SO I decided to make a test of how far I can jump, and I only jumped a to square gap with a platform level to mine. So I made a three block gap with a level platform but I couldn't make the jump, so I lowered the opposite platform to make up for the distance between me and that platform. The cycle went on for a while, so enough of the story and on to the data.
O = Me
P = Platform
_ = Gap
JUMP ONE - ONE BLOCK GAP
O_P
Process: Obviously I made the jump, so I moved up the platform by one block, and still made the jump, though with common minecraft knowledge, you can't jump up two squares, so I left it at that
Results: A one block gap allows me to jump upwards one block
JUMP TWO - TWO BLOCK GAP
O__P
Process: So I made the jump, but barely, so I added one block to the platform and after a few tries, made it
Results: A two block gap allows for a one block incline
JUMP THREE - THREE BLOCK GAP
O___P
Process: Did not make the jump, so I dropped the platform down a block and made it
Results: A three block gap requires a one block decline
JUMP FOUR - FOUR BLOCK GAP
O____P
Process: Remembering the last jump, I dropped it down a level, but didn't make it, that lead to me dropping it down yet another block. There might be a one block decline after every increase in the gap after this
Results: A four block gap requires a two block decline
JUMP FIVE - FIVE BLOCK GAP
O_____P
Process: I dropped it down to the ground, since that was one block lower than the four block gap, and I didn't make it, so I raised the ground that I jumped off of and still didn't make the jump, I did this three times and never made it
Results: A five block gap is impossible, no matter how far you drop. Even If you did manage to make the gap you would die after breaking your legs
CONCLUSION
After a trial and error based process, I know it is only safe to jump four blocks as long as there is a two block decline. NEVER attempt a five block gap, UNLESS you are being chased down by a whole army and you have important items with you.
PICTURES - The important part
The four block wide thing I'm looking at is what I stood on (it used to be five but I took that down)
The columns I jumped to (the fifth column is the floor)
