[titzer]

> The number of live objects is proportional to the amount of total memory allocated.

No, that's not right. The number (or ratio) of live objects depends on application behavior. According to the weak generational hypothesis, most objects die young, so a garbage collector that only touches live objects (e.g. tracing) does no work at all for the most objects.

The actual survival rate is complex and depends on application behavior, but typical well-tuned GC systems often see survival rates from young generation collections around 10%--that means that only 10% of objects ever occur any GC overhead. Those 90% of quickly dying objects do, however, take up memory and cache space until they are reclaimed. IMO that is only remaining situation where manual memory management can outperform GC by wide margins: when a program can carefully reuse recently allocated memory to keep reusing the same cache lines.