Why do we still use analog gain with ISO invariant sensors?

using ISO 1600 we'd get more highlight protection and about the same noise.

Why do cameras not do this? Is there a problem I'm not seeing?
Aside from the fact that the images on the back of the camera would be mostly black, what about the shadows? Crushed shadows are far more apparent than a lack of dynamic range in the highlights.
 
So why does ISO typically operate via analog gain [snip]
I don't think that it does. I've lurked/participated in countless discussions about this here at DPR, and have learned that calling ISO "sensor sensitivity" is a) not correct and b) will kick off many arguments. What I've gathered is that no one can say exactly what turning the ISO dial does in a given camera (it's a secret sauce; delivering better high-ISO performance is a closely guarded trade secret), but it is likely accomplished by some combination of physical signal amplification (ie analog gain) and digital amplification (adding/multiplying numbers).

Bobn2 is a great one to ask about this, if you can find him.

Aaron
Not too difficult to figure out; compare the Raw histograms of the same scene shot with the same exposure at different ISO settings. Analog gain just shifts the histogram; digital gain also generates missing codes because of the round-off errors and constant bit depth.
I'm not sure that's a given these days. It was true in the days that cameras had simple 16-bit processors, but nowadays they have 32-bit processors with floating point capability. Although software rigor mortis is a common affliction, I would think that at least some cameras would be using FP calculations somewhere in the image chain. If they are doing raw manipulation, which won't be covered by a specialised JPEG pipeline, it make sense.
 
Ok, time for some experimentation. I took two photos at 1/1000 and f/13. The first one at ISO 51200 and the second one at ISO 100.
In other words, you took two pictures with the SAME exposure, with the SAME scene illumination, with ISOs that were off by a factor of 512x (9 stops). Not at all the case which I was discussing, where the reason for setting a high ISO is to give the camera permission to underexpose the sensor (by a factor of 512x, at that!).
 
So why does ISO typically operate via analog gain [snip]
I don't think that it does. I've lurked/participated in countless discussions about this here at DPR, and have learned that calling ISO "sensor sensitivity" is a) not correct
Which is why ISO 12232:2019 calls it the sensitivity of the "digital still camera" (DSC). And, as you say, leaves it up to the individual designers as to how it is implemented.
and b) will kick off many arguments. What I've gathered is that no one can say exactly what turning the ISO dial does in a given camera (it's a secret sauce; delivering better high-ISO performance is a closely guarded trade secret), but it is likely accomplished by some combination of physical signal amplification (ie analog gain) and digital amplification (adding/multiplying numbers).

Bobn2 is a great one to ask about this, if you can find him.

Aaron
 
Autonerd wrote:What I've gathered is that no one can say exactly what turning the ISO dial does in a given camera …
Yup. That’s why I decided to stop worrying and leave it on auto. Mostly.
 
So why does ISO typically operate via analog gain [snip]
I don't think that it does. I've lurked/participated in countless discussions about this here at DPR, and have learned that calling ISO "sensor sensitivity" is a) not correct and b) will kick off many arguments. What I've gathered is that no one can say exactly what turning the ISO dial does in a given camera (it's a secret sauce; delivering better high-ISO performance is a closely guarded trade secret), but it is likely accomplished by some combination of physical signal amplification (ie analog gain) and digital amplification (adding/multiplying numbers).

Bobn2 is a great one to ask about this, if you can find him.

Aaron
Not too difficult to figure out; compare the Raw histograms of the same scene shot with the same exposure at different ISO settings. Analog gain just shifts the histogram; digital gain also generates missing codes because of the round-off errors and constant bit depth.
I'm not sure that's a given these days. It was true in the days that cameras had simple 16-bit processors, but nowadays they have 32-bit processors with floating point capability. Although software rigor mortis is a common affliction, I would think that at least some cameras would be using FP calculations somewhere in the image chain. If they are doing raw manipulation, which won't be covered by a specialised JPEG pipeline, it make sense.
This is becoming a deep topic for a DPReview chatroom. If the variable digital ISO is just gain, you will get missing codes. If it also does noise-shaping, you can fill in the missing codes, but you take a sharpness hit. There's no free lunch.

I'm old-school. Variable analog gain has much lower noise than any sensor or A/D and the delay is zero. Not bad.
 
