Is the self like a rainbow and is it just as real?

the deluded self is not like a rainbow.

the delusive self is not formed from five aggregates but is merely a thought (sankhara; SN 22.81)

therefore the delusive self does not dissolve into any constituent elements because the delusive self is merely a thought and all that dissolves is the thought of self

when there is a rainbow, the different colors can be clearly seen. even a child can discern red, orange, yellow, green, blue, indigo and violet

but the deluded puthujjana (worldling) cannot clearly discern the various aggregates clung to & identified with that cause the becoming/creation of the delusive self. the deluded puthujjana (worldling) cannot discern the various manifestations of form, feeling, perceptions, mental formations & consciousness

the analogy of the rainbow appears unwarranted & merely theoretical

the buddha didnt asset that not-self is the dissolution of the self. nor that nonapprehension of yourself is the meaning of selflessness.

that deluded ppl lose the capacity to clearly ascertain in deep sleep or even recognise dreams as dreams is standard but has nothing to do with examples of ascertaining reality. falling asleep and failing to ascertain urself is not a perception of not-self

If a rainbow was a mind created phenomenon, then a camera, which has no mind or consciousness, would not be able to photograph it.

Hold on. If rainbow was mind created phenomena, wouldn't the camera also be mind created, wouldn't the eye be mind-made and if these are likewise mind-made then why wouldn't the camera be able to photograph it? Seems like photographing would be the only thing a camera should do, it is not going to cognize the shape & color of a tree or see it, the instrument is essentially an extention to the nervous system and is not supposed to do what mind does.

Similarly, a meditator might perceive a dissolution of the self into its constituent elements and thus conclude that the self does not truly exist,

There is something that can be spoken of as 'a sign' in your analogy, the sign is complete with form & color, which is perceived as it is grasped & interpreted by the nervous system to be 'a rainbow' or 'sign of a rainbow'.

That which is thought about & called 'sign' can be said to be an abstract expression of what is thought to be the sign's causes & conditions coming into play. If the causes & conditions prompting the expression are understood then there is no confusion in regards to the expression and it's meaning is rightly seen with intellect.

Interpreting & grasping the signs correctly is the directed development, grasping correctly one acts correctly, acting correctly one begets the correct sign which is associated with the consummation of the 5 faculties.

When a person grasps with underdeveloped intellect he reacts badly, in example a person grasps the sign of a bodypart and assumes that it is personal or that it is a self and makes an evaluation. Based on this evaluation he may become glad or aversive. Experiencing this excitement the intellect is clouded, one is not thinking straight and is carried away on the currents of bad intention, due to bad intention there is a wrong directing of attention and a weakening of the faculties due to frequent giving of attention to unwholesome themes which become the inclination of the mind due to a frequent giving of attention.

In this way a person might grasp something as self and be stuck thinking along those lines due to obliviousness to that which is his best knowledge.

Then having calmed down one might realize that he has been stuck interpreting the signs according to the false doctrine of 'self' and having become aware he is no longer entertaining those lines of reasoning based on delusion and is at that time interpreting the signs correctly.

There is this kind of dissolution of self. I don't know another.

As a comparison, if one is asleep and dreaming, one loses awareness of the body and the external world, yet both still exist for others,

Well yeas but the others, like the dream, don't exist for you until you start perceiving them, so the others are here semantically just as real as the dream because both elements come into play only when they are perceived by the observer and you have absolutely no way to establish these as a truth or reality beyond a particular person's seeing, hearing, smelling, tasting, feeling with the body and grasping with intellect.

To say that external world persists beyond it's conception & perception on a base primary frame of reference is akin to saying that dreams are a place you go to and that it persists while you are awake without your participation.

Thus, only awareness would have ceased, not the objects of awareness.

It is kind of amusing how people first establish something as a truth based on it essentially being an "objects of awareness" and then attempt to remove the 'of awareness' part.

It is not defined as an object which is sometimes of awareness and sometimes not of awareness. You don't get to take something defined & understood exclusively to be an object of awareness and talk about it as an not an object of perception.

That is a mistake of mixing two mutually negating contexts and you get a contradiction where you basically say 'this object of awareness is not an object of awareness because it's an object' and on this basis you create a doctrine about an object disconnected from everything meaningful as if a term's meaning is changed by using a shorter expression, in particular 'object of awareness' to 'object [not of awareness]', that doesn't work.

