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Stephen Hawking was highly prolific. Compared to a regular person, how quickly could he communicate language to the people assisting him with his research? (e.g. compared to the human average of 40 or 200 characters per minute).

What was this process exactly like? Did he rely on any third person to help him visualize and write down equations and develop his theories?

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I think this covers the actual question:

While working to receive his Ph.D. and make a name for himself at [Oxford], Stephen proved himself able to handle great levels of theoretic equations in his head

Then later

Most of his [most famous work on black holes and space time] was done while working with Roger Penrose, a mathematician who wrote the equations as Stephen communicated them while they worked together during several years on their theory

http://www.cpp.edu/~nova/scientists/articles/hawk.html

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The basic answer is yes, he was dependent on a few nurses and a research assistant or two.

From Wikipedia - the article you brought forth:

Nurses were hired for the three shifts required to provide the round-the-clock support he required. One of those employed was Elaine Mason, who was to become Hawking's second wife. For his communication, Hawking initially raised his eyebrows to choose letters on a spelling card. But he then received a computer program called the "Equalizer" from Walt Woltosz. In a method he uses to this day, using a switch he selects phrases, words or letters from a bank of about 2500–3000 that are scanned. The program was originally run on a desktop computer. However, Elaine Mason's husband, David, a computer engineer, adapted a small computer and attached it to his wheelchair.

Wall-of-text $\to$ At first, nurses kept him alive and healthy and helped him communicate. Then his condition stabilized, and a computer with a voice synthesizer speaks for him. He controls it with facial movements.


This confirms the nurses- and voice-synthesizer- details, and notes specifically that

Through the program, and the help of assistants, Stephen Hawking has continued to write at a prolific rate.


From here (emphasis mine):

As part of his condition, Hawking has lost his ability to speak, so he utilizes device that can translate his eye movements (since he can no longer utilize a keypad) to speak in a digitized voice.


Best, of all, from the official website:

My main interface to the computer is through a program called EZ Keys, written by Words Plus Inc. This provides a software keyboard on the screen. A cursor automatically scans across this keyboard by row or by column. I can select a character by moving my cheek to stop the cursor. My cheek movement is detected by an infrared switch that is mounted on my spectacles. This switch is my only interface with the computer. EZ Keys includes a word prediction algorithm, so I usually only have to type the first couple of characters before I can select the whole word. When I have built up a sentence, I can send it to my speech synthesizer. I use a separate hardware synthesizer, made by Speech+. It is the best I have heard, although it gives me an accent that has been described variously as Scandinavian, American or Scottish.

This contradicts the "eye movements" source, although I have read (sorry, I can't find a source for this!) that the mode of operation has changed as Hawking has lost facial mobility.

In a nutshell (pun intended): Nurses keep Hawking healthy, a computer lets him "speak", and his brain does the rest.

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