Mistakes Concerning Infinity

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Mistakes Concerning Infinity

G. Stolyarov II

The Rational Argumentator--A Journal for Western Man

Issue XXIV-- July 21, 2004

"Infinity" is one of the most frequently encountered terms in the modern culture, and one of the least understood. Too often has its invocation been an attempt to justify mysticism, irrationalism, and contradiction, especially in the natural sciences. It is the province of filosofy, as a foundational science, to set the very framework without which the natural sciences cannot operate. Unfortunately, numerous modern scientists have stepped far outside their field in making generalizations about the nature of existence, and of infinity, deliberations which properly belong in the realm of filosofy and which filosofers must employ to weed absurd and contradictory statements from the natural sciences.

Infinity and Existence

Reality is absolute and every existent has an identity. According to the filosofy of Objectivism, existence and identity are inextricable corollaries. To be is to be something and to be something in particular. To be something in particular means to have a set, deliberate, fathomable nature. It is no coincidence that the word "to fathom" means both "to measure" and "to understand." In order to be understood by man, a given entity must have attributes that can be measured on some scale, be it a qualitative or a quantitative one. In order to be measurable, an entity must demonstrate a finite quantity of each measurable attribute. A particular given entity, say, a dog, must have finite mass and length, and its fur must reflect light of a finite frequency. A concept, such as dog, is formed by omitting the particular measurements of every dog and claiming that a dog must have dog-like qualities in some quantity, but could have them in any of a range of quantities. To claim that any dog has infinite measurements of given qualities is absurd: if something is infinite, and does not have a set, delimited quantity to be measured, how can it be measurable? If it is not measurable in some manner, absolute or relative, how can it serve as a necessary quality in the definition of a concept? Thus, infinite, that is, limitless measurements of qualities cannot exist if concept formation is to continue to maintain its legitimacy.

Using this as a foundation, we now proceed to investigate prevalent misconceptions and faulty logic in the examination of the notion of infinity and where it is applicable.

Mistake 1: If nothing can be infinite, then everything will have to be destroyed someday.

This in no way follows from the assertion that no entity may ever have an infinite quantity of anything. Let us say that an architect has designed a tower of such durability that no known substance can erode or puncture it. There is absolutely no guarantee that this tower will ever be destroyed. It can be said to be invincible, but it will always have a finite age! After one thousand years, it will be one thousand years old. After one million years, it will be one million years old. No matter how old it becomes, its age can still be measurable, and thus is not infinite. Thus, it is possible for things to last indefinitely, and there is no inherent guarantee that everything will someday be destroyed. While man's mind cannot envision infinite size or infinite smallness, it can conceive of the possibility of "infinite" longevity of anything: buildings, planets, animals, men, so long as these entities had a certain origin in time.

This fenomenon can be referred to as a chronological infinity, though I use this term with reservation, because it does not truly describe an infinity, for all the measurements concerning it must be in all cases finite. The true infinity, or a simultaneous infinity, concerns either coexistence of infinite and finite measurements or the presence of all infinite measurements within an entity. God has been defined by the religious as an object of allegedly infinite quantities of everything, i.e. omnipotence and omniscience. However, the rational man would need to reject God by this definition, because it implies a simultaneous infinity: the technique of measurement-omission cannot be applied to the formation of the concept, "God," and, thus, "God" cannot be a legitimate concept unless it is a hypothetical God that does have a finite age, and exhibits delimited qualities and abilities. (And, simply because something is conceivable, does not guarantee that it exists; the existence of such a conceptually legitimate God would still need to be proven to be within the realm of reason.)

Mistake 2: Singularities and black holes exist which have an infinite density.

Filosofy must urgently employ its veto power over the natural sciences to refute this illogical theory. Density is the ratio of mass per unit volume. An infinite density implies the existence of unlimited mass within a limited volume. Mass is not a chronological attribute, and exists all at the same time. To claim that infinite densities can exist is to acknowledge the existence of simultaneous infinities, which immediately renders one's concept or theory illegitimate.

One must ask the modern fysicists the following questions: "What properties does a finite volume have to enable it to hold infinite mass without expanding? If a finite volume can hold any quantity of mass, no matter how large it is, does it not follow, then, that each individual unit of mass must occupy zero volume? If one unit of mass has zero volume, and zero multiplied by anything remains zero, then must a singularity, too, not have zero volume? But how can it also be claimed to have a certain finite non-zero volume?" This is a contradiction that cannot be reconciled. The fysicist, if he thinks rationally, will be forced to admit that the singularity does indeed have zero volume, that is, it does not exist.
It is conceivable that an object may have a very high density, exhibiting a very large mass to volume ratio. It is also possible that there exist what are now called black holes and singularities, and that they can explode outward or attract matter into themselves. But, a "singularity" can only release some very large amount of matter in an explosion; it cannot be an inexhaustible fount of matter. A "black hole" cannot be said to have an infinite holding capacity for objects, either. Throughout its existence, it must have attracted some finite quantity of objects into it, which quantity affects its mass. But, if it also has some finite density, any intake of matter must also have amplified its volume in some manner. Even if this matter were to become compacted to an immense extent in the "black hole," it would not be possible to compact this matter infinitely.

This is what filosofy tells us in regard to modern cosmology. It informs us what propositions must be false, but it does not guarantee that even a conceptually feasible notion of black holes and singularities is true. Such proof would be a task for empirical observation to undertake. Filosofy can, however, catch scientists spouting senseless generalizations and propositions, and inform them whenever they venture into a realm for which the filosofically unsystematic scientist is quite ill-equipped.

Mistake 3: If any entity must have a finite age, then the universe must also have originated at some point in time.

Yes, any entity must have a finite age at any point in time. The mistake here, however, is quite simple: the universe is not an entity! It is a mere collection of everything that exists. The purpose of the term ��universe�� is to serve as intellectual shorthand that substitutes listing every single existent when one wishes to speak of universal principles that are applicable to everything (such as the axioms of existence and identity). The term "universe" is not in itself a legitimate concept. If the sum of Chicago, Quasimodo, a telescope, and a hippopotamus cannot be a legitimate concept, how can the sum of Chicago, Quasimodo, a telescope, a hippopotamus, and everything else be a legitimate concept?

If one were to say that Chicago, Quasimodo, a telescope, and a hippopotamus had a certain single origin in time, the statement would evidently be ludicrous, from any perspective. The more expansive such a statement becomes, however, the more reverence is given to it in contemporary academia! Rationally, though, it must be all the more ludicrous for it. There is no such one thing as "everything," nor even "the potentiality of everything." If there is no such one thing, it cannot have a single origin in time. (It cannot, per se, have any quality, not being a single thing!) Thus, all the modern cosmological speculations about a Big Bang that occurred to "initiate everything" and a Big Crunch to occur that will "destroy everything" are sheer blunders, caused by the inability to understand the limitations of a term such as "everything" (or its equivalent, "universe.") Filosofy instructs the rational man to reject these superstitions right away.

The universe cannot have a beginning or an end, for the term "universe" is synonymous with "existence." Existence exists. Existence can never not exist or not have existed. A=A.

Mistake 4: Matter is infinitely divisible.

I could take a sheet of metal and slice it in two pieces. It could be said then, that the metal is divisible by two. I could, using advanced futuristic technology, dismember it into its constituent atoms. It can then be said to be divisible by about 6.022 * 10²³ (assuming we have a mole of metal to begin with). I may also be able to extract the cores of these atoms and separate them into their constituent nucleons, and, subsequently, split those nucleons into the quarks that comprise them. Matter can be divisible by a very large factor, and this factor may be far greater than we presently even suspect. Only science can inform us of the precise extent of matter's divisibility. But can matter ever be infinitely divisible?

Can we ever have an infinity of particles originating from some finite object? Just like having infinite mass in a finite volume, this is a simultaneous infinity, and is thus impossible. After all, this would imply that each of these particles would have zero volume, and would thus simply not exist. How one can form an existent piece of metal out of non-existent particles, no matter how many of them there are, is beyond rational comprehension. I will wager my life savings that nobody will ever be able to do this!
Thus, matter cannot be infinitely divisible. We do not know the extent of matter's divisibility, and we may be able to continue dividing it for vast periods of time, and still find new division to be possible. But we will only know matter to be divisible as far as we will have divided it. Since simultaneous infinities cannot exist, we will never reach a state where infinite divisibility can be empirically verified. Thus, it is not a legitimate proposition, scientifically or filosofically.

Mistake 5: Division by zero gives infinity. Thus, infinite quantities must exist.

There is no such operation in the real world called ��division by zero.�� I can split a pie into three pieces, or five thousand pieces (if I have a microscopic cutting tool). I cannot split it into zero pieces. Matter does not originate ex nihilo, nor can it be annihilated. The fundamental fabric of that which exists (i.e. matter) cannot all of a sudden stop existing for no apparent reason. The scientific principle of matter conservation is in fact a filosofical proposition which must be true in order to exclude magic from the realm of science.

Division by zero is in fact not even a valid mathematical operation, but rather the description of a trend: the magnitude of the quotient is inversely proportional to the magnitude of the number by which the dividend is divided. Similarly, all other uses of infinity in mathematics are mere convenient shorthand notation to the identification of trends. For example, a quantity ��approaching infinity�� is the same as a quantity increasing without bound. At any particular time, it will still be a finite quantity.

Mistake 6: If infinite quantities cannot exist, then space itself is finite.

All quantities are attributes of existents. Space is not an existent. It is a mere positional relation of existents with respect to each other. There cannot simultaneously exist an infinite amount of existents, but space itself cannot be said to be finite or infinite. It cannot be said to be. Something, i.e. an existent, is. Nothing, i.e. space, is not.

This is why all coordinate systems are inherently relative: they must presume an arbitrary origin at some point. But, just as an entity can be conceived to exist at (0,0,0), so can it be conceived to exist at (10⁸⁷, 9*10⁶⁵, 2.79*10⁹⁸⁸⁷⁵⁷), which is just a set of numbers describing its relation to an entity that could exist at (0,0,0). A spaceship with recyclable fuel could be equipped to distance itself from other existents indefinitely. At any time, it will still be a measurable distance from those existents, and its distance would be finite. No matter how large this distance is, however, it could always become larger. 2.79*10⁹⁸⁸⁷⁵⁷+1 is a conceivable number, but infinity is not.

Space is neither finite nor infinite, but it can be said to be indefinite.

Mistake 7: If everything is finite, time must have had an origin.

Time, too, is not an entity. Just like space is a relationship in three dimensions, time is a relationship in the fourth dimension. It can be measured by any uniform standard we deem fit, and something can be chronologically remote to something else in either direction to any finite quantity. Though this quantity must be finite, there is no limit to how large this quantity can be. Like space, time is neither finite nor infinite, but rather indefinite in two directions (earlier and later).

Here, it is fitting to note that each dimension (and there are only four) describes a particular relationship, and is indefinite in two directions: time (earlier and later), height (up and down), length (front and back), and width (left and right). This is a filosofical insight that science cannot nullify by any amount of theorizing or observation.
Mathematics, being a sister foundational science to filosofy, calls this truth in the three spatial dimensions Euclidean space. Perhaps it would be fitting to refer to it in all four dimensions as Euclidean space/time, which is based on arbitrarily designated uniform units. Euclidean space/time is to science a metafysical given that it must accept if it is to function in this world. Neither science nor mathematics can legitimately claim the existence of more than three spatial dimensions and one chronological dimension. Thus, dimensions with numbers like 6, 2.34, or the square root of pi+ 3/4 must be immediately rejected as unreal and logically absurd.

Conclusion

Consistent and rational application of filosofy can indeed tell us many things about the nature of existence: indefinite Euclidean space-time, the impossibility of simultaneous infinities, the possibility of indefinite, but not infinite, measurements of all qualities, including the four dimensions of Euclidean space-time, and the nonexistence of infinite divisibility. Filosofy can also help alleviate senseless scares about the "inevitable end of everything," which threaten, by no legitimate logical basis, to render the long-term purpose of existence itself meaningless.
Whenever one uses the term "infinity," one treads a thin line (though not an infinitely thin one!). I make no apologies for the term's existence, however; like "universe" it can be a convenient intellectual shortcut to lengthier expressions of mathematical and natural trends. It can also be used to point out logical impossibilities. It is convenient, for example to inform an opponent in debate, "You claim the existence of a simultaneous infinity. This means you have committed a logical fallacy." But, in the vast majority of cases, the term "indefiniteness" is far more suitable to describing an entity or fenomenon than "infinity." The latter term suffers from improper cultural use, and has far exceeded its boundaries, ironically enough. It is time to constrain the term "infinity" to its proper limits.

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Post 1

Friday, July 23, 2004 - 11:03am

"any entity must have a finite age at any point in time."

What about an electron? Couldn't an electron have existed forever?

"Can we ever have an infinity of particles originating from some finite object? Just like having infinite mass in a finite volume, this is a simultaneous infinity, and is thus impossible."

This is a mistake. This is the kind of mistake people make all the time when thinking about infinity. If the little particles that make up this finite object get *smaller and smaller*, then it's possible to have infinitely many tiny particles that altogether add up only to a finite mass.

This is related to the fact that some infinite series of numbers have finite sums. For example, 1/2 + 1/4 + 1/8 + 1/16 +...=1.

Perhaps you could discover some particle in the universe with a mass of one unit, and then break it up into two particles with masses of 1/2, then break one of those particles into two particles which each have a mass of 1/4, then break one of those new particles into two new mass 1/8 particles, and so on.... Then we would have discovered that the original particle is actually made up of infinitely many subparticles, with masses 1/2, 1/4, 1/8, 1/16, 1/32, ...... There is no contradiction here. All the masses of all the infinitely many little particles add up to 1. Similarly, their volumes could add up to some finite volume.

Does such a particle or object actually exist in nature? Well, that is something we have to check by *looking at nature* to see if it actually happens. It is *not* something that we can decide just by thinking.

Post 2

Friday, July 23, 2004 - 11:20am

"If a finite volume can hold any quantity of mass, no matter how large it is, does it not follow, then, that each individual unit of mass must occupy zero volume?"

This is a mistake. Again, it's important to remember that an infinite series can have a finite sum. Imagine taking a region of space that has volume one. Cut it in half. Each half has volume 1/2. Take one of those halves, and cut it in half, giving you two new regions which each have volume 1/4. Continuing like this, you can see that the original region of volume 1 is actually the union of infinitely many subregions, having volumes 1/2, 1/4, 1/8, 1/16, .... Now imagine putting an object of mass 1 inside each of these subregions. Then what would be the mass of all the stuff inside the original volume? Well, the original volume now contains infinitely many objects, each of which has mass 1. So, there is an infinite amount of mass now stuffed inside the original volume.

There is no logical contradiction here.

Is such a thing actually possible in the real world? To find that out, we would have to look carefully at the real world, and see if it ever happens or not. It's not a question that can be decided just by thinking.

Post 3

Friday, July 23, 2004 - 11:31am

"Filosofy must urgently employ its veto power over the natural sciences to refute this illogical theory."

Let's say a philosopher actually discovered a mistake a scientist had made. I don't know if this has ever happened in history, but let's just say it did happen. Well, then, I wouldn't say the philosopher had "vetoed" the scientist's idea--I would just say he had pointed out a mistake that the scientist hadn't caught.

Post 4

Friday, July 23, 2004 - 2:30pm

Greetings.

Mr. O'Connor: What about an electron? Couldn't an electron have existed forever?

Mr. Stolyarov: How? Was there a year called Infinity B.C., when this electron was formed? To "have existed forever" is a logical impossibility. We can examine the history of a particular electron and say that it existed in the year 4 billion B.C., or in 4 trillion B.C., but this tells us nothing about whether it "existed forever." The proposition that an electron, or anything, "existed forever," is entirely outside the sfere of human knowledge and utility, and, thus, must be absurd, as I will later show.

We know that matter cannot be created or destroyed. But there is no such entity as "matter." Matter just happens to be what entities are made of. It is not in itself an entity, nor does it have any qualities outside of the qualities of the entities it comprises, be those entities atoms, electrons, or human beings.

Here is the general rule of thumb: if it is an entity, it must have had a chronological origin. If it is not an entity, then questions of chronological origin are meaningless. "Universe," "matter," "time," "color," and "height" are examples of non-entities, but descriptions of intellectual shorthand, qualities, dimensions, and constituents of entities, where applicable.

Mr. O'Connor: If the little particles that make up this finite object get *smaller and smaller*, then it's possible to have infinitely many tiny particles that altogether add up only to a finite mass.

Mr. Stolyarov: All right, let us say particles get smaller and smaller. We might have a particle that has 10^-160 units of volume, or 10^-1230000 units of volume, or even 10^-9999999999999999999999999 units of volume. All of these figures express some volume conceivable to the human mind. But exactly when (that is, upon which division) do we get a particle with a volume of 10^-infinity? We do not. And we cannot. No matter how far we keep dividing, we can never empirically verify the proposition that matter is infinitely divisible, though we may someday be able to say that is divisible by a factor of 10^9999999999999999999999999. Thus, the proposition of infinite divisibility is outside the realm of the natural sciences.

It is also outside the realm of the foundational sciences, since an "infinite" quantity cannot be properly conceptualized by the human mind and logical apparatus, which are the tools that study the foundational sciences based on "commonsense" (i.e. unavoidable) apprehension of the external world (as opposed to the focused special observation of the natural sciences).

If a proposition is outside any means of human cognition, empirical or abstract, it has no meaning! It has no relation to man's existence or the universe in which man exists. It cannot tell us anything true or useful. It, too, has zero volume. :)

Mr. O'Connor: Perhaps you could discover some particle in the universe with a mass of one unit, and then break it up into two particles with masses of 1/2, then break one of those particles into two particles which each have a mass of 1/4, then break one of those new particles into two new mass 1/8 particles, and so on....

Mr. Stolyarov: You omit the time factor involved. Mathematical operations are somehow assumed to take place simultaneously, but, in the real world, each single division requires a certain amount of time. No matter how much time has passed while one divides this particle, one will always have a finite amount of parts! Upon no division do we reach the state of infinity parts.

The operation of division requires that which divides. Some entity, sentient or not, must perform it. It could be particle decay, or the hand of man. But every entity has an origin in time. Thus, no entity which initiates the dividing force can ever have infinite time to perform infinite divisions. Neither infinite time nor infinite divisions exist, though indefinite time exists, and the possibility of indefinite division may exist.

Mr. O'Connor: Does such a particle or object actually exist in nature? Well, that is something we have to check by *looking at nature* to see if it actually happens. It is *not* something that we can decide just by thinking.

Mr. Stolyarov: I contend that this proposition is impossible to check by looking at nature. This means that, if it is verifiable, it is only verifiable "just by thinking." It turns out not to be. Thus, it must be rejected as irrelevant in all contexts.

Mr. O'Connor: Again, it's important to remember that an infinite series can have a finite sum. Imagine taking a region of space that has volume one. Cut it in half. Each half has volume 1/2. Take one of those halves, and cut it in half, giving you two new regions which each have volume 1/4. Continuing like this, you can see that the original region of volume 1 is actually the union of infinitely many subregions, having volumes 1/2, 1/4, 1/8, 1/16, .... Now imagine putting an object of mass 1 inside each of these subregions. Then what would be the mass of all the stuff inside the original volume? Well, the original volume now contains infinitely many objects, each of which has mass 1. So, there is an infinite amount of mass now stuffed inside the original volume.

Mr. Stolyarov: Since at each point in time, we shall have only a finite amount of already divided parts before us, we can stuff them with a finite amount of units of mass 1. Thus, we will have volume 1 with some finite mass, a perfectly conceivable situation, with no simultaneous infinities!

I challenge you or anyone or anything else to make, in the real world, an infinite amount of divisions by the method you propose, and thus produce an object of limited volume, but infinite mass. I am willing to offer my life savings as the prize to anyone who manages this.

I am
G. Stolyarov II

The Prologue: http://www.geocities.com/rationalargumentator/eac_prologue.html

Chapter I: Protector's Summons: http://www.geocities.com/rational_argumentator/eac_chapter1.html

Order Eden against the Colossus at http://www.lulu.com/content/63699.

Post 5

Friday, July 23, 2004 - 2:44pm

Greetings.

Mr. O'Connor: Let's say a philosopher actually discovered a mistake a scientist had made. I don't know if this has ever happened in history, but let's just say it did happen. Well, then, I wouldn't say the philosopher had "vetoed" the scientist's idea--I would just say he had pointed out a mistake that the scientist hadn't caught.

Mr. Stolyarov: The areas where filosofy has veto power over the natural sciences are where scientists, after conducting certain empirical observations, venture to make filosofical generalizations on their basis that contradict known filosofical propositions such as the absolutism of reality, the validity of reason, or the universality of such concepts as Euclidean space/time. This is really tantamount to a raiding party from the realm of the natural sciences invading the realm of filosofy. The problem is, the realm of filosofy is at the foundation of the natural sciences, and, by undercutting it, the modern scientists undercut themselves.

Filosofers questioning filosofical propositions as filosofers can be right or wrong. Scientists questioning filosofical propositions as scientists are outside their province. If they would question filosofical propositions, they must do so in the role of filosofers (there is nothing preventing any given man from being both). Yet what the modern cosmological orthodoxy is doing can be compared to questioning the discipline of architecture by stating: "There is C major contained in every brick. This implies gloom and doom for everything and everybody!"

I am
G. Stolyarov II

Post 6

Saturday, July 24, 2004 - 8:01am

I can split a pie into three pieces, or five thousand pieces (if I have a microscopic cutting tool). I cannot split it into zero pieces.

This statement refers to multiplication.

"I can multiply one by three and get three, or one by five thousand and get five thousand, but I cannot multiply one by any known number and arrive at zero."

It looks like the fact that one is the identity number for both multiplication and division threw you off.

Post 7

Saturday, July 24, 2004 - 4:45pm

Greetings.

Mr. Ryan: This statement refers to multiplication.

"I can multiply one by three and get three, or one by five thousand and get five thousand, but I cannot multiply one by any known number and arrive at zero."

Mr. Stolyarov: I meant it in a different way: "After I divide one by three, I get three parts that each measure one-third." Similarly, I slice a pie into three pieces to get pieces of volume 1/3. 1 divided by 3= 1/3. 1 divided by 0 does not equal anything; it is not a legitimate operation in the real world. I cannot divide a pie into zero pieces, each with volume 1/0, or volume infinity.

I am
G. Stolyarov II

Post 8

Saturday, July 24, 2004 - 8:51pm

The point I was making was one related to mathematics specifically. What you are saying, by using that model of division, is that 1/0 (and, by implication, any number divided by zero) is nonsensical.

The trouble with using that kind of analysis is that it throws a lot of math out the window. How would I divide a pie into negative three pieces? As far as the pie itself: it is impossible, for a pie of exact circumference, to describe with numbers the exact diameter - and vice versa. I have to use a symbol representing a number whose exact value is unknown.

You could change the model while still making the same point; this is true. The line of reasoning used to derive the answer "infinity" instead of "nonsensical" for the answer to 1/0 is purely abstract; such an exercise could be considered merely a successful attempt to fill a hole that, if unfilled, would lead to a loss of certitude among mathematicians. I'm not sure how much descriptive value the function a/0 [where a is not equal to zero] has; its use might be confined to an exercise in cleverness derived from a technique that has use all over the realm of higher mathematics.

The above criticism, I should add, does not bear upon what I think of the overall content of your article. Would you say that mistakes relating to the use of infinity result from using the word in a loose way?

Post 9

Sunday, July 25, 2004 - 7:58am

Mr. Stolyarov,

I have some brief comments and questions, mostly of agreement.

First, what does this mean: "...measured on some scale, be it a qualitative or a quantitative one..."

This may have been only an expression, but I do not know what a "qualitative scale," would be. Not all qualities are measurable, for example, absolute qualities of relationship (uncle, parent, child, inside, outside) or state (on, off, true, false).

For example:

A concept, such as dog, is formed by omitting the particular measurements of every dog and claiming that a dog must have dog-like qualities in some quantity, but could have them in any of a range of quantities.

Rand's definition of a concept, (a concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted,) unfortunately, does not work well for anything other than non-living physical entities. A dog is a dog or it isn't. The abstract quality dogness (which I assume you mean by "dog-like") is either true of an animal (which means it is a dog) or isn't true of an animal (which means it is not a dog). Any given dog may vary in its possible qualities, but must have those qualities necessary to a dog. It is those qualities necessary to a dog that we refer to as dogness; and, include such qualities as mammal and canine, for example. There are no degrees or measurements of mammalness or canineness. A thing is a mammal or it isn't. A thing is a canine or it isn't. The attempt to force everything under this notion of, "measurability," leads to absurdities.

Now for your specific arguments:

If the following is meant as a hypothetical argument for the possibility of physical existent lasting indefinitely, it is fallacious:

Let us say that an architect has designed a tower of such durability that no known substance can erode or puncture it.

The assumptions begs the question. The thing to be proved is that it is possible for a physical entity to exist that "no known substance can erode or puncture it," that is, that it is indestructible, and therefore will endure indefinitely. But you cannot assume that, and use that assumption as you proof.

Density is the ratio of mass per unit volume. An infinite density implies the existence of unlimited mass within a limited volume.

The exact expression, I think is infinite density and zero volume, the "amount" of mass is irrelevant, except that is must be greater than the threshold for a black-hole to form. The concept of infinity in this expression is the result of the "space-time" view of physical existence. Mathematically, the gravitation force of a given mass or greater will cause itself to collapse indefinitely. Since the decrease in volume an indefinite collapse would produce results in zero, per your own formula (density is the ratio of mass per unit volume), the density would be infinite.

The problem is the reification of the math notions to physical reality and, I think, a mistake in the math. The relativistic increase in mass as it accelerates inward on itself is neglected. As the velocity of the mass increases under that acceleration, its relativistic mass approaches infinity. There must be some point at which the gravitational force and relativistic mass both become (mathematically) infinite, and that point would be before zero volume is reached, or, if it is reached, both the relativistic mass and its gravitational force would instantly vanish. Then, what happens to the momentum?

I agree with your conclusion that infinite density and zero volume is a mistake, but for different reasons. Of course the simple answer is that zero is not the measure of anything. If something is "zero," it doesn't exist at all, and anything that must have some quality (e.g. volume) to exist, having a zero quantity of it, simply does not exist. I think that is essentially your argument, isn't it?

the universe is not an entity!
That is correct.

On the question of matter being infinitely divisible, I think you miss the point, at least from an Objectivist point of view. Objectivism assumes the entity ontology rather than the matter ontology. Like the universe, "matter" is not an entity. It is, for Objectivists, a quality of physical existents, not a "something."

Your examples all deal with the divisibility of entities, which obviously are not infinitely divisible. But, the mistake with the idea that matter is infinitely divisible is there is no such thing.

There is no such operation in the real world called "division by zero."

That is correct, not only in the real world, but in mathematics as well. The Calculus preforms an operation (derivatives) that is essentially a method of discovering the value of a function, "as if," a thing were actually divided by zero.

Space is not an existent.

That is correct. It is a concept for the relationships between existents, and exists only in that sense. The mistake is not a very bad one however; because most people think of "space" meaning "room" (there is not enough space here for any more furniture), or if we mean the universe (there must be enough space for everything that exists). In that sense, space is, "indefinite," but still not infinite.

Time, too, is not an entity

That is also correct. But I disagree that time is a dimension. The dimensions (of which "three" is only the method we have settled on as the best for dealing with the nature of spatial relationships) pertain only to static relationships. "Time," does not exist without motion, and is a way of measuring the relationships between motions. The fact that time may be treated as a dimension in the mathematical formulas for dynamic phenomena, and interchanged with the other dimensional variables leads to the mistaken notion that time itself is a dimension.

About Life and Logevity

Now, Mr. Stolyarov, an organism is a physical entity, and as a physical entity cannot be indestructible. Furthermore, an organism is a unique kind of physical entity that can exist only so long as the self-sustained process of life continues. It is the life of the organism that makes the organism what it is.

Living organisms are extremely fragile, relative to other physical existents, and the least likely of physical existents to endure over time. The life process is also extremely complex and the more complex the life form, the more dependencies it has on external conditions and resources. The more complex any process is and the more dependencies it has, the more vulnerable it is to destructive events and conditions. The fact that man is the most "adaptable" of living creatures does not make man, in terms of longevity, the most successful life form. Trees and turtles are both much successful.

At our present level of knowledge and technology, the belief that all possible dangers to the life of human beings can be eliminated is a gross superstition. The possible variety of infectious diseases alone is infinite, and while man has slowly eliminated one or two of the most devastating diseases, new ones, never before known, are being discovered almost daily, and those that were nearly eliminated or manageable, are now becoming more virulent, and deadly. It is very strange that we have made so little progress in this one tiny area of threats to human life, and yet some people think we are on the verge of immortality. The next world-wide plague will put an end to that silly notion.

Regi

Post 10

Sunday, July 25, 2004 - 4:36pm

Greetings.

Mr. Ryan: The trouble with using that kind of analysis is that it throws a lot of math out the window. How would I divide a pie into negative three pieces?

Mr. Stolyarov: Actually, 1/-3 is shorthand for (1/3)* -1, or vice versa. I can divide a pie into three pieces, and then give a piece to Jack, in which case I will possess 1/3 of a pie less. Or I can give the pie to Jack first, and have him cut it into three pieces and eat one himself.

Any of the four basic operations (addition, subtraction, multiplication, division) in the real world can have meaning in a particular situation. I can lose 3000 dollars in a given month. In the next month I can gain one-third as much as I had lost in the previous month. The mathematical operation for this is -3000/-3= $1000.

Nothing of the sort can be done with division by zero.

Mr. Ryan: The line of reasoning used to derive the answer "infinity" instead of "nonsensical" for the answer to 1/0 is purely abstract; such an exercise could be considered merely a successful attempt to fill a hole that, if unfilled, would lead to a loss of certitude among mathematicians. I'm not sure how much descriptive value the function a/0 [where a is not equal to zero] has; its use might be confined to an exercise in cleverness derived from a technique that has use all over the realm of higher mathematics.

Mr. Stolyarov: But there is no conceivable purpose for mathematicians to try derive a precise "answer" to a single operation that does not make sense, just as there is no purporse for mathematicians to attempt to figure out what cos(i) equals. The very proposition is non-sensical!

I think division by zero as a single operation could more precisely be replaced by an expression of an indefinite trend.

Mr. Ryan: The above criticism, I should add, does not bear upon what I think of the overall content of your article. Would you say that mistakes relating to the use of infinity result from using the word in a loose way?

Mr. Stolyarov: Largely, and among laymen, this is the case. Most uses of the word "infinity" occur where "indefiniteness" is more proper. On the other hand, I doubt that the modern cosmological orthodoxy is merely committing an honest mistake by using the word too loosely. Michael Miller writes that the renowned astronomer Halton Arp was barred by the majority of research institutions from using their equipment, and his works have been placed under academic ban, as a result of him questioning the Big Bang theory and the redshift fenomenon following his extensive observation. Given that the entire Big Bang theory evolves from the fallacious notion of an "origin" to the universe, derived from a misunderstanding and misuse of "infinity," I would say the cosmologists have quite a personal zeal for their errors.

Thank you for your thoughtful comments.

I am
G. Stolyarov II

Post 11

Sunday, July 25, 2004 - 5:24pm

Greetings.

Mr. Firehammer: This may have been only an expression, but I do not know what a "qualitative scale," would be. Not all qualities are measurable, for example, absolute qualities of relationship (uncle, parent, child, inside, outside) or state (on, off, true, false).

Mr. Stolyarov: How about this: Richard Cobden is more pro-free-market than John Stuart Mill, who is more pro-free-market than Benjamin Disraeli. There are no specific units of measurement to quantify �pro-free-marketness,� but a relative hierarchy nevertheless exists. This is a qualitative scale, which is indeed different from the absolute relationships you mention.

Mr. Firehammer: Any given dog may vary in its possible qualities, but must have those qualities necessary to a dog. It is those qualities necessary to a dog that we refer to as dogness; and, include such qualities as mammal and canine, for example. There are no degrees or measurements of mammalness or canineness. A thing is a mammal or it isn't. A thing is a canine or it isn't. The attempt to force everything under this notion of, "measurability," leads to absurdities.

Mr. Stolyarov: Let us presume that paws are a necessary quality of a dog. A dog must have paws, but the length of its paws may vary, as may the degree to which the dog uses them, and the mass that paws can have in a dog. Whether or not paws are present is an either-or question, but the paws entail measurable quantities of each quality about them.

The information sciences have an answer to measuring either-or qualities. Therein, the �on� state, or the presence of a quality, is designated as �1,� and the �off� state is designated as �0.� In this way, could either-or qualities also not be considered measurable within a range, except the range only encompasses two integers and is exclusive to integers?

Mr. Firehammer: Let us say that an architect has designed a tower of such durability that no known substance can erode or puncture it.

Mr. Stolyarov: Let us say the architect has tested every known substance against the tower, and nothing happened to the tower. Each time a new substance is discovered, the architect tests it, and nothing happens. This is what I meant to say.

By the way, since all simultaneous quantities must be finite, do you concede that there exist 1) a finite quantity of existents, 2) a finite quantity of matter, and 3) a finite quantity of diseases at any given time?

(Do you see where this is leading to?)

Mr. Firehammer: I agree with your conclusion that infinite density and zero volume is a mistake, but for different reasons. Of course the simple answer is that zero is not the measure of anything. If something is "zero," it doesn't exist at all, and anything that must have some quality (e.g. volume) to exist, having a zero quantity of it, simply does not exist. I think that is essentially your argument, isn't it?

Mr. Stolyarov: Yes, it is. I point out that the modern theory of singularities, if consistently applied, would have to concede this, and thus disprove itself.

Mr. Firehammer: Your examples all deal with the divisibility of entities, which obviously are not infinitely divisible. But, the mistake with the idea that matter is infinitely divisible is there is no such thing.

Mr. Stolyarov: I agree that matter is not an entity. It is a constituent of entities. To some extent, is can be called a quality in that the quality, �mass,� is defined as �the amount of matter in an object.� However, the question, �Is matter infinitely divisible?� asks, �Can anything be made of infinitely smaller mass?� It can be refrased as, �Can a measurement of mass be infinitely small?� I claim that this question is outside the realm of man�s utility and cognition; it is devoid of value.

Your discussion of time and longevity will be addressed shortly. Of course, you can expect vehement disagreement on the latter issue.

I am
G. Stolyarov II

The Prologue: http://www.geocities.com/rationalargumentator/eac_prologue.html

Chapter I: Protector's Summons: http://www.geocities.com/rational_argumentator/eac_chapter1.html

Order Eden against the Colossus at http://www.lulu.com/content/63699.

Post 12

Sunday, July 25, 2004 - 6:41pm

Your discussion of time and longevity will be addressed shortly. Of course, you can expect vehement disagreement on the latter issue.

I expect it, and it better be good.

Thanks for the comments.

Regi

Post 13

Sunday, July 25, 2004 - 9:31pm

Greetings.

Mr. Firehammer: The dimensions (of which "three" is only the method we have settled on as the best for dealing with the nature of spatial relationships) pertain only to static relationships. "Time," does not exist without motion, and is a way of measuring the relationships between motions.

Mr. Stolyarov: I have a problem with your last statement. Let us imagine a state of affairs in which very little movement takes place, even on a molecular level (let us say that a certain environment has come to exhibit a temperature very near absolute zero). Does time in that environment pass more slowly than in the status quo? I would answer with a resounding, �No!�

Time, in order to have any meaning as an abstract measurement tool, must be uniform. It is not time that follows from motion, but motion that follows from time. The chronological �distance� between two isolated acts of motion is analogous (though not the same) as the spatial distance between two objects. The greater this distance, the slower an object moves. But, in order to accurately determine which objects are faster than other objects, a uniform time scale is needed, which is not �relative� to the object, but rather absolute and universal (time relations are expressed in the sense of �earlier� or �later,� but these are not measurements themselves). The scale�s units would need to be arbitrary, but uniform still.

I would say that, if an object does not move or change, there is still need for the concept of time, except we do not know how far chronologically its next state is separated from its present one; its next state has not yet occurred, and the duration of its present state is indefinite. But the uniform meter of time keeps beating, and if, suddenly, a molecule shifts in that object, there will be a difference between whether that molecule shifted 15 million years after the static object was first observed, or 15 billion years. The moment the molecule shifted would not be the beginning of time.

Now, on to the longevity discussion.

Mr. Firehammer: Living organisms are extremely fragile, relative to other physical existents, and the least likely of physical existents to endure over time. The life process is also extremely complex and the more complex the life form, the more dependencies it has on external conditions and resources.

Mr. Stolyarov: This does not make the more complex entity necessarily more fragile. For example, a skyscraper is more complex than a mud hovel. Yet it is also more endurant. The skyscraper�s complexity reinforces its structure and durability, just like the human organism�s complexity and need for various resources reinforces its ability to creatively adapt to and survive in conditions that simpler creatures, who require a smaller variety of resources, cannot endure in.

For example, it is well known that a species that can digest only a single type of food is far more likely to go extinct with the slightest fluctuation of environmental conditions than an omnivorous species whose digestive system is more complex and has more �options� built in, thus being able to process a greater variety of food.

Thus, the length, quality, and prospects of man�s life will only increase as his surroundings and needs become more complex. Each need answered results in many newly discovered ones, as an individual advances on the hierarchy of needs. An individual in an ever-progressing environment will constantly get more, but his appetite for even greater acquisitions will increase, and at an accelerating pace. This is why men of our time are so concerned with cleanliness, sanitation, or freedom from household pests, qualities that almost all pre-industrial peoples could not even conceive of. This is a wonderful trend! The fact that you need more does not preclude the fact that you had also gotten what you needed before, which fortifies your chances of survival and prosperity.

Mr. Firehammer: The fact that man is the most "adaptable" of living creatures does not make man, in terms of longevity, the most successful life form. Trees and turtles are both much successful.

Mr. Stolyarov: But only man can study the genotypes of trees and turtles to determine what makes them so long-living. And only man can use genetic engineering to adjust his own genome accordingly. (The human genome has already been mapped, and new genes are being identified as we speak; the turtle genome should be a lot easier to decode.) Other life forms cannot change their life expectancy because they do not have the rational faculty to purposefully exploit and alter their environment. Man does, and man has used it to quintuple his average life expectancy (which, in the pre-agricultural age, could not have exceeded 15 years) thus far, with the last century yielding a 29-year growth in the United States. The rate of progress has accelerated, and, with increased technological capacity and sufficient political freedom, there is no reason why this should not continue. I stress the latter criterion: nature is passive more often than not; if man tries to put it under its yoke, it will obediently comply. The only thing that can truly stop man from becoming as formidable as he seeks is man, in the form of his own self-doubt, or the ideological paradigms and political restrictions that others inflict.

The plot of Eden against the Colossus revolves around this idea, and how, with sufficient technology, the fully rational man will become impervious to the antiprogressive influences of others.

Mr. Firehammer: At our present level of knowledge and technology, the belief that all possible dangers to the life of human beings can be eliminated is a gross superstition.

Mr. Stolyarov: Dr. Aubrey de Grey of Cambridge University (to an interview with whom Mr. Geddes had linked on the �Affirming Life� thread) states:

http://www.betterhumans.com/Features/Reports/report.aspx?articleID=2003-08-25-3
�So, am I optimistic? Certainly with regard to indefinite lifespan, yes. As I said earlier, I think there will be only a short interval between the time when we first have genuine life extension treatments and the time when we're improving those treatments faster than we're aging, which is all that's necessary to give us an indefinite lifespan. We currently have no idea what sort of treatments we'll need to keep us going when we're 200, but that's okay, because we won't need those treatments for over another 100 years. So long as we look hard at 180-year-olds as soon as we have any, and also at 80-year-old chimpanzees once we have them (which will be sooner, of course) for signs of trouble on the horizon, we'll have time to head off that trouble before it kills anyone.�

In addition:

�If my plan works in the timeframe I have mentioned, no one presently under 30 in wealthy nations need have a life expectancy under about 1,000 years (which is how long we'd live now if our risk of death per unit time at any age were the same as it currently is at age 15 or so). In practice we will be a lot more risk-averse, so I expect life expectancy to be at least 5,000 years. So, even if it takes 500 years to develop, most of us who stick around long enough to get an indefinite lifespan will still be around for "slow teleportation" (presuming it's possible at all).�

I have quite a compelling interest in the matter, for, you see, I am under 30, and, even by my present life expectancy (which, for a regularly exercising and fairly affluent nonsmoker is in the high eighties), can live well into the latter half of the century. The technologies that will be available then, given a concerted scientific and ideological effort toward life extension, might give me the indefinite life. I rather look forward to not fighting a losing battle with a declining organism.

Mr. Firehammer: The possible variety of infectious diseases alone is infinite, and while man has slowly eliminated one or two of the most devastating diseases, new ones, never before known, are being discovered almost daily, and those that were nearly eliminated or manageable, are now becoming more virulent, and deadly.

Mr. Stolyarov: First of all, it is necessary to admit that there is a finite, not �infinite,� amount of diseases currently in existence. The number of entities simultaneously existing must always be finite. Technology will someday find the means to combat each individual disease, because there is a finite amount of them, but technology will have indefinite time to progress. Moreover, new diseases can only originate by evolving from old diseases. With our already rapidly growing knowledge of genetics, we can preempt the mechanisms that result in the necessary mutations for new disease evolution and assume absolute control over the genetic code of each living entity (by steps, of course, and spanning a lengthy period of time). Each man will be master of his own code, and all non-rational life can be designated as somebody�s property, and the owners shall see it in their interests that their property is genetically altered to serve only benign, not malignant, purposes.

Mr. Firehammer: The next world-wide plague will put an end to that silly notion.

Mr. Stolyarov: You must mean the next Third-World-wide plague, because of the immense gap in living standards that exists between the developed countries and the Third World. The plague is not a major peril in any industrialized nation; antibiotics can easily remove it, and its cases have been virtually non-existent since the Industrial Revolution.

Atrocious things happen in the Third World every minute, mostly because of the horrendous tyrannies that its denizens are subject to, and the premature withdrawal of the colonial powers, who left tribal savages with automatic rifles to replace them. This has very little bearing on what happens here, however, though, if the Third World suddenly awakened to Reason, more economic connections might improve our standard of living.

I am
G. Stolyarov II

The Prologue: http://www.geocities.com/rationalargumentator/eac_prologue.html

Chapter I: Protector's Summons: http://www.geocities.com/rational_argumentator/eac_chapter1.html

Order Eden against the Colossus at http://www.lulu.com/content/63699.

Post 14

Sunday, July 25, 2004 - 10:14pm

Greetings.

Mr. Firehammer, the following is an excellent illustration of my point:

"The Fable of the Dragon-Tyrant" by Nick Bostrom: http://www.nickbostrom.com/fable/dragon.html

I am
G. Stolyarov II

Post 15

Monday, July 26, 2004 - 6:48pm

Hi G.

Thanks for the always thoughtful responses.

How about this: Richard Cobden is more pro-free-market than John Stuart Mill, who is more pro-free-market than Benjamin Disraeli. There are no specific units of measurement to quantify �pro-free-marketness,� but a relative hierarchy nevertheless exists. This is a qualitative scale, which is indeed different from the absolute relationships you mention.

Of course there are qualities that are measurable in the comparative sense, but my point is that some qualities are not measurable. In those cases, Rand's definition of a concept does not work.

Whether or not paws are present is an either-or question, but the paws entail measurable quantities of each quality about them. ... the �on� state, or the presence of a quality, is designated as �1,� and the �off� state is designated as �0.� In this way, could either-or qualities also not be considered measurable within a range, except the range only encompasses two integers and is exclusive to integers?

Sure, to both examples, but both are a stretch, and unnecessary ones. Rand was mistaken and only needed to change "particular measure left out," to, "particular differentiating qualities left out," (since "measurement" is itself a quality), and her definition would have fit all possible cases and would not require the mental gymnastics that is required to force everything under the "measurement" definition.

Let us say the architect has tested every known substance against the tower, and nothing happened to the tower. Each time a new substance is discovered, the architect tests it, and nothing happens. This is what I meant to say.

I do not see how this changes your argument, it just delays it indefinitely. In any case, however many new substances he tests, none preclude the future existence of a substance that can destroy the tower. Unless you assume this has already gone on forever, it cannot be used as an argument that the tower is indestructible, (or that such a tower is possible).