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With a fixed shutter speed and aperture, there are two ways we can brighten an image:

- by using a higher ISO (analog gain)

- by increasing the exposure slider in post (digital gain)

My understanding is that most modern sensors are approximately ISO invariant (beyond a second base ISO, if they have one), meaning that these two approaches will produce very similar noise levels in the final image.
Roughly, but ISO-invariance is not perfect. Push the shadows enough, especially in very warm light where blue is weak, or deep forest shade lacking in red, and the ugliness of post-gain read noise can raise its head.

You probably won't notice much difference between the ISO 400 and 100 settings for an ISO 400 exposure, but you certainly will see a huge difference at ISO 100 vs 25.6K for an ISO 25.6K exposure.
But the digital gain approach retains the maximum amount of highlight room, while every additional stop of ISO decreases highlight room by a stop. As a result, by using ISO instead of digital gain we could lose multiple stops of dynamic range without seeing any real noise improvement.
There's certainly a trade-off, and there is another benefit to one analog gain and digitization, too; compressed RAW files are much smaller when most of the most significant bits are unused. That would make higher-ISO RAW files smaller; not larger.
Wouldn't we be better off if, beyond their second base ISO, cameras just baked an exposure adjustment into the exif info instead of applying more analog gain? So if "proper" image brightness required ISO 1600, the camera would instead use its highest base ISO (say, ISO 400) and then tell Lightroom to start at +2 on the exposure slider. Compared to using ISO 1600 we'd get more highlight protection and about the same noise.

Why do cameras not do this? Is there a problem I'm not seeing?
Well, some cameras actually lean a little in that direction; usually the ones that start at ISO 200, or you might get an option for it, like HTP with Canons (but that is only one stop).

One issue which exists, but shouldn't exist, is sloppy blackpoint level assumptions, which get far worse, giving green or magenta casts to shadows, when RAW data is heavily pushed.
 
There's certainly a trade-off, and there is another benefit to one analog gain and digitization, too; compressed RAW files are much smaller when most of the most significant bits are unused. That would make higher-ISO RAW files smaller; not larger.
I'm not sure which way round you mean this. If read-chain gain is increased at high ISO settings the lower bits get filled with (useless) noise, which impedes compression. If the upper bits are just zeros (no variable gain) they will compress well.

In the end, the ISO control is probably redundant. The camera processor has all the information that it needs to optimally pack the sensor information into the available ADC width, varying the read chain gain if needs be. The JFIF engine has all the information that it needs from the raw file to make a rendering. At most, ISO should be a cue to help signal the photographers intent, though I think that a rendering intent control would be better. Auto ISO is a kind of poor effort at that.
 
I'm old-school. Variable analog gain has much lower noise than any sensor or A/D and the delay is zero. Not bad.
I agree. It's in most cases a better engineering solution than a wider ADC. I'm not a fan of the term 'analog gain'. You're not gaining analogs, and 'gain' itself is an analog concept, applied to whatever quantity is being 'gained' (in the case of a camera VGA it's voltage). In the digital domain, if you make a number larger it's called multiplication.
 
There's certainly a trade-off, and there is another benefit to one analog gain and digitization, too; compressed RAW files are much smaller when most of the most significant bits are unused. That would make higher-ISO RAW files smaller; not larger.
I'm not sure which way round you mean this. If read-chain gain is increased at high ISO settings the lower bits get filled with (useless) noise, which impedes compression. If the upper bits are just zeros (no variable gain) they will compress well.

In the end, the ISO control is probably redundant. The camera processor has all the information that it needs to optimally pack the sensor information into the available ADC width, varying the read chain gain if needs be. The JFIF engine has all the information that it needs from the raw file to make a rendering. At most, ISO should be a cue to help signal the photographers intent, though I think that a rendering intent control would be better. Auto ISO is a kind of poor effort at that.
Discussions of digital camera ISO always seem to follow the same story arc on DPR. A naïf asks a question that incorporates a false assumption. There is an initial clarifying response or two, but then gradually the discussion becomes more and more abstruse. After a while the whole topic becomes clear as milk.

For example, the damnable control is redundant, something entirely different is needed, and it’s not clear what that is. It isn’t clear that there is any helpful guidance for the innocent in the meantime.
 
