It will therefore be a question of inducing experimental pain in patients with Alzheimer's disease, in the early stages of the disease and to check whether pain-related changes in the autonomic nervous system via the Nociception Level index (NoL® system) differ from a control group of subjects matched in age, gender and education level. To induce pain, the investigators will use the "cold pressor test" technique, which consists of leaving the arm immersed in ice water for as long as the pain is bearable. The investigators will also record before, during and after the immersion, the variations of several parameters derived from the autonomic nervous system during the painful stimulation via the NoL® system. During this experience, the participants will be filmed in their entirety to observe the facial emotions related to pain.