GFT identity
The same calculation as the widget, but as a reproducible script.
Expected: residual < 1e-12
View script
idle
Mathematical atlas
PT mathematics / tool
tool
Persistence calculator
Directly manipulating the GFT partition between entropy and persistent information.
Plain
The idea
The calculator makes GFT tactile: choose a distribution and see the total budget split between persistent structure and uncertainty.
When the distribution is uniform, everything is entropy. When it is concentrated, persistence rises.
GFT calculator
Standard
Standard reading
The tool computes $H(P)$, $D_{KL}(P\|U_m)$, and $\log_2(m)$ for a normalized discrete distribution.
It visually shows that the sum does not move: shifting probability mass does not change the total budget, only its partition.
Takeaways
- A simple tool to understand the fundamental principle.
- Uniform: maximal entropy, zero persistence.
- Concentrated: strong persistence, low entropy.
Technical
Technical formulation
Computations use base 2: $H=-\sum p_i\log_2 p_i$ and $D_{KL}=\sum p_i\log_2(p_i/(1/m))$. Zeros are ignored in logarithmic sums.
This page illustrates the GFT identity; it depends on no fit and no empirical data.
Monograph: ch04_gft.
Formulas
$H(P)=-\sum_i p_i\log_2 p_i$
$D_{KL}(P\|U_m)=\sum_i p_i\log_2(mp_i)$
$\log_2(m)=D_{KL}+H$
public code
Code and scripts
The links below point to public resources or planned GitHub repositories. No local working path is exposed to the reader.
tool
Manipulate GFT
Move the sliders: the sum stays equal to the total budget.
log₂(m)
2.000
D_KL
0.000
H
2.000