The problem arises when you talk about an object of awareness as an object and then insist on overriding normal usage in making the assumption that it's affirmation of a truth & reality isn't presumed to be dependent on contact and awareness.

"Monks, I will teach you the All. Listen & pay close attention. I will speak."

"As you say, lord," the monks responded.

The Blessed One said, "What is the All? Simply the eye & forms, ear & sounds, nose & aromas, tongue & flavors, body & tactile sensations, intellect & ideas. This, monks, is called the All. [1] Anyone who would say, 'Repudiating this All, I will describe another,' if questioned on what exactly might be the grounds for his statement, would be unable to explain, and furthermore, would be put to grief. Why? Because it lies beyond range."

To say that the perceived world & it's objects exist independently of a single observer's frame of reference is not to be done because without an observer the world can't even be talked about in terms of the electromagnetic process because there [that frame of reference] is then not a process, not without an observer to collapse the wave function.

In non physics terms;

There being no observation there is no contact, there being no contact there is no expression of causes & conditions, there being no expression there are no signs, there being no signs there is no awareness of signs, there being no awareness of signs there is no awareness and that exactly because awareness is also always associated with a sign or an object of the 6 sense doors as it's existence is postulated on it being demonstrably implicated in contact which is a requisite for expression of a sign. There being no awareness there is then no awareness of a before & after and hence it is not a process.

Think about this.

If you and i both look at a rainbow, we are actually conceiving & perceiving two different worlds altogether because you can calculate the distance light travels to hit your eye and compare it to the distance light has to travel to hit my eye and take note of the fact that it's not even technically the same light that does the travelling.

Let alone the fact that we are technically only seeing the light that was emitted before contact occured and our seeing depends on it but we are not seeing things change simultaneously. Given the variance in the distances the sign of the rainbow will even dissolve at different time assuming our clocks were calibrated correctly and we could even prove it by making timestamped video.

Of course the distance between us would have to be enormous for light to be measurably delayed but as a thought experiment..

Suppose you are looking at a rainbow from a helicopter and i teleported instantly 1 light year away, i wouldn't even see the rainbow for a year no matter what optical zoom i have because the light from the rainbow won't make contact for a year whilst my watch would still be aligned with yours if i were to teleport right back.

Furthermore were i to immediately look back at earth with superzoom, i wouldn't see the rainbow at all and would be looking at events from 1 year ago.

Furthermore with this kind of teleportation powers i could teleport and watch myself teleport to my current location appearing as a second me beside because apparently i got faster than light travel...

"When the four bases of spiritual power have been developed and cultivated in this way, a bhikkhu (monk) wields the various kinds of spiritual power: having been one, he becomes many; having been many, he becomes one; he appears and vanishes;

note: here by light speed i talk about just the speed of the smallest discernable change in the electromagnetic process. It is entirely dependent on the instrument of measure.

Someone may say the rainbow doesn't exist.

But you can see it with your eyes and you can take photos of it, so it surely exists.

Similarly, someone told the Buddha that the self-doer doesn't exist at all.

But the Buddha said, hey, one could decide to move forwards and backwards by his own volition, so a self-doer surely exists. Or I may say, if it looks like a duck and quacks like a duck, then it must be a duck.

“Venerable Gotama, I am one of such a doctrine, of such a view: ‘There is no self-doer, there is no other-doer.’” ...

“So, brahmin, when there is the element of endeavoring, endeavoring beings are clearly discerned; of such beings, this is the self-doer, this, the other-doer. I have not, brahmin, seen or heard such a doctrine, such a view as yours. How, indeed, could one — moving forward by himself, moving back by himself — say ‘There is no self-doer, there is no other-doer’?”
AN 6.38

On the other hand, if you look closely at the rainbow, it doesn't exist as a single standalone object or entity. Rather, it is an emergent phenomena.

The Buddha used a similar analogy - a stringed musical instrument called the lute. The lute produces music. But if you break it down into its constituent parts, you cannot find music as a single standalone object or entity.

Similarly, the self doesn't exist as a single standalone object or entity. Rather, it's an emergent phenomena that appears when the five aggregates (form, feeling, perception, consciousness, mental formations) work together according to dependent origination, just as music is an emergent phenomena that appears when different parts of the lute work together.