I'm old-school. Variable analog gain has much lower noise than any sensor or A/D and the delay is zero. Not bad.
I agree. It's in most cases a better engineering solution than a wider ADC. I'm not a fan of the term 'analog gain'. You're not gaining analogs, and 'gain' itself is an analog concept, applied to whatever quantity is being 'gained' (in the case of a camera VGA it's voltage). In the digital domain, if you make a number larger it's called multiplication.
Analog gain and digital gain were very commonly used terms when I did electronic design, but that was decades ago. However I just did a Google search and they are still commonly used by circuit designers.

I've never heard the terms "gaining analogs" or "gaining a quantity" though.

And gain can be greater or less than unity in an electronic circuit.
 
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I'm old-school. Variable analog gain has much lower noise than any sensor or A/D and the delay is zero. Not bad.
I agree. It's in most cases a better engineering solution than a wider ADC. I'm not a fan of the term 'analog gain'. You're not gaining analogs, and 'gain' itself is an analog concept, applied to whatever quantity is being 'gained' (in the case of a camera VGA it's voltage). In the digital domain, if you make a number larger it's called multiplication.
Analog gain and digital gain were very commonly used terms when I did electronic design, but that was decades ago. However I just did a Google search and they are still commonly used by circuit designers.

I've never heard the terms "gaining analogs" or "gaining a quantity" though.
As I said, you're not gaining analogs, which was the point. On the quantity, electronic engineers will talk about voltage gain or current gain and occasionally charge gain. That's 'gaining a quantity', the quantity being voltage, current or charge.
And gain can be greater or less than unity in an electronic circuit.
Yes, they are. Within a discipline people tend to have their own framework of jargon. Electronic engineers are well accustomed to talking about 'gain', but the will say in general which kind of gain it is (unless it's obvious by contexts) so they'll talk about 'current gain' or 'voltage gain'. When digital circuits began to be incorporated into analog systems, they they found that digital multiplication operators could provide the same function as could 'gain', so they called it 'digital gain'.

In the world of computer science things were different. Circuits that performed multiplication were called 'multipliers'. For analog computing the variable gain amplifiers that did this function were still called 'multipliers' (and still are).

Photography is neither electronic engineering or computer science, so if we adopt those communities' terminology without understanding then we confuse ourselves. I say this with a fair amount of confidence, because I am an electronic engineer, a computer scientist and a photographer.

The reason I'm concerned about terminology is that poor use can lead thought patterns down a garden path. That's the case here. If we consider a camera as a black box, it takes light in at one end and puts out perceptual specifications at the other. It doesn't emit light. Inside the black box a translation is made from the input to the output, and gain is no part of that translation. There is no reason why any arbitrary amount of light might not be translated to any arbitrary lightness (lightness being the component of that perceptual specification which says how light or dark something should look). Internal 'gains' are as irrelevant to the essence that conversion as are the details of the computer code used to do it. So, you do not need to invoke 'gain' to explain how a smaller amount of light translates to a lighter image. And doing so sometimes leads to erroneous thought patterns. People logically assume that 'gain' means that something is being 'gained', and then the thing that is gained is either light or some unspecified analog to light they they often call 'signal'.
 
There's certainly a trade-off, and there is another benefit to one analog gain and digitization, too; compressed RAW files are much smaller when most of the most significant bits are unused. That would make higher-ISO RAW files smaller; not larger.
I'm not sure which way round you mean this. If read-chain gain is increased at high ISO settings the lower bits get filled with (useless) noise, which impedes compression. If the upper bits are just zeros (no variable gain) they will compress well.

In the end, the ISO control is probably redundant. The camera processor has all the information that it needs to optimally pack the sensor information into the available ADC width, varying the read chain gain if needs be. The JFIF engine has all the information that it needs from the raw file to make a rendering. At most, ISO should be a cue to help signal the photographers intent, though I think that a rendering intent control would be better. Auto ISO is a kind of poor effort at that.
Discussions of digital camera ISO always seem to follow the same story arc on DPR. A naïf asks a question that incorporates a false assumption.
I'm not sure that naïf is entirely appropriate here. When we talk about 'analog gain' and 'ISO invariant sensors' we're already well into the abstruse from the get-go. These are fringe topics in the photography community, so if you want to just stick to the mainstream, don't choose to participate in threads of this kind.
There is an initial clarifying response or two, but then gradually the discussion becomes more and more abstruse. After a while the whole topic becomes clear as milk.
That's about it. That's the nature of the topic.
For example, the damnable control is redundant, something entirely different is needed, and it’s not clear what that is. It isn’t clear that there is any helpful guidance for the innocent in the meantime.
One of the nice things about forums is discussion. Someone puts a half-formed idea out there, other people contribute and in the end, people learn and sometimes even innovate. I think that's great. For some people it's outside their comfort zone, but participation is not compulsory.
 
