Observations on a Mathematical Thread Linking Kinematic and Dynamic Ratios

J. Rogers, SE Ohio

Overview

When examining the fundamental equations of physics through the lens of unit-free ratios, an interesting mathematical consistency appears. This thread seems to connect the disparate worlds of Newtonian gravity, Special Relativity, and General Relativity. By stripping away the Jacobian scaling factors required for SI units, we can observe how these "different" laws may actually be expressions of a single geometric relationship.

1. The Proportionality of Force (

        $I_1 \cdot I_2$
      

)

If we consider a "natural" force as the interaction between two dimensionless densities, we find a curious simplification of Newton’s Law of Gravitation. In the substrate, where we deal with proportions of the total physical scale rather than kilograms and meters, "Force" can be expressed as:

        $$F_{natural} = I_1 \cdot I_2$$

Where

        $I$
      

is the unit-free ratio of mass to distance. In this form, the gravitational constant

        $G$
      

is no longer seen as a standalone parameter, but as the scaling factor required to translate this simple product into the misaligned units of the SI system.

2. The Identity of Velocity and Potential (

        $\beta^2 = 2I$
      

)

A particularly interesting result arises when we re-examine the classical relation for orbital or escape energy:

        $$\frac{1}{2}{v}^2=\frac{GM}{r}$$

If we express the velocity

        $v$
      

as a ratio of the maximum substrate flow (

        $\beta = v/c$
      

), the equation becomes:

        $$\frac{1}{2}\beta^2 c^2 = \frac{GM}{r}$$

Rearranging for

        $\beta^2$
      

:

        $${\beta }^2=\frac{2GM}{c^{2}r}$$

If we define

        $I$
      

as the "natural" mass-to-radius ratio (

        $m/r$
      

), we see that the term

        $\frac{2G}{c^2}$
      

acts as the unit-scaling bridge. In a unit-free environment, the relationship reduces to a striking identity:

        $${\beta }^2=2I$$

This suggests that, at the substrate level, the "Speed" of an object (

        $\beta^2$
      

) and the "Gravitational Potential" (

        $2I$

) are mathematically indistinguishable ratios.

3. The Unified Lorentz Factor (

        $\gamma$

)

The most notable part of this thread is found when we plug this identity into the Lorentz factor (

        $\gamma$

), which is the core of Special Relativity:

        $$\gamma =\frac{1}{\sqrt{1-{\beta }^2}}$$

By substituting

        $\beta^2 = 2I$
      

, we obtain:

        $$\gamma =\frac{1}{\sqrt{1-2I}}$$

This result is curious because it is identical to the formula for gravitational time dilation in a weak field (the Schwarzschild temporal component).

4. The Boundary Condition (

        $r = 2M$
      

)

A final interesting observation occurs at the mathematical limit of these formulas. In the substrate expression for time dilation, a singularity occurs when the denominator reaches zero. This happens when:

        $$1=2I$$

Substituting our definition of the natural ratio

        $I = m/r$
      

:

        $$1=2(m\mathrm{/}r)\hspace{0.25em} ⟹\hspace{0.25em} \mathbf{r}=\mathbf{2}\mathbf{m}$$

In the language of natural ratios, the point where "Speed" hits its limit (

        $\beta = 1$
      

) is the exact same point where the geometry hits the Schwarzschild radius (

        $r = 2m$
      

). This suggests that the "Speed of Light" limit and the "Black Hole" limit are the same geometric boundary, expressed through different coordinate lenses.

Conclusion

These derivations are interesting because they suggest that many of our "fundamental laws" are not independent discoveries, but different views of the same underlying tautology.

The thread reveals that:

• Force is a product of densities.

• Velocity squared is a measure of potential.

• Time dilation (

          $\gamma$
        

  ) is a geometric consequence of your position in that potential.

• The event horizon is the point where the unit-scaling ratio reaches unity.

