Tree Rings as a Natural Model of Dual Time
私はこの論文「Tree Rings as a Natural Model of Dual Time」を Oxford Academic の Analysis に投稿しましたが、採択には至りませんでした。
それでも、私が提案する「年輪モデル」は、客観的時間と主観的時間がどのように共存しているのかを考えるうえで、有益な視点を与えてくれるのではないかと感じています。また、note のコミュニティにとっても、哲学的な思索を深める一助になればと思い、ここで共有することにしました。
論文そのものは、学術投稿の慣例に従い実名で執筆しています。
後ほど、日本語版も note にアップロードする予定ですので、英語と日本語の両方で読んでいただければ幸いです。少しでも何かの気づきや思考のきっかけになれば嬉しく思います。
I originally submitted this paper, “Tree Rings as a Natural Model of Dual Time,” to Analysis (Oxford Academic), but it was not accepted.
Even so, I still feel that the “tree‑ring model” I propose may offer a useful way of thinking about how objective time and subjective time coexist. I also believe that sharing it here may contribute to deeper philosophical reflection within the note community.
The paper itself was written under my real name, as is customary for academic submissions.
I plan to upload a Japanese version on note as well, so that readers can engage with the ideas in both languages. I hope this work provides some insight or sparks further thought.
Tree Rings as a Natural Model of Dual Time
Kazumasa Shimamatsu, MD, PhD
Abstract
This paper introduces a simple naturalistic model that visualizes the coexistence of physical time and subjective time. Tree rings provide a structure in which these two temporal dimensions are simultaneously inscribed: the number of rings corresponds to the homogeneous progression of physical time, while the width of each ring reflects the heterogeneous character of subjective time. Because both records are physically co‑located within a single structure, the model offers a concise way to conceptualize the dual structure of temporal experience.
1. Introduction
Philosophers and scientists commonly distinguish between two kinds of time.
Physical time is homogeneous, measurable, and independent of any subject. It is the time described by physics, exemplified by Einstein’s relativistic framework (Einstein 2019).
Subjective time, by contrast, is heterogeneous, elastic, and dependent on the internal states of the subject. This notion is central to Bergson’s account of durée (Bergson 2014).
Although this duality is widely acknowledged, we lack a simple model that shows how these two temporal dimensions can coexist within a single structure. This paper proposes that the growth rings of a tree provide precisely such a model. Unlike many metaphors for subjective time, tree rings offer a physical structure in which a metric temporal sequence and a qualitative temporal record are simultaneously inscribed.
2. Tree Rings as Physical Time
Tree rings are formed annually through the interaction of a tree’s biological processes with external environmental conditions. Because each ring corresponds to one year of growth, the number of rings represents a sequence of discrete, homogeneous temporal units. This makes tree rings a natural analogue of physical time:
They accumulate in a linear, irreversible order.
They are countable and measurable.
Their formation depends on external physical conditions rather than internal experience.
Thus, the ring count visualizes the objective passage of time as understood in physics.
3. Ring Width as Subjective Time
While the number of rings is uniform, the width of each ring varies significantly. These variations reflect the tree’s internal condition during each year: favorable conditions produce wide rings, while stress or scarcity produce narrow ones (Fritts 2001).
This variability can be interpreted as a natural analogue of subjective time:
Some years are “long” in the sense of being rich in growth.
Some years are “short” in the sense of being constrained or stagnant.
The qualitative character of a year is encoded in the width, not the count.
Just as human subjective time expands or contracts depending on emotional, cognitive, and experiential factors (Libet 2005), the tree’s “experienced time” is reflected in the non‑uniform spacing of its rings.
4. The Tree Ring Model
The central claim of this paper is that tree rings provide a single physical structure in which two temporal dimensions are simultaneously represented:
Physical time → the number of rings
Subjective time → the width of each ring
This dual inscription is not merely metaphorical but structural. The tree does not symbolize the coexistence of two times; it embodies them. The model therefore offers a concise visualization of a longstanding philosophical distinction. It shows how a subject (in this case, a tree) can inhabit a world governed by homogeneous physical time while simultaneously generating a heterogeneous internal temporal record.
5. Why Trees?
The model is not chosen for metaphorical convenience. Tree rings constitute one of the few familiar natural structures in which a metric temporal sequence and a qualitative temporal record are physically co‑inscribed. The duality is not imposed by interpretation but arises from the tree’s own biological processes. This makes the structure uniquely suited to illustrating the coexistence of physical and subjective time.
6. Philosophical Implications
The tree ring model has several conceptual advantages:
(1) A naturalistic representation of dual time
It provides a concrete structure rather than an abstract analogy.
(2) Compatibility with both physical and phenomenological accounts
The model accommodates Einsteinian physical time and Bergsonian durée without conflating them.
(3) A framework for thinking about memory and temporal quality
The tree’s internal record resembles the way human memory encodes the qualitative texture of lived time.
(4) A minimal model for broader applications
The model may be extended to discussions of biological time, psychological time, and metaphysical accounts that distinguish between metric time and experiential time (Ismael 2021).
(5) What the model explains
The model clarifies how two temporal dimensions can be simultaneously instantiated within a single subject. It also shows that qualitative temporal variation need not be represented as a distortion of physical time but can be encoded independently alongside it.
7. Objection and Reply
Objection.
The model anthropomorphizes the tree by treating ring width as “experienced time.”
Reply.
The model does not attribute consciousness to the tree. It uses the tree’s internal physiological record as a structural analogue of subjective temporal heterogeneity. The point is not that the tree experiences time, but that its growth produces a physical pattern that mirrors the dual structure of temporal experience.
8. Conclusion
This paper has introduced a simple model for understanding the coexistence of physical and subjective time. Tree rings provide a natural structure in which these two temporal dimensions are simultaneously inscribed: the number of rings corresponds to the homogeneous progression of physical time, while the width of each ring reflects the heterogeneous character of subjective time.
The aim of this paper has been limited to presenting the model itself. Further work may explore its implications for theories of consciousness, memory, biological temporality, and the metaphysics of time.
References
Bergson, H. 2014. Time and Free Will: An Essay on the Immediate Data of Consciousness. Trans. F. L. Poson. Overland Park: Digireads.Com Publishing.
Einstein, A. 2019. Relativity: The Special and the General Theory – 100th Anniversary Edition. Trans. H. Gutfreund. Princeton: Princeton University Press.
Fritts, H. C. 2001. Tree Rings and Climate. Caldwell: The Blackburn Press.
Ismael, J. 2021. Time: A Very Short Introduction. Oxford: OUP Oxford.
Libet, B. 2005. Mind Time: The Temporal Factor in Consciousness. Cambridge: Harvard University Press.
