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Correct me if I'm wrong, but I thought the difference between flash cast and normal cast is that flash doesn't require a CAD because the caster already has the magic memorized.
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You need to understand the function of CAD in the first place. IIRC they're like computers that will do your calculation for you. In other words, the magic 'data' will be calculated first through CAD before it manifest in real world. Using CAD is like using a calculator where you put a bunch strings of value and command to get the result. In using calculator, a person need to put in the value and work on the command before getting the result. Flash cast, on the other hand, is like seeing a superhuman who can calculate things instantly using his/her brain (i.e manual but instant).
Still talking about that analogy, depending on the calculation a person can calculate it quickly or slowly. For example 1+1=2 can be done almost instantly (without using calculator) but a calculation where we got something like 4^2^3^4 can't be done in a second...though there could be a freaking genius who possibly can do it in a second. That kind of complex calculation needs calculator to get the result almost instantly.
Now I think this is what makes Tatsuya a bit different.. you see, whenever someone see a math question and try to answer it, they still need to calculate it in their brains before getting the result. What I believe is that for Tatsuya, all the questions AND answers are already implanted in his brain. As a result, he can give a result WITHOUT doing any calculation..
To summarize, I don't think not using CAD means that he/she is using flash cast. IIRC there's a line that mention that magicians can actually use magic without it but it will take too long to cast or something.. and I also vaguely remember something about ancient magician who rarely use it though I'm not so sure about this.
What flash cast ultimately is that no-casting spell, 0 delay, etc
