Is Kolmogorov Complexity Infinite for All Noncomputable Irrational Numbers?

[cragar]

How would I figure out the Kolmogorov complexity of an irrational number?
Could I just look at the shortest formula to compute that number.
If it is an uncomputable real, does it have infinite complexity?

 

[mXSCNT]

Yes, and yes.

 

[SteveL27]

How would I figure out the Kolmogorov complexity of an irrational number?
Could I just look at the shortest formula to compute that number.
If it is an uncomputable real, does it have infinite complexity?

I saw an interesting example online the other day. Take a noncomputable number and interperse 0's in every other digit position. Then for each finite-length initial segment, it takes just a little more than half as much information to compute the number with the 0's in every other position as it does to compute the original number. So not all noncomputable numbers are equally random. It's tricker than I'd realized.

 

[cragar]

where did you see this example

 

[haruspex]

I saw an interesting example online the other day. Take a noncomputable number and interperse 0's in every other digit position. Then for each finite-length initial segment, it takes just a little more than half as much information to compute the number with the 0's in every other position as it does to compute the original number. So not all noncomputable numbers are equally random. It's tricker than I'd realized.

That sounds suspiciously like infinity/2 = infinity.