Mujitsu and Tairaku's Shakuhachi BBQ

johnstrr · 2006-04-04 09:29:41

For those of you who seek the truth that lies beyond beliefs and egocentric thought.

"In lak'ech"

Play the Void

johnstrr · 2006-05-11 11:47:46

I found some excerpts I wrote out a while back:

On the Subject of Zero – Paraphrased from J.D. Wheatley’s “The Nature of Consciousness, The Structure of Reality” Ch. 18-20

We will consider the equation:

1/0 = infinity

In this form the idea is zero (0) should divide into one (1) an infinite (Character doesn’t work) number of times. It has been a controversial equation. The following is another variation of the equation, the one we will consider:

1 = 0 x infinity

This equation looks impossible at first glance. Do we not assert 0 x n = 0? If this is granted, would not 1 = 0 x infinity reduce to 1 = 0? This does not “appear” acceptable. This conclusion is contradictory; hence, its apparent unacceptability. Regardless, let’s proceed and see what we can learn.

There are three ways to begin an understanding of the equation. They are the following:

First consideration: the simple and conventional mathematical understanding of the individual terms of the equation.

Second consideration: the factors (“0”) and (“infinity”) are understandable in terms of each other.

Third consideration: each factor (“0” and “infinity”) can be understood in terms of the (“1”).

Let’s examine each of these interpretations. We use physical examples to better understand.

First consideration. Convention posits the following:

One (“1”) denotes the least of any number. It can also represent the least of any something. Using “water” for instance, (“1”) would denote the least of that which can be denoted water, namely, one water molecule: two chemically combined hydrogen atoms with one atom of oxygen.

Zero (“0”) denotes lack of a number: a “placeholder.” It can also represent nothing: “no thing” – not something. In our example: No water, and no molecules of water.

Infinity entails the natural numbers without end, viz, 1, 2, 3… It can represent an unending number of things. The earth (or the universe) could be said to harbor a quantity of water molecules approaching an infinite number.
We concede the definition of infinity “representing” any limitation to the number of things is less than mathematically satisfying. For example, to say there is an infinite number of things, like water molecules, is foolhardy when we also acknowledge there also exist things other than water molecules.

Even if infinity represented everything, we still find ourselves in the same uncomfortable situation. What if one of these “things,” after our “defining” of infinity, gives “birth” to another “thing?” Doing this adds one more thing to “everything.”

A more serious problem is defining “thing.” For example, how do we consider the atoms (oxygen, hydrogen) composing a water molecule? To say “adding numbers to every number does not increase the value of infinity” does little to understand such a concept.

Let’s restate our progress in understanding. We notice an inherent problem in defining infinity in any countable or uncountable manner. If uncountable, adding one more to “infinity” changes it. The definition of uncountability appears unsatisfactory because it is “indefinite.” Infinity must be defined in terms other than mere endless sequentiality.

We learn one thing in the first consideration. Using things to “represent” numbers may benefit understanding the fundamentals of mathematics. Existents might help recognize problems that were artificially created in the effort to solve certain problems (viz, paradoxes and contradictions).

Using conventional definitions we conclude the following: Zero infers no value (of any number or anything). Zero represents no number or no thing. Infinity represents the greatest value (of any number or anything). This definition is “countably undefinable.” But, is this not a definition? Yes, and no.

There is an apparent contradiction. A term should not be definable and undefinable at the same time. (We define infinity as endlessly countable and therefore undefinable.) That is a problem. A contradiction exists by these definitions. Maybe the problem is not what is being defined. Perhaps the problem is the definition itself.

Question: Should the factors (“0” and “infinity”) defined individually as in the first consideration, dictate the understanding of the equation? If they do, what are the consequences?

Let’s use an approximation of the first consideration to better understand the equation. Here, we consider defining an approximation of both zero and infinity in terms of each other. In the second consideration we examine the factors as approximations of their ideal.

The second consideration. Pragmatism suggests the following:

Zero (“0”) is approximated by 1/1, ½, 1/3…

Infinity is approximated by 1, 2, 3…

One (“1”) is a constant of proportionality.

Pragmatism contends via the equation the two factors (the[“0”] and [“infinity’]) vary inversely to each other because of the constant one (“1”). This is a relation of complement.

