Hi Bluesky65RS,
I'm going through the DM training right now as well. According to my instructor I have a pretty good explanation of half-times.
There are a few things to make sure you understand. The first is that compartments, half-times and M-values all relate to a theoretical model that has no direction correlation to the human body but that years of research have shown they seem to be a good model.
That said, different body tissues absorb/release nitrogen at different rates. Dr. Haldane decided his model would assume there are six different body tissues. So he created six compartments.
Rather than look at all the compartments at once, lets look at the 5-minute and 20-minute compartment. If we go to a depth of 60 feet for 60 minutes, here is what happens to the two compartments. First the 5-minute compartment:
After 05 minutes: 30.000' or 50% of 60'
After 10 minutes: 45.000' or 75% of 60' (50% + 25%)
After 15 minutes: 52.500' or 87.5% of 60' (50% + 25% + 12.5%)
After 20 minutes: 56.250' or 93.75% of 60' (50% + 25% + 12.5% + 6.25%)
After 25 minutes: 58.125' or 96.875% of 60' (50% + 25% + 12.5% + 6.25% + 3.125%)
After 30 minutes: 60.000' or 100% of 60'
You'll notice that 25% is half of 50%, 12.5% is half of 25%, 6.25% is half of 12.5%. In other words, every 5 minutes half as much is added. Also, half of 3.125% is 1.5625% but on the last iteration we round up to 100%. I.e. the sixth half time is always 100%.
After 30 minutes the 5-minute compartment stays at 100%. It is full and cannot hold any more. Because our example is a 60 minute dive, the 5-minute compartment will be full after 30 minutes and will stay full for the rest of the dive.
Now let's look at the 20-minute compartment:
After 20 minutes: 30.0' or 50% of 60'
After 40 minutes: 45.0' or 75% of 60'
After 60 minutes: 52.5' or 87.5% of 60'
Because it is only a 60 minute dive, the 20-minute compartment will never be full.
On top of whether or not the compartment is full, there are M-values for each compartment. If the M-value is reached then you have reached an No Deco Limit (NDL). So you might hit an NDL before any of the compartments are full.
For example, if the M-value for the 20-minute compartment was 50' (it is not) then we would hit the NDL because of the 20-minute compartment before the 60 minute mark.
You might also want to read
Understanding M-Values.
Finally, the examples in the book leave out a lot of information and are based on Dr. Haldane's model. If you try comparing the examples in the book to the RDP don't bother. The RDP is based on a completely different model.