Warning 512 error, I make the tmp dir writable and I get more errors

This is driving me crazy and I have googled this and nothing that I
have found is fixing this problem I'm having.

I'm getting the typical Warning 512 error where it says that my "app/
tmp/cache/ is not writable". I go to chmod 777 this directory and all
hell brakes loose on me and I get a whole bunch of errors.

Warning: unlink(/Users/myname/Sites/myapp/app/tmp/cache/persistent/
cake_core_core_paths) [function.unlink]: Permission denied in /Users/
myname/Sites/myapp/cake/libs/file.php on line 279

Warning: fopen(/Users/myname/Sites/myapp/app/tmp/cache/persistent/
cake_core_core_paths) [function.fopen]: failed to open stream:
Permission denied in /Users/myname/Sites/myapp/cake/libs/file.php on
line 146

What's happening here and how can I fix this?
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