even or odd

[AntonioLao]

If all the different things in the entire universe can be counted, would the answer be an even number or an odd number? This is the same as asking the question that if infinity is a number would it be an even number or an odd number.

Solely relying on inductive reasoning it can be shown that the universe is approximately 67% probable to contain even number of things and 33% probable to contain odd number of things. Take any two numbers at random and apply the binary operation of addition, the following numerical statements are always true. (1) Odd + odd = even, (2) even + even = even, (3) even + odd = odd. Statement 3 suggests hidden perfect symmetry of additive commutativity such that even + odd = odd + even. However, if statement 3 is not commutative then a statement 4 must be added such that odd + even = odd. The addition of statement 4 changes the rule of probability to 50% even and 50% odd for the counts of things in the physical universe.

[Meem]

Uni-verse, an odd-one. All things in the universe counted = one ... uni-verse.

[SteveA]

If all the different things in the entire universe can be counted, would the answer be an even number or an odd number? This is the same as asking the question that if infinity is a number would it be an even number or an odd number.

Solely relying on inductive reasoning it can be shown that the universe is approximately 67% probable to contain even number of things and 33% probable to contain odd number of things. Take any two numbers at random and apply the binary operation of addition, the following numerical statements are always true. (1) Odd + odd = even, (2) even + even = even, (3) even + odd = odd. Statement 3 suggests hidden perfect symmetry of additive commutativity such that even + odd = odd + even. However, if statement 3 is not commutative then a statement 4 must be added such that odd + even = odd. The addition of statement 4 changes the rule of probability to 50% even and 50% odd for the counts of things in the physical universe.

That's cute. When I saw the list of 3 combinations, I knew there was something missing, but it took a bit for me to figure it out and then I saw you'd already mentioned it.

Ok, if we're to refine this probability, we need a bit more detail. Including the probability of this addition being commutative, and if it is commutative, then we'd need to know the probability of each element similarly being a sum as in that case you'd have the probabilities as nested dependencies.

Let's hypothetically say that the universe contains 2 summed parts that are commutative, but that each part is similarly a sum of 2 commutative parts etc. Then the probability at each level of this binary tree for the volume to be even would approach 100% also.

(I'm skeptical of the commutative idea though because that would imply that at least for the purpose of commutation, the values would be identical and undifferentiated, which leads to a question of how we know which is the right side and which is the left side - there would not appear to be a right side element nor a specifically left side element either and you'd need some other manner to maintain them as distinct)

It's still a cute idea. (Something else to consider, similar to Meem's comment is whether or not there's a bias to the range of values in this sum. If we had an exponentially decaying probability, then there would be a bias toward the minimum value etc.)

I do think that the size of the universe could be described as a potentially changing value over time and likely there are some solutions to which values could be possible to observe. For example, if something determines that it must be representable as both a square surface and a cubic volume, then the volume of space would need to be a value with both a square root and a cube root, so it would be of a form n^6. (That's just a hypothetical example, but depending upon the model there can be constraints on which are valid and it may be that physical instants only occur as some decaying fraction of the growth of this volume and the rest are undetected moments - so the universe could continually "fill up" until it finds new valid physical configuration to the solution and then continue this evolution as determined by the need to satisfy multiple constraints, such as being an odd or even volume, if there's a manner to determine this)

[AntonioLao]

The uncertainty of knowing even or odd might be a problem of connectiveness between two space-time events. In the one dimensional real number line, take three points A, B, and C. A could always be connected to B assuming they are contiguous numbers. However, A could never be directly connected to C unless it passes thru B. Now, consider an infinity of points located in an arbitrary 'inside' and another infinity in an 'outside' bounded by an infinity of points, the inside cannot see the outside unless it see thru the boundary which must be necessarily transparent to both light and thoughts.

[SteveA]

The uncertainty of knowing even or odd might be a problem of connectiveness between two space-time events. In the one dimensional real number line, take three points A, B, and C. A could always be connected to B assuming they are contiguous numbers. However, A could never be directly connected to C unless it passes thru B. Now, consider an infinity of points located in an arbitrary 'inside' and another infinity in an 'outside' bounded by an infinity of points, the inside cannot see the outside unless it see thru the boundary which must be necessarily transparent to both light and thoughts.

A good question here is over how we're measuring that it's tightly packed or dense over some segment of the line. If we simply constructed a real number line ...<a<b<c<d<..., there's nothing non-uniform about this.

