# How the Universe Got Its Spots

Most of us feel the need to implant our ideas at the very least in others’ memories so they don’t expire when our own memories become inadequate. No one wants to be the tree falling in the forest. But we all risk the obscurity ushered by forgetfulness and indifference.

Nature packs infinity in the most humble interval.

I try to find a simple expression for my ideas. I figure if there is none, the ideas might be wrong. ... The simpler the insight, the more profound the conclusion.

We are intrinsically bound to this space and this time. We cannot jump off it or live outside it. We are meaningless without it. This is our universe – the vast extent of our curved spacetime. People always ask: what’s outside the universe? The answer is nothing. It lives nowhere. There is no meaning to the questions where or when if there is no space or time. The tendency is to imagine a curved space as bent into something, embedded in another space. Whether or not that’s the case, it is totally unnecessary. It is completely possible that that is all there is: (3 +1)-dimensional curved spacetime.

The electron does not have a precise location and a precise speed until we, the observers measure it. This phenomenon, known as the collapse of the wave function, has ensnared physicists and philosophers since its discovery. The full import of this conclusion always sends me careening. This interference between the observer and observed is truly profound. We are part of the system: as austere and distant and objective as we try to be in our scientific investigations, there is a theoretical limit to how precisely we can remove ourselves from our object of investigation. The questions we ask in some part determine the answers.

There is another incarnation of the uncertainty principle, which states that there is an uncertainty in the energy and the time of an event. If, for instance, the energy of a particle is very precisely measured then the time it took to perform the measurement will be correspondingly long. The deeper implication is that a particle does not have an exact energy at an exact moment.

The conservation law states that we can always – at least in principle – account for all of the energy in a system. Energy never disappears into nothingness or appears out of nowhere. However, the uncertainty principle allows violations of the conservation of energy if the duration of time is short enough.

I don’t know of any easy way to mesh ambiguity and uncertainty into a profound definition of self-determination. If this life were to repeat over and over again, there would be some finite probability of my making a different set of choices, not out of wisdom or free will, but from sheer chance. Chance is not choice.

Human-made signals tend to be extremely regular in contrast to naturally made signals. For this reason, extremely regular patterns are used as code, a kind of universal symbol of civilization versus natural phenomenon. In essence, we are relying on math transcending language.

Seems easier to explain infinity to my silent, absent audience. When I concentrate on math, the stress of the present wanes and is replaced by the uncomfortable paradoxes surrounding infinity.

A four-dimensional hypersphere intersecting our three-dimensional world would look like a point initially, then a growing sphere, only to shrink and disappear again. We wouldn’t know where to look to find out where it came from. Any manner of objects could be dropped from the fourth dimension, passing through our three-dimensional volume tilted and askew to reveal to our wide-eyed selves the miraculous appearance of smoothly mutating polyhedra that just as unexpectedly disappear.

Maybe there is a way to push the interpretation further and really view ourselves as four-dimensional objects that only perceive our intersections with a three-volume. So in a sense we are solid in four dimensions, there is no time, only the sequence of our perceptions as we intersect a three-surface that we interpret as the spatial world. It becomes clumsy trying to discard time. It’s difficult to imagine motion of any kind without a concept of time. So even the sequence of intersections implies an ordering of that series which contains in it something we might as well call time. Any discussion of time has time ensnared in it.

"Time is what keeps everything from happening at once."

Individual three-dimensional blobs may be connected at their roots in four dimensions. To be extreme for the sake of argument, while we may feel fully encased in three dimensions and convinced of our individuality, our separateness, the isolation imposed by our skins, we may be like the fingers of a four-dimensional hand, connected and integrated at our roots in a fourth dimension. A modern version of this scenario is conceivable where individual particles may really be endpoints of a string or a network that wiggles in the inaccessible extra dimensions.

Distance and perspective are everything. With distance and perspective I can understand life on a connected surface fairly effortlessly, while the same visual is incomprehensible to a two-dimensional

animal trapped on the surface, its vision blurred by sheer proximity. We can hold all of these two-dimensional surfaces in our hands, roll them around, hold them at arm’s length. All of these two-dimensional surfaces are easy to visualize because we can view them from the outside. Both distance and perspective are lost when we try to view our own universe. We can’t jump off space and see it from ‘outside’. There is no outside. We will move along the curves like a travelling stain migrating around the fabric of space.

animal trapped on the surface, its vision blurred by sheer proximity. We can hold all of these two-dimensional surfaces in our hands, roll them around, hold them at arm’s length. All of these two-dimensional surfaces are easy to visualize because we can view them from the outside. Both distance and perspective are lost when we try to view our own universe. We can’t jump off space and see it from ‘outside’. There is no outside. We will move along the curves like a travelling stain migrating around the fabric of space.

If the fluctuations were entirely random in the early universe, we would expect to see a spectrum of hot and cold spots approaching white noise: that is, a random and structureless superposition of temperature spots of any size. If instead the fluctuations are confined to a finite box, namely a finite universe, the shape and geometry of that box will mould the spectrum of fluctuations. By looking for the discrete harmonics of the different shapes of space, we could determine if the universe was compact and connected, we could hear the shape of the drum. If we cannot see the discrete harmonics, we’d have to conclude that the universe is too big to see all the way through it, but we may never be able to assert that the cosmos is actually infinite.

Life feels far more complicated to us. We experience electricity and gravity and nuclear forces, all of which seem distinct. But ultimately all these forces may be different phases of the same thing, just as water, ice and steam are different phases of the molecule H₂O.

The word ‘chaos’ conjures up an image of hysteria and things out of control. In a sense this is right. Chaos theory is used to describe systems with a loss of predictability, systems too complex for us to predict how they are going to behave.

But remarkable order is known to precipitate out of chaos. Fractals are the most striking example. The snowflake that repeats the same structure on smaller and smaller scales is a fractal; a complex, geometrical object that repeats a bulk structure on smaller and smaller scales. Chaos is a natural consequence of life in a finite space. As light and matter orbit the compact space their paths cross and tangle, forming an intricate fractal pattern. When galaxies do finally form as the universe ages, they can condense along these scars, like dirt collecting in scratches on an otherwise smooth surface.

In complex systems the emergent properties of the collective exceed the sum of the parts, just as meaning that emerges from a sentence exceeds the sum of the constituent letters.

There would be no one truth, not even layers of truth but a complex organization of competing truths.

And if we were playing this game in person, we might agree that geometry is a structure we can define as the set of relations and causal structures. This is probably what spacetime is in the sense that it is not really a cloth in my hand. So spacetime isn’t a thing but rather a collection of events and their relations. Even more disarming, we may not even be things, just events.

Maybe the most abstracted is the language of mathematics and the most symbolic is the language of art. Or maybe it’s the other way around.

To manage the overwhelming visual information in our everyday lives we symbolize. We assign a name and an abstract concept to the things we see. By dismissing these everyday symbols, another level of symbol surfaces and visual representation can expose a barer meaning, like dreams do.

Writing this as the events unfold is different from writing about the events with the clarity of hindsight. The inane and the mundane are given equal importance in the present before select events acquire special importance in the context of a memory that stretches far into the past and far enough into the future.

Even time can be made compact. If time is compact, every event will repeat precisely as set by the age of that very peculiar world.

If space itself were to collapse, we would be crushed back into the dust of the earth from which we came: the atoms that the sun, the earth and we ourselves stole from a dying star would be returned to space and broken into their subatomic constituents, to the stuff of pure energy where gravity and matter and light merge indistinct. As nature rushes to its demise, the entire universe would become smaller than a discarded speck of dust, and smaller still, and perhaps then it could start all over again.