SN 56.47 uses the same analogy but doesn’t mention arising of the Tathagata and his Dhamma teaching
I think the analogy is just meant to illustrate how something is very rare.
The overall message seems to be that it’s very rare to be human and at the same time have access to the Buddha’s Dhamma.
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it’s difficult to ignore the explicit assertion by chance
https://suttacentral.net/define/adhicca 2nd meaning, in which nothing suggests rarity, but an event without a cause
There’s a note to Bhikkhu Bodhi’s translation of SN56.48:
Adhiccam idaṁ. The statement has to be taken as rhetorical rather than philosophical in intent. At the doctrinal level, all three occurrences mentioned here come about through precise causes and conditions, not by chance.
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ok, however does Ven Bodhi explain why this has to be taken as rhetorical rather than philosophical in intent?
because anything claimed anywhere else in the suttas can similarly be relegated to rhetoric and discounted as a philosophical point
what would be a criterion for such a decision? quantitative value of a statement for the Canon?
“It would be by chance, venerable sir, that that blind turtle, coming to
the surface once every hundred years, would insert its neck into that
yoke with a single hole.”
In the context of the turtle simile, it is pretty clear that ‘by chance’ means “an event that has a low probability of happening”.
A philosophical interpretation means this sutta is saying that blind turtles are exempt from causality.
i don’t see why one would have vanishing chances of human birth if one is endowed with virtues and thus is sure to obtain a favorable rebirth as explicitly stated in numerous other suttas
this is not exactly a straightforward sutta, one needs to resort to interpretations to bring it into accordance with the main Teaching
I think the vanishing chance is having a human birth and having access to the teachings of the Buddha at the same time.
It seems there are periods of time where the true Dhamma is not around and a Buddha does not arise. You can’t do as much with a human birth then 
I got the note from the discussion in dharmawheel and the dropbox download here, didn’t see any further explanation though.
Dear Fxam
It is stated in Finger Nail Sutta Nakhasikha Sutta
"The great earth is far greater, lord. The little bit of dust the Blessed One has picked up with the tip of his fingernail is next to nothing. It doesn’t even count. It’s no comparison. It’s not even a fraction, this little bit of dust the Blessed One has picked up with the tip of his fingernail, when compared with the great earth.
“In the same way, monks, few are the beings reborn among human beings. Far more are those reborn elsewhere. Thus you should train yourselves: ‘We will live heedfully.’ That’s how you should train yourselves.”
and
Blind Turtle Sutta Kanakacchapa-sutta
O Bhikkhus, the obtaining of the opportunity of becoming a man again by a man who has expired and is reborn once in any of the four realms of misery. The occurrence of the yoking of the blind tortoise is not worth thinking of as a difficult occurrence in comparison therewith.
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it’s dhaRmawheel site 
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Finger Nail Sutta Nakhasikha Sutta
Blind Turtle Sutta Kanakacchapa-sutta
I tend to think these are more about the rarity of human birth; not so much about demonstrating that human birth being more conducive to practice.
Under “Teacher of the Devas”
When a deva faces death, his aura begins to fade and dirt appears on his clothes for the first time. When the gods see these indications of impending death, they tell their friend:
“Go from here, friend, to a good bourn. Having gone to a good bourn, gain that which is good to gain. Having gained that which is good to gain, become firmly established in it.”
The Buddha then explained the devas’ concept of a good birth and of what is “good to gain”:
“It is human existence, bhikkhus, that is reckoned by the devas to be a good bourn. When a human being acquires faith in the Dhamma-Vinaya taught by the Tathagata, this is reckoned by the devas to be a gain that is good to gain. When faith is steadfast in him, firmly rooted, established and strong, not to be destroyed by any recluse or brahman or deva or Mara or brahma or by anyone else in the world, this is reckoned by the devas to be firmly established.”
The Buddha explained that the devas view a human existence as an excellent opportunity for growth in morality, giving, faith, and understanding. With compassionate concern for their dying cohort, they say:
as per (Iti 83):
Go, friend, to a good bourn,
To the fellowship of humans.
On becoming human acquire faith
Unsurpassed in the true Dhamma.
That faith made steadfast,
Become rooted and standing firm,
Will be unshakeable for life
In the true Dhamma well proclaimed. … … …
In the sutta preceding the one quoted above (Iti 82), the Buddha spoke of “joyous utterances” devas give forth in three situations: (1) when a man is preparing to ordain as a bhikkhu; (2) when a person is “engaged in cultivating the… requisites of enlightenment”; and (3) when someone attains the goal, utterly destroying the mental defilements. Whenever devas notice people engaged in the first two deeds, they rejoice saying, “A noble disciple is doing battle with Mara.” When the devas see that someone on the human plane has become fully awakened, they declare: “A noble disciple has won the battle. He was in the forefront of the fight and now dwells victorious.”
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Richard Gombrich agrees
Brahma heavens (brahmaloka or bambalova), and below them are six divine heavens (divyaloka or devlova) which constitute the top segment of the sphere of desire. The inhabitants of these divyaloka enjoy divine bliss (dev sapa vindinava). These heavens have a drawback: they are so pleasant that no one bothers to meditate and make spiritual progress.
in “Buddhist Precept and Practice”, p. 182
I want to bring up the issue of chance that was raised earlier. I feel like the standard takes on this issue do not do much justice to a nuanced understanding of how chance or randomness work.
Just because something is due to causes does not also mean that there is not what we would call chance involved. If we don’t allow room for some randomness then we risk going to determinism, that is all causes must lead to a particular result at a particular time in a particular way. We also risk making spiritual practice impossible because our past kamma determines everything (AN 3.61).