"Suppose there were a king or king's minister who had never heard the sound of a lute before. He might hear the sound of a lute and say, 'What, my good men, is that sound — so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling?' They would say, 'That, sire, is called a lute, whose sound is so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling.' Then he would say, 'Go & fetch me that lute.' They would fetch the lute and say, 'Here, sire, is the lute whose sound is so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling.' He would say, 'Enough of your lute. Fetch me just the sound.' Then they would say, 'This lute, sire, is made of numerous components, a great many components. It's through the activity of numerous components that it sounds: that is, in dependence on the body, the skin, the neck, the frame, the strings, the bridge, and the appropriate human effort. Thus it is that this lute — made of numerous components, a great many components — sounds through the activity of numerous components.'

"Then the king would split the lute into ten pieces, a hundred pieces. Having split the lute into ten pieces, a hundred pieces, he would shave it to splinters. Having shaved it to splinters, he would burn it in a fire. Having burned it in a fire, he would reduce it to ashes. Having reduced it to ashes, he would winnow it before a high wind or let it be washed away by a swift-flowing stream. He would then say, 'A sorry thing, this lute — whatever a lute may be — by which people have been so thoroughly tricked & deceived.'

"In the same way, a monk investigates form, however far form may go. He investigates feeling... perception... fabrications... consciousness, however far consciousness may go. As he is investigating form... feeling... perception... fabrications... consciousness, however far consciousness may go, any thoughts of 'me' or 'mine' or 'I am' do not occur to him."
SN 35.205

Is the self like a rainbow and is it just as real?

A rainbow is not real. It is a concept. What is really going on is the process of seeing, i.e. visible forms come into contact with the eye faculty whereafter eye-consciousness arises and passes away. After that arises a mind-door process wherein the object just seen is being cognized. If one is not mindful before that point, conceptual proliferation will take place.

The self doesn't exist. It is a concept as well. It's an idea that belongs to the 4th aggregate of mental formations. A self cannot (nor anything pertaining to a self) be found inside the 5 aggregates of clinging.

OP: "No one can deny that a rainbow is as real as the term can be defined in any meaningful way."

In fact, I can define 'real' as follows:

real (adjective): actually existing in just the same way it appears to exist

In this sense, then neither the self nor the rainbow can be considered real. In the case of the rainbow, it appears to exist as a shimmering/solid object in the sky. It actually exists as an interplay of reflection/refraction of light with water moisture in the sky. Thus, a rainbow is not real.

Similarly, it can be said that the 'self' is not real as it appears to truly exist in a substantial and independent way, but it utterly does not. Thus, the self is not real.

This definition can be found in the "Explanation of the Presentation of Objects and Object-Possessors as well as Awarenesses and Knowers" by Pur-bu-chok and is the definition used in the the Tibetan Gelugpa tradition of Buddhism.

OP: "Is the Buddhist conception of a self similar to that of a rainbow or not?"

It can be said given the above definition that both are not real. However, the same can be said of (nearly) all things. That is, phenomenal things in this world appear to have true existence, but they utterly do not.

This is why it is said in the Diamond Cutter sutra:

“As a star, a visual aberration, a lamp, an illusion, dew, a bubble, a dream, lightning, and a cloud – view all the compounded like that.”

And as it says in the Lump of Foam sutta:

“Form is like a lump of foam; feeling is like a bubble; perception seems like a mirage; choices like a banana tree; and consciousness like a magic trick: so taught the Kinsman of the Sun."

Excellent question, and the analogy is very appropriate in a Buddhist context. I would point to instructions that one receives for meditation practices, to meditate on the meditator (in different ways). The objective is to see the ‘self’ that we habitually cling to, as you have described seeing a rainbow up close. When we, as you say, fly up to it in a helicopter (meditation practice ☺️) we can no longer see it. And yet, until we reach a certain stage in our meditation practice, that self causes all sorts of mayhem. You can see what I mean exhibited all around us, even here.

So is the self as real as a rainbow? Hearing your intent in asking your question, rather than focusing on word definitions and imposing idiosyncratic or otherwise scholarly meanings on them, I would say, yes, the self is as real as a rainbow. And I would add that while a rainbow is real, flying into one won’t kill you, whereas, getting hit by a bus will.

And yet, both the rainbow and the bus, when analyzed, lack a permanent and intrinsic self existence. Emaho ☺️