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Nothing repeats in this world. Nothing happens as much similar to another thing already happened that #2 can be assigned to it, even superficially.

Can intelligent life exist in such world?

By Intelligent Life I mean any organism that can learn.

Planets and stars form in this world, gravity exists - just not in repeatable enough sense that an orbit can be said to be repeating - this time orbit is an ellipse (like in our world), another time its some other shape. Perhaps storing some orbital energy this time by bulging part of orbit (towards center) to use it another time by expanding part of orbit (away from center). When it bulge and when it expand, and what part of orbit bulge or expand, is truely random.

People can identify aspects (qualities or defects) of things but things which are similar in one aspect are so much different in other aspects that they cannot be called instances of same class of things.

Without things repeating in close enough way to be numbered can there still be patterns? Failing that, can organisms still learn (and so can be called intelligent) in absence of patterns?

For example, in our world, we cannot formulate when a particular atom decay, there is no pattern, we do still learned that atoms decay and made tons of science about it, so decaying of atoms, a truely randomly occuring phenomena is indeed very intelligible.

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    $\begingroup$ More coherence needed $\endgroup$
    – Priska
    Oct 22, 2019 at 5:03
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    $\begingroup$ Pattern recognition, by definition, is recognizing similar things happening. Without repetition there can be no patterns, and without patterns there can be no pattern recognition. While it may be possible to come up with an intelligent species that has no concept of numbers for other reasons, you cannot make this an intrinsic property of your world and expect anything resembling intelligence to exist. $\endgroup$ Oct 22, 2019 at 6:02
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    $\begingroup$ Life is a repeating pattern. Reproduction, evolution, growth: without those things it doesn't make sense to call something "life", let alone intelligent life. $\endgroup$
    – ckersch
    Oct 22, 2019 at 6:12
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    $\begingroup$ Your definition of planetary orbit sounds like quantum uncertainty at a global scale. This can be quantified, but not directly. For example, one cannot say that the orbit of a planet is precisely a given number of AUs, but rather that there is a probability field ( like a cloud ) where the planet is most likely to be ( in terms of predicting where it's path will be next week, for example ). And the density of that cloud disperses the further away from it's star you get. So still quantifiable, but not in discrete terms ( whole number terms ). $\endgroup$
    – Nolo
    Oct 22, 2019 at 6:17
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    $\begingroup$ The premise that "making everything random means the concept of numbers can't exist" is flawed - I can count things without requiring any commonality between them. "A dog", "the color blue", "the emotion of love", and "gravity" are still four things, even though none of them are "instances of same class of things". $\endgroup$ Oct 22, 2019 at 7:14

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Nothing repeats in this world

then nothing exists in this world, because forming any more than 1 elemental particle, be it a quark, a lepton, a barion, whatever you want to take as elemental, requires the event to be repeated.

And those particles come in existence waaaaaaay earlier than life, let alone intelligent life.

After your edit:

gravity exists - just not in repeatable enough sense that an orbit can be said to be repeating - this time orbit is an ellipse (like in our world), another time its some other shape.

this makes little to no sense. If gravity is not invariant with time, then how would two or more masses get to coalesce together?

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Can intelligent life exist in such world?

The question itself is a bit messed up, you could identify intelligence on various levels.

You may consider a dog or a monkey as intelligent, or a caveman, or a civilization that just discovered farming and sheep herding and of-course the modern-day man and space-faring civilization, all are intelligent in their own rights.

If your world doesn't need numbers then you will need some way to identify certain quantities.

for instance, if your people just learned sheep herding, fishing or farming, they will need some way to classify theirs produces like, no goods, small, somewhat-good, good, large, very large and so on.

This may be feasible for the short run, but as development sets-in, your people will need more sophisticated ways of precision counting, for processes like tax collection, a very basic need for any advanced civilization, and needs higher precision of numbers.

So, you can start with no numbers, but the development may stagnate without them.

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There is a difference between the headline and text of your question. Sentient beings have concepts, and it would be difficult but perhaps not impossible to envision a civilization without numbers.

Cause and effect, and repeating effects after repeating causes, are central to the development of life itself. Definitions of life differ, but a metabolism and reaction to stimuli are usually on the list.

For that matter, do you expect planets to form in your universe? Is gravity predictable enough to form stars out of stellar clouds?

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"No repeat" is inconsistent, you can always find some similarities between two beings in a set of beings unless there is only one being or no being at all.

Do you in fact mean no consistent/stable physical rules? intelligent being is a product developed by nature for billions for years with countless small improvements. Every time the rules change, your previous design won't work that well as before. So even in a world that the basic rules change occasionally, there won't be such products that can last longer than the next change.

So this depends one the rate of rule change and the speed of evolution towards intelligent being and the real effect of the change on the existing non-intelligence being already evolved at the time of change.

Human beings evolved successfully before the next fatal rule change, and we will be wiped away by some minor change in the galaxy context in the future without changing the basic rules.

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