Gooober - I'll email you about it sometime, but it's something from within me and not taught so... it could be far out. Please remind me about it.
It's more of a study of human nature and applying numbers to a type of human behaviour. But, I'll say this.
Imagine that 1 is the colour RED and it's higher octaves like 10, 19, 28, 37, and 46 are different shades of RED. The RED would stand for a certain major archetype in human behaviour and how this archetype can express itself according to it's environment.
Eg. RED would look slightly ORANGE-like if it was in a YELLOW environment. It would still have the original RED in it, but it would be altered a bit or a bit of the RED would be overshadowed/converted/destroyed/canceled.
Now, this would be easier to understand if you view RED (colour) as light or as a wave (which it is) and it's frequency being a certain number. RED light is a frequency with a long wavelength (distance from crest to crest) and it is the lowest wave in the visible light spectrum. The lowest number in real numbers is 1. RED is associated with base emotions or primal behaviour in human behaviour. In chakras it represents the lowest chakra, the energy level which represents actions/behaviors/personalities which are instinctual and active like sex, anger, or more precisely - emotions and behaviours which are a product of the Reptilian nature of the human being or one can say (the part that wants to dominate or be dominated, consume or be consumed).
Well, you can check that out for yourself to understand the RED vibe but it associated with a certain archetype. Linda says Sun, but I see a whole lot of similarities with Mars. In truth, the planet/number connection is the last thing I'll do. I just mentioned it here because Lara is into astro.
But... the SUN is exalted in Aries (Mars) so... 1t could be represented by the SUN, but I think you have to decide for yourself as I am not decided on this, either.
1st House represents (SELF)
1st Sign Represents (ACTION or first cause)
Both these things SELF and FIRST CAUSE are characteristics of the number 1.
So, what I did was put aside the astrological stuff and got myself really acquainted with number 1's feel/RED and all of number 1's person, character or 1's personality and then I went to astrology to and used the astrological method of finding harmony i.e trine, sextile or conjunct in some cases. I then applied this to the numbers, but I am still struggling a bit since there are 9 numbers and 12 houses/signs - and how Venus (libra/Taurus) can square and trine Earth (Capricorn).
Anyway, to cut a long story short... 1 and 9 ended up being numbers that are compatible but it can get more complicated than that, just as Sun signs aren't enough to tell you much about people's compatibility.
1 also gets along with 4 and 5 in some degree too, especially in a non-romantic context because
take 1's INITIATIVE, put it to 4's INNOVATION and you get yourself something really genius and powerfully so.
take 1's LEADERSHIP or AUTHORITIVE presence and add it to 5's ability to communicate and you get yourself something really charismatic and powerfully so.
but romance can happen here too.
1 can be said to SQUARE 8 because 1's PRIMAL nature and 8's CAUTIOUS nature couls result in behaviours which are opposite in nature. Can they get along? Yes.
Through out using numbers as a compatibility tool, I try not to forget that I am talking about waves - energy or frequencies and the interraction of waves, not solid things. So, if a wave if out of phase, and it opposes another wave, it produces NOTHINGNESS or it cancels out the other wave.
I'm sure you can use your own way of imagining this. I just identify with colour and sound. I can see sound as colour and visa versa. And both sound waves and light waves are waves which have frequencies = frequencies can be measured in numbers.
Just keep in mind that just like anything, there is a source and the simplest form of something, so to speak. If the universe was white light, people, their behaviour and their personalities would be unique and different parts of that source being expressed, just as all colours, even those that aren't visible, come from white light. What we call black, the stuff colour black is a colour that many artist can produce by mixing a few colours, and so the absence of light is not the same as the "colour black". As far as our eyes are concerned, things we can't see or understand are "black", e.g. infra-red/ultra-violet are black until you we change their environment to make them visible to the eye. (shoot! I went off there.)
9 and 1 are quite compatible, but if their combined vibration/frequencies are weak and are overshadowed by a discordant vibration, the compatibility seems be of less effect. And if their environment doesn't allow them to be seen, (oh, that's why I spoke about black) they could be as good as non-existent.
The OCTAVES of each number represent the waves's amplitude (size/volume). Different amplitudes can be harmonious. It's different frequencies of the same thing. Different wavelengths are of different natures (personalities or archetypes). These are not the same thing but they can be "compatible" as far as human nature is concerned.
I've never had to explain this so it might come out confusing.