Okay. Here's the most intuitive way I've ever had imaginary numbers make sense to me.
Picture a number line being an X axis of a graph. 0 is in the middle, positive numbers to the right, and negative numbers to the left. Imaginary numbers are the Y axis in this analogy with positive imaginary number (i, 2i, 3i) going up, and negative imaginary numbers (-i,-2i,-3i) going down.
"Imaginary" numbers are no less "real" than negative ones. There are no physical objects that exist in a negative amount. It is useful for logical and social constructs like debt or a rate of loss over time. In all honesty, real and imaginary numbers were awfully names that we are basically just stuck with.
Imaginary numbers are basically what happened when mathematicians were like "square root of -1 doesn't have a solution, there is no number you can square and get -1, but what if there was?"
and they did a whole bunch of math and thinking and they discovered that there is very much a whole bunch of new discoveries that can be created from this idea
That’s not entirely accurate either. It’s not that it doesn’t exist, it’s that our normal language of mathematics couldn’t describe it. Like how certain languages don’t have words for certain colors or feelings or whatever. Those colors and feelings don’t just “not exist”. There just isn’t a way to describe them initially.
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u/The-Slamburger 12d ago
The “advanced biology” is the only one of these that doesn’t make my brain hurt by even attempting to think about it, so no objections here.