AI progress rate ode

ode.py

import numpy as np
from scipy.integrate import solve_ivp
import matplotlib.pyplot as plt

superhuman_coder_accel = 3.6
superhuman_coder_accel_add = superhuman_coder_accel-1
current_accel = 1.05
current_accel_add = current_accel -1

# Define the ODE
def ode(_, T):
    return 1 + current_accel_add * (superhuman_coder_accel_add/current_accel_add)**(T/5)

# Initial condition
T0 = [0]

# Time span for the solution
t_span = (0, 3.6)
t_eval = np.linspace(t_span[0], t_span[1], 500)

# Solve the ODE
solution = solve_ivp(ode, t_span, T0, t_eval=t_eval)

eval_individual = [1.3, 2, 2.5, 3, 3.5]
solution_individual_points = solve_ivp(ode, t_span, T0, t_eval=eval_individual)
print(list(zip(solution_individual_points.t, ode(None, solution_individual_points.y[0]))))

# Plot the solution
plt.plot(solution.t, solution.y[0], label="Y (years of AI progress at the (unaccelerated) current rate)")
plt.plot(solution.t, ode(None, solution.y[0]), label="dY/dt (multiplier on the rate of AI progress)")
plt.title(f"Accelerated AI progress")
plt.xlabel("Calendar years (t)")
plt.legend()
plt.grid(True)
plt.savefig("ode.png")
# plt.show()