You can believe something without knowing it. You can know something without believing it. Further, there are different types of belief.
Example: I believe my wife will want this color.
Example: I know you just said it, but I can't believe it.
I want to share an anecdote that exposes the difference between belief and knowledge on a more personal level. I hope that you can get something out of this story.
I knew I could run two miles in less than 11:54. No doubt in my mind. It wasn't bravado, I didn't brag to my buddies that I could and would do it. It was my goal and I knew I could do it.
How did I know? Because I was faster than people that had done it. I just needed to do it on Physical Fitness test day.
A time of eleven minutes and fifty four seconds on a two mile run earned you 100% of the points on the running section of the PT test if you were male and under 22 years old. After 22 years old, the time increased to 12:35. (Now, for comparison, the 100% time is 13:00.)
My very first 2 mile run was 14:20. I was dying the whole way, walked a lot. Man, I was out of shape. The next was two weeks later and it was 13:10. That beat the time of my drill sergeants (former Rangers in their mid-20's) and I was surprised. The next was 12:30. From then on, I never was slower than 12:30.
During basic training we'd run in ability groups. When I joined the second to fastest group (13:10), I was told I didn't belong there. But I stayed because my time qualified me to be there. I didn't stay long. I soon moved up to the next group. In that group we would run two miles in 12 minutes, and then run two more.
In Germany, my Battery Captain loved to run. He'd organize these cross country course and he and I would race. It wasn't much of a race really as I'd just stay in front of him and speed up when he moved to pass me.
Once, on a regular run, segregated by speed, he let me be the pacer. (By regular run, I mean we ran in formation, which really sucked since it was always slow.) But now, the pacer, I could change that. He warned me to keep it steady and keep us together. Screw that! I wanted to make the lungs of the other runners turn to ash and their hearts to explode.
I ran the first mile at a comfortable pace, around 7:00. I ran the second mile at 6:00. There were some fall outs and a lot of complaining. The Captain though, he was always up for a challenge. So, I ran the third mile as fast as I could, which was in the low 5 minutes. I don't know the exact time because the person with the stop watch was long gone. But he said he timed me and watched me finish the course. I turned the formation of 20 into a formation of one.
They never let me pace again.
But on test day I could never beat the 11:54. I could get 12:10, 12, 12:20...but I'd always start off too fast and bonk.
Then I turned 23. My new time for 100% score was 12:35. No problem. I could do that without issue. I dogged the run, took it easy. At the mile point the time was just over 6 minutes. No problem. I didn't push until the last half mile. I was expecting to hear 12:15 or so as I crossed the finish. But what I heard as I got closer was Sergeant Skipper (really his name) counting eleven 21, 22, 23, ... I put it in high gear and crossed at 11:30.
It occurred to me later that while I knew I could run that fast, I didn't really believe it. There was always a shadow of doubt. When running with other people, they paced me. I was right by them and had someone pushing me. On these test runs, if you were around people, you were two minutes slower than I was.
Maybe I absorbed the physical impression I made on people. That is that my ideal body was is in the mid 150's, but I was 210, had no neck and had legs like tree stumps. The impressions was, "This guy must really lumber down the track." Maybe it's because I knew I didn't deserve to run that fast. A lot of people I knew, and helped, worked really hard and couldn't get any where close to me.
The real puzzle is, why do we sometimes perform better when our confidence is high? When you know how have done and believe you'll do it again, your chances of success are great.
Now I know that for people that really run, 11:30 isn't much to brag about. But for me, it is and was a big deal. That's my personal best. It's a time I'd sorely love to beat now. But now, I know pain a lot better than I did then. Now, I don't know if I can do it. So the belief is of the sort that's just a guess. Believe this, I'm going to find out.
I used what I learned in this experience to better perform on my first (and to date, only) road bike race. I had a goal pace and I kept that pace on all training rides, always. Only once did I drop below that pace and there were some incredible conditions slowing me down. I knew that nobody would be on their best race in those conditions.
So on race day, I was confident. I knew I could meet my goal and I believed I would. Why did I believe it? Because I'd done it again and again and again. It was never easy, but I never gave in. I knew that to meet my goal when it was official, I had to do it when it wasn't official. It was the training that counted, not the performance! The race makes it official for everybody else. But I knew I would do it because I always had.
When trying to run 11:54, I knew I could do it because I had the potential. I didn't believe it because I had not yet realized that potential. I hadn't done it when it really counted. It counts in training.