There's certainly a trade-off, and there is another benefit to one analog gain and digitization, too; compressed RAW files are much smaller when most of the most significant bits are unused. That would make higher-ISO RAW files smaller; not larger.
I'm not sure which way round you mean this. If read-chain gain is increased at high ISO settings the lower bits get filled with (useless) noise, which impedes compression. If the upper bits are just zeros (no variable gain) they will compress well.

In the end, the ISO control is probably redundant. The camera processor has all the information that it needs to optimally pack the sensor information into the available ADC width, varying the read chain gain if needs be. The JFIF engine has all the information that it needs from the raw file to make a rendering. At most, ISO should be a cue to help signal the photographers intent, though I think that a rendering intent control would be better. Auto ISO is a kind of poor effort at that.
Discussions of digital camera ISO always seem to follow the same story arc on DPR. A naïf asks a question that incorporates a false assumption.
I'm not sure that naïf is entirely appropriate here. When we talk about 'analog gain' and 'ISO invariant sensors' we're already well into the abstruse from the get-go. These are fringe topics in the photography community, so if you want to just stick to the mainstream, don't choose to participate in threads of this kind.
There is an initial clarifying response or two, but then gradually the discussion becomes more and more abstruse. After a while the whole topic becomes clear as milk.
That's about it. That's the nature of the topic.
Good, at least it’s not just my imagination!
For example, the damnable control is redundant, something entirely different is needed, and it’s not clear what that is. It isn’t clear that there is any helpful guidance for the innocent in the meantime.
One of the nice things about forums is discussion. Someone puts a half-formed idea out there, other people contribute and in the end, people learn and sometimes even innovate. I think that's great. For some people it's outside their comfort zone, but participation is not compulsory.
 
There's certainly a trade-off, and there is another benefit to one analog gain and digitization, too; compressed RAW files are much smaller when most of the most significant bits are unused. That would make higher-ISO RAW files smaller; not larger.
I'm not sure which way round you mean this. If read-chain gain is increased at high ISO settings the lower bits get filled with (useless) noise, which impedes compression. If the upper bits are just zeros (no variable gain) they will compress well.

In the end, the ISO control is probably redundant. The camera processor has all the information that it needs to optimally pack the sensor information into the available ADC width, varying the read chain gain if needs be. The JFIF engine has all the information that it needs from the raw file to make a rendering. At most, ISO should be a cue to help signal the photographers intent, though I think that a rendering intent control would be better. Auto ISO is a kind of poor effort at that.
Discussions of digital camera ISO always seem to follow the same story arc on DPR. A naïf asks a question that incorporates a false assumption. There is an initial clarifying response or two, but then gradually the discussion becomes more and more abstruse. After a while the whole topic becomes clear as milk.
In my case I’m not so sure that the discussion is abstruse but rather that I am obtuse 🤣
For example, the damnable control is redundant, something entirely different is needed, and it’s not clear what that is. It isn’t clear that there is any helpful guidance for the innocent in the meantime.
 
There's certainly a trade-off, and there is another benefit to one analog gain and digitization, too; compressed RAW files are much smaller when most of the most significant bits are unused. That would make higher-ISO RAW files smaller; not larger.
I'm not sure which way round you mean this. If read-chain gain is increased at high ISO settings the lower bits get filled with (useless) noise, which impedes compression. If the upper bits are just zeros (no variable gain) they will compress well.

