Why do tilting high speed trains tilt in the same direction of the turn?

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From what I read on Wikipedia, it is to counteract the G forces of turning at such high speeds. Wouldn’t it make more sense to tilt the opposite way? I was on a High Speed train in Italy once, but the tilting system broke and it had to go really slow. They gave us our money back, but I don’t understand how the tilting works.

In: Physics

So when you go around a turn, you get thrown to the outside, you can try this is in a car. The faster you go, the more you get pushed to the outside. If you go fast enough, you can tip over (or spin out in a car). If you have a tilt, it turns some of the getting thrown to the side into getting thrown “down” towards the bottom of the car or train, it’s more stable and easier to make stuff do. So it’ll make it a bit less like you’re getting pushed into the side of your seat and more like you’re getting pushed into the bottom of your seat.