Consider these decimal counts represented in Round8:
Our Columnar Marquee System demonstrates this efficiency:
Round8 UnHex Binary
0 000 000 000 001 111 = 8
0 000 000 001 111 111 = 88
0 000 001 111 111 111 = 8,88
0 001 111 111 111 111 = 88,88
1 111 111 001 111 111 = 1,88,88 | Count of 70,216
Every internet packet would carry 7% more data. Every 16-bit operation would be 7% more efficient.
Within this framework, we have sufficient capacity to implement Round8 for any information equal to or greater than 16 bits, beginning at the baseline with a remarkable 7% more digits represented in binary than hex.
Comparison with Hexed Binary:
Hexed Binary
1111 1111 , 1111 1111 16 bits @ 65,536
1111 , 1111 1111 , 1111 1111 20 bits @ 1,048,576
1111 1111 , 1111 1111 , 1111 1111 24 bits @ 16,777,216
The major breakthrough that Round8 brings involves the study of abstractions and their underlying manifolds. This enables the creation of Bidirectional Higher-Ordered Look-Up Tables, or Manifold Spools, which leverage the relative position of bits for increased combinations.
Critically, this approach provides immunity from Shor's Factorization Attack on binary operands. Counter-intuitively, where many would fail to understand this paradigm shift is precisely the point where this system becomes quantum-proof by current measurement techniques.
Prior to 16 bits, the system is not as efficient as hexed binary. However, after 16 bits, the advantages compound significantly.
What was once a Y2K-level challenge for civilization stands at our doorstep once again.
Note: This method uses binary operations to inform modern switches. Our approach employs signals relatively alongside bidirectional higher-ordered compositional principles. There is no intended value judgment on arbitrary symbol creation. This demonstrates the limited perceptual scope of unidirectional associations without bidirectional validation.
Round8 is based on a spatial coordinate system with only one zero at its origin, while truncating the need for a 10th placeholder position. This means the usual expectations of an octal counting system do not apply, yet it maintains a non-columnar design.
How does this work?
Due to the truncation of arbitrary placeholder positions in the baseline, we have an extra two counts available. Once the rotation completes, rather than creating an arbitrary 10th place, the next counting position activates and adds to the stack of counts.
The reason Round8 functions as a spatial coordinate system relates to its design for graphs. The only true zero in reality is the origin of a graph. The limitation of eight counts derives from how we subdivide circles on a graph.
Consider this progression:
In Base 10 Decimal, starting with a count of 10 for the total representation of degrees in a subdivided circle:
You cannot subdivide the space further without maintaining a fraction or decimal.
If we limit circle subdivisions to round numbers: 2, 4, 8, 16. At 16, you encounter the same issue. In Base 10 Decimal, the extra position for the 10th place imposes an offset in the symbol space. Therefore, our round counts can only be represented via 2 through 8, where 8 is the maximum expression space prior to requiring a 10th place.
Roman numerals were once the standard. They represented counts, but the true advent of mathematics came with the Arabic numeral system and the invention of zero. However, with zero came placeholder positions in the counting system. The issue is that there is no such thing as zero outside of absolute zero within our physics system.
This is where the bidirectional nature of this counting system emerges. We stand on the shoulders of giants.
With our circle degrees represented as 8:
It's a complete round counting system. In geometry, we already acknowledge this—we don't divide circles into tenths expecting to divide further than fifths. Once you do, the division is no longer round, which distinguishes this system from base systems.
So what is the maximum count of 64 bits? Our current base mathematics system has an offset and cannot represent higher-accuracy round numbers, especially in higher ranges. While Round8 is Base 72 starting at two rotations (or two positions of 8s), the reason is that the base system equals 8 × 9. The first 8 represents the first rotation, and the next 8s represent the second rotation, counting the number of 8s by 8. This pattern continues for the entire length.
Base octal systems are limited to 70 number representations in the same space. We can see this as a compounding error rate at higher ranges. This also applies to our Base 10 system. It's important to acknowledge that while Base 10 counts to 10 and 100, within that same space of counts, fewer counts are possible within the same symbol space.
Comparison:
The eventual RoundX as Base 100 will provide the means of converting from Round8 to Base 10 Decimal.
Using finger positions:
Notice how we reach our maximum count and still have a pinky available? The thumb acts like a Round8 marquee, relative to the other fingers.
XX: (Hang ten / Hang loose) on two hands X × X = XX
88: Index + Middle + (Ring + Thumb) + Pinky + Thumb in play on both hands
Within the same amount of space on your hands, you can represent more information in the same space.
Where 1,000,000,000 = X,XX,XX,XX,XX
(X,XX,XX,XX,XX - Hang ten / Hang loose) on two hands X × 4 shakes = XX,XX,XX,XX
In RoundX, we don't need a placeholder. However, when we do count in that position—like our Round8 marquees—it exists, but we don't need to represent it until we start counting the next level.
Key Distinctions:
Our counts are accurate, but if you're working in geometric space, you still would not divide a circle into Xths as in our base system—instead, it would be represented by rounds.
In RoundX, we compose a linear counting system that flattens the curve that Round8 matches in its compounding rotations. That exact curve is precisely why predicting the maximum range in Round8 without the eventual mapping of RoundX remains on the roadmap.
What is that curve? The limit of our spatial reality—without it, there would be no circles, squares, or triangles.
Round8 orders information more efficiently than binary operand operations. Its clear methodology, aligned with higher-order data structures as manifolds and spools, enables us to have a safe, secure future in a post-Shor's world without requiring upgrades to every computer.
This system is neither a compression method nor encryption. It's too expansive and counter-intuitive for conventional linear counting. These very qualities make it the perfect hex replacement. It enhances current encryption by interchanging the storage method, removing Shor's attack vector of factorization. Instead, we utilize manifolds with clear and set operations.
Consider the 7% power savings for each component—RAM, storage, and internet communication. In total world energy savings, we have a formative method of creating a marketplace in the same space. This is not extraction; this is value creation and represents the essence of the purest form of capitalism: the creation of marketplaces where none existed before.
Key Questions:
This represents the largest invisible problem of our modern age, and 7% is the floor of energy savings. Through coordinated effort and redirection of funds due to energy savings across our economies, we create capital, create good work and jobs, and create the possibility for more capital formation—a true unlimited marketplace in the same space.
Within those savings are jobs—the essence of capitalism as a method of value creation. This is not about burning our finite resources and discarding them into landfills and oceans. That represents loss of value, not the value creation central to the truest form of capitalism.
This introduces Formative Capitalism: the idea that the formation of capital is the value that capital produces.
The ceiling is not:
The potential: 70%+ less fuel and resources wasted through every computer system on the planet.
Consider the climate change discussion. This advent addresses that challenge fundamentally while creating a starting floor of 7% more capital from assets spent on bit crumbling to circulate into our economies, increasing GDP worldwide.
Crowdfunding and subsequent training materials coming soon.
Thank you for your patience in this Formative Capitalism advent. This represents the Precision and Error Correction Marketplace—the one poised to break ground and enable the rest on an unlimited frontier bounded by our reasonability.
Cheers, MTK @ PhuirE Research