Alternatively, I think that a mixed understanding fits reality much better and allows for understanding the word ‘chance’ more clearly in the context of the suttas.
In this way we can look at someone being born a human, as this is the issue at hand. In order to be born human you would have to make good kamma generally and perhaps some sort of specific kamma that leads to a human rebirth. Now presumably this kamma would not be the only kamma a being has created in their current life or in previous lives.
At the time of rebirth that good and human kamma may or may not be the specific cause of the next rebirth, it will depend on many factors (that are beyond our comprehension). Meaning the factors that will be causally active is a complex issue. So while all those factors may have a cause, there may be so many interacting in such a complex way that is effectively random, if not actually random to some degree (chaos theory looks at these kinds of issues). What I mean by that is that once a system gets complex enough, even a rule based one, it becomes random such that what happens is essentially unpredictable. Think about a using a simulation of the Big Bang to predict the shape North America.
In a specific case, if rebirth occurs outside of the human realm, it is still due to a cause, but there is some level of functional randomness determining which particular outcome within the possible set of outcomes occurs. The good/human kamma does not go away and will ripen at some later point, but when that is would seem to be indeterminate to some degree. This being because most beings make a mix of kamma. Which is not to say some beings can’t have such strong kamma that it overrides all the other kamma (ie, killing parents=go to hell).
Once one is in an animal realm (or lower) it seems like the likelihood of activating the human kamma is lowered because you are making kamma associated with that realm. Which means it could be a long time before another fortunate rebirth when all the conditions come together for a human birth to happen.
In this way, I think it is reasonable to say that a human birth is both due to specific causes and ‘chance’. We can see just a thing in chemistry with the decay of an isotope. We can predict the rate of decay very precisely, but we cannot predict which specific molecule will decay next at all. In the same way we can say an action/intention will lead to a kammic result, but we cannot say when, where or in exactly what form that will happen.
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with respect to birth i would not call it randomness or fortuity, it only may so appear to us wordlings incapable to comprehend the intricacies of kamma as was discussed here
Saying rebirth is fully controlled by kamma, even if unknowable still strikes me as determinism. The Buddha discusses the types of action and then what result they have, but there is obviously some variation based on mitigating factors. However, it would seem some of those factors would have to be outside kamma if you don’t want to make kamma into an omnipotent creator God. Kamma does not sculpt reality or rebirth to ‘perfectly’ match our kamma.
To be more specific imagine that someone has very strong kamma to be reborn poor and human. Now the set of beings that rebirth can occur for is fixed by the abailable embryos in the world. That means that the specific circumstances and genetic makeup of the new being will be determined by the interaction of the rebirth process and the available circumstances for rebirth. That embryo will not be designed by kamma to perfectly match that beings kamma. Kamma would have to work within the physical world to have its results.
In the same way unless you hold to hard determinism, rebirth between realms will be influenced by factors outside kamma. It seems to me that what will be determined by kamma, in a highly complex way, is how that rebirth moves within and between what options are available/possible.
It is the difference between prediction and hindsight. After an event occurs it is possible to say exactly why something happened, but to predict that will happen is not necessarily possible. It seems the Buddha acknowledged causes outside kamma in the world, which means kamma is not a closed system. If it is not a closed system I would say that there is room for what we might call ‘chance’ at least colloquially.
Check out this article on random walks. It shows how the exact same deterministic process can still lead to a wide variety of results (the parallel being that the same kamma could lead to different rebirths).
as far as i’ve been able to understand the Buddha’s message, during life a being is subject to factors other than kammic, however rebirth is determined by kamma and mind state at the moment of death, and it must be, otherwise spiritual development wouldn’t make much sense, in this case form and spehere of noble persons’ rebirth would also be volatile and contingent without kamma guaranteeing sotapanna rebirth only in human realm and above and sakadagami - only one other rebirth in kamaloka
or we would have to restrict determinism of rebirth to certain situations and/or characteristics
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I think this would have to be more accurate. It doesn’t seem reasonable to me to say that all rebirth is fully deterministic. I don’t think the state of mind in a specific sense is in the early suttas. The last mind moment is a later interpolation. In a general sense though mind state at death would be effective, say a stream enterer not being able to be born in the lower realms.
My best interpretation is that there are degrees of causal efficacy. Just as a mango seed cannot make an avocado tree, a non-returner cannot be reborn anywhere except into the pure abodes. However, just because a mango seed can only become a mango tree does not tell us everything we need to know about that tree. The characterisitics of that tree will be based on its genetics, the soil, the water, the sun etc.
MN 136 illustrates this well. In it the Buddha discusses how people who make good kamma can be reborn in hell and people who make bad kamma can be reborn in heaven. Based on this, others mis-understand kamma. This shows the complexity of kamma and that knowing how kamma will interact with the circumstances to produce results is both complex and perhaps unpredictable (though still explainable in hindsight by one with vision, i.e. a buddha).
Based on this, to me it seems possible for spiritual progress to have definite effects without saying that rebirth kamma is fully deterministic.
This is imprecise, and in fact not quite correct. While the statement “short life is one of the result of killing living beings” accords with the Cūlakammavibhaṅga-sutta (MN 135), the statement “Not trusted by others is the result of lying and poverty is the result of stealing” is not quite right, since it gets things the wrong way around. This sutta, rather, states that one result of lying is not being trusted. This leaves open the possibility that there could be other reasons for not being trusted, such as it just being what happens sometimes. The same thing applies to the connection between stealing and poverty.
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