Why did God harden Pharaoh's heart?
On the contrary. Read the verses carefully (Exodus ch. 7 to 12) and you'll see that God hardened Pharaoh's heart on only three occasions (Exodus 9:12, and 10:20 and 27), and only after five Plagues had passed in which Pharaoh hardened his own heart. That itself explains the reason. After a person misuses his free-will repeatedly, he sometimes sees it diminished (like a person who has ruined his health through bad habits and is warned to henceforth stay away from alcohol, or sweets, etc).
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A mathematical technique which involves tracing theoretical rays of light within a mathematically defined world. Render-Boy uses this technique to render images.
How to kill myself without anyone knowing?
Go on a vacation and kill yourself,
they will never know what happened
It splits in differents colors according to their different wave length. An example of refracted light is a rainbow.
The ray is split in 7 colors: red, orange, yellow, green, blue, indigo and violet.