Longer pipes
Little Red Rooster (obviously a Stones fan?) true you will get more torque with a longer inlet, however the inlet comes after the throttle plate.
Race bikes have the carb or throttle body as close to the cylinder head/inlet as possible with as big an opening as is permitted. This means that the engine may have sod all torque and power below for example 3/4000 rpm or even much higher, but at the top end of the rev range alot more available power.
To produce a slogging engine i.e. for trials riding then the inlet tract is longer.
If Mr. Tickle were to put the throttle bodies as far back as the reinforcing area of the air hose then he would notice a tremendous difference, the torque would be alot lower down but the top end power would tail off perhaps too early for normal road riding.
In effect cutting off a piece of the air hose is no different to making extra air holes in the air box of any bike it will simply allow more air in to be used by the engine (that it can draw in), we used to cut 2 inch holes into the sides of 250 and 350 Yamaha LC's up the jetting and then watch them fly. BMW and any other manufacturer design the air box and subsequent hose work to produce a compromise between good power characteristics and torque curves for the purpose the bike was intended. No doubt with some cutting and drilling here and there differences will be noticed.
The flutes (curved edges) are there to prevent the air being drawn in from literally bouncing off the now flat edge. Add a trumpet to a straight cut inlet and power increase, not dramatically but by at least 2-3%.
So Mr. Tickle if you measure the inside of the piece cut off at the fluted end you may find it to be narrower than the new entrance now created. If you can I would try to gently radius the edges of the cut tubing or modify your air pipes so that the original flutes can be incorporated.
Probably the main reason that someone has done this is to give a slight increase in induction noise which is in it self mind over matter as 'more noise mut equal more power'.
Be interested to see a Dyno print out.
Overall Mr BMW has now had his harmonics altered.