The presence of constants like

        $c^2$
      

and

        $G$
      

in our standard formulas appears to be the "tax" paid for using instruments calibrated to different historical standards. When those calibrations are removed, we are left with a very simple, unit-free geometry where the orbit, the speed, and the time dilation are all functions of the same substrate proportion.

Who Watches the Watchers? Tracking "Hidden" Indexers in Linux

J. Rogers, SE Ohio

If you’ve ever noticed your laptop fans spinning up or your terabyte-scale storage thrashing while you aren’t doing anything, you’ve likely met tracker-miner. In modern desktop environments like GNOME, these services are designed to index your files to provide "instant search" But for power users who live in the terminal and manage massive data sets, this isn't a feature—it's a background process digging through your private data without your explicit permission.

Even worse, these indexers create a centralized metadata database. In the event of a security breach, an attacker doesn't need to spend hours scanning your disks; they can simply query this "pre-digested" database to find your most sensitive documents in seconds.

Here is how to reclaim your system and use Honeyfiles to catch these silent trackers red-handed.

Step 1: The "Honeyfile" Trap

A Honeyfile is a decoy file designed to attract unauthorized access. By placing one in your home directory, you can detect any background service—or human intruder—that snoops where it shouldn't.

Create your bait:

bash  

mkdir -p ~/Documents/Secret touch ~/Documents/Secret/financial_passwords.txt

Of course, pick a filename that blends in on your system to look innocuous.  You can also watch files that contain sensitive data as well. 

Step 2: Set Up the Watcher

To see who touches this file, we use the Linux Audit Daemon (auditd). This kernel-level tool logs every system call that interacts with your chosen file.Install the Audit Framework:

bash

sudo apt update && sudo apt install auditd -y

Add a "Read" Watch Rule:

We will tag this rule with the key honey_trap so we can filter the logs later

bash

sudo auditctl -w /home/$USER/Documents/Secret/financial_passwords.txt -p r -k honey_trap

Step 3: Caught Red-Handed

Now, simply wait. If tracker-miner or any other background process tries to index your "financial passwords," auditd will record the event silently.

Search the logs for activity:

bash

sudo ausearch -k honey_trap -i

What to look for in the output:comm: The specific command that accessed the file (e.g., tracker-miner-fs-3).

exe: The path to the binary.

auid: The User ID responsible for the process.

You can also monitor the honeyfile in real time to catch events immediately:

 

bash

tail -f /var/log/audit/audit.log 

    -- or -- 

aureport --follow

Step 4: The Final Kill-Switch

If your "Honeyfile" confirms that the system is indexing your private data against your wishes, it’s time to shut it down for good. On Debian, you can’t easily uninstall these services without breaking the desktop, so we mask them to prevent them from ever starting.  This is what worked for me.  You may also want to reboot to catch a running instance if it did not quit with the following commands.

bash

sudo systemctl --global mask tracker-miner-fs-3.service

sudo systemctl --global mask tracker-xdg-portal-3.service

sudo tracker3 reset -s -r

The Takeaway

Your OS should be a toolbox, not a "manager" that snoops on your storage to offer convenience you didn't ask for. By using auditd and honeyfiles, you move from being a passive user to an active auditor of your own hardware. Stay lean, stay private, and keep your IOPS for yourself.

The Planck Scale Is Not a "Pixel": It’s a Measure of You

J. Rogers, SE Ohio

For decades, we’ve been told the same story about the Planck Length. Science popularizers often call it the "pixel size of the universe" or the "smallest possible length." We are told that at an unimaginably small scale—a decimal point followed by thirty-four zeros and then a one—space-time turns into a bubbly foam and physics breaks down. It feels like a fundamental wall of reality.

But what if that is backward? What if the Planck Length isn't a property of the universe at all, but a measurement of human convenience?

A provocative paper by independent researcher J. Rogers suggests that we have been looking at our rulers from the wrong end. The paper argues that the tiny numbers we associate with the Planck scale are actually a measure of how far humans had to "zoom out" from nature’s reality to make our lives comfortable by writing small numbers in our day to day experiences.

