Is Light intangible to other Light? And how does all the intersecting light exist in space? I was thinking of how light actually gets into my eyes, and thought about my light bulb shining rays to every part of my bedroom wall, and reflecting them towards me. but then i realized, i could be at many different locations and still see all that light, so it must either be bouncing off in all directions, or the light that shined elsewhere has bounced around the room to end up reflecting off the wall in all other directions.
so i can view the entire wall from bazillions of atom offsets of spaces in my room. but lets just concentrate on two atom positions directly on my index fingers. the entire wall is shining directly into those two atoms. so light is passing through other light that is heading towards another direction.
just with this simple scenario of the wall shining towards two positions, in my imagination, two pyramids of light colliding with each other, which is hard to imagine how that works, let alone the bazillions more intersecting, constant flowing of light that reveals the slightest of dust in the air on sunny days, from all places in your room, and how it can travel out into space, like the stars do towards earth from light years away, just concentrating into smaller and smaller amounts of atoms space. it really breaks my mind at how light even works.
so i guess my question is, pretty much, how does light travel?
 A: Let's neglect a specific phenomenon known as interference for now, which is important for special cases, not like a normal light bulb or starlight. Let's also ignore gravitational effects.
"Is light intangible to other light?"
Yes. Two, or more, photons can occupy the same place at the same time. Many photons, or electromagnetic (light) waves, can pass right through each other and not affect each other. So light can intersect with no problem. Like PM 2Ring commented, water waves do the same thing. 
Sound waves do too. If you are at a party and everyone is talking, the sound waves from their voices are overlapping while traveling to your, and everyone's,  ears, but they do not bounce off or destroy each other. It may seem like they really mess each other up, but that's because your ears cannot focus like your eyes. If you had a really high quality directional microphone you could point it at someone in a crowd and hear them  much better. (Also there are some buildings with rooms (maybe the ceiling) shaped like an ellipse or ellipsoid that if you stand at one focal point,  you can hear someone  talking softly at the other focal point, even if the room is full of people taking.  
So  back to light.  The light from your lamp hits all  the points on the walls, and from each point some reflects off in  all directions and passes through light from other points on the walls to your eyes and fingers or whatever. It travels  in straight lines and does not get deflected by other light it passes through.
A: Light is an electromagnetic wave and Maxwell's theory of electromagnetism explains very well how electromagnetic waves propagate in space by the mutual concatenation of time-varying electric and magnetic fields described by Maxwell's equations. Thus it is well understood how light travels in time and space. 
Furthermore, Maxwell's equations lead to linear wave equations for the electromagnetic fields. This means that different solutions of them, i.e. different light waves, can be superimposed in space without influencing each other. This might explain what you probably meant by "Is light intangible to other light?"  
A: As the other answers state, both in the classical mathematical modeling of the behavior of light and in the quantum mechanical where classical  light is composed of a superposition of photons, there is no interaction of light, to first order.
The italics to emphasize that in the underlying quantum mechanical frame there exists a photon photon interaction/scattering in higher orders ,with a very very small  small probability in the visible frequencies. 

The diagram is a shorthand for an integral which  allows to calculate the probability of photon photon (two incoming squiggles) scattering off each other (two outgoing squiggles) at energies of visible light. The four electromagnetic vertices make the contribution so small , it can be ignored for visible light frequencies.
The diagrams go on to higher orders in a converging series expansion with diminishing contributions from higher orders, because each  vertex gives a $(1/137)^{1/2}$ multiplicative contribution to the final value of the diagram, and the above diagram goes to  the fourth power, so already the probability of scattering falls by $\sim 10^{-5}$. Higher orders for visible light means diagrams with more vertices with even smaller contribution.
The electromagnetic spectrum has higher energy photons though, up to gamma rays, and the probability of photons scattering goes up with energy, as students of physics will find when they reach a quantum mechanical level course.
There are even proposals for gamma gamma colliders.
