It happened to me today. For a lot of my nuke classes, we use government databases for tabulated information on neutron and photon cross sections. The websites that host these databases have all been shutdown. This means that I actually had to physically track down an ancient thing called a "book" to do my homework today. It didn't even give links to the studies/methodologies that were used to get the data.
Mark my words; someone is going to pay for this.
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It didn't affect me directly but my friend is having to help pay for his moms bills. She works for the VA (Veterans Association) and doesn't get paid till the shutdown is over.