The Problem with Being Human-Sized

Think about why a meter is a meter. It is roughly the length of a human stride. Why is a second a second? It is about the interval of a resting heartbeat. Why is a kilogram a kilogram? It is roughly the weight of a liter of water—a convenient amount of liquid to carry.

Our units of measurement are ergonomic. We designed them to fit our bodies and our daily lives. This is great for building houses and trading groceries, but Rogers argues it creates a massive distortion when we try to do fundamental physics.

The Tax for Using the Wrong Ruler

Rogers describes constants like the speed of light or the gravitational constant as conversion factors. In mathematics, these are often called Jacobian entries. They are simply the "tax" you pay when you move between different ways of measuring things.

Imagine you are measuring a rug. If you use inches and your friend uses centimeters, you will need a constant number—2.54—to talk to each other. That number 2.54 isn't a fundamental law of the universe; it is just the bridge between two different rulers.

According to the paper, the speed of light, the gravity constant, and the Planck constant are that exact same kind of bridge. They only exist because we insist on measuring the universe in strides and heartbeats rather than in the universe's own natural language.

The Inversion: Why the Planck Length is Tiny

This brings us to the Planck Length. In standard physics, we see the Planck Length as an incredibly small "thing" out there in space. Rogers flips this on its head.

In his view, the Planck Length is the "unity point" of nature. It is the place where the universe’s internal math simply says "one." The reason the number looks so tiny to us—that long string of zeros—isn't because the universe is made of tiny grains. It is because we chose a ruler (the meter) that is trillions upon trillions of times larger than nature's "one."

The Planck Length doesn't measure a grain of space. It measures the distance between a human stride and the baseline of reality. It tells us how far we moved our coordinates away from the heart of nature to make them fit our own bodies.

The Ant Civilization

To prove this, Rogers proposes a thought experiment involving a civilization of ants. Imagine ants develop advanced physics. Their "meter" is the length of an ant (one millimeter). Their "kilogram" is the mass of an ant. When they calculate the Planck Length using their ant-units, they get a different number than we do.

Does the universe’s "pixel size" change because the ants have a different ruler? Of course not. The only thing that changed was the choice of the observer. This shows that the Planck Length is an artifact of our coordinates, not a physical boundary built into space.

Why It Matters

This isn’t just about making math easier; it dissolves massive philosophical headaches.

For example, people often talk about "fine-tuning"—the idea that if the gravity constant were slightly different, stars couldn't form, and therefore the universe was made for us. Rogers shows this is a misunderstanding. If you change the gravity constant, you are just changing your ruler. Stars form just fine even if you use a completely different unit system where the gravity constant is a massive, round number.

The universe doesn't care about meters, kilograms, or seconds. It operates on a single scale with its own unit free ratios between things.

The Planck Scale isn't a mysterious limit on how small we can go. It is a reminder of where we started. We walked away from nature's baseline to create a world of strides and liters, and the fundamental constants are just the breadcrumbs we left behind to find our way back. The Planck Length isn't the size of the universe's pixels—it is the length of the shadow we cast upon it.

The Constraint Console: A Proposal for a Modular Gaming Ecosystem Focused on Systemic Creativity

J. Rogers, SE Ohio 

Abstract

This paper proposes a new paradigm for video game consoles: a hardware platform built around a fixed, comprehensive, and updatable set of core software libraries. In this model, the console itself contains the essential "engine" components—physics, rendering, audio, AI, input handling—as a permanent, optimized part of the system. Games are not self-contained applications but rather lightweight modules that utilize these shared libraries, consisting primarily of level data, assets, scripts, and gameplay logic. This paper argues that such a system, by establishing firm technical and creative constraints, would refocus game development from technological one-upmanship toward systemic innovation and artistic expression, drawing direct parallels to the creatively fertile era of 8-bit computing exemplified by the Commodore 64.

