Is there an alternative encoding scheme to binary where similarity of pattern correlates with size of number? If I compare binary for 7

111


and binary for 8

1000


there is no correlation between these two patterns that suggests that the numbers are sequentially close to each other.

Is there a recognized, efficient encoding scheme using 1s and 0s for base ten numbers in which the more similar two patterns are, the closer the base ten numbers are?

Of course you could just have

1 -&gt; 1
2 -&gt; 11
3 -&gt; 111
4 -&gt; 1111


etc, but there must be more compact ways to do it!
Yeah, this is what I'm asking. So essentially Gray code is what I'm envisioning, with 0's substituting decimals which are only applied after a given number to separate from the next. I don't see why it is necessary to compact if your goal is not for speed, but rather for truth. I mean couldn't we use a dual system where binary code is used for communication purposes and "gray" code is used for information(facts). I don't agree that we live in an Information Age, or atleast a logical Information Age...perhaps we live in an emotional Information Age as evidenced by blogs, news, and other mediums from which all we are doing is translating our thoughts from human language to binary to back to human language. I'm a hard believer in facts and principals (principles?) and would be nice to segregate both. I believe philosophically that the universe is infinite and that as we move forward to quantifying our problems we should realize that everything is a division of that whole infinity and so instead of taking a scientific bottom-up approach, we should take a top-bottom approach. Creating an established system that records only fact will allow us to then quantify quicker or atleast verify or recognize falsehoods. One interesting thing that you should note is that as my philosophy repeatedly calls on the truth, it acknowledges that falsehoods are not the opposite of truths, but rather the result of truths overlapping. Picture a binagram, Venn diagram with two truths overlapping making the middle a falsehood. 

I think that by putting this system in place, we will be solving entscheidungsproblem in terms of effectively calculating questions with a universal language. Call it the mega algorithm. 

I've read Freeman Dysons: Scientist as a Rebel 
and he was ragging on reductionism and those who followed it like Einstein later in life and Hilbert also later in life, but i think that there is some real meat to what they were doing trying to find a way to theoretically find all the answers to the universe, like Einstein's grand unified theory.
Yeah, this is what I'm asking. So essentially Gray code is what I'm envisioning, with 0's substituting decimals which are only applied after a given number to separate from the next. I don't see why it is necessary to compact if your goal is not for speed, but rather for truth. I mean couldn't we use a dual system where binary code is used for communication purposes and "gray" code is used for information(facts). I don't agree that we live in an Information Age, or atleast a logical Information Age...perhaps we live in an emotional Information Age as evidenced by blogs, news, and other mediums from which all we are doing is translating our thoughts from human language to binary to back to human language. I'm a hard believer in facts and principals (principles?) and would be nice to segregate both. I believe philosophically that the universe is infinite and that as we move forward to quantifying our problems we should realize that everything is a division of that whole infinity and so instead of taking a scientific bottom-up approach, we should take a top-bottom approach. Creating an established system that records only fact will allow us to then quantify quicker or atleast verify or recognize falsehoods. One interesting thing that you should note is that as my philosophy repeatedly calls on the truth, it acknowledges that falsehoods are not the opposite of truths, but rather the result of truths overlapping. Picture a binagram, Venn diagram with two truths overlapping making the middle a falsehood. 

I think that by putting this system in place, we will be solving entscheidungsproblem in terms of effectively calculating questions with a universal language. Call it the mega algorithm. 

I've read Freeman Dysons: Scientist as a Rebel 
and he was ragging on reductionism and those who followed it like Einstein later in life and Hilbert also later in life, but i think that there is some real meat to what they were doing trying to find a way to theoretically find all the answers to the universe, like Einstein's grand unified theory.