A permanent exhibition on the second floor of Espacio Fundación Telefónica opens with a light installation built around one number: the telephone took fifty years to reach 100 million users, the mobile phone took twelve, Instagram took two, and ChatGPT took two months. Exponential. From Analog to Digital (Exponencial. De analógicos a digitales) spends the rest of its run unpacking what telecommunications has done to how people live.
What it is
Launched in 2024 to mark Telefónica's centenary, the exhibition is built around three ideas, Habla, Vive and Imagina, tracing the shift from 19th-century analogue telephones through to the internet, mobile telephony and artificial intelligence. Visitors move past 80 objects drawn from Telefónica's Technological Heritage collection of more than 10,000 pieces, among them early switchboards once staffed by telefonistas, vintage phone booths that can be picked up and used, and a shoe-sized early mobile phone nicknamed the zapatófono.
Nine interactive installations run alongside the objects, including a space where voice commands prompt reflection on the future of work, education and housing. Part of the exhibition is dedicated specifically to the telefonistas, the women who staffed Spain's telephone exchanges for decades, a job not phased out until the town of Polopos switched to automatic dialling in 1988; their training manuals and switchboard equipment are set up for visitors to try operating themselves.
Why it's worth attending
Free, permanent and in the centre of Madrid, this is an easy addition to a visit already built around Espacio Fundación Telefónica's temporary exhibitions, and the hands-on objects give it a more tactile feel than a typical corporate history display. The focus stays on individual stories, telefonistas, phone-booth culture, the sudden disappearance of the landline, rather than a straight timeline of company milestones.
Practical info
Individual guided tours run Thursdays at 17:00, booked in advance via Eventbrite. Group visits (maximum 15 people) run Tuesday to Friday between 11:00 and 18:00, booked in advance by email; groups with specific access needs can also book through the Acerca Cultura platform. A free audio guide is available on-site.
FAQ
Is entry to Exponencial free?
Yes, admission to this permanent exhibition is completely free.
Can I interact with the exhibits?
Yes, several pieces, including phone booths and a vintage switchboard, are designed for visitors to try using themselves.
Do I need to book the guided tours in advance?
Yes, individual guided tours run Thursdays at 17:00 and require booking through Eventbrite.
Can groups visit Exponencial?
Yes, groups of up to 15 people can visit Tuesday to Friday between 11:00 and 18:00 with advance booking by email.
Which floor is the exhibition on?
The second floor of Espacio Fundación Telefónica.