To understand this “pragmatic” definition (of the factors zero and infinity) let’s do the following. Instead of the zero (“0”) substitute a series of even smaller fractions. 1/10, 1/100, 1/1000, and so on. (We could use the sequence of reciprocals of the natural numbers ½, 1/3, 1/4…) Let’s represent this graphically (using Cartesian coordinates). As the fraction decreases in value, it more closely approaches zero (as an asymptote). The zero is approached infinitesimally.

Similarly, proportionately substitute the infinity factor with 10, 100, 1000, (or 10^n…) and so on. As the value increases, it approaches ever closer to ideal infinity.

The second consideration posits zero is approached as the fraction (e.g. 1/10^x…) decreases in value. And, infinity is approached as the natural numbers (here in exponential multiples of 10) increase without limit.

The second consideration approximates the meaning of the individual definitions offered in the first consideration. Therefore, approaching zero is said to come ever closer to infinity itself. Approaching infinity is thought to come ever closer to infinity itself. We just do not know what “zero in-itself” or “infinity in-itself” means. They are still undefined. If we cannot specifically pinpoint our terms, can they be explicitly defined? The catch, zero is nothing, and infinity is “endless” by definition. What can be accomplished with definitions like these?

In the second consideration, we conclude zero is less than any enumerable value while infinity is greater than any enumerable value. The difference between the first and second consideration is that zero in the second consideration is only approached (approximated) as “nothingness.” This may not be the same as nothingness in-itself.

However close we approach either zero or infinity that (itself) is not necessarily the same as either zero or infinity in themselves (we differentiate between an “apparent,” or approximate, and “actual” zero and infinity). And that leaves an unsettling problem. If there is a difference (between apparent and actual zero and infinity) however minute or undefinable, there may be a difference in understanding..

Question: Should the factors (“0” and “infinity”) define the understanding of the equation; therefore, define the “1” (as previously asked in the second consideration) or should the equation (“1”) dictate the understanding of the individual factors (“0” and “infinity”)? Maybe this consideration will lead to a difference in understanding (between “apparent” and “actual” definitions).

Specifically, can we incorporate the individual definitions of the factors, as in the first consideration, into an understanding of the equation? For example, can we define zero as nothing and yet maintain that definition within the equation? Does the equation permit defining zero as nothingness? Here, we suggest the proper meaning of zero and infinity depends on their role (or meaning) in the equation. A vague way of stating this is the following. “Do the terms define the meaning of the equation as is customary, or in this case, does the equation (uncustomarily) define the terms?” Let’s examine the possibility.

The third consideration. Each factor can be defined by how it functions in the equation.

Zero (“0”) represents a “zero divisibility” aspect of the one (“1”).

Infinity represents an “infinite divisibility” aspect of the (“1”).

One (“1”) is unity. Unity equivalently represents a complementary combination of zero and infinity.

The equation’s left side (i.e. “1” or unity) is equivalent to its right side (0 x infinity). In the second consideration: We found the “approximating” factors (respectively 1/n…, n…) for zero and for infinity are complementary. Zero and infinity are complementary aspects governed by the constancy of unity.

There is a leap from an “apparent” (approximating) definition to an “actual” definition when defining zero and infinity in themselves. Our task is to follow this leap and maintain complementarity.

One is said to be unity. What is the meaning of unity? Specifically, what defines unity? The equation suggests that one is definable by two factors—is equivalent to a relation between zero and infinity. How do the terms zero and infinity explain one? Can we understand zero and infinity by how they relate to unity?

The third consideration suggests zero is an aspect (of “1”) indicating “no divisibility” (of the “1”); i.e., [“1/0]. Infinity represents an “endless divisibility” aspect of the “1”; i.e., [“1/infinity”].

We surmise unity is definable by two aspects—the factors zero and infinity. Unity is analyzable in terms of “no-divisibility” (0) and “infinite-divisibility” (1/infinity). Unity is also analyzable in terms of any division: it need not be a limitless division. A single unit of water is analyzable through its components, viz, oxygen and hydrogen. Unity implies we are concerned with something that is a completed composition. Let’s pursue this line of inquiry.

Most people would say (“1”) signifies a unit. Offered for examples are: one foot, one yard, one meter, and one kilometer. The same idea applies to any individual thing: one car, one person, and one country. The concept of unity abstractly delimits and demarcates identity. One water (identity) molecule meets this criterion. A water molecule is identifiable by its composition (H-O-H).

Using the above understanding: We say the concept of unity (categorically) denotes an individual object. It does not explicitly pertain to an object in terms of its composition. Although composition is suggested, it has not been traditionally considered an explicit aspect of the concept of unity.

Though implied, unity has not “conventionally” inferred divisibility of itself. Unity typically describes the individual (or object): with or without regard to its composition (or divisibility). Be mindful, we are associating numbers with (physical) things to better understand concepts entailed by the Primary Equation (1 = 0 x infinity).

Last edited by johnstrr (2006-05-11 11:54:21)

johnstrr · 2006-05-11 11:49:27

Entropy and Negentropy – Wheatley

The First Law of thermodynamics is the conservation of energy. Total energy of the universe is constant. Energy cannot be created (within the physical universe) but only transformed from one state to another. (Our initial consideration concerns the physical universe.) What happens to the “given” energy of the universe? Matter is a form of energy.

In the 1820’s a Frenchman named S. Carnot tried to understand the mechanics of steam engines. He understood the energy process results from a state of high-heat concentration --- “flowing” to a state of low-heat concentration.

In 1854 the German physicist R. Clausius generalized the idea heat cannot pass from a cold area to a hot one. The process of heat distribution ends when both areas achieve equilibrium, vis, “settle” at the same temperature.

In 1868, Clausius coined the word entropy. Clausius believed entropy (of any closed system) would evolve toward a maximum value. That is, as heat energy dissipates it becomes less available for work (activity).

Entropy defines the Second Law of thermodynamics. Entropy is sometimes likened to an ”energy” fluid or carrier. Entropy is the thermo-process that is expressed as a function of a system’s energy. The energy content of a system is measured before and after an interval of time. Energy (difference) is a measure of activity. Temperature is a measure of heat—typically correlated with molecular-kinetic energy. Entropy is associated with the disordering of parts.

Englishman B. Thompson believed entropy has cosmological consequences. The German H. Helmholtz realized when all physical energy is expended—the universe ends in “heat death.” When all activity ceases, there is maximal disorder (and minimal order). No available energy means no transformation of material arrangement is possible.

Let’s use what we learned under the previous heading and connect it to extreme cosmological settings. The extremes of reality are the wholeness of space and its infinite energy (i.e., of the vacuum).

Space is the ultimate wholeness function. It is formness itself. It is complete order: pure form—form without content. There is no disorder in formness because (considered alone) there is no “activity” of parts (which can “deform” the form). At first thought, it may not be easily grasped how there could be a connection between “that which has no parts” and the form of every possible thing. Once it is understood that things have no form but for the wholeness function, the difficulty of grasping this connection lessens.

The energy of the vacuum is the final-functional breakdown of space itself. There is no order (form) in the random activity (“foaming”) of the vacuum’s energy. It is total chaos—formlessness. Chaos describes the final parts-function. This is easily understood. Order is contrasted with disorder. If there is that (space as a whole) which is characterized by complete order, then there must be that which is characterized by total disorder (viz, vacuum energy).

Between the extremes of reality are found everyday things. We have seen that ordinary things are “structurally” constituted in the extreme by (the wholeness of) space (itself) and its opposing-infinite energy (molecular to atomic on down to vacuum energy). Considering the cosmological setting, what is the relationship between energy and change of structure?

At the beginning of the physical universe (inauguration of Big Bang and extremely high-energy density—high temperatures) order is “potentially” maximized. As the universe expands and matter cools, some energy is freed for use.

Energy can be transformed. Electrical or heat energy is usable for mechanical activity. Activity implies motion and hence (potential if not actual) work. Energy makes possible the building of structural forms.

Form changes as energy is consumed. Burning coal hears water—transforming it into steam. Steam turns an engine turbine generating electrical energy. Electricity can be harnesses for work. After coal burns to ashes, it has practically no form and no usable energy.