---

1. Introduction: The Escalating Arms Race

The history of home video game consoles is largely a history of technological escalation. Each new generation markets itself on raw power increases: more polygons, higher resolutions, faster frame rates, and photorealistic lighting. While this progression has yielded graphical marvels, it has also created significant industry-wide inefficiencies. Game development budgets have ballooned to blockbuster proportions, driven by the need to build or license ever-more-complex engines from scratch for each title. Consequently, the industry has become risk-averse, favoring sequels and established franchises over novel concepts.

Furthermore, this focus on hardware capability often positions the game itself as a mere demonstration of the technology, rather than the technology serving the game. This paper explores an alternative: a console designed not as a blank slate for developers to rebuild the wheel, but as a complete, modular creative instrument. This "Constraint Console" would internalize the platform, allowing games to become focused expressions within its limits, much like a musician composes a sonata within the fixed constraints of a piano.

2. The Proposed Architecture: The Console as an Instrument

The proposed system, which we will term the "Constraint Console," operates on a fundamental shift in the relationship between hardware, platform, and software.

2.1 The Core Libraries (The Instrument)
The console ships with a comprehensive suite of highly optimized, low-level software libraries permanently installed in its firmware. These libraries cover all standard game functions:

• Rendering Pipeline: A fixed-function but highly flexible renderer capable of specific visual styles (e.g., cel-shaded, pixel-art, low-poly 3D).

• Physics Engine: A robust system for collision detection, rigid body dynamics, and particle effects.

• Audio Synthesis & Playback: A powerful sound engine, potentially including a software emulation of a classic synthesizer chip (like the SID) alongside modern playback capabilities.

• AI Framework: A library of pathfinding, state machines, and behavior trees.

• Input Handling: Standardized mappings for all controller inputs.

These libraries are not static; they can be updated by the console manufacturer to improve performance, fix bugs, or add new core functions. However, they are universal. Every game running on the console uses the same version of the physics engine, the same renderer.

2.2 Games as Modules (The Compositions)
A game for the Constraint Console is not a standalone executable. It is a lightweight module containing:

• Unique Assets: 3D models, textures, 2D sprites, sound effects, and music.

• Level Data: Geometry placement, object spawn points, trigger zones.

• Scripts & Logic: High-level code that dictates gameplay rules, enemy behavior, and interactive elements, all written to interface with the core libraries.

When a user purchases and downloads a game, they are primarily downloading this unique content. The game "runs" by instructing the console's core libraries on how to assemble and utilize its assets.

2.3 The Subscription Model (The Genre)
To further structure the ecosystem, games could be categorized by genre, which might require a specific "genre pack"—a curated subset or configuration of the core libraries. A player might subscribe to a "First-Person Shooter Pack" or a "2D Platformer Pack." This subscription would unlock the relevant core functionalities and provide a curated storefront for games built within those specific constraints. This model ensures that a player's library of games is guaranteed to be compatible with their console's capabilities.

3. The C-64 Precedent: Constraint as a Catalyst for Creativity

The primary objection to such a system is often the fear of creative stagnation—that fixed libraries will lead to homogeneous games. However, the history of the Commodore 64 (C-64) serves as a powerful counter-argument. The C-64 presented developers with a set of rigid, unchangeable hardware constraints:

• A fixed color palette.

• A specific, idiosyncratic sound chip (the SID).

• A limited amount of RAM and processing power.

Far from stifling creativity, these constraints became its engine. Developers, unable to compete on raw technical prowess, were forced to innovate in other areas. They developed clever programming tricks to squeeze more color out of the system, pushed the SID chip to produce sounds its designers never intended (including crude speech synthesis), and designed gameplay loops of incredible depth within tiny memory footprints. The result was a library of games that were not only technically impressive for their time but remain celebrated for their artistic vision and distinct personalities—from the open-world exploration of The Last Ninja to the emergent simulation of Little Computer People.

The Constraint Console aims to replicate this environment on a modern, digital scale. The core libraries are the new "hardware." They are the known quantity, the instrument. The developer's challenge is no longer "how many shaders can we write?" but "what unique gameplay experience can we compose using this fixed set of tools?"

