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The "No Science At All Version".

Take a bottle of coke and shake it up.  Now, if you loosen the top, it'll try to fizz over, but if you tighten it again quickly before it gets to the top, you can prevent the fizzy mess and wait for the bubbles to go away, then repeat the cycle until you can open the top safely.  That's kind of like the Buhlmann tables, depressurise until you are about to bend then stop and de-fizz.

Deep stops figure that you need to be a bit more sensible, and never let the bubbles get near the top of the neck.  Doing deep stops are like loosening the cap gently and only letting a few bubbles form.  The gradient factors are a mathamatical way of saying how fizzy it is allowed to get before you have to stop, and how much they have to subside before you can start again.

Pyle stops you can do in your head, but Eric Bakers gradient factors are too much maths to be doing under pressure (but would appear to be better) so don't worry about the maths bits.
 

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(Not correcting you, Matt, just saying a bit more on the subject.)

The "Some Science Version".

When you do deco dives, you have a "virtual overhead situation", there is a virtual ceiling which is the point at which  the equations say you will get bent if you go over.  The ceiling gets higher as you decompress.  Eventually it breaks the surface and you can get out.  The way deco software/tables work is that they pick a convenient set of steps for the stop depths, and keep you at each stop depth until your ceiling clears then next one, whereupon you ascend to it.

If you have been reading the articles, then you will have come across the "M-Value line" and the "Ambient Pressure Line"  The M-Value line is the Buhlmann ceiling, the Ambient Pressure Line is wherever you happen to be.  The Gradient Factors represent where the ceiling you are using lies relative to these two lines.  Zero means the Ambient pressure line, and 100% (or 1.0) means the M-Value Line.

The deepest possible stop is the next stop depth after at least one bit of you could possibly be considered to decompress and is the point at which the Low Factor is applied, the shallowest stop is the point at which the High Factor is applied.  

These two points define a line themselves which represents the ceiling you are using for the dive. The line maintains a smooth change from one factor to the other, so only the High Factor actually applies to a real stop since stopping at the deepest possible stop isn't usually sensible.  Using 0/0 would mean that you could never ascend since your ceiling is always your current depth.  Using 100/100 is the same as normal Bulhmann stuff.  

Using 80/20 means that you are pulling back a bit from Buhlmann's ceiling at the shallow stops, but are really conservative at depth, thus you get deep stops, but aren't penalised when you get shallow like you would if you just made the Buhlmann equations more conservative.

Caveat emptor.
 
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