Thermodynamic processes have a “direction.” Entropy has been linked to the flow of time. Eddington said entropy is the “arrow of time.” The idea entropy defines temporal directionality is deduced from Helmholtz’s idea the universe is winding down (to a heat death). A that point, motion ceases and energy is unavailable. Until then, things change inexorably. Direction of change defines the flow of time.

Physical motion is attributable to the universe being in a state of nonequilibrium. Without motion, there would be no determination of temporality. Time flow is associated with motion of parts and temporal directionality is determined by entropy. The natural process of energy use in a given universe specifies temporal directionality.

Temporal directionality is defined by increasing entropy in Phase I of the cosmic cycle. The physical universe becomes more disordered as its energy is consumed. Entropy defines the primary process of change in the physical universe.

Negative entropy, also called negentropy, is the opposite of entropy. Negentropy defines a system that becomes more ordered. Order is associated with structure building (and work).

Negentropy is not the dominant energy process in the physical universe. Even where life forms are thought to develop contrary to entropy, there is no problem in understanding that the source of free energy (used to increase order found in structure building) defers to outside (of living) systems. The main energy source for physical life is sunlight.

Sun energy (electromagnetic radiation) “drives” life processes. Plants obtain nutrition through the photosynthetic process. Sun energy drives photosynthesis. Plants are food for animals.

Negentropy occurs in the physical universe only because it is enabled by the free energy by-product of entropic processes (system degradation). If dynamic symmetry applies to cosmic structure, we expect there to be a universe where negentropy dominates (system building). Phase II of the cosmic cycle is probably dominated by the negentropic process.

Saying development of physical life forms, which defy entropy, is balanced by greater entropy elsewhere, avoids addressing the “bigger picture” (actually balancing entropic energy processes).

Entropy has also been applied to the loss of information about a system. The more disordered a system becomes; the less information represents the “order” of the system. We presume the more ordered a system is, the more it is associated with knowledge. Complete order (no disorder) is then associated with total knowledge—formness itself.

dstone · 2006-05-11 16:57:46

johnstrr wrote:
I found some excerpts I wrote out a while back:
"Zero (“0”) is approximated by 1/1, ½, 1/3…
Infinity is approximated by 1, 2, 3…"

Hi John. That looks like a good book. Nobody else has responded, so I'll throw something out there on the topic of zero...

Let me start by saying I love zero, mostly because there are so many ways to see it. And we must keep in mind that zero (or infinity) doesn't really exist; it's just a convenient label, a map, a finger pointing a the moon, etc. Zero is a recent idea, created by man.

But putting my dualistic hat on... I wrestle with that particular way of looking at zero, above. It's true that the given infinite series approachs zero asymptotically, but I think that's creating complexity where it doesn't need to be. I understand the author is trying to establish a complementary relationship between zero and infinity to support a grander scheme, but approximating zero with a series just seems like so much about nothing! Ha ha.

Zero, if it exists, doesn't seem quite as special as infinity. We can count, in integers or reals, in evenly spaced units to, from, and across zero. -3, -2, -1, 0, 1, 2, 3. We can easily perform math with it. This is unlike infinity. Approximating infinity with a series seems more reasonable to me, since it's truly not countable, or depictable on a number line, or add-able, or subtractable, etc.

Another thought in regards to zero... He suggests an asymptote approaching zero from the positive side. This approaches positive zero. (Zero is a fabrication, so "positive zero" is fair game.) There is a similar asymptote approaching from the negative side, towards negative zero. There are numbering systems in use today and historically that have two distinct representations for zero, both positive zero and negative zero. So maybe there's something to this idea of approximating zero, after all...

Anyways, if the book has sound math and causes this much contemplation and questioning, it automatically gets added it to my "wish list"... Cheers.

-Darren.

johnstrr · 2006-05-11 21:49:11

That's great... I won't even attempt to summarize it, but I promise that he leaves no stone unturned. The multicontextual layers of the three "numbers" will change your mind on any one being more special than the other... ;-)

It's the rabbit hole, and you are on your way down... I see the world differently because of this guy... truly amazing.

Cheers.

dstone · 2006-05-11 22:58:46

I love rabbit holes. But before I submit... a question... at the Amazon book link you provided, something raised a red flag for me. Maybe this isn't what the Wheatley himself said, but in the "From the Publisher" note at that link, it reads "He reasoned how to prove 0 = 1."

