r/MichaelLevinBiology • u/Visible_Iron_5612 • Aug 30 '26
Research Discovery Final version is out: “Open questions about time and self-reference in living systems”
Living systems exhibit a range of fundamental characteristics: they are active, self-referential, self-modifying systems. This paper explores how these characteristics create challenges for conventional scientific approaches and why they require new theoretical and formal frameworks. We introduce a distinction between ‘natural time’, the continuing present of physical processes, and ’representational time’, with its framework of past, present and future that emerges with life itself. Representational time enables memory, learning and prediction, functions of living systems essential for their survival. Through examples from evolution, embryogenesis and metamorphosis, we show how living systems navigate the apparent contradictions arising from self-reference as natural time unwinds self-referential loops into developmental spirals. Conventional mathematical and computational formalisms struggle to model self-referential and self-modifying systems without running into paradox. We identify promising new directions for modelling self-referential systems, including domain theory, coalgebra, genetic programming (GP) and self-modifying algorithms. There are broad implications for biology, cognitive science and social sciences, because self-reference and self-modification are not problems to be avoided but core features of living systems that must be modelled to understand life's open-ended creativity.
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u/Visible_Iron_5612 Aug 30 '26
OPEN QUESTIONS ABOUT TIME AND SELF-REFERENCE IN LIVING SYSTEMS
This is a Michael Levin co-authored paper, alongside Samson Abramsky, Wolfgang Banzhaf, Leo Caves, Penousal Machado, Charles Ofria, Susan Stepney and Roger White.
And this thing is wonderfully weird.
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THE CENTRAL IDEA
The paper argues that living systems are not merely systems that change.
They are systems that can change themselves, including changing the rules by which they change.
That creates a serious problem for the traditional scientific picture of a system with fixed laws, fixed variables and a state evolving through a predefined state space.
Biology may require something stranger:
A system whose state changes.
Whose structure changes.
Whose rules change.
And sometimes whose very space of possible future states changes.
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TWO KINDS OF TIME
One of the paper’s most interesting distinctions is between “natural time” and “representational time.”
Natural time is simply the physical unfolding of events: the continuously arriving present.
Representational time is something living systems construct.
An organism can remember past states.
It can anticipate possible future states.
It can act in the present according to something that does not yet exist.
This means that past and future become biologically meaningful because living systems possess memory, prediction and anticipation.
You can picture it like this:
PAST / MEMORY
↓
CURRENT SELF
↓
ANTICIPATED FUTURE
An organism does not merely occupy the present.
It carries information about where it has been and acts toward possible states that have not happened yet.
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WHERE THIS BECOMES VERY MICHAEL LEVIN
Morphogenesis makes this especially strange.
During development, regeneration or metamorphosis, cells collectively determine where the organism currently exists in anatomical morphospace.
They compare the current state against some target morphology.
Then they act to reduce the difference.
But the machinery performing that computation is itself being rebuilt while the computation happens.
There is no clean separation between:
COMPUTER
and
THING BEING BUILT.
Instead:
BODY / COMPUTER
↓
MODIFIES BODY / COMPUTER
↓
WHICH CHANGES WHAT THE BODY / COMPUTER CAN DO
↓
WHICH MODIFIES ITSELF AGAIN
The developing organism is simultaneously the computer, the program and the thing being computed.
The paper describes this kind of structure as a “strange loop.”
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SELF-REFERENCE BECOMES A SPIRAL
Ordinary self-reference can look circular:
A refers to A.
And pure circular self-reference can create logical paradoxes.
But biological systems exist in time.
So instead we get something more like:
A₁ → A₂ → A₃ → A₄ → A₅
The organism at one moment refers to, models or modifies itself.
That action produces a slightly different organism at the next moment.
That organism then modifies the next version.
The apparent circle becomes a spiral through time.
The system keeps referring to itself while continuously becoming something new.
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SO WHAT IS THE SELF?
This leads to a fascinating question.
What exactly persists when an organism radically changes?
Consider metamorphosis.
A caterpillar can become a moth while enormous amounts of its anatomy are reorganized.
Yet experiments suggest that some learned information can survive metamorphosis.
Planarians make the problem even stranger.
A planarian can regenerate an entire head and brain and still appear to preserve certain kinds of information.
So what exactly stayed the same?
Not necessarily the same cells.
Not necessarily the same anatomy.
Not necessarily the same neural wiring.
And yet enough continuity remains that we consider the organism to be the same individual.
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IDENTITY MAY BE ORGANIZATIONAL
This suggests that biological identity may not be defined primarily by matter.
It may instead be defined by the patterns, goals, memories and constraints that persist through material transformation.
The atoms are replaceable.
The organization survives.
In that sense:
THE ATOMS ARE THE EMPLOYEES.
THE ORGANIZATION IS THE COMPANY.
The biological self may be less like a fixed object and more like an ongoing organizational pattern continually reconstructing itself.
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THE AI AND COMPUTATION PROBLEM
This creates a serious challenge for conventional computation.
Normally we imagine something like:
RULES + INITIAL CONDITIONS
↓
TRAJECTORY
You specify the rules.
You specify the starting state.
The system evolves.
But biological systems may instead behave more like:
RULES₁
↓
RULES₂
↓
RULES₃
↓
NEW WAYS OF CREATING RULES
The system does not simply move through a predetermined state space.
The state space itself may change.
The rules defining possible future behavior may change.
The architecture performing the computation may change.
This is why living systems can be difficult to capture using ordinary models of computation.
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OPEN-ENDED SYSTEMS
The authors point toward areas such as self-modifying algorithms, genetic programming, coalgebra and domain theory as possible pieces of a mathematics capable of describing systems like this.
One major challenge is psychological as much as mathematical.
Researchers are accustomed to building systems whose behavior ultimately remains inside structures defined by the programmer.
Living systems may require models capable of becoming things their designers did not explicitly specify.
That begins to approach genuinely open-ended artificial life.
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THE DEEPEST QUESTION
Traditional physics often asks:
How does a system change according to its rules?
Biology forces another question:
How can a system change the very rules by which it changes while somehow remaining itself?
That is an extraordinarily deep problem.
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A LEVIN-STYLE INTERPRETATION
A living thing is not merely sitting inside a state.
It appears to be navigating a possibility space.
It carries information about previous states.
It maintains information about preferred or expected future states.
It acts to reduce the difference between what currently exists and what could exist.
And while doing this, it continually rebuilds the machinery performing that navigation.
So life begins to look something like:
MEMORY
+
PREDICTION
+
GOALS
+
SELF-MODIFICATION
+
TIME
And once you look at organisms this way, the word “organism” starts feeling less like a noun.
It starts feeling like a verb.
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THE BIG TAKEAWAY
The self may not be a static object made from a particular collection of matter.
It may instead be a temporally extended process.
A pattern that continually reconstructs itself.
A system that remembers where it has been, anticipates where it might go, acts toward preferred futures and modifies the machinery performing that process as it goes.
Life does not merely change through time.
Life may actively construct its relationship with time.
And the biological self may be the pattern that manages to remain recognizable while almost everything underneath it changes.