Developments in microprocessor technology have seen address buses increase in width from 8 to 16, 24, 32, to 64 bits. IPv6 uses 128 bits to address network nodes – but how many bits does it take to address the universe?
To address the universe, we need to be able to specify four dimensions 1) a point in time since the beginning of the known universe and 2) a 3-D point in space.
Lets take a point of time as having the duration of a Planck Time. One second is about 1.9×1043 Planck times.
The age of the known universe is approximately 13.7 billion years or 8 x 1060 Planck Times. This number is in the order of 2203 so we will need 203 bits to specify a point in time since the beginning of the known universe.
Lets take points in space as having dimensions of the Planck Length. There are approximately 1.6 × 1035 Planck Lengths in a metre, and 1.51×1051 Planck Lengths in a Light Year.
The radius of the observable universe is approximately 46.5 billion light-years or 7.04×1061 Planck Lengths. This gives a volume of the observable universe of 4.65×10185 Cubic Planck Lengths. This number is in the same order as 2617 and so we need 617 bits to specify a point in the observable universe.
Taking the time and space dimensions together we need 820 bits to specify a unique point in space at a unique point in time.
[[Update: I just noticed that the Age of the Universe in Planck Times (8 x 1060) and the Radius of the Universe in Planck Lengths (7.04×1061) are almost identical. I bet this is no coincidence!]]
Factoid
The number 2820 is also a generous upper bound on the number of computer instructions that could possibly have been performed since the beginning of the known universe. How so? If we assume that every Cubic Planck Length in the universe contains a computing element that performs one instruction every Planck Time then the number of instructions processed would be 2203 Planck Times * 2617 computing elements = 2820 Instructions performed.
Another Factoid
This is a random pattern of 841 bits generated courtesy of random.org . If my calculations above are correct, then there are more variations of this pattern than there have been unique points in space and time!
- BTW this means that only a minute fraction of the possible combinations of 841 bits have ever existed in all the Petabytes of data generated by the Googleplex and all the rest of the computers in the world!
- It also means that unless this pattern is saved it will never ever be seen again by any observer wholly inside the observable universe.
Taking the logical positivist stance that there is no actual infinite, could 2^841 be considered the largest actual meaningful finite number? Though it’s reasonable to assume that the universe doesn’t end at the limits of telescope range, however much more space is outside that volume, it’s existence still isn’t empirically meaningful from a strict positivist stance, any more than all the unrealized combinations of those 841 bits. Not to say I think positivism is correct; I’m not convinced there can’t be an actual infinite. But from within that framework, could there be a larger, empirically meaningful, actually embodied number than 2^841?
Hello – I just happened on this article and the volume calculation is bothering me. Assuming you were trying to use a spherical model for the observable universe, you forgot to multiply in pi, which boosts your volume to 1.46×10^186 cubic Planck lengths, which is 619 bits, not 618.
That isn’t what I wanted to comment on, however – the problem is geometry. More specifically, what kind of geometry a programmer might use to describe the observable universe.
While spherical geometry (r,?,?) might make sense at first glance, the angular size needed to delineate a Planck length at increasing distances makes this unreasonable. For example, if we use 7.04×10^61 Planck lengths as the radius of the observable universe, the angular distance between two points one Planck length apart at the edge of the observable universe is 8.139×10^-61 degrees. You would need 209 bits to cover all possible angular distances for ? and 208 bits to cover all possible angular distances for ?. Add that to the 206 bits that you would need to cover all possible values of r, and that comes out to 623 bits (826 once you include time). The problem is even worse, however – the programmer would have to recalculate his angles every so often because the universe is still expanding.
Using rectangular geometry (x,y,z) actually saves space – not to mention removing the need to recalculate the entire universe every few billion years. Each of the three spatial dimensions would be 207 bits long (remember you need the *diameter* of the observable universe for this part), and so the space of the observable universe can be delineated with only 621 bits (824 once you include time).
Of course, describing anything in physics requires momentum as well – but then we run into the Heisenberg Uncertainty Principle and I really don’t feel like trying to work that out on a work night.
One more thing – saying that the 841-bit pattern will never ever be seen again is incorrect (I suspect it was a mis-wording) as the time until the heat death of the universe will be approximately 10^106 years = 5.8534×10^156 Planck times = 521 bits. Given that the observable universe will be quite a lot larger by then too, the total measurement of the entire possible observable universe (without taking momentum into account) will require well over 2 kilobits.
Just so I’m clear, this really is mostly semantic quibbling, and I really enjoyed the post. I plan to check out the rest of your blog now.
In response to Daniel above, the largest number that will ever be empirically meaningful in the observable universe would be 2^[the number of bits representing Planck time at heat death + 3×the number of bits representing the diameter of the universe in Planck lengths at heat death + 3×the number of bits representing the largest possible momentum in the universe at any point during its age (please don’t ask me to calculate this) which would probably be well before heat death]. Just don’t ask me what that number is.
David, excellent blog post. Current thinking in physics seem to point towards there making no sense to reason about ‘absolute’ address for space – that each planck volume can only be referenced to with regards to its surroundings – ie since point A and B could never agree about what the origo of the coordinate system is – I guess that that would point to some kind of cubic tree structure, which would probably need immensely larger numbers. I think you’d need to factor in the speed of light there somewhere.
Responding to your comment:
Update: I just noticed that the Age of the Universe in Planck Times (8 x 1060) and the Radius of the Universe in Planck Lengths (7.04×1061) are almost identical. I bet this is no coincidence!
If I’m understanding things correctly, that’s not a coincidence. The size of the observable universe is bound by the speed of light, and Planck time is defined as the time it would take to cross one Planck length at the speed of light.