Roger's Web Site of Metaphysics, Physics, Cosmology and Set Theory Ideas
Hi. Welcome to my web site. My name is Roger. I'm a biochemist in Columbus, Ohio, but one of my hobbies is thinking about infinite sets, philosophy, metaphysics and physics. Some of my ideas about these subjects are listed below. As with most ideas, mine are built on all the thinking that has come before me. So, I'd like to credit all those who have contributed in this area in the past and who are doing so today. Please forgive me if I do not reference everything directly. In developing these ideas, my philosophy has been to assume as little as possible, even about the most basic of things, and then try to develop logical and internally consistent ideas. Because I'm an amateur, many academics would consider me a "crackpot" and dismiss the ideas out of hand. However, in reading these ideas, I hope that you consider them on their individual merits and not based on their amateur source. After the ideas, some links to other, not all related, sites are also listed. Thanks.
New: I've added a couple of pages of new ideas on the question of "why is there something rather than nothing?" at the bottom. Thanks.
Infinite Sets: A Contextual, or "Physiological", View of the Relative Size of an Infinite Subset Compared to its Parent Infinite Set
Brief overview:
This paper relates to the mathematical method for comparing the relative size
of a single infinite set (say, the set of all positive integers) with one of
its subsets (say, the subset of all even integers). Starting with the single
infinite set of all the positive integers as the experimental system being studied, the goal is to determine the number of even integers relative to the total number of all the positive integers within the context of this single set. Traditionally, this size comparison is done by extracting the evens as a separate subset and then pairing off its elements one-to-one with those of the original set in order to show the counterintuitive result that they are the same size, as opposed to the intuitive view that there are only one-half as many evens as total positive integers. However, it is suggested here that even though this size comparison is done in the mind, it is still an "experiment" and should follow sound principles for conducting an experiment. One of these principles is that when the experimental processing changes the system being studied compared to the original system, then the results obtained are not necessarily what would happen in the original system. That is, an experimetal artifact and incorrect results can be created. By considering the even integers as a separate subset, one in effect removes them from the single, original, set, which necessarilly changes the relationships present between elements in the single set system. This means that in the separate subset of evens, there is no accompanying of each even with an odd, as there is in the single, original set. This lack of accompanying odds in the subset is what then allows the one-to-one pairing off of evens and the set of all positive integers. Only when maintained as an integral part of their natural millieu, the single set, where the fixed relationships of the evens with the odds is maintained can the true number of evens relative to the total integers in the single set system be ascertained. An analogy in biochemistry is that when a nucleus is removed from an intact cell, relationships between the nucleus and the rest of the cell are changed and often different than what occurs in the intact cell. In conclusion, it is suggested that, when considering a single, infinite set system, the traditional method for infinite set-subset size comparison creates experimental artifacts (changes brought on by "experimental processing"), which render questionable the result that the subset and the original set are the same size.
Infinite Sets: How Do Internal and External Observers View Infinite Sets?
Brief overview:
It is suggested that how a hypothetical observer would "view" an infinite
set depends on whether or not that observer is internal to or external to
the set. A finite-sized, internal observer would see the set as being
composed of discrete chunks, whereas a hypothetical, infinite, external
observer would not be able to distinguish individual elements and would,
thus, view it as being composed of a continuous space. Similarities of
these differing views of a single infinite set and the discrete and
continuous views of the universe as seen by quantum physics and relativity,
respectively, are noted.
Ideas and Concepts and Their Relationships to "Real World" Objects and Cosmology
Brief overview:
This paper discusses the relationships between ideas (in the mind reference
frame) and "real world" objects (in the external-to-the-mind reference
frame). First, an idea is defined as a complete description of something.
Assuming the materialist view that the mind is composed of biochemical
molecules, then an idea in the mind frame is a complete description where this
description is composed of biochemical molecules, which are themselves
composed of atoms, particles, etc. A simple idea is defined as a complete
description with a specific time and place stamp (that is, the idea of Fido
the dog in Denver on Saturday). A concept is defined as a complete
description without a specific time and place stamp (that is, a generic dog at
any place and time). Moving to the external-to-the-mind reference frame, a
"real world" object in this frame is defined as a collection of atoms,
particles, etc. that is a complete description of itself. Thus, except for
the reference frame, ideas and objects have similar definitions. This leads
to the conclusions that objects, within the external-to-the-mind reference
frame, can also be thought of as ideas, in that frame, and that the
external-to-the-mind reference frame can be thought of as a type of mind (a
reference frame containing ideas). An application to cosmology is the
suggested answer to the question of how one gets a real universe from
mathematical concepts or bits of information that describe it. The proposed
answer is that one doesn't. The concepts/bits are themselves the constituents
of the universe. After all, concepts and objects have the same definitions.