As an additional preview of this book, is it possible for you to briefly share how or if Wheatley proves 0 = 1? This man obviously dedicated his life to some important and rigorous thinking, so I don't want to suggest that he's going to pass off a bad math joke. But... This seems suspicious. And I've seen some bad (but fun!) proofs of similar contradictions.

-Darren.

Karmajampa · 2006-05-12 00:23:35

I have an opinion on how 0=1...thought about this a long time ago, never been very useful though.

1, being a solitary object, cannot be compared, because there is nothing to compare it to, and cannot be proven even to exist. Therefore it can equal 0.

Okay, perhaps that doesn't make any sense, but that is also OK.

Kel.

johnstrr · 2006-05-12 01:21:57

I'll try Darren..

johnstrr · 2006-07-11 10:07:57

Ok,

These are the key points from the end of Chapter 18, Page 516-518:

- We "conceptualized" an interesting equation: the Primary Equation. The first task was "fitting" the concept of space to the equation. The problem was space behaved as though it possessed at least one characteristic, viz, that space expands according to the Big Bang Theory of the universe. (Tests of Special Relativity indicate space can expand and contract.)

- That space can expand and contract suggests it is characterizable as though it is a "something." An immediate question was "how can space be defined as nothing and yet be characterized as though it were a something?" It seemed that space had to be defined as though it were both nothing (otherwise, how can we call it nothingness) and (also) something (in that it can expand and contract). How can space both be nothing and not nothing (i.e. something)? The issue of temporality also sneaks into any possible resolution.

- We began our search for a deeper understanding of the basic nature of everything. We settled on correlating space with the zero ("0") in the equation. There is no other choice. We acknowledge this concession despite not seeing how we could reconcile this complementary definition (of nothing -- something) with the Law of Contradiction. How can the same (space) both be and not be? Permitting such a realization violates the logical Law of contradiction.

- If the Law of Contradiction is violated, the very understanding of consistency becomes the issue. This realization forced us to examine logic.

- We said one (1) represented the unity of Reality. We could say unity is "space-time." The next question is how can the other two factors of the equation "explain" unity? After saying zero represents space, we are left to say the infinity factor represents time. (We continue our quest to understand the nature of time in the next chapter.)

- Unity is the constant of proportionality. Zero represents "actual" infinity. The infinity factor represents "potential" infinity (1,2,3,. . . ). Actual infinity includes potential infinity. How else can the equation be interpreted? Unity signifies completed Reality (space-time). Reality is constituted of two aspects. Space (zero aspect) includes the infinite (infinity aspect) energy of the vacuum.

- There is a complementary relation between zero and infinity. As the infinity factor increases toward infinity, the zero factor decreases to zero: toward nothing at All. eventually, we take a (conceptual) "leap" from an infinitesimal fraction (which "approaches" zero as a limit) to nothingness (zero itself). Nothingness includes infinity. This is a role (functional) reversal of the "apparent" idea infinity (potential) includes the natural numbers.

- We reinterpreted our understanding of the equation using set theory. We noticed the problem of defining space without contradiction (such that it could remain "nothing" and yet behave, as though it were something) was akin to Russell's Paradox in set theory.

- We reasoned the following. A unit is a set and its members. Zero is setness itself. Infinity represents every possible member of the set. Setness itself can be understood as a "form" or a "wholeness" function. Elements or members of a set are correlated with "contents" or "parts" function.

- Unity is the "set of a set." Parts are generated from a wholeness function by its (the whole) "fractionation." Relevancy: The "infinity" of natural numbers are generated by a continual partitioning of zero ("0"). “Zero to one” (unity) is the continuum. The empty set is a de facto member of every set.

- Every possible discrete number is found within the partitioning of the continuum. Nondiscrete numbers result from the “synthetic” appending of irrational numbers to the continuum. Complex numbers are not derivable without a basis in the natural numbers.

- The primary problem of understanding space (represented by zero) reduced to justifying the generating of the natural numbers. Specifically, how is the number one ("1") originated? Merely erecting a series of "operational" axioms, telling us how to carry out numerical inductions, does not in itself "explain" how unity ("1") is originally derived. One ("1") is obtained by functionally fractionating zero ("0").

