Trinity Analogy - Human Nature

 In a discussion between a Christian and Muslim, I heard the following analogy. To understand how God can be three persons and one nature, think of three humans. You have three persons, but all one nature, the human nature. 

Preliminary comment. All analogies for understanding God will come short in some respect since God is totally unique. God can't be compared to anything, so no analogy is appropriate. That said, they are helpful. We just need to understand that they will have limits. 

The limit here is that one could easily respond with: yes, there are three persons, and they all are of the same nature, human. But there are also three humans, which would mean you would have to say there are also three gods. That's an unacceptable consequence for a Trinitarian, and it's often what Muslims will say Christians are forced to believe. 

I read the following explanation from J.P. Moreland some years ago, I forgot the title of the book, but a similar analogy, which I think doesn't fall into that mistake as easily, is as follows. How many words in the following sentence? "Red, red, red." In one sense, one word, and in another sense, three words. More accurately, there is one word type, and three word tokens. There is one divine substance, and three divine persons. 

You could probably push it to the same absurd conclusion as the human nature analogy, but I think it would require more work, and so this second example is a bit more illustrative.