In the end, the ISO control is probably redundant. The camera processor has all the information that it needs to optimally pack the sensor information into the available ADC width, varying the read chain gain if needs be. The JFIF engine has all the information that it needs from the raw file to make a rendering. At most, ISO should be a cue to help signal the photographers intent, though I think that a rendering intent control would be better. Auto ISO is a kind of poor effort at that.
Discussions of digital camera ISO always seem to follow the same story arc on DPR. A naïf asks a question that incorporates a false assumption.
I'm not sure that naïf is entirely appropriate here. When we talk about 'analog gain' and 'ISO invariant sensors' we're already well into the abstruse from the get-go. These are fringe topics in the photography community, so if you want to just stick to the mainstream, don't choose to participate in threads of this kind.
There is an initial clarifying response or two, but then gradually the discussion becomes more and more abstruse. After a while the whole topic becomes clear as milk.
That's about it. That's the nature of the topic.
For example, the damnable control is redundant, something entirely different is needed, and it’s not clear what that is. It isn’t clear that there is any helpful guidance for the innocent in the meantime.
One of the nice things about forums is discussion. Someone puts a half-formed idea out there, other people contribute and in the end, people learn and sometimes even innovate. I think that's great. For some people it's outside their comfort zone, but participation is not compulsory.
I do not have a college degree and freely admit I don’t understand a lot of this discussion but I feel that if one keeps their mouth shut, reads what is offered and then do some research on their own, understanding can be the reward.
 
There's certainly a trade-off, and there is another benefit to one analog gain and digitization, too; compressed RAW files are much smaller when most of the most significant bits are unused. That would make higher-ISO RAW files smaller; not larger.
I'm not sure which way round you mean this. If read-chain gain is increased at high ISO settings the lower bits get filled with (useless) noise, which impedes compression. If the upper bits are just zeros (no variable gain) they will compress well.

In the end, the ISO control is probably redundant. The camera processor has all the information that it needs to optimally pack the sensor information into the available ADC width, varying the read chain gain if needs be. The JFIF engine has all the information that it needs from the raw file to make a rendering. At most, ISO should be a cue to help signal the photographers intent, though I think that a rendering intent control would be better. Auto ISO is a kind of poor effort at that.
Discussions of digital camera ISO always seem to follow the same story arc on DPR. A naïf asks a question that incorporates a false assumption.
I'm not sure that naïf is entirely appropriate here. When we talk about 'analog gain' and 'ISO invariant sensors' we're already well into the abstruse from the get-go. These are fringe topics in the photography community, so if you want to just stick to the mainstream, don't choose to participate in threads of this kind.
My naïf self has definitely appreciated this discussion! In particular, this was very interesting and basically the answer I was looking for:

"In the end, the ISO control is probably redundant. The camera processor has all the information that it needs to optimally pack the sensor information into the available ADC width, varying the read chain gain if needs be."

There is an initial clarifying response or two, but then gradually the discussion becomes more and more abstruse. After a while the whole topic becomes clear as milk.
That's about it. That's the nature of the topic.
For example, the damnable control is redundant, something entirely different is needed, and it’s not clear what that is. It isn’t clear that there is any helpful guidance for the innocent in the meantime.
One of the nice things about forums is discussion. Someone puts a half-formed idea out there, other people contribute and in the end, people learn and sometimes even innovate. I think that's great. For some people it's outside their comfort zone, but participation is not compulsory.
 
There's certainly a trade-off, and there is another benefit to one analog gain and digitization, too; compressed RAW files are much smaller when most of the most significant bits are unused. That would make higher-ISO RAW files smaller; not larger.
I'm not sure which way round you mean this. If read-chain gain is increased at high ISO settings the lower bits get filled with (useless) noise, which impedes compression. If the upper bits are just zeros (no variable gain) they will compress well.

In the end, the ISO control is probably redundant. The camera processor has all the information that it needs to optimally pack the sensor information into the available ADC width, varying the read chain gain if needs be. The JFIF engine has all the information that it needs from the raw file to make a rendering. At most, ISO should be a cue to help signal the photographers intent, though I think that a rendering intent control would be better. Auto ISO is a kind of poor effort at that.
Discussions of digital camera ISO always seem to follow the same story arc on DPR. A naïf asks a question that incorporates a false assumption.
I'm not sure that naïf is entirely appropriate here. When we talk about 'analog gain' and 'ISO invariant sensors' we're already well into the abstruse from the get-go. These are fringe topics in the photography community, so if you want to just stick to the mainstream, don't choose to participate in threads of this kind.
My naïf self has definitely appreciated this discussion! In particular, this was very interesting and basically the answer I was looking for:

