Saturday, September 17, 2005
Dimension - The Catechism
What do we know about dimension? There are many unknown vagaries to the space-time continuum that we are not aware of, probably because we do not possess the cognizance enough to even imagine one such. We extrapolate things with reference to the known 4 dimensions in our sci-fi stories and what we come out with is a parallel universe very much like our own.
Questions:
- What other qualities do you think this extra dimension might add? Would it add fluidity to your movements?
- Would it give your basic atoms the ability to disperse and re-group as you wish?
- Would it take on the qualities of not absorbing any part of the light spectrum and in turn make you invisible?
- Would it remove the limitations that you suffer due to the specific directions that you have to adhere to while following your basic brownian movement?
- Even if it did allow all these possibilities and more, would you use it to cease the current way of your living and take on a different view of things?
Would you be able to see in the new dimension?
// posted by Swetha @ 6:48 PM 
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Ever thought of Thought as a dimension? If not, here’s why you could:
Thought possesses characteristics similar to those of the other conventionally accepted dimensions:
• It defines the state of existence of an entity in unambiguous terms.
• It can be perceived, but can not be quantified as an absolute measure.
• It defines the transport and transformation of an entity whose state with respect to the other dimensions remains invariant to the said transformation.
Mathematical characteristics
• Continuity and differentiability: Thought has existed, exists and will exist. It is a continuous function defined everywhere in its domain, and is therefore analytically differentiable.
• Mutual independence: Thought and its perception are not constrained by the state of an entity in the other dimensions, nor does it directly influence the said states in any manner.
• Measure and orientation: Thought as an absolute does not exist. It can only be measured with respect to a reference in its own domain. Thought has neither a beginning nor an ending. It is not constrained by any restrictions on location or orientation as long its mutual independence from the other dimensions is guaranteed.
• Domain and range: Due to its innate immeasurability in absolutes, Thought can be arbitrarily assigned to the real, complex or hypercomplex domains. Consequent to this, the range of thought too is arbitrary in real, complex or hypercomplex measure.
Behavioral characteristics
• Existence and conservation: Though its perception and application may require the presence of an entity that can not survive in vacuum, Thought by itself does not require an existential medium. The non-perception of Thought does not necessarily imply its non-existence, just as its non-application does not lead to conservation: Thought once expended, can not be re-created.
• Perception in the intrinsic: An entity does not need to be taught nor trained to acknowledge the perception of Thought: it is only its application that requires experience and external impetus.
• Indispensability of measure: The description of an entity is incomplete without mention of the state of its Thought: lack of information leads to ambiguity in state quantization.
• Adherence to Heisenberg’s uncertainty: It is impossible to measure with certainty the state of an entity in Thought simultaneously with its state in other dimensions, for Thought is automatically expended in the said measurement.
Thought possesses characteristics similar to those of the other conventionally accepted dimensions:
• It defines the state of existence of an entity in unambiguous terms.
• It can be perceived, but can not be quantified as an absolute measure.
• It defines the transport and transformation of an entity whose state with respect to the other dimensions remains invariant to the said transformation.
Mathematical characteristics
• Continuity and differentiability: Thought has existed, exists and will exist. It is a continuous function defined everywhere in its domain, and is therefore analytically differentiable.
• Mutual independence: Thought and its perception are not constrained by the state of an entity in the other dimensions, nor does it directly influence the said states in any manner.
• Measure and orientation: Thought as an absolute does not exist. It can only be measured with respect to a reference in its own domain. Thought has neither a beginning nor an ending. It is not constrained by any restrictions on location or orientation as long its mutual independence from the other dimensions is guaranteed.
• Domain and range: Due to its innate immeasurability in absolutes, Thought can be arbitrarily assigned to the real, complex or hypercomplex domains. Consequent to this, the range of thought too is arbitrary in real, complex or hypercomplex measure.
Behavioral characteristics
• Existence and conservation: Though its perception and application may require the presence of an entity that can not survive in vacuum, Thought by itself does not require an existential medium. The non-perception of Thought does not necessarily imply its non-existence, just as its non-application does not lead to conservation: Thought once expended, can not be re-created.
• Perception in the intrinsic: An entity does not need to be taught nor trained to acknowledge the perception of Thought: it is only its application that requires experience and external impetus.
• Indispensability of measure: The description of an entity is incomplete without mention of the state of its Thought: lack of information leads to ambiguity in state quantization.
• Adherence to Heisenberg’s uncertainty: It is impossible to measure with certainty the state of an entity in Thought simultaneously with its state in other dimensions, for Thought is automatically expended in the said measurement.
In a given environment, the properties of an entity are constant and absolute (although our perception of the same is not). A dimension, by itself, is only an abstract concept that can not transform an entity in any manner: it can only aid in a change of perception of the state of the entity. A change in the properties of an entity due to its movement to a new environment, as perceived by a change in its state in a dimension, can only be attributed to the entity and its interaction with the said environment, and not to the dimension itself.
Wikipedia tells me Brownian motion is a limiting instance of the random walk. It is mathematically improbable to achieve motion any more random than the simple random walk. The realization of new dimensions may help us “see” the motion of an entity in new light, but can not alter the underlying motion itself.
For instance, consider an entity (‘X’) whose state (‘x’) is defined in time (‘t’). Further, assume that X is subject to a simple random walk in ‘t’:
x(t) = x(t-1) + u
where, for argument’s sake, ‘u’ is binary with possible values 1 and -1.
The realization of a new dimension‘d’ can now allow us to perceive the state as a simultaneous function of ‘t’ and ‘d’ i.e.
x(t,d) = x(t-1,d) + u
which is still representative of the random walk in ‘t’.
However, given that we only possess knowledge of a measurement of x at a specific‘t’ and‘d’ slice i.e. x(t,d), it is possible to interpret the underlying motion differently. For example, we could interpret x(t,d) to be
x(t,d) = x(t-1,d-1) + u
which may be mathematically correct, but is no longer necessarily a simple random walk in ‘t’.
Maybe the example is convoluted but the thought I wish to convey is that the availability of a new dimension permits us to perceive the behavior of an entity in a hitherto unacknowledged manner, without actually altering the said behavior in any way.
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Wikipedia tells me Brownian motion is a limiting instance of the random walk. It is mathematically improbable to achieve motion any more random than the simple random walk. The realization of new dimensions may help us “see” the motion of an entity in new light, but can not alter the underlying motion itself.
For instance, consider an entity (‘X’) whose state (‘x’) is defined in time (‘t’). Further, assume that X is subject to a simple random walk in ‘t’:
x(t) = x(t-1) + u
where, for argument’s sake, ‘u’ is binary with possible values 1 and -1.
The realization of a new dimension‘d’ can now allow us to perceive the state as a simultaneous function of ‘t’ and ‘d’ i.e.
x(t,d) = x(t-1,d) + u
which is still representative of the random walk in ‘t’.
However, given that we only possess knowledge of a measurement of x at a specific‘t’ and‘d’ slice i.e. x(t,d), it is possible to interpret the underlying motion differently. For example, we could interpret x(t,d) to be
x(t,d) = x(t-1,d-1) + u
which may be mathematically correct, but is no longer necessarily a simple random walk in ‘t’.
Maybe the example is convoluted but the thought I wish to convey is that the availability of a new dimension permits us to perceive the behavior of an entity in a hitherto unacknowledged manner, without actually altering the said behavior in any way.
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