Thoughts on CH

[Joe Shipman]

There are some questions about integers which we are never going to know the answer to, and we’re ok with that.

For example: either there is a sequence of a googolplex consecutive identical digits in the decimal expansion of pi that is both the first such sequence and involves an even digit, or not.

It seems very plausible that there is just no way we could ever come to know the answer to that question. But does anyone think that it is a sentence whose meaning is unclear?

I don’t understand why so few mathematicians are willing to say “of course CH is either true or false, but we don’t have access to the answer because it makes no difference to physics, and with no direct access to uncountable sets we can’t prove anything about it.”

No one seems to think it’s a problem we can’t answer my question about pi. Why is it such a problem that we can’t answer CH?

— JS

Sent from my iPhone