[Phithagoras]

CS, pure math, physics, and applied math are all around the same level of upwind in terms of what your education gives you in terms of critical thinking. In terms or workforce, CS is probably more upwind, especially as an undergrad degree. Even more upwind is electrical/computer engineering (in Canada at least, where engineering is tightly regulated).

It is unlikely that the skills you are taught will limit your long term success; after an undergrad in CS you can still get an MBA or to go grad school in many many fields. However, you'll be ahead of many people with only an undergrad degree: math and physics undergrads often find themselves with a skill set that doesn't apply particularly well to any specific job. CS and comp/elec eng are pretty universal, and you'll have flexibility with who you can work for. If you decide in 7 years that you're done "workin for the man" in "the system" you could go work in IT at Jackson Hole and ski your brains out.