Infinite Dimensionality

The argument in brief

1. Framing. Griggs labels the piece a "thinking out loud" post rather than a polished essay: speculative notes on how optimization, dimensionality and the free energy principle might inform a future of advanced technology and human flourishing.
2. Universal optimization. The universe optimizes at every scale (least action, free energy, evolution). Life seems uniquely able to move "upstream," but perhaps it is not defying optimization so much as optimizing at higher dimensions.
3. The dialectic. Optimization compresses dimensionality for efficiency; dimensionality expends energy to extend optimization to higher dimensions.
4. Infinite dimensionality. In active inference, optimization means increasing homeostatic certainty, which requires modeling greater dimensionality. Human models vastly exceed a bacterium's, and almost all of that expansion is due to technology. Since the desire for certainty is infinite, technology's ultimate goal could be "infinite dimensionality," making life an "infinite game."
5. Alignment. Dimensionality is expensive, so we optimize against it with heuristics and gut instincts. Good optimization compresses rather than collapses dimensionality, which yields criteria for aligned and misaligned technology. Higher dimensionality also raises the risks and costs of over-optimization (collapse) and stasis (a local maximum).
6. Dimensional poverty. Viable paradigms contain enough dimensionality to model reality. Ours do not: technology expands reality's dimensions while institutions remain low-dimensional, fragmenting our models and leaving no uniting "outer meta-blanket."
7. Technology's role. Technology should reveal and create novel dimensionality, compress it for optimization, reduce the energy cost of expansion, and enable higher-dimensional paradigms, illustrated by speculative "affective" technologies.

Key claims

• Griggs suggests life's most defining attribute may be that "when everything is going downstream, life will move upstream."
• Technology expands perception and action, improves prediction, and enables larger collectives; it is "the natural extension of our desire to optimize for certainty."
• Satisficing, heuristics and gut instincts are evolved "dimensional optimizations" that conserve energy.
• Optimization is good when it compresses rather than collapses dimensionality.
• Low-dimensional paradigms he lists include representative democracy, science as parsimony, health as diagnosis, land as asset, value as money, art as commerce, self as autonomous individual, education as testing, and quality as quantity.
• Our paradigms are "leaking" so much dimensionality that a critical threshold has been reached and new paradigms are required; in a pluralistic world, "every religion is leaking dimensionality."
• A hypothesis of the Tech for Life Substack is that only life itself can serve as the uniting outer meta-blanket.
• Feelings are an effective paradigm for dimensional compression: at maximum compression a feeling reads as positive or negative valence, yet it can be decompressed into constituent feelings.
• He imagines felt senses of "security," "agency" and "progress" that include planetary, relational and second- and third-order dimensions, a future in which "every model would engage with reality at its appropriate level of dimensional optimization."

What is distinctive about this view

Griggs repurposes concepts from the free energy principle and active inference, usually applied to brains and organisms, as a normative theory of technology: technology is life's instrument for expanding the dimensionality of its models, and alignment becomes a question of whether information is compressed or collapsed. This lets him treat alignment, the meta-crisis and institutional failure within one frame. The essay itself cites active inference, the free energy principle, Kolmogorov complexity, satisficing, finite and infinite games, the meta-crisis, and an account of feelings as valence. These notes are an early statement of ideas, including "dimensional poverty," that Griggs develops more fully in "The High-Dimensional Society."

Questions this essay answers

What is R.B. Griggs's theory of infinite dimensionality?

In "Infinite Dimensionality" (2024), a self-described speculative note, R.B. Griggs proposes that life optimizes for certainty by modeling ever more dimensions of its environment, and that technology is the main way humans expand that dimensionality. Because the desire for certainty is infinite, he suggests technology's ultimate goal could be called infinite dimensionality.

How can you tell if a technology is aligned, according to Griggs?

R.B. Griggs argues in "Infinite Dimensionality" that technology is aligned when it expands dimensionality and improves our ability to compress it for optimization, and misaligned when it reduces dimensionality or accelerates its collapse. The key distinction is that compressed information can be recovered while collapsed information is lost forever; he suggests Kolmogorov complexity as a possible formalization.

What does "dimensional poverty" mean?

In "Infinite Dimensionality," R.B. Griggs describes dimensional poverty as the felt sense that civilization can no longer model the full dimensionality it contains. Technology has expanded reality through global connectivity, information abundance and planetary-scale agency, but institutions like representative democracy, money and testing-based education remain low-dimensional. He offers this as another way to describe the "meta crisis."

How does the free energy principle relate to technology?

R.B. Griggs uses active inference, a theory linked to the free energy principle, to define optimization as increasing homeostatic certainty, which requires modeling greater dimensionality. In "Infinite Dimensionality," he argues that technology extends this drive by expanding perception, action, prediction and collective intelligence.

Connections to other essays

• The High-Dimensional Society develops dimensional poverty and the critique of low-dimensional proxies into a full account of AI-mediated coordination.
• Tech for Life is linked from this essay as the source of its view of "life itself" as the uniting frame for technology.
• The Price of Innovation cites this essay when calling for human judgement that can capture the increasing dimensionality of the future.
• Homo Digitalis applies the free energy principle to how digital immersion changes our relationship with uncertainty.
• The Plurality: a Better Myth for AI revisits optimization and the value of the suboptimal in the evolution of intelligence.

Note: this is a “thinking out loud” post, not a polished essay. Consider these speculative notes about how concepts like optimization, dimensionality, and the free energy principle could help inform a viable future with advanced technology and human flourishing.

Universal optimization

The universe optimizes at all scales and all levels. Its most generalizable principles— least action, free energy, evolution—all explain different aspects of optimization. The path of the universe is that of least resistance.

But how does life relate to optimization? Life seems to have the unique ability to defy or subvert optimization. When everything is going downstream, life will move upstream. This is perhaps life’s most defining attribute.

How should we characterize this? Perhaps life is that internal drive to put optimization in service of value. Perhaps life explains intrinsic optimization rather than extrinsic optimization. Or motivated optimization rather than lawful optimization.

But is life truly “defying” optimization? Or is it simply optimizing at higher dimensions? Perhaps life is that which can defy optimization at one dimension to pursue optimization at higher dimensions.

This would indicate a dialectic between optimization and dimensionality:

• Optimization occurs by compressing dimensionality to increase efficiency at lower dimensions.

• Dimensionality occurs by expending energy to expand optimization to higher dimensions

Playing with this dialectic can take us to some strange places.

Infinite dimensionality

Active inference is a theory related to the predictive brain hypothesis that seeks to explain much of how our perception, learning, and action works. In essence, we are always trying to minimize the difference between what we need from the environment versus what we actually experience. The more certain we are that our environment can meet these predictions for what we need, the better.

Active inference would define optimization as the increase of homeostatic certainty. Increased certainty requires the ability to infer and model increasingly greater dimensionality.

For example, if you contrast the "dimensionality" contained in the model of a bacteria with that of a human, human models are vastly more dimensional:

• We have a far greater scale and scope of action

• We can consider more variables and relationships, and project those farther into the future.

• We can vastly improve the accuracy of our predictions through simulations, counterfactuals, etc.

• We can embed ourselves in collective intelligences that encompasses more and more of our environment.

And almost all of this dimensional expansion is due to technology. Technology expands our capacities of perception and action, it enables us to form better predictions for explaining our environments, and it expands our ability to form larger collectives.

In this sense, technology is the natural extension of our desire to optimize for certainty. Because this desire is infinite, the ultimate goal of technology could be said to be infinite dimensionality.

This is, in essence, the fundamental “drive” of life. And because there is no ultimate certainty, life is playing the ultimate infinite game.

The alignment problem

The problem is that dimensionality is expensive. Simple models are cheaper to process. This means we are driven to relentlessly optimize against dimensionality. Satisficing, heuristics, and “gut instincts” are examples of dimensional optimizations that humans have evolved to use in order to conserve energy.