Notice that there's an implicit "other" number line we're using measure that the density of the real numbers varies.

If we're looking at it in physical terms - nothing can travel faster than light anyway, so there's no way to see "past" the point you're at, unless your points expands somehow and then you're detecting a volume of space with effectively faster than light communication because you're able to differentiate more information over time than if you solely had access to a single point.

Anyway, it doesn't matter how closely packed the points are if they're connected together because the information still propagates at the same subjectively constant rate unless there's some alternate route that can be viewed that differs in length - but what would that be?

[SteveA]

Actually, there may be some other restrictions on what volume a space can have if we add in some possible restrictions due to perceptions and knowledge - perceptions do not appear able to make distinctions on very fine or very large scales of time or space and we mentally append or compare and subdivide these units to points of being intangible yet physical features are still assumed to exist on these scales and there should only be a small set of possible operations that can be performed on wavelength or periods of time that are humanly observable and so this generates a natural spectrum of mental constructs dependent upon this human scale periods/wavelengths of interaction, so that could be another form of restriction upon perceivable space.

[AntonioLao]

that differs in length - but what would that be?

We could define a quantum of length as the Planck length for a fundamental metric of space-time. This is the minimum distance between 2 events in a space-time continuum.

[SteveA]

We could define a quantum of length as the Planck length for a fundamental metric of space-time. This is the minimum distance between 2 events in a space-time continuum.

I agree very much that there should exist a single metric unit shared by everything in a space and a unit of time, or similarly difference (all differences are equal in magnitude - short or long, large or small etc. arise when comparing quantities of inequalities, but a lowest distinguishable difference should be equal for any two objects - and two objects must be distinct otherwise they would be the same object)

So if we had a number line and wanted the density of this line to change, there would need to be some other reference added parallel to it and interconnected, this would form a loop (or lattice if we extended this) around that location allow two pathways of communication between endpoints - either the "uniformly" dense pathway or the "non-uniformly" dense pathway - but then again, which is which? If there's not a deterministic way for a signal to select one path or the other then we immediately jump into statistical descriptions and classical mechanics.

The only way to remove all the uncertainty is to have everything in a single line and so there would be no variation in density within it, if we have a lattice the we could potentially imagine a "non-uniform" flow of information within it, but then this would similarly require yet another "uniform" lattice be attached to it to provide references as to what is uniformity - once again, this can be seen as forming loops in another dimension and we continue on trying to construct ever higher and higher dimensional references as defining what is the uniform reference for space that everything else changes relative to, when in reality it was the first dimension the entire time.

Notice that even if we had a lattice of points interacting with each other, if the system is deterministic we could still remap this into a single number to describe the state and once again the evolution of this over time is linear and assuming anything other than a constant rate of time (and similarly a uniform density of samples points over time) would only add uncertainty and force the model to be statistical, even if it was entirely precise and did not need a statistical description.

I messed around with this idea some and it looks like this path leads to some mind bending twists and turns, though it's dependent upon the question of whether or not we could describe time as a string of inequalities. If we can, then it looks like all the funky quantum wierdness comes into play, though ultimately there may be some hard rules underlying it and it's all mathematical and logical.

What do you think? Are there ever entirely identical things that exist in time or does everything at least possess a single element that makes it unique? (It would seem everything must be unique and distinct otherwise it would have already been the same thing at the same time).

[AntonioLao]

Are there ever entirely identical things that exist in time or does everything at least possess a single element that makes it unique?

Continuous absolute angular acceleration as constant change of direction and such that the scalar product with the local infinitesimal metric is a constant the square of light speed: a × r = c²

[SteveA]

Continuous absolute angular acceleration as constant change of direction and such that the scalar product with the local infinitesimal metric is a constant the square of light speed: a × r = c²

Ok, that could be assumed constant, but notice that this is not directly measurable but deduced to be constant.

What physical properties are being measured for this?

Notice that if we were to attempt to verify a change in direction, we'd need sensors at different positions to do this, otherwise the change in direction would not be detectable.

If these detection repeated across one or more sensors we'd still need memory to maintain them as distinct over time.

In the end, we'd still be measuring a sequence of distinct/unique/non-identical observations even though the assumed underlying property was constant.

Consider that if events over time all have at least one unique component to them, then this could be seen similar to an incompressible component to the information.

