Wednesday, January 16, 2008

Infinity and the Boltzmann Brains

A link to this video can be found at

Last week, in an entry called "Google, Memes, and Randomness" we talked about how something as complex as our universe and the multiverse of other universes really could spring from randomness. Now, here's a link to a fascinating article in yesterday's New York Times:

This article includes a reference to the Boltzmann Brains conundrum: an idea that ties very nicely to some of the ideas we explore regularly in this blog. Let me try to sum up Boltzmann's idea: by the time we're imagining a fabric that includes every possible expression of matter and energy, that must mean there are many expressions which are not complete universes, but rather just fragmentary bits of order, and those fragmentary bits could be observed by something approximating a mind within each fragmentary universe. The disturbing idea this leads to is that within the multiverse of all possible universes there could be all these "brains" floating around (not physical brains of course, but this startling image helps to make the idea stick in our minds). This is all discussed in the above article, which also touches on some of the more metaphysical ramifications of all this.

To be clear, the Boltzmann Brain scenario is similar to the tale of Schrödinger’s Cat: it was originally offered as an extreme example of the absurd conclusions that might be drawn from applying quantum thinking to the macro world. The idea does have more power, though, when we accept the proof offered by a team of scientists at Oxford equating quantum probability states with our macro-world's probability states. Is it really such a great leap to imagine there could be organized systems representing an "observer" in many of those other universes within the infinite set of all possible universes?

Infinity or Infinities?
We keep returning to the concept of infinity with this project: some people like to think of infinity as being only one thing, and therefore they jump to the conclusion that I'm talking nonsense when my way of visualizing the dimensions uses phrases like "draw a line to yet another infinity". Here's a simple example of the same concept: the numbers following the sequence 1,2,3,4,5... extend out to infinity. But let's take any two of those numbers, 1 and 2 for instance: how many numbers are there between 1 and 2? There's 1.1, there's 1.2, there's 1.75689425... there are an infinite set of numbers between 1 and 2. Finding different ways to get to infinity is what this is all about: and as Michel from Norway recently reminded me in the tenth dimension forum, "two parallel lines meet at infinity".

Thinking of infinity as being the unobserved fabric of quantum indeterminacy shows a way to imagine how all those infinities connect together, and the parallel universes resulting from choice, chance and circumstance for our universe (as infinite as those branches appear to be) is still just one more subset of all the possible expressions of matter and energy, memes and spimes that we're playing with here.

Here's another way to describe the dimensions, which acknowledges that every single dimension extends out to its own version of infinity:

0 - a point of indeterminate size
In this way of imagining, 0 and 10 are very similar concepts - both are of indeterminate size. The common practice of referring to "0" as infinitely small isn't really correct then: a point on a graph can be any size we care to imagine it being because its size is not relevant, just its location. And to be clear, 0 is not a dimension, it's just where we start our description.

1 - a line created by a certain set of "points", extending to infinity
Start with a point, add a second point, join them together with a line. The line you have drawn is a line segment with those two points as its endpoints, but that line can be extended out in either direction to infinity

2 - a plane created by a certain set of 1D lines, extending to infinity
Draw a second line. As long as the second line is not directly on top of the first, those two lines are now part of an infinite plane that passes through those two lines.

3 - a space created by a certain set of 2D planes, extending to infinity
Any two planes that are not directly on top of each other become part of an infinite 3D space that passes through those two planes.

4 - a line created be a certain set of "3D points", extending to infinity
So 3 is our 3-dimensional space. What would "not directly on top of each other" be for 3D space? It would be 3D space in a different state. Look at your watch: let's call whatever time you see at the instant you looked "now", or the universe in one state, and we'll call that a point. Three o'clock tomorrow afternoon is another state, and we'll call that our second point. Joining those two points creates a line segment, and the ends of that line can be extended back to the Big Bang and forward to the end of the universe.

But as I've said many times here, the big bang is an illusion, it's better to think of it the way physicist Seth Lloyd describes it - the first binary yes/no that separates a particular universe out from the indeterminate background. So the fourth dimension can be thought of as a line that extends to infinity in either direction, and the big bang is just a point on that line, same with the "end" of the universe.

