Kurzweil Law Accelerating Returns Lookup
Compare early and late annualized log growth across a caller-supplied milestone series to test for accelerating returns.
Description
Accelerating returns can be screened by comparing early and late annualized log growth in supplied milestones.
Accelerating returns can be screened by comparing early and late annualized log growth in supplied milestones. Growth and acceleration are distinct.1
The returned values include Growth accelerating, Late minus early annualized growth, Early annualized growth percent, Late annualized growth percent. The How section below explains the calculation, input rules and interpretation.
When to use Kurzweil Law Accelerating Returns Lookup
Use Kurzweil Law Accelerating Returns Lookup when you need to evaluate the supplied records under the calculation and evidence rules below. This compares equal-weight segment means, not a fitted universal law or discrete compound growth rate.
Define the question, evidence and scenario assumptions first. Supply the chosen score scales, time horizons or reference selection explicitly. Interpret generated text as a discussion template and screen labels as the stated rules.
How to use Kurzweil Law Accelerating Returns Lookup and understand its results
- Define the question, evidence and scenario assumptions first. Supply the chosen score scales, time horizons or reference selection explicitly. Interpret generated text as a discussion template and screen labels as the stated rules.
- Enter milestoneValues, milestoneYears using the field table and calculation rules, then run the tool.
- Read accelerating, annualizedGrowthDifferencePercent, earlyAnnualizedGrowthPercent, lateAnnualizedGrowthPercent. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| milestoneValues | At least two positive values in chronological order. | list of number | Required |
| milestoneYears | At least two strictly increasing years. | list of number | Required |
Require aligned at least two strictly increasing finite years and positive finite values. Split segment rates after ceil(segmentCount/2), average each half and compare signed difference>0. With only two milestones the late half is empty and its mean is nonfinite, so the tool reports an input error. At least three milestones are needed for a returned comparison.
segment=100ln(nextValue/currentValue)/(nextYear−currentYear); difference=meanLate−meanEarly Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| accelerating | Growth accelerating | boolean |
| annualizedGrowthDifferencePercent | Late minus early annualized growth (%) | number |
| earlyAnnualizedGrowthPercent | Early annualized growth percent (%) | number |
| lateAnnualizedGrowthPercent | Late annualized growth percent (%) | number |
{
"input": {
"milestoneValues": [
10,
20,
60,
240
],
"milestoneYears": [
2000,
2005,
2010,
2015
]
},
"output": {
"accelerating": true,
"annualizedGrowthDifferencePercent": 9.80829253011726,
"earlyAnnualizedGrowthPercent": 17.91759469228055,
"lateAnnualizedGrowthPercent": 27.72588722239781
}
}Limitations and assumptions
This compares equal-weight segment means, not a fitted universal law or discrete compound growth rate.
Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Core numeric and string lists are limited to 100,000 entries; text entries are subject to the general large-text limit. Follow any smaller calculation limits above. Missing fields without a declared default, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use Wright Law Learning Curve Cost Doubling Lookup: Learning curves express a hypothetical unit-cost reduction per doubling of cumulative production. The chosen rate is an assumption, not an observed future trend. For a complementary task, use Extrapolation Horizon Limit Warning Checker: An extrapolation can assume uncertainty grows at a constant annual compound rate. Explicit thresholds provide an illustrative warning screen.
References
-
Kurzweil Law Accelerating Returns Lookup — tool.io
Similar or alternative tools
- Wright Law Learning Curve Cost Doubling Lookup
Learning curves express a hypothetical unit-cost reduction per doubling of cumulative production. The chosen rate is an assumption, not an observed future trend.
- Extrapolation Horizon Limit Warning Checker
An extrapolation can assume uncertainty grows at a constant annual compound rate. Explicit thresholds provide an illustrative warning screen.