Furthermore, relative to one another, two concepts or bits of information
would appear to be as real to each other as two "real world" particles appear
to each other. Whether or not a description is called a concept or an object
is an arbitrary distinction only. Thinking of objects as ideas also allows
one to see interesting similarities between the formation of an idea space in
the mind (ie, the process in which, starting with the picture of a single
concept, such as that of a ball, the mind can then instantly picture a larger
number of concepts, or balls, surrounding it) and the big bang process (starts
with singularity and goes to larger space-time), symmetry breaking (in going
from concept to simple idea, see below), non-locality (the mind can seemingly
instantaneously envision a larger number of concepts), and the
observer-observed relationship (first concept is the observer; once it exists,
the succeeding concepts, or observed, can form)
Why Do Things Exist? Proposed Definitions For the Terms "Existence", "Exists", "What Is", and "Location"
Brief overview:
The principal findings of this paper are proposed definitions of the words
and phrases "existence", "exists", "what is", and "location". They are
all centered around the concept of a whole, or an entirety. A whole, by
virtue of its wholeness or completeness, has an edge or boundary (wholes
without edges or boundaries, indicating their completeness, wouldn't be
wholes). This edge is not a specific structure but is, rather, just the
wholeness, entiretyness or completeness of the whole itself. Because it
has an edge or boundary, a whole becomes something that has substance;
that is, it is a "thing"; it "exists"; it "is". The edge is the key to
making any whole real and capable of being called "existent" or "is". The
above leads to the definition of "existence" as a whole (with its
associated edge) and of "exists" as the property of being whole. An edge
also allows a whole to be observed and, thus, described as occupying
spatial volume. One application of the idea that things that "exist" are
whole amounts (with their associated edges) is that it provides a natural
explanation for why there are three spatial dimensions. Three dimensions
is the smallest number of dimensions needed to fully enclose a
whole/volume with an edge and, thus, make it "exist". The definitions of
"what is" and "location" are also based on the concept of a whole.
Why Is There Something Rather Than Nothing? Evidence that "Non-Existence" Can
be Considered to "Exist"
Brief Overview:
Based on the concept of a "whole" and its use in the definition of existence
given in the above paper, evidence is presented here that what is
traditionally thought of as non-existence can actually be considered to
exist. Briefly, assume that everything that is normally thought of as
existing (including physical objects, energy, space-time, vacuum, the mind,
mathematics, ideas, concepts, etc.) takes up non-zero volume as seen from our
reference frame (ie, obervation point). This leads to the next assumption,
then, that total zero volume as seen from our reference frame would be what is
normally called non-existence. It is suggested here that this zero volume
meets the definition for being a whole and, therefore, exists as shown by the
answers to the following questions: 1.) Does zero volume include all? Yes.
2.) With zero volume, is any volume, thing or part lacking, missing or
omitted? No. 3.) With zero volume, is there any volume or thing anywhere
else? No. Therefore, zero volume, by definition, is a whole or entirety.
And, by virtue of this wholeness, it has an edge, indicating its wholeness or
completeness. The edge gives substance to the wholeness of zero volume and
makes it capable of being called "existent" or "is". This edge is not a
separate structure but is just the wholeness/entiretyness of the zero volume
itself. The existence of zero volume can only be perceived from a reference
frame that can see the wholeness of the zero volume. Arguments supporting
this hypothesis are presented. In sum, this paper proposes that an answer
to the philosophical question of why there is something rather than nothing?".
It suggests that this question is misleading in that "nothing" (ie,
non-existence) and "something" (ie, existence) are one-and-the-same.
Why Is There Something Rather Than Nothing? Mechanism for the Expansion of
the Zero Absolute Volume State of Non-Existence into the Non-Zero Relative
Volume of Existence
Brief Overview:
A long standing question in philosophy has been "why is there something
rather than nothing?". A mechanism for the formation of the non-zero relative
volume of our universe (ie, "something") from the zero absolute volume of the
existent state of non-existence (ie, "nothing") is proposed here. Briefly:
1.) Non-existence is defined as zero volume.
2.) The zero volume of non-existence meets the definition of a whole.
3.) Wholes have edges, or boundaries, indicating their wholeness, and "exist".
A hypothetical observer that could see the wholeness, or edge, of the
existent state of non-existence would view this state as a sphere because
the zero volume inside the edge is the same distance "across" as seen from
all perspectives. This is the definition of a sphere.
4.) Edges have outsides. Assuming zero volume, what is outside the edge of
the state of non-existence? There can only be more zero volume (ie, a
lack of volume). That is, a second instance of zero volume along the
outside of the edge of the initial state of non-existence has been
formed. Because there can be no distance smaller than the diameter of the
state of non-existence, the zero volume along the outside of the spherical
circumference of the initial state of non-existence is quantized into
chunks, or "locations" equal in size to the diameter of the state of
non-existence. The zero volume at each of these "locations" is a whole,
has an edge and exists. Therefore, a second layer of states of
non-existence has been formed around the spherical outside circumference
of the initial state of non-existence.
5.) Each state of non-existence in the second layer (ie, around the outside of
the edge of the first state of non-existence) also has an edge with an
outside that forms a third layer of instances of the state of
non-existence. This process continues ad infinitum.
6.) Each of the edges of the states of non-existence formed in the above
process is in a different location (relative to one another), meaning
that, between them, non-zero relative volume has been formed. Also, each
state of non-existence would look as real, relative to one another, as two
units/particles of what we call existence would look to one another.
Therefore, overall, a non-zero relative volume of "real-looking" existent
states (ie, "something") has been formed from the zero absolute volume of
non-existence (ie, "nothing").
In conclusion, a mechanism for the expansion of the zero absolute volume
of what is traditionally called non-existence (ie, "nothing") into the
non-zero relative volume of existence (ie, "something") is proposed. In this
mechanism, the state of non-existence is the fundamental building block, or
quantum unit, of what we call existence. In standing with this idea, the
above process shows several similarities to physics and cosmology as well as
providing a mechanism for the presence of energy. For instance, it shows
similarites to the big bang process with its early symmetry breaking,
non-locality, the observer-observed relationship of quantum physics, the
holographic principle of string theory and time.
Why Is There Something Rather Than Nothing? Summary.
Brief Overview:
The above two papers proposed a possible solution to the question in
philosophy of "why is there something rather than nothing?". That is, a
possible mechanism for the formation of the non-zero relative volume of our
universe (ie, "something") from the zero absolute volume of the existent state
of non-existence (ie, "nothