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Please enlighten us how purely theoretical mathematical constructs, that are impossible to test, help us understand anything about our universe.
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Imaginary numbers are purely theoretical, but they turn out very helpful in almost every engineering discipline
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Sure, let me know when any of these imaginary physics is useful for predicting anything that can be observed.
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Imaginary numbers are a helpful tool for calculating things in our universe. All these holographic theories and their insights are based on a universe that behaves basically opposite to ours.
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From Wikipedia, imaginary numbers...

> Originally coined in the 17th century by René Descartes[4] as a derogatory term and regarded as fictitious or useless, the concept gained wide acceptance following the work of Leonhard Euler in the 18th century, and Augustin-Louis Cauchy and Carl Friedrich Gauss in the early 19th century.

I think the jury is still out wrt utility of AdS spaces. They could be useless toys, or they could be in the Descartes phase rn.

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Lots of science is impossible to test practically for hundreds of years before it is actually experimentally verified
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Not actually science until you can test it.
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> It is not about producing results that you personally think are important. It is understanding the nature of the universe for the sake of it.

Is this actually stated somewhere by the institutions that take taxpayer money for this research, or just your opinion?

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If you’re talking about taxpayer money and you’re in the United States, maybe a better starting point is the ‘jobs program’ they’re running for military personnel
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Science and math are not the same thing, though. The concern is that physics, a science, has been sliding too much into math research - specifically talking about the foundations of particle physics.

That is, the concern is that instead of studying the real world, theoretical physicists are spending more and more time studying mathematical constructs and their properties.

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There's a lot of ire for string theory. It's non-testable and wound up attracting lots of minds, funding, and resources. It hasn't seemingly led to any tangible results. Many scientists express anger about it and claim entire generations of progress were lost.
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