- Why are we interested in numbers? Arithmetic is manipulation of numbers. Physics is "formulated" in mathematical terms. Physics concerns "things." Mathematics reduces to the arithmetic of the natural numbers. Numbers can represent every possible thing in abstraction. Understanding how zero can generate unity is to possibly explain how something (the focus of physics) can be generated from nothing. Abstractly, it (zero) also enables the axiomatization of arithmetic.

- The problem narrowed to explaining arithmetic. Peano axioms are an example of the attempt to "explain" arithmetic. Russell's Paradox seemed to make it difficult to erect a complete axiomatic treatment of arithmetic. Other attempts were made to "patch up" an axiomatic basis for arithmetic using logic. Zermelo-Franke''s axioms and later attempts were made to readdress the logical basis of arithmetic. Godel's incompleteness Theorems suggested there cannot be any complete and consistent axiom for B. Russell's logical treatment of arithmetic.

-The search for understanding of things reduced to the consistency of logic itself. Is logical consistency, as defined by the Law of Contradiction, also the test of consistency of logic? We found the answer to be no. The Law of Noncontradiction defines the consistency of logic.

- Law of Noncontradiction is representable in Boolean algebra as 0 = 1 x 0. We found an equation that allows the derivation of one (1) from zero (0). The negation of the Law of Contradiction yields the Law of Noncontradiction, which defines the consistency of logic. It is inescapable, 0 = 1. Why? Because zero is the whole, one (1) "has" the same whole as (which defines) zero (0) but one (1) has functioning parts. No one will deny that a whole pie is equivalent to the same (whole) pie cut into pieces. Although the whole pie is still present (equivalent) the functionality has changed (from wholeness to unity). There cannot be more than the whole of what is. These are not definitions that typically characterize zero and one in the usual sense of numeration (where 0 does not equal 1). These definitions reflect the understanding of zero and one in there own right (wholeness and unity).

- (It is true that) zero is "nonfunctioningly" equivalent to ONE ("1"). It is false that zero is "functioningly" equivalent to ONE ("1").

- A proposition proving anything and everything—proves nothing at all. All is no-thing: nothing. Nothing proves anything and everything. The Law of Noncontradiction defines the criterion nothingness must meet. The Law of Contradiction defines the criterion for anything and everything.

The next chapter concerns applying what we learned in this chapter. Can what we learned about logic (through Boolean algebra) and our equation (1=0xinfinity) better explain physics? Particularly, besides explaining space and time, what else in physics can logic and our equation explain?

Harry · 2006-08-07 11:12:15

"For those of you who think that zero is nothing... try imagining a few more of them at the end of your pay check... nice, isn't it?" Sogyal Rinpoche (On the subject of shunyata).

Interesting topic, thanks for the recommendation.

Regards,

Harry.

evan kubota · 2006-08-07 14:19:21

Whenever I see 'negentropy' used so casually in a thermodynamic context without specifically citing its origins and acknowledging that it's a totally unnecessary term, it bugs me. Schrodinger used the word so that the loss of entropy could be cited as a positive - instead of losing entropy, the system is gaining negentropy. The fact that this author cites 'negentropy' as something substantatively different from entropy is also misleading. Negentropy is simply the loss of entropy - and entropy is *not* just 'disorder' as the author states, overly simplistically.

Mujitsu and Tairaku's Shakuhachi BBQ

#1 2006-04-04 09:29:41

Book Recommendation

#2 2006-05-11 11:47:46

Re: Book Recommendation

#3 2006-05-11 11:49:27

Re: Book Recommendation

#4 2006-05-11 16:57:46

Re: Book Recommendation

johnstrr wrote:

#5 2006-05-11 21:49:11

Re: Book Recommendation

#6 2006-05-11 22:58:46

Re: Book Recommendation

#7 2006-05-12 00:23:35

Re: Book Recommendation

#8 2006-05-12 01:21:57

Re: Book Recommendation

#9 2006-07-11 10:07:57

Re: Book Recommendation

#10 2006-08-07 11:12:15

Re: Book Recommendation

#11 2006-08-07 14:19:21

Re: Book Recommendation

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