When Edward and Alphonse try to transmute their mother, how come they didn't gain anything?


So, to my understanding, the idea of alchemy is equivalent exchange, in which
you get in return as much as you gave.

This doesn't make sense to me, as in the beginning when they tried to
transmute their mother back, Alphonse lost everything, and Edward lost his
leg. They didn't get anything in return, or at least anything worth of a soul
and a body. After this Edward transmuted his arm to get Alphonse back.

So, put in a calculation:

Things lost

  * Random piled ingredients which were supposed to compose the average human
  * Alphonse's body
  * Alphonse's soul
  * Edward's arm
  * Edward's leg

Things gained

  * A blob of purple stuff with Alphonse's soul affixed to it ( for a while )
  * Alphonse's soul

So, where the hell did the rest of the stuff go? And more importantly, why
could they not just have transmuted everything back?




**_Unmarked spoilers for both_ Brotherhood _and the 2003 series follow._**

You're missing a key bit of information: they _did_ gain something for their
loss[1], just as Izumi did.

The boys gained the knowledge of what was beyond the gate. Unparalleled truths
of alchemy reside beyond the gate, and no mortals are ever allowed access to
it--unless they commit the taboo.[2]

Both Edward and Alphonse were shoved through the gate and absorbed as much
material as they could from it, Edward even wanting to go back to get more. In
the 2003 series, Alphonse never recalls this, though in _Brotherhood_ , he
recalls it after having blood spilled on his seal. Ed remembers it from the
beginning, and this knowledge is what allows him (and later, Alphonse) to
transmute without a circle.

The reason they couldn't just transmute everything back is because they had
already committed the sin. If you steal something, and are caught, but then
give it back, do the police let you go? No; and this is also the way of The
Truth. Performing the sin is the punishable act; transmuting it back would be
futile.

**1**   Keep in mind that by the end of the series (at least in _Brotherhood_
's case, original _FMA_ was not as forgiving), much of what was lost is
regained through further equivalent exchanges.  
**2**   It's a bit more complicated than this, but it will suffice for this
explanation.




**_Unmarked spoilers for both_ Brotherhood _and the 2003 series follow._**

You're missing a key bit of information: they _did_ gain something for their
loss[1], just as Izumi did.

The boys gained the knowledge of what was beyond the gate. Unparalleled truths
of alchemy reside beyond the gate, and no mortals are ever allowed access to
it--unless they commit the taboo.[2]

Both Edward and Alphonse were shoved through the gate and absorbed as much
material as they could from it, Edward even wanting to go back to get more. In
the 2003 series, Alphonse never recalls this, though in _Brotherhood_ , he
recalls it after having blood spilled on his seal. Ed remembers it from the
beginning, and this knowledge is what allows him (and later, Alphonse) to
transmute without a circle.

The reason they couldn't just transmute everything back is because they had
already committed the sin. If you steal something, and are caught, but then
give it back, do the police let you go? No; and this is also the way of The
Truth. Performing the sin is the punishable act; transmuting it back would be
futile.

**1**   Keep in mind that by the end of the series (at least in _Brotherhood_
's case, original _FMA_ was not as forgiving), much of what was lost is
regained through further equivalent exchanges.  
**2**   It's a bit more complicated than this, but it will suffice for this
explanation.

