Technology

Yes, of course. Monte Carlo killed my father.

You know what the problem is? You think that you're too smart to be caught with a meth addiction. See, your neighbor got fucked up, lost a bunch of his teeth, but you, you know about microdosing.

Your other neighbor fell off a construction site that was missing its guard rails, but that wouldn't happen to you; you have excellent balance.

The movie Jurassic Park is literally about people like you.

Do you have a reason to restrict Gaussian mixture models you'd like to give me, or are we just pissing in the same bush?

You know what all those methods have in common? FUCKING evaluation of smooth continuous functions based on a limited number of samples.

REAL MEN WRITE REAL PROOFS. They don't use God damned computational methods which completely IGNORE non-converging regions.

I used opus to generate this lean-verifiable proof that you in particular are full of shit!

import Mathlib
open Real

noncomputable def f (x : ℝ) : ℝ := sin (π * x) * exp (-x^2)

lemma f_smooth : ContDiff ℝ ⊤ f :=
  (contDiff_sin.comp (contDiff_const.mul contDiff_id)).mul
    (contDiff_exp.comp (contDiff_id.pow 2).neg)

lemma f_zero_on_ints : ∀ n : ℤ, f n = 0 := by
  intro n
  show sin (π * (n : ℝ)) * exp (-((n : ℝ))^2) = 0
  rw [mul_comm π (n : ℝ), sin_int_mul_pi, zero_mul]

lemma f_ne_zero : f ≠ 0 := fun h => by
  have h₁ : f (1/2) = 0 := congrFun h (1/2)
  have h₂ : f (1/2) = exp (-(1/2)^2) := by
    show sin (π * (1/2)) * exp (-(1/2)^2) = exp (-(1/2)^2)
    rw [show π * (1/2) = π/2 from by ring, sin_pi_div_two, one_mul]
  exact (exp_pos _).ne' (h₂ ▸ h₁)

theorem sampling_is_a_lie :
    ∃ f : ℝ → ℝ,
      ContDiff ℝ ⊤ f ∧
      (∀ n : ℤ, f n = 0) ∧
      f ≠ 0 :=
  ⟨f, f_smooth, f_zero_on_ints, f_ne_zero⟩