4. Advantages of a Constraint-Based Ecosystem

Shifting the development focus from engine-building to content-creation offers profound benefits for developers, players, and the industry as a whole.

4.1 For Developers: Lower Barriers and Focused Innovation

• Reduced Development Costs & Time: By eliminating the need to develop or heavily customize a game engine, studios can focus their resources on what makes a game unique: its art, story, level design, and core mechanics.

• Democratized Development: Smaller teams and even solo developers could create polished, professional-feeling games by leveraging the console's powerful core libraries.

• Systemic Mastery: Developers would become virtuosos of the platform. Over time, they would learn the intricacies and hidden potentials of the core libraries, leading to emergent techniques and styles that become the console's signature. Creativity would flourish not in spite of the constraints, but because of them.

4.2 For Players: A Streamlined and Cohesive Experience

• Smaller Downloads & Instant Play: Games, stripped of redundant engine code, would be dramatically smaller. A complex role-playing game might be only a few hundred megabytes, allowing for near-instantaneous downloading.

• Consistent Performance & Polish: Because the core rendering and physics libraries are optimized by the console manufacturer, games would run with a guaranteed level of smoothness and stability. A bug in the physics engine, once fixed by an update, would improve every single game that uses it.

• A Focus on Gameplay: Players would evaluate games based on their artistic merit and gameplay innovation, rather than being swayed by graphical fidelity. A new title would be anticipated for its novel mechanics, not its use of a new ray-tracing technique.

4.3 For the Industry: A Sustainable Model

• Reduced "Crunch": By streamlining the development process, the industry-wide problem of unsustainable "crunch time" could be significantly mitigated.

• A Hedge Against Obsolescence: Games written for the Constraint Console would be inherently forward-compatible. As long as the console's core libraries are maintained and updated, a game released on day one would still function perfectly on a console purchased ten years later, as it relies on the same fundamental API. This preserves gaming history and the player's investment.

5. Addressing Potential Challenges

No system is without its challenges, and a model this radical would require careful consideration.

• The Risk of Stagnation: While the C-64 example is compelling, a poorly designed library could indeed lead to monotony. The key is to design core libraries that are not just functional, but expressive. They must offer deep, combinable systems that allow for a wide spectrum of outcomes. The libraries should be more like the rules of chess than a paint-by-numbers kit.

• Versioning and Compatibility: How does the system handle a major update to the physics library that might break older games? This could be solved through a virtualized layer, where games are tagged with the core library version they were designed for, and the console seamlessly emulates that version when running the game.

• The "God Game" Problem: What if a developer has a visionary idea that the core libraries simply cannot accommodate? The solution is not to remove constraints, but to design the libraries with extensibility in mind. Developers could be allowed to submit "library extensions" or new core modules for approval and integration into a future system update, enriching the platform for everyone.

6. Conclusion: A Return to Systemic Depth

The current trajectory of the video game industry, driven by an endless pursuit of graphical and technological advancement, is economically and creatively unsustainable. The Constraint Console offers a viable and compelling alternative. By shifting the foundation of a game from its underlying technology to its content and systems, this model refocuses development on what truly matters: the player's experience.

Inspired by the golden age of 8-bit computing, where fixed hardware gave rise to boundless creativity, this proposed ecosystem treats the console not as a passive box to be overpowered, but as an active instrument to be mastered. Games would no longer be monolithic showcases of new display tech, but rather diverse and inventive compositions written within a shared, powerful language. The result would be an industry that is more sustainable, more accessible, and, most importantly, more creatively vibrant than ever before.

---

References

• Montfort, N., & Bogost, I. (2009). Racing the Beam: The Atari Video Computer System. MIT Press.

• Rogers, J. (2026). Beyond the Processor: A Technical and Cultural Analysis of Creative Constraint in Commodore 64 Game Development

• Costikyan, G. (2013). Uncertainty in Games. MIT Press. (Discusses how constraints shape gameplay).

• Juul, J. (2005). Half-Real: Video Games between Real Rules and Fictional Worlds. MIT Press. (Explores the relationship between game rules and fiction).