So if we had a string of observations over time and we extracted the commonalities across them, this should be the laws of physics (which can easily appear symmetrical in both directions in time if we're not paying close attention to which reference for time is actually being used - if you're looking at a machine making some measurements, which form of time are you using to indirectly observe what it's "seeing"? You're using your own ability to distinguish between moments of time and so are not directly witnessing what it's see with respect to its time. In the end, it would be time as you perceive it that determines what events are seen as existing in time and these are highly non-symmetrical in time).

As a sidenote, conscious perceptual qualities appear to be constant - the colors of the rainbow, or the feel of a piece of paper do not morph from moment to moment (though they may or may not be present in an experience), or the familiarity of remembering something etc. so these might be considered the constant alphabet by which information is communicated, but they're arranged differently over time and so a conscious moment still contains a unique configuration of these as a figurative "perceptual word".

It may seem as though a machine making fine physical measurements or a precise atomic clock is more accurate than conscious perception, but that's not necessarily the case - in order to make these machines or known of their accuracy etc., their measurements must be verifiable and communicable within the limits of perceptions, so if we had a row of various clocks and had to determine which was the most reliable it would ultimately be the one that most closely agreed with our own interpretation of time and though it could potentially measure wavelengths outside those of hearing or sight or touch or atomic interactions in taste or smell etc., these are constructed mentally in a spectrum with respect to those wavelengths that we can consciously perceive.

Anyway, if all moments in time contain a unique element then any communication over time requires a quantity of those unique elements and you can't specifically point to them, nor change their rate (because they already exist as an incompressible quantity - space is also incompressible, information is built from incompressible components), but you can make relative measurements between such quantities and say that the rate of time measured by one clock is different than the rate of time measured by another, but subjectively the rate remains the same as it has to include all these quantities and the quantity is always equal to itself.

You can't go backward in time because these elements are unique - selecting a prior element would require two of these to be identical, but identities describe physical laws common across them, so you could see physical laws, in this respect as similar to being able to select components from prior moments (memories - physical laws would become incomprehensible random experiences without memory to hold sequences together and allow for correlations to be constructed across them).

So, assuming that all moments in time contain unique elements, experiences over time regard quantities and communications in time are fundamentally derived from numbers. (They're placed within a context of conscious perception and expanded via. laws/logic from memory to construct the perception of the physical universe)

A good analogy here would be of a source of white noise playing through a musical instrument. Once the characteristics of the instrument are learned, we can compensation for its predictable components and effectively "see" the instrument and allow us to "see through it" as well by inverting this process (though there are some processes that destroy information and are not invertable and are obscuring or obstructive or possibly imagined only), but there's still the energy or white noise "behind" it.

Though there's another perspective as well - this energy is continually being compressed as new correlations are discovered/created/imagined etc. and so the instrument is being built instead, but in this event there still remains that energy/noise/information/space/time/chaos/quantum foam etc. from which it was constructed and these are fundamentally a collection of unique and non-identical things and so they exist as quantities and specifically describable or localizable, except when the mind places them within a structure as memory (in this case the objects themselves would be perceptions themself - though that may be a cyclic reference and paradoxical if it could be said that they were perceived as perceptions - at least one perception would need to be unique in this respect as being that which perceives perceptions).

There's actually a lot of mathematics that we can attach to these structures, especially if we make an assumption of a constant velocity space and non-linear interactions within it (non-linearity appears unique in that it changes the density of representations in a space and can be seen as compressive or intelligent - data compression and intelligence are closely related - if you had an algorithm capable of very high video compression ratios, it would effectively be understanding the scene and simply storing what new elements were added to a scene and potentially even predicting the visible properties of the evolution of those elements over time - of course the uncompressed remainder still has to be stored in a linear memory in order to retain an ability to temporally recall the sequence - if we moved beyond a linear/serial/sequential memory then we have an ability to edit those scenes, but that wouldn't be a deterministic dimension unless the causes for those edits were themselves predictable and if we're to learn of those causes in time, then ultimately this second dimension of time/memory etc. would still be constructed by looping the first dimension back with associations to itself, similar to folding a DNA strand and this could construct an arbitrarily large number of dimensions, it there were no predefined limits - the size of memory and quantity of perceptually distinct experiencies determines this dimensional limit unless the structure is simply allowed to move indeterminantly - in which case we couldn't objectively communicate much about that)