By the way, since all simultaneous quantities must be finite, do you concede that there exist 1) a finite quantity of existents, 2) a finite quantity of matter, and 3) a finite quantity of diseases at any given time?

(Why do you say "simultaneous quantities" when just "quantities" would do. All measureable quantities must be finite.) So, 1- yes, 2-it depends on what you mean by matter, if you mean, "mass," [an attribute of physical existents], yes, if you mean matter as an ontological something out of which things are made, I do not believe there is any such thing, and 3-yes.

(Do you see where this is leading to?)

Sorry, Gennady, I do not.

I agree that matter is not an entity. It is a constituent of entities.

It is not terribly important but I cannot quite agree that matter is a "constituent" of entities. That is known as the matter ontology, which Objectivism flatly rejects, and I agree with Objectivism on that point. Existence consists only of existents. Those existents are physical, or "material" and the term "matter" only has meaning as an extension of the qualities of physical existents, that is, "matter" is any physical existent or existents, and apart from physical existents, the term "matter" has no meaning.

Ayn Rand was a bit confused by this notion, by the way, and sometimes made statements that implied a matter ontology rather than an entity ontology, like, "matter cannot be created or destroyed, it can only be changed," which I assume means there is some kind of absolute totality of physical existence, probably in terms of total mass, although I'm not sure she would have understood what that means. I am quite frankly not sure what she meant. She was not talking about the conservation of matter and energy, as far as I know, even though it sounds like that.

Thanks again.

Regi

Post 16

Tuesday, July 27, 2004 - 4:52am

As with most threads that become really long before I even see them, I've only read about 10% of this one. I hate announcing it every now and then, but I have a sick-assed demonic vision impairment (otherwise known as macular degeneration), and thus can only read so much per second. I say this so it makes sense if I post something that another member has already posted or whatever, which is better than not revealing my situation and coming off as a near politician instead, a slug-brained fool.

Anyway, in the random paragraphs I did read in this thread, someone said that no part of existence can be eternal, or thereabouts. Which is something I take issue with, in my uneducated arrogance. While explaining my reasons for this view, I'll focus on what I call the "experiencer," often labelled consciousness and such by others.

Now, if an experiencer isn't eternal, then that means it's reducible to two or more parts, right? Whereas I don't think that an experiencer can be reduced. Or, conversely, built. To my possibly nuts way of thinking, the experiencer is eternal. And by the way, I don't pose this theory as a challenge against Objectivism; I see it as being a question that Objectivism kind of tinkers with like a hobby. Whether I'm right or wrong, Objectivism is still valid in the here and now.

When two separate parts of existence merge, they form a new part. However, that part in total is still a unity of two. It's not really one at all, for where can you say "one" actually exists? Prick it somewhere with the pin of pins and you'll touch something that isn't a singularity at all, precisely because it can be pricked in the first place. Whereas, the experiencer is different - it is a singularity. If two parts were able to form an experiencer, as people claim they can, a third would exist, if you ask me - making it impossible. I mean, if two or more parts can create an experiencer, it's like saying one plus one can equal three. What's doing the experiencing if reducible parts can build the entity that's experiencing? How can an experiencer be by itself while other individual parts form it, creating more than is in their capacity to achieve? Jesus christ this is hard to explain!!!! LOL

Ask yourself this: when something experiences, what is doing it? Nothing that can be created, in my view. There's always a third that two can't become. Always a single beyond our mental building-block creations, a single part more than is possible to be built by however many parts we try to warp into it.

If some scientist or the like has an explanation for how experience is possible (or consciousness or whatever), let me know. I'm very interested in this subject.

I once tried explaining everything above to a poet friend of mine (now dead LOL) and he just looked at me with twin zeros in his eyes. Sheesh.

-D

(Edited by Darin on 7/27, 5:01am)

Post 17

Tuesday, July 27, 2004 - 6:17am

Hi Gennady,

About time. I think you have been overly influenced by Mr. Einstein. You think of both time and space as, "things," whether you intend to or not. For example, "Time, in order to have any meaning as an abstract measurement tool, must be uniform." Only things need to be uniform.

Here is what I mean. If the universe were static everything in that universe could be described in terms of its "shape" and relationship to other things. Now both shape and relationships in a static world would be purely "geometric," that is, described in terms of positional relationships. A thing's shape would be described by all the points (positions) in all its parts. The relationship between things wold be described by their relative position to one another.

Even in this world, when its dynamic aspects are ignored, the only attribute that is required to describe it is position. To describe any position only two qualities, or metrics, are required: distance and direction. The direction and distance of all things is "measured" by some unit of "measure" which is usually some actual positional relationship (the distance between the beginning and end of the King's heel and toe is a foot, the angular difference between the direction of the physical north pole and any other point is east, northwest by west, etc.).

But the dynamic world introduces a new aspect, "change." In the case of motion, the change is change of position. A change of position means a change in the two "metrics" by which positions are measured, distance and direction. Any motion may be described simply by describing the change in the relationship of anything to everything else in terms of its change in position and direction. (A moved three feet in the direction C.)

But just as positions are measured in relationship to other positions, motions can be measured in relationship to other motions. The metrics by which the relationship between motions is measured are time and velocity.

Time compares a motion to some standard motion (like a clock) and is measured in terms of how much the standard motion moves (e.g. one minute) relative to some "measured" motion (change in position in terms of distance, e.g. on mile). Velocity compares the distance moved to some standard motion (like a clock) and is measured in terms of how much the measured motion moves (changes position, e.g. sixty miles) relative to a fixed change in the standard motion (1 hour).

Just as direction and distance are interdependent aspects of positional relationships, time and velocity are interdependent aspect of change in position (motion). Where there is no change in position, there is no motion, and neither time or velocity would have any meaning.

The mistake I think you are making is in assuming the word "relative" means non-determined. The relationships defined by the metrics, direction, distance, time, and velocity are absolute, and what they are whether we measure them or are even aware of them. But time is only the measurement of a relationship between the motion of existents, not a thing in itself.

(The next level of change is change in motion, or acceleration, by the way. Both mass and energy can be defined entirely in terms of acceleration.)

Now, on to the longevity discussion.

Yes.

... the more complex entity [is not] necessarily more fragile. For example, a skyscraper is more complex than a mud hovel. Yet it is also more endurant. The skyscraper�s complexity reinforces its structure and durability, just like the human organism�s complexity and need for various resources reinforces its ability to creatively adapt to and survive in conditions that simpler creatures, who require a smaller variety of resources, cannot endure in.

It is true that complexity alone does not make a thing more vulnerable, but, all other things being equal (or even similar) the more complex is always more vulnerable. The skyscraper/mud hovel comparison is not germane. The proper comparison would be two skyscrapers, one of a simple design and one of a complex design.

As for living organisms, the simpler organisms are always less vulnerable; it is why they survive. The more complex organisms require a great deal more to sustain themselves; complexity demands more complexity.

Notice the subtle switch from the durability of existents to "species." For example, it is well known that a species that can digest only a single type of food is far more likely to go extinct with the slightest fluctuation of environmental conditions than an omnivorous species whose digestive system is more complex and has more �options� built in, thus being able to process a greater variety of food.

It is well known that an organism that only requires a single type of food is more likely to survive, if there is only that kind of food in the environment than an omnivorous organsim that requires many different kinds of nutrients to survive. Go to the desert and see how many omnivores are able to survive.