5 - a plane created by a certain set of 4D timelines, extending to infinity
5 is our "probability space", or "spacetime tree" as some have described it in the tenth dimension forum. The "bush-like branching structure" of the David Deutsch team's recent proof is equivalent to this, which means this occurs at both the quantum and the macro level. So: take one timeline that could extend forward or back from this moment (this "now", as we called it), then think of another alternate version that could also occur from that same "now", and those two lines define an infinite plane that passes through any versions of our spacetime that are logically consistent with our current "now".

6 - a space created by a certain set of 5D planes, extending to infinity
Stay with me now: the spacetime tree for our particular "now" doesn't include a version of the universe where it's 2008 and Kurt Cobain is still alive. That would be a different fifth-dimensional "plane". Imagining that other "Kurt alive" plane along with the "Kurt dead" plane that we find ourselves to be in, then, is the same conceptual leap as imagining one 2D plane and another different 2D plane, and extrapolating how 3D space is derived from that.

Why do we say "certain set of timeline branches", then? Here's why: the version of the 6th dimension that our current timeline is/must be part of is still constrained by the basic physical laws that are unique to our universe. No amount of choice, chance, and circumstance, at either the quantum or the macro level, moves us to a universe where the laws are different, and that is what we mean by a "certain set" of timelines in this context.

Could there be more than one version of the big bang that this infinite observed/unobserved sixth-dimensional structure passes through on its way out to infinity? Certainly, but only to the extent that there are always random fluctuations, quantum outcomes, small decisions made that in the big picture do not affect things for our overall universe to the point that its existence is no longer possible. But the 6th dimension, like the other dimensions, is an infinity. That infinity encompasses all the possible "beginnings" and "endings" for our particular universe, and it includes all of the possible paths that are not available to us from our current position in spacetime but which are still constrained by our basic physical laws. The idea proposed by physicists like John Wheeler of "reverse fine tuning" of our universe through quantum observation was discussed in my blog entry "Boredom and Consciousness", and this gives us a way to imagine how our current universe really could have multiple slightly-different-versions of the Big Bang within its 6D space.

7 - a line created be a certain set of "6D points", extending to infinity
Take the 6th dimensional structure we've just imagined, that is a point in the seventh dimension. Take the structure representing all possible outcomes for some other universe that has different basic physical laws, that is a different point in the seventh dimension. The line that passes through those two points extends to infinity in either direction.

8 - a plane created by a certain set of 7D lines, extending to infinity
Now think of the seventh dimensional line that passes through the point representing our universe, and the point representing another universe where the value for gravity is different. That line extends out to infinity in either direction, but it doesn't pass through universes where some other constant varies. To get to the infinite plane that passes through those two different lines takes us to the 8th dimension.

9 - a space created by a certain set of 8D planes, extending to infinity
The 9th dimension is the way you get from one of those planes we've just imagined to another, and the space that passes through those planes may not, as I've said many time before, be able to actually express any physical realities itself - at that point we are dealing only with the "information" side of the "information equals reality" concept. But once again, there is a timeless unobserved infinity that this 9th dimension stretches out to. Imagining the 9th dimension, then, as being filled with "Boltzmann Brains", each being an observer of some fragmentary organized bit of information/reality, is what the above New York Times article is referring to. In my book and this project, I have preferred to imagine the 9th dimension as being the place where "big picture memes" are found: organized patterns that have the potential to generate one kind of reality over another in the dimensions below.

10 - 9D as a point of indeterminate size, everything as potential only
Ten, then is the infinite unobserved quantum fabric. Attempting to observe any aspect of this collapses us into some or all of the dimensions below.

Our poll question ending soon is about Google and the way it has changed the way we interact wth information. If Information Equals Reality, then that is a very big question indeed for all of us as Boltzmann Brains floating in our perceived reality.

Enjoy the journey,

Rob Bryanton

PS Two other blog entries that work through a way to imagine our hierarchy of dimensions are "You Can't Get There From Here" and "How to Make a Universe". Now, for fun, here's a new video created by Ryan Hill, for my song "Big Bang to Entropy".

A link to this video can be found at

No comments:

Tenth Dimension Vlog playlist