5 ms·
It's not circular. It rearranges into a standard quadratic equation: x^2 − 24Sx + 24 = 0. α is derived as the root of this equation.
by albert_roca 9mo ago
It's not circular. It rearranges into a standard quadratic equation: x^2 − 24Sx + 24 = 0. α is derived as the root of this equation.
- fatbrowndog 9mo agoDoesn't fix or predict Fan et al. 2024 latest dataset. Try harder.
- albert_roca 9mo agoThis is moving the goalposts, but ok. The model matches the international standard of CODATA 2022 to 0.005 ppm. If and when this value is updated, the prediction can be re-evaluated. Until then, I stick to the standard.
- fatbrowndog 9mo agohi, the formula should allow both. you have an integral and order^ power.
- fatbrowndog 9mo agoα⁻¹ = S - 1/(24α) α⁻¹·24α = 24αS - 1 24α²S - 24α - 1 = 0 α = (24 ± √(576 + 96S))/(48S) α = (24 + √(576 + 96·137.036...))/(48·137.036...) α = (24 + √13,723.66...)/(6577.74...) α = (24 + 117.12...)/(6577.74...) α = 141.12.../6577.74... α ≈ 0.021454... α⁻¹ ≈ 46.61 ??? That's wrong!
- fatbrowndog 9mo agoα⁻¹ = S - 1/(24α) α⁻¹·24α = 24αS - 1 24α²S - 24α - 1 = 0 α = (24 ± √(576 + 96S))/(48S) α = (24 + √(576 + 96·137.036...))/(48·137.036...) α = (24 + √13,723.66...)/(6577.74...) α = (24 + 117.12...)/(6577.74...) α = 141.12.../6577.74... α ≈ 0.021454... α⁻¹ ≈ 46.61 ??? That's wrong!
- albert_roca 9mo agoYou transcribed the formula incorrectly. The term is -(alpha / 24). You calculated -1 / (24 · alpha). The correct derivation is: 1 / alpha = S - (alpha / 24) 1 = S · alpha - (alpha^2) / 24 alpha^2 - 24 · S · alpha + 24 = 0 Solving this with S = 4 · π^3 + π^2 + π yields the correct value.