But not all optimization is equal. Optimization could be said to be “good” when it compresses, rather than collapses, dimensionality. Dimensionality that is compressed for optimization can be decompressed with no loss of information, while dimensionality that is c_ollapsed_ is irretrievably lost. Kolmogorov complexity offers a possible formalization of alignment as conserving information through compression.

This gives us a model for thinking about aligning technology.

• Technology is “aligned” when it expands dimensionality AND increases our ability to compress dimensionality in service of optimization.

• Technology is “misaligned” when it reduces dimensionality OR accelerates the collapse of dimensional optimization.

But this dialectic is always negotiating trade-offs. As optimization occurs at greater dimensionality, more and more energy is required—both to compress dimensionality and defy optimization to pursue even greater dimensionality. So as dimensionality increases, there will be greater risks for over-optimization (a collapse of dimensionality) or for stasis (a local dimensional maxima), and the costs for both will be greater.

Dimensional poverty

Civilization paradigms (like cultures, institutions, and religions) can be considered “viable” when they contain sufficient dimensionality to effectively model reality. Viable paradigms can compress all available dimensionality for optimization, conserving energy for expanding dimensionality.

Our current civilizational paradigm could be characterized as insufficiently “dimensional”.

Technology increasingly expands our dimensional reality:

• global interconnectivity

• information abundance

• human agency at planetary scales

• expanding collective intelligence

• omni engineering (bio, geo)

• crypto primitives, virtualization, etc.

Yet our means of interfacing with reality remain mired in low-dimensional paradigms:

• representative democracy (in almost all forms)

• science as parsimony

• health as diagnosis

• land as asset

• value as money

• art as commerce

• self as autonomous individual

• education as testing

• quality as quantity

These paradigms have been relentlessly optimized for lower dimensionality. This leads to a felt sense of living in dimensional “poverty”—the sense that our civilization is no longer able to effectively model the full dimensionality that it contains. This would be another way to characterize the “meta crisis”—our civilizational paradigms are “leaking” so much dimensionality that a critical threshold has been reached. New paradigms are required.

This also leads to a fragmentation of our models. We have fewer outer meta-blankets that can unite our collective models by compressing maximal dimensionality. Religions used to play this role, compressing all dimensions of reality into legible forms that even the smallest model could optimize. Today that is no longer true. In an interconnected and pluralistic world, every religion is leaking dimensionality.

One hypothesis of this Substack is that only life itself is sufficiently “omni-dimensional” to serve as that outer meta-blanket that can surround and unite our collective blankets.

Technology’s role

From this perspective, the normative role of technology is to optimize certainty in the broadest sense, and thus to optimize the expansion of dimensionality. Technology should thus strive to:

• Reveal and create novel dimensionality

• Compress dimensionality in service of optimization

• Reduce the energy cost of dimensional expansion

• Enable new paradigms for modeling higher dimensionality

At its most abstract, technology should seek paradigms that can support infinite dimensionality. These “infinite” technologies would enable scale-invariant dimensional expansion and compression.

For example, the role that feelings play in human consciousness is an effective paradigm for dimensional compression. At its maximal compression, a feeling is legible as positive or negative valence. Yet any affect can be decompressed into its constituent feelings, up to maximum dimensionality.

This may look like “affective” technologies where even planetary valence can be compressed into affect that can still be legible to the most efficient models. At the highest compression these “affects” would translate to a simple “good” or “bad” valence, yet they could be decompressed for any model with sufficient energy to process their maximum dimensionality.

Imagine if every state’s felt sense of “security” included some component of the security of our planetary collective? Or if our felt sense of “agency” could include the entirety of our interconnected relations? Or if our felt sense of “progress” included second and third order impacts?

This would be a future of infinite dimensionality, yet one where our models would never be at risk of being overwhelmed. Every model would engage with reality at its appropriate level of dimensional optimization.

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