Takeda Sokaku defined aiki in the following way:
“ The secret of aiki is to overpower the opponent mentally at a glance and to win without fighting. ”
Tokimune Takeda, speaking on the same subject during an interview, said:
“ Could you explain in a little more detail about the concept of aiki?
Aiki is to pull when you are pushed, and to push when you are pulled. It is the spirit of slowness and speed, of harmonizing your movement with your opponent's ki. Its opposite, kiai, is to push to the limit, while aiki never resists.
The term aiki has been used since ancient times and is not unique to Daito-ryu. The ki in aiki is go no sen, meaning to respond to an attack.
... Daito-ryu is all go no sen—you first evade your opponent's attack and then strike or control him. Likewise, Itto-ryu is primarily go no sen. You attack because an opponent attacks you. This implies not cutting your opponent. This is called katsujinken (life-giving sword). Its opposite is called setsuninken (death-dealing sword).
Aiki is different from the victory of sen sen, and is applied in situations of go no sen, such as when an opponent thrusts at you. Therein lies the essence of katsujinken and setsuninken. You block the attack when an opponent approaches; at his second attack you break his sword and spare his life. This is katsujinken. When an opponent strikes at you and your sword pierces his stomach it is setsuninken. These two concepts are the essence of the sword.
The above taken from http://en.wikipedia.org/wiki/Daitō-ryū_Aiki-jūjutsu
On pages 72-73, of Tatsuo Kimura's book, at least in the Japanese version, Sagawa talks about aiki a bit differently more so on the physical side of sthings. My japanese ability had been considerably reduced as I havent regularly spoken or read japanese in a few years, but I can attempt a poor translation if you like.
I think the section has been quoted before in the 2005-2007 time frame, it is kind of amusing actually if you read it. As I recall it was fairly explicit and didn't require much interpretation or IS knowledge.
I'm not so sure if I would want to pull if pushed and push if pulled ala judo. As I mentioned in another thread that works fine on non IS people, but if you try it with someone who is working on IS and understands how to use it, it fails.