[Disclaimer: It is generally frowned upon to take the ideas of quantum physics and mathematics and use them philosophically. So instead I'm trying to work my way backwards and take standard philosophical concepts such as the self and ideas and thoughts and interpret them through quantum physics and mathematics.]
What if, hypothetically speaking, we are like the particles of quantum mechanics. We are corpuscular (that is to say, we are particles), which is easily stated, because we are single objects. Mathematically speaking we are topologically equivalent to a sphere or any other object of genus 0 (one could argue that our orifices would make us more akin to a torus or double torus, but this argument is fairly immaterial). But we don't need mathematics to see our particulate nature, we can do a much simpler exercise, we can zoom out. We can zoom out far enough that we still see people, but we see them as tiny little specs, dots, moving around chaotically like some confused liquid. So the idea that humanity is corpuscular is not extremely hard to wrap your brain around, it may be somewhat abstract but it's fairly easy to grasp. Now in order for me to make my supposition that we are like the particles of quantum mechanics, that is to say both wave and particle, I must now elucidate how we are like the wave.
The conscious mind is a very mysterious entity, the subject of thousands of years of debate, and I certainly don't attest to have solved any of those mysteries. But I would say that what arises from consciousness and the human mind are some very wave like qualities. For one thing, the activity of the mind is an ever fluctuating thing, a series of ons and offs, of peaks and crests. We have moments of inspiration, during which many areas of our mind our light up with neural (electrical) activity, and we have periods of sleep (specifically stage 3 and 4) during which our mind is quiet and restful. But this analogy to the wave form is fairly weak, for it is more of a two dimension comparison than it is an actual mapping. What I would like to attempt, is to successfully transpose the concept of a wave on to the concept of humanity (or vice versa) and even on to the individual person. First let's think about waves for a moment. Imagine the surface of the earth to be one single tranquil sheet of water. Just a perfect blue sphere floating in space, held together by gravity, and for the moment it is completely calm, not a single ripple on its surface. Now imagine a massive meteor crashes into the sphere and disrupts its perfect surface. We watch as a huge wave will form, emanating from that focal point of the meteor crash, growing in size as it heads towards it's peak. The wave is so massive that the ripple goes around the entirety of the earth until it meets itself on the other side of the planet, crashing with tremendous force and sending smaller waves that crest and crash and strike each other and send out more smaller waves. So we see from the initial impact, the entire system is now in a state of flux and activity, and the whole of the surface is disrupted with waves and ripples and motion, all of them rising and falling, cresting and crashing. This is the action of a wave in three dimensional spherical geometry. Now something similar to this is happening every day but the medium I'm speaking of is not simple water molecules, comprised of two hydrogen atoms and one oxygen atom, rather it is a drastically more complex molecule which interacts in drastically more complex ways: The Human Molecule. The wave form is the idea; a development of the conscious mind. And the medium through which it travels is sight and sound (waves), and it is received by other human molecules, where it picks up steam and it grows and it crests and it crashes, and again subsequent ripples are formed. But this time there is a new dimension, the axis of time is added for the ideas exist not just in the present moment, but they linger on as wave cresting through our linear progression of time, rising and falling with the trends of humanity in what could conceptually be called an infinite number of times. Like a religion, or an economy, or a song or a social movement: like war and peace, like love and hate, they are dips and troughs on a wave rippling through the liquid surface of humanity.
And so at the same time as we are walking physical objects we are also ideas and waves which ripple through humanity: such is my conception of the dual wave-particle nature of man.