So, in preparation of my ISTP profile, I decided to write a description of Ti. There are many misconceptions of what Ti is (specifically, the common conception of Ti is actually closer to TiNe), and an understanding of how it works is essential to understanding the ISTP.
First, what Ti is not:
Ti is not inherently logical.
Ti is not linear.
Ti is not theoretical.
Ti is not objective-oriented (though it is object-oriented).
Now that that's out of the way, my Ti description:
Introverted Thinking
Ti is an introverted judging process. It takes data given by Extraverted Perceiving and judges it. Ti basically takes the data, and “melds” with it, it analyzes it from all angles until it understands the essential qualities of it completely. This is a non-linear, almost unconscious process, and it does not make use of logic. The logic of Ti comes from the fact that the data is understood completely, including all the rules of how it operates, which is logical. For example, if you use a hammer on a nail, Ti figures out how the force of the hammer causes the nail to be driven into the wood, and how far, and at what angle, etc. It takes in all the variables simultaneously and figures out how the system as a whole works, but if asked, it's answer will likely be something along the lines of “because that's how it works, can't you see that?”. Whereas a Te approach would be to take the force of the swing, the weight of the hammer, surface area, length of the nail, density of the wood, angle the nail is hit, etc and preform a lengthy and complicated math problem. As you can see, Te is just plain inefficient here (ironically, considering Te is all about efficiency). Furthermore, Ti is experiential. It relies upon actual real world data seen personally by the individual. Here is where much of the confusion arises. Because of the nature of Ne, it allows you to see things that don't actually physically exist, and Ti is able to utilize that data, but fundamentally, the individual is still experiencing it. The experiential nature of Ti is much more noticeable when paired with Se. Se gives physical external data which Ti uses. The above hammer example is TiSe in action. Another place where Ti is evident is in music. Where a Te approach to learning to play an instrument would be to learn the scales and chords and how to read sheet music and all that, Ti would learn by doing. It would learn by experimenting with the instrument, by listening to music and hearing the underlying structure and then applying that to the individual's own playing. It learns how different sounds fit together by hearing it, as opposed to someone telling you for example, “the first plus third plus fifth notes in a scale make a major chord which sounds good” in a very mathematical and mechanical way.
And stuff. Yes I know it needs editing, I'll do that later.