It a common argument I hear in epistemological discussion I have from time to time: We cannot hear or touch or see electromagnetic waves, but we know they exist. Apart from the fallacy that seeing is feeling the electromagnetic waves we know as light, this is a great example of how we come to knowledge through science. Hans Christian Ørsted noticed that electric current produced magnetic forces. Faraday took this observation further, and through his experiments showed changing magnetic forces create electric current. Both of these were descriptive laws, however no mathematical derivation from first principles were provided. It was Maxwell who combined these laws in his equations, which made testable predictions such as the existence of radio waves which were capable of action at distance. Hertz demonstrated that this is the case, and it is thanks to these people you are able to read this post. Long story summarized, scientific method works!
This wonderful picture is another beautiful demonstration why scientific method works:
Researcher at the IBM Research Zurich were able to "photograph" a single pentacene molecule. To be exact, they were able to touch the molecule, using their fingertips made up of a single carbon monoxide molecule, and just like a blind person reading from a Braille text, they painted what they felt. Textbooks predicted the molecule would look something like this:
Isn't it incredible, how accurate the scientific prediction described the reality?