In 1960, J.C.R Licklider wrote a text called Man-Computer Symbiosis.
In it, he drew the path towards the ultimate vision of the relationship between a person and a computer, envisioned as a symbiosis.

A symbiosis is between two beings, so the person AND the computer have an independent reality. The computer is not only a deadly mere machine, it has a kind of soul.
A symbiosis profits from the two's skills to solve problems surrounding them.
A symbiosis is a mutual dependency as each needs the other.

This text is from 1960, a year when neither personal computers or the Internet or higher level languages were made.
However, as the famous "As we may think" from Vanevar Bush, it really paved the way to the future.
Looking at where we are now, in the nascent "iPhone" era and what may be next, I think we are on the verge to fulfill Licklider's vision by the end of this decade, closing the loop in 50 years.

1) A symbiotic computer will be more than personal

In 50 years, we moved from big corporation's computers to personal computer.
The latest version of it, iPhone, like any mobile phones, is really becoming personal, a perfect one-to-one matching between a person and a computer.
A symbiotic computer will be more than personal.
It will survive to hardware lifecycle, getting faster and faster but never losing what it learnt.
It will live nearer than a bag or a pocket, may be on a person's wrist, being more often here and less often lost, crashed or stolen.
It will see, read and hear most of what a person can see, read and hear to remember it as digits on a hard drive.
It will get better ones for a person to read, see and hear because it will be the only one to remember everything.
It will be a person's and in a person's computer, not those of Facebook or Google, opened to non authorized third parties.

2) An aware computer will be more than connected.

In 2007, a person has still to think about how to "connect" to the Internet and how to another person or group of persons by HTTP domain names, SMTP email addresses, IBAN bank accounts, ZIP building addresses, ENUM phone numbers or whatever...
In the same way, a person has still to ask a computer to remember what he saw, hear, read or do.
To tell a computer how to do something, a person must know some bizarre languages, different from what he already knows.
An aware computer will remember whitout a person asking for it and will know how to a person without a person to ask by some cryptic computers' protocol.
An aware computer will do from a person without these bizarre languages.

3) A person with a symbiotic aware computer will be more than a person.

Persons quit the hazardous and uncontrolled genetic evolution since a long time.
What makes persons different is that we can make for a purpose.
A person with a symbiotic aware computer will be more than a person.
He will remember everything he saw, read, heard or did.
He will be able to get and post with persons much more easility and faster than before.
He will taylor the world to his ends, cure his diseases and know about changes faster.

In a sense, a person with his symbiotic computer will represent the ultimate step in humanity's journey : human-machine symbiosis.