"In the end, the ISO control is probably redundant. The camera processor has all the information that it needs to optimally pack the sensor information into the available ADC width, varying the read chain gain if needs be."
There is an initial clarifying response or two, but then gradually the discussion becomes more and more abstruse. After a while the whole topic becomes clear as milk.
That's about it. That's the nature of the topic.
For example, the damnable control is redundant, something entirely different is needed, and it’s not clear what that is. It isn’t clear that there is any helpful guidance for the innocent in the meantime.
One of the nice things about forums is discussion. Someone puts a half-formed idea out there, other people contribute and in the end, people learn and sometimes even innovate. I think that's great. For some people it's outside their comfort zone, but participation is not compulsory.
Alas, you were not the naïf I had in mind. No one in this thread was. I was thinking about many other threads over the years.

With respect to the answer that you were looking for and got, let me ask this question: what practical maxim(s) would you derive from it?
 
There's certainly a trade-off, and there is another benefit to one analog gain and digitization, too; compressed RAW files are much smaller when most of the most significant bits are unused. That would make higher-ISO RAW files smaller; not larger.
I'm not sure which way round you mean this. If read-chain gain is increased at high ISO settings the lower bits get filled with (useless) noise, which impedes compression. If the upper bits are just zeros (no variable gain) they will compress well.

In the end, the ISO control is probably redundant. The camera processor has all the information that it needs to optimally pack the sensor information into the available ADC width, varying the read chain gain if needs be. The JFIF engine has all the information that it needs from the raw file to make a rendering. At most, ISO should be a cue to help signal the photographers intent, though I think that a rendering intent control would be better. Auto ISO is a kind of poor effort at that.
Discussions of digital camera ISO always seem to follow the same story arc on DPR. A naïf asks a question that incorporates a false assumption.
I'm not sure that naïf is entirely appropriate here. When we talk about 'analog gain' and 'ISO invariant sensors' we're already well into the abstruse from the get-go. These are fringe topics in the photography community, so if you want to just stick to the mainstream, don't choose to participate in threads of this kind.
My naïf self has definitely appreciated this discussion! In particular, this was very interesting and basically the answer I was looking for:

"In the end, the ISO control is probably redundant. The camera processor has all the information that it needs to optimally pack the sensor information into the available ADC width, varying the read chain gain if needs be."
There is an initial clarifying response or two, but then gradually the discussion becomes more and more abstruse. After a while the whole topic becomes clear as milk.
That's about it. That's the nature of the topic.
For example, the damnable control is redundant, something entirely different is needed, and it’s not clear what that is. It isn’t clear that there is any helpful guidance for the innocent in the meantime.
One of the nice things about forums is discussion. Someone puts a half-formed idea out there, other people contribute and in the end, people learn and sometimes even innovate. I think that's great. For some people it's outside their comfort zone, but participation is not compulsory.
Alas, you were not the naïf I had in mind. No one in this thread was. I was thinking about many other threads over the years.

With respect to the answer that you were looking for and got, let me ask this question: what practical maxim(s) would you derive from it?
Good question. I'm always interested in understanding things better even if there aren't obvious practical consequences. But still:

- Cameras' implementations of ISO are more mysterious than I had thought, so it's worth testing this on my own camera rather than trying to generalize.

- If it is the case that my camera can get a lot more highlight room with very little loss of shadow detail by shooting at base ISO when auto ISO would choose a higher one, I'll ... well I'm not sure what I'll do! Perhaps worry less about "underexposure" in low light and curse Sony for an ISO implementation that makes me choose between a dark image preview and optimal use of the camera's dynamic range!
 
One of the nice things about forums is discussion. Someone puts a half-formed idea out there, other people contribute and in the end, people learn and sometimes even innovate. I think that's great. For some people it's outside their comfort zone, but participation is not compulsory.
I do not have a college degree and freely admit I don’t understand a lot of this discussion but I feel that if one keeps their mouth shut, reads what is offered and then do some research on their own, understanding can be the reward.
A good sentiment. I don't see why you need to keep your mouth shut. On a forum, you can ask questions if you don't understand, and plenty of people will contribute to clarifying things for you with a good will.

The people who tend to take umbrage about this kind of discussion are often those that already have a fixed idea of things and don't like to find that it might be erroneous. Also, there are people that feel being found to be wrong about something is deeply shaming. Of course it's not, we're all wrong about a lot of things, and the best way to not be wrong is to learn when you find that you are.
 

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