Thus, the length, quality, and prospects of man�s life will only increase as his surroundings and needs become more complex. Each need answered results in many newly discovered ones, as an individual advances on the hierarchy of needs. An individual in an ever-progressing environment will constantly get more, but his appetite for even greater acquisitions will increase, and at an accelerating pace. This is why men of our time are so concerned with cleanliness, sanitation, or freedom from household pests, qualities that almost all pre-industrial peoples could not even conceive of. This is a wonderful trend! The fact that you need more does not preclude the fact that you had also gotten what you needed before, which fortifies your chances of survival and prosperity.

Now you have mixed individuals, "An individual in an ever-progressing environment will constantly get more ..." and species, "prospects of man�s life will only increase as his surroundings and needs become more complex." Is it the survival of "man's life," or "a man's life," that are supposedly advanced by complexity of the organism (not the complexity of society and culture)?

I am not suggesting an advanced industrial society is not preferable or that it does not make possible both a longer and more enjoyable life for individuals. I am saying that the vulnerabilities increase as well. Certainly the life of an individual working in a skyscraper is preferable to one toiling from dawn to dusk in the dirt just to feed himself. But consider 300,000 such poor individuals. It wold be almost impossible for a single event to kill them all, but put them in a skyscraper and two hijacked planes will do it.

Man does, and man has used it to quintuple his average life expectancy (which, in the pre-agricultural age, could not have exceeded 15 years)

Please check you facts, or in this case, just think about it. In pre-industrial ages, puberty was greatly delayed. Humans would have become extinct if they only lived to 15 years, because they never would have reproduced. In every period of known history, there have been societies in which most men lived to the sixties. Some societies (probably due more to genetic characteristics and cultural differences) had average ages exceeding 80.

My point is that if it were only living as long as possible that were the purpose of life, men are failures at the purpose of life, or at least comparative failures relative to other organisms. Longevity is not the purpose of life. The purpose of life pertains only to individual organisms. The purpose of one's life is to enjoy it, not to make it last as long as possible.

Regarding Dr. Aubrey de Grey of Cambridge University

The world is full of quacks and crackpots and they come in all flavors, from college professors to social reformers. All of them, without exception, are extremely convincing fellows, else you would never have heard of them. I have no interest in people's opinions, especially if they are, "experts." I am convinced by clear explanations which I can understand. If you or anyone else believes human life is going to be extended to any great degree in the near future, explain exactly how it is going to be done; but, please, do not expect rational people to be convinced by blather such as, "I think there will be only a short interval between the time when we first have genuine life extension treatments and the time when we're improving those treatments faster than we're aging, which is all that's necessary to give us an indefinite lifespan. We currently have no idea what sort of treatments we'll need to keep us going when we're 200, but that's okay, because we won't need those treatments for over another 100 years."

He has absolutely no idea what treatments we'll need, but he's absolutely certain we'll have them. Sure.

I have quite a compelling interest in the matter, for, you see, I am under 30, and, even by my present life expectancy (which, for a regularly exercising and fairly affluent nonsmoker is in the high eighties) ...

My life expectancy is in the nineties for a smoker who lives a very risky life. All my relatives live into their nineties. My grandfather was a pharmacist and worked every day of his life, including the day he died, because he loved and enjoyed his work. He was a chain-smoker his entire life, as were his children. One of my aunts (his daughter) recently died sitting at her kitchen table. She had just extinguished a cigarette. She was 97. Yesterday my father celebrated his 89th birthday with a drive to the mountains. He may not live as long as the others. He quit smoking about 10 years ago. Nicotine helps keep the mind sharp and staves off Alzheimers and Parkinson's disease. It is unhealthy for some people to not smoke. No one is a statistic. Everyone is different.

Technology will someday find the means to combat each individual disease, because there is a finite amount of them, but technology will have indefinite time to progress.

At any time in history there are a finite number of diseases, but at any time in history there are a finite number of cures. There are always more diseases than there are cures, (else no one would be sick), because new diseases form for which there are not cures yet. There is no reason in the world to suppose cures will be developed faster than the emergence of new diseases. I am not saying that cannot be, only that there is no reason at the present time to think so.

You must mean the next Third-World-wide plague, because of the immense gap in living standards that exists between the developed countries and the Third World.

Nope! I mean world-wide, pandemic like the 1918 flu epidemic.

" ... in 1918 the Great Flu Epidemic felled the young and healthy virtually overnight. An estimated forty million people died as the pandemic raged. Children were left orphaned and families were devastated. More American soldiers were killed by the 1918 flu than were killed in battle during World War I. And no area of the globe was safe. Eskimos living in remote outposts in the frozen tundra succumbed to the flu in such numbers that entire villages were wiped out. If such a plague returned today, taking a comparable percentage of the U.S. population with it, 1.5 million Americans would die, which is more than the number killed in a single year by heart disease, cancers, strokes, chronic pulmonary disease, AIDS, and Alzheimer's combined."

Mr. Stolyarov, there is no cure for flu. There is no known reason why there cannot be another flu pandemic. It is not known if a vaccine is even possible. There is still not a vaccine against SARS, which, if only a little more virulent and not contained might easily have been another great pandemic.

So this, The plague is not a major peril in any industrialized nation; antibiotics can easily remove it, and its cases have been virtually non-existent since the Industrial Revolution, is just a mistake. Unless you are referring specifically to bubonic and pneumonic plague (variations of the same disease), the entire industrialized world was "plagued" by pandemic flu in 1918.

Regi

Post 18

Tuesday, July 27, 2004 - 8:33pm

Greetings.

Mr. Firehammer: Rand was mistaken and only needed to change "particular measure left out," to, "particular differentiating qualities left out," (since "measurement" is itself a quality), and her definition would have fit all possible cases and would not require the mental gymnastics that is required to force everything under the "measurement" definition.

Mr. Stolyarov: It is interesting to speculate as to what Rand actually meant by the word "measurement" and whether her meaning encompassed the examples I had provided. Perhaps you are correct, and I shall ponder this over further.

Mr. Firehammer: I do not see how this changes your argument, it just delays it indefinitely. In any case, however many new substances he tests, none preclude the future existence of a substance that can destroy the tower. Unless you assume this has already gone on forever, it cannot be used as an argument that the tower is indestructible, (or that such a tower is possible).

Mr. Stolyarov: Perhaps this does not preclude the coming about of a new substance that will destroy the tower, but there is no guarantee that this substance exists or will come about; thus it is absolutely improper to say that the tower will inevitably be destroyed someday. We do not know this, and the tower could have an indefinite existence. For the moment, we know of nothing that could destroy it.

Mr. Firehammer: (Why do you say "simultaneous quantities" when just "quantities" would do. All measureable quantities must be finite.)

Mr. Stolyarov: To differentiate from quantities that accumulate chronologically. For example, there need be no finite quantity of "years passing before an entity ceases to exist," as I explained in my tower example. We do not know if the entity will ever cease to exist! At any chronological instant, however, all quantities are finite, ages included.

Nor can we adequately answer the question: "How many entities have ever existed?" if we assume a time scale that is indefinite in both directions. This may not be a necessary question, and I have yet to decide whether it is an absurd one. However, I do not know whether there could have ever been a time when the first entity came to be. What caused it to be? All actions, that could have caused it to be, must have been performed by some other entity. Thus, I am inclined to think that there was no first entity! (Rather, entities have become increasingly more complex with the passage of time).

I am interested in hearing your thoughts on this issue? Is this question a valid one, and can a finite quantity ever address it? It is because of problems such as these that I choose to use the term "simultaneous quantities," however.

I will continue this soon.

I am
G. Stolyarov II

Post 19

Wednesday, July 28, 2004 - 10:16am