Symbols are local definitions
Read the manuscript’s unity score without treating its name as a measurement.
Course lessons · 1 of 5
Evaluate the unity score and distinguish its variable, target, and output.
Read the expression as instructions
The manuscript defines a scalar score by subtracting a chosen target, taking an absolute distance, adding one, and taking the reciprocal. The variable x is the input. The symbol Φ names the output of this particular function. Parentheses decide which operation happens first.
A Greek letter does not carry one universal meaning across the archive. Other pages use Φ for a partition-based information quantity. Always read the local definition before transferring an interpretation from another document.
Translate the formula into behavior
At x = 1 the distance is zero, so the score reaches one. Values equally far to the left and right produce the same score. As the distance grows, the denominator grows and the score decreases.
The manuscript proposes a consciousness-related interpretation. The calculation itself measures proximity to the selected target one. Evaluating it successfully establishes that arithmetic, while the proposed interpretation needs its own evidence.
Evaluate the score at x = 3
1Find the distance
Subtract the target before taking the absolute value. The distance between three and one is two.
2Construct the denominator
The added one prevents a zero denominator at the target.
3Take the reciprocal
The result is one third. It is a scalar similarity score under the chosen definition.
Make the idea respond
Change one input at a time. Predict what should happen, then compare the computed result with your prediction.
Teaching model · computed in your browser
Distance from unity
Move the input, watch the distance from 1 change, and calculate the score yourself.
x is a real input and |x − 1| is its absolute distance from 1. The displayed domain is −3 ≤ x ≤ 5; the mathematical function is defined for every real x.
Try this: compare x = 0 and x = 2. Why do they produce the same score?
The default worked example is shown below.
Substitute, then simplify: U(1) = 1 ÷ (1 + 0) = 1. Equal distances on either side of 1 give equal scores. A score of 1 is a property of this function; it is not evidence of consciousness.
| x | Distance from 1 | U(x) |
|---|---|---|
| -1 | 2 | 0.3333 |
| 0 | 1 | 0.5 |
| 1 | 0 | 1 |
| 2 | 1 | 0.5 |
| 3 | 2 | 0.3333 |
Your turn.
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What is Φ(1) for Φ(x) = 1/(1 + |x − 1|)?
Read the solution
The denominator is 1 + 0 = 1, so the reciprocal is 1.
What is Φ(0)?
Read the solution
The distance is one, so Φ(0) = 1/2 = 0.5.
Which input has the same score as x = 3?
- x = 1
- x = 0
- x = −1
- x = −3
Read the solution
Both −1 and 3 are two units from one, so both score 1/3.
What does calculating a large value of this Φ establish directly?
- An exact information partition was found.
- The source program is running on a remote computer.
- The input is close to the chosen target.
- A system has conscious experience.
Read the solution
A high score directly indicates small distance from one under this formula.
Follow the original record
Use the definitions you just practiced to read the project’s own notation, assumptions, and evidence.
The ideas to keep
- Define symbols within the current source.
- Evaluate inner operations before outer ones.
- Separate a calculated score from its proposed interpretation.
Reading completion is separate from your practice evidence.
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