Tensions in Practice: A fixed channel amount in tension with a fixed share¶
Two output channels · changing total
A lossless splitter sends one input into channels A and B. At input 20, both of the illustrated settings send 10 to each channel. At input 40, they diverge: holding A at 10 leaves 30 for B, while holding A at one half sends 20 to each. A’s fixed amount becomes a smaller share; its fixed share becomes a larger amount.
Hold A’s amount constant
Deliver ten units to A while sending additional input to B.
Hold A’s fraction constant
Keep A at one half as the available input changes.
Why these aims pull against each other
An amount and its fraction share a changing denominator. Once input changes, the two invariants cannot both be preserved.
Choose an arrangement to see what changes and what remains difficult.
Finite illustrative comparisons. Text states carry the meaning; color is not a measured score or universal preference.
What this choice protects
What it costs
When it fits
Compare the arrangements
Fixed amount
Stipulate a metered split A=10 and B=input−10 for the shown inputs, both at least ten.
| Amount A | Share A | Amount B | |
|---|---|---|---|
| Input 20 | 10 | 50% | 10 |
| Input 40 | 10 | 25% | 30 |
- What it protects
- A receives the same ten units while B receives all of the increase.
- What it costs
- A’s fraction falls from one half to one quarter and it receives none of the growth.
- When it fits
- The intended channel service is a fixed ten-unit quantity and B can receive the remainder.
Illustration note: The finite setting and values are editorial assumptions, not measured effects or recommended operating settings. This metering rule is an editorial design assumption. Input Partition supplies the accounting relation, not the mechanism, priority or desirability of the rule.
Fixed share
Stipulate A=input/2 and B=input/2 for both shown inputs.
| Amount A | Share A | Amount B | |
|---|---|---|---|
| Input 20 | 10 | 50% | 10 |
| Input 40 | 20 | 50% | 20 |
- What it protects
- Both channels preserve their fractions as the input doubles.
- What it costs
- A’s amount doubles; B receives only ten of the twenty additional units instead of all twenty.
- When it fits
- Both channels are intended to scale with the common input and can accept the resulting amounts.
Illustration note: The finite setting and values are editorial assumptions, not measured effects or recommended operating settings. No storage, leakage or conversion channel is included. Each row’s two amounts exhaust its declared input.
What this illustration does—and does not—establish
Input Partition: Fixed input versus changing denominator supplies the amount/share distinction and Input Partition: Passive split versus deliberate allocation prevents deriving a causal or normative rule from the arithmetic alone.
- The rule for inputs below ten is outside the fixed-amount illustration.
- The prime does not itself justify either routing rule or establish a fair allocation.
- Quantities are per the same accounting interval; no unstated rate or unit conversion is used.
Source entries
Input Partition
Input Partition: Fixed input versus changing denominator supplies the conflict examined here.
Fixed input versus changing denominator
A channel amount can rise while its share falls if total input rises faster. Amount and fraction must not be interchanged.
Structural Tensions
The same numerical table can arise from physical routing or a decision among claimants. The causal and normative interpretation must come from another abstraction.