Actually, the reverse is true.
Nope. Higher ISO settings in general produce less noise. That's a demonstrable fact. It's why cameras are engineered as they are.
Less noise than what?
If we study i random mages taken by random photographers at different ISOs, and without any noise reduction applied, we'll find a strong correlation "higher ISO -> higher noise". Now whether it's also a causation is a different story, but the correlation is definitely there.
Your statement is only true in a special case: a higher ISO image may produce lower visible noise compared to an image taken with the same exposure and a lower ISO setting, and then brightned up in Lightroom. So your statement implies a) same exposure b) visible noise after certain processing that equalises the brightness.
It's not a 'special case'. It's the default case if you want to separate out the effect of different variables. In this case we have the variable 'ISO' and the variable 'exposure' and we want to know what each variable does independently. If we change them together we don't know which is responsible for what.
DPR now provides examples of this in its 'ISO invariance' tests. So, for instance
Exposure does not change, ISO does. We can see very clearly that as the ISO increases, noise decreases.
Here are the same ISOs different exposure
(unfortunately we've added another variable here, EFC, but its effect is minimal). Now compare each patch with the same ISO patch above. It shows that the patch with more exposure is the noisier. So we have two independent variables. ISO, which has quite a small effect on noise, and its noise decreases as ISO increases; and exposure, which has a larger effect, and its noise decreases as exposure increases. So, the rule is, for lowest noise maximise exposure. Set the ISO as high as you can for that exposure.
This is where the most common methods of exposure management get it wrong. I get the impression that the most popular exposure mode is A, so lets run with that. Suppose that you're at some kind of event taking photos as you see them. I suppose that using A you'll set the aperture first, for whatever reason you choose an aperture. Then you set the ISO, either by guess or by adjusting it until you get the shutter speed you feel OK with. Whichever way you did it, by setting the ISO you have fixed the exposure that you'll be using. Thereafter the camera will adjust the shutter speed to keep the exposure constant. So now you go around snapping, and the light changes. Sometimes it will be brighter than it was when you set the ISO, and the shutter speed will increase. But, when it is brighter, you could have left the shutter speed the same, had more exposure and thus, as above, a less noisy photo. Other times the light will be darker and the shutter speed will go below what you're happy with. So this fixed ISO, automatic exposure technique is sub-optimal, because it will often lead to you having a noisier photo than you needed or a slower shutter speed than you're happy with. You could say that you can choose a higher ISO at the start to get some margin in the shutter speed, but then most of your photos will end up noisier than they need to have been.
Now contrast this to using M with auto ISO. You set the aperture you want, you set the shutter speed that' your happy with. As the light changes the ISO changes, and with it the exposure. But, that exposure is always the biggest exposure that will work with the shutter speed and aperture that you chose. Thus in every case it is the least noisy photo that those constraints allow.
Going back to the point of whether it is 'ISO' that causes noise, I think we have shown that it's not, it is exposure (or the lack of it). You see many cases here where people have tied themselves in a knot because of the misunderstanding that ISO causes noise. They set a very low ISO because they don't want noise, then they suffer camera shake or insufficient DOF, so they decide to underexpose at the low ISO (because they think that raising the ISO causes noise), and thus suffer a double whammy, the extra noise that the low ISO setting gives them plus the noise of the low exposure. Understanding the separated effects of noise and exposure is important.
As a final point, the idea that it is 'and then brightened up in Lightroom' is a misconception if you're working in raw. A raw file has no intrinsic lightness. The lightness is set when you process it. So you're not 'brightening up', you're just choosing what is the lightness that you want, and there is no additional penalty for doing so.
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Is it always wrong
for one to have the hots for
Comrade Kim Yo Jong?