has one of two possible fundamental states, either digital
. If digital, than there is a smallest possible unit
to which everything can be reduced, said unit being attunable to one of a discrete number of states, with a binary
exposition being a quite possible option.
Current scientific knowledge proposes the Planck length
and the Planck time
as the smallest units of significance with respect to each such measure -- not necessarily the smallest length
"possible" but the smallest at which any activity
impacting the states of our Universe can occur. The Planck length is estimated at about 1x10E-35 metres, and the Plank time at about 1X10E-42 seconds. The question as to whether the nature of our Universe is fundamentally digital or analog is really a question of whether the Planck units are a bottom (or perhaps some smaller subsets thereof are a bottom) or if there is no
bottom limit, and things can be offset to each other by any fractional amount conceivable.
But if our Universe is indeed digital, with exclusive discrete "packets" of space/time, then we can actually calculate
the number of possible outcomes for any Universe of given size X. If our Universe is, to be generous
(and enable easy rounding
), 100 billion light years in diameter (which is a few billion more than current estimates) that's 1x10E25 meters, or 1x10E60 Planck lengths, for a radius of 5x10E59 Planck lengths. The volume of a sphere
is 4/3 (pi
*r)E3, so presuming our Universe to be spherical
(which is the maximization of size following the longest axis
from the presumption of approximately even distribution from an original point) that would be 4/3 (pi
*5x10E59)E3, or very roughly 2.1x10E63 Planck cube units.
Each such unit can be characterised as a "bit
" -- a unit of information
which, combined with neighboring units, can convey complex coding. If we presume that any of these units has one of two bit-states (basically on
), and the Planck time is indeed a minimum threshold, then our Universe would be capable of experiencing up to 2.1x10E105 bit-states per second. With 31,536,000 seconds in a year, that's only 6.6x10E125 possible bit-states over the course of a hundred trillion years. Naturally, the formula
by which this presumption is generated presumes the size of our Universe to be constant
(which obviously it's not), but even presuming expansion at a thousand times the speed of light and the highest bound estimate for the size of the Universe, we're still comfortably within the range of 6.6x10E160 possible bit-states.
To bring this down to a more comprehensible level, imagine a jar
filled with marble
s. There is a certain set number of marbles that can fit within the jar -- let's say it's 300
. If each marble is capable of being either orange or green, and of changing color once per second, and we hold that jar up for one minute, then there are 300x60, or 18,000 bit states; basically 18,000 blank slates onto which color can be projected. The fact that the marbles occupy volume is actually irrelevant, for the same possible number of results will follow if you have 300 marbles lined up in a row (or, of you have a row of 300 bits, either of which could be a zero or a one).
To calculate the number of actual possible states, we go factorial
, which means that there are 6.6x10E160!
possible actual states. As a practical matter most of the "possible actual states" are only theoretical and would turn out to be, in fact, impossible in practice given the real factors of how existing bit-states affect neighboring bits moving into their next state. Going back to the marbles, if there are some rules about when a marble can turn blue if it is surrounded by other blue marbles, or by red marbles, this reduces the total possible number of options. At a quantum
level, we currently know neither the character of the smallest bits, nor the rules governing their changes. If we did, we'd be God
The point of all this, lest it be lost in the shuffle, is that if
our Universe is fundamentally digital at its lowest level, then despite the truly incomprehensibly massive number of total possible states, that number is a finite number. If that gigantic number is designated as "ZUX," it is still absolutely paltry compared to ZUX*10E10. But if our Universe is fundamentally analog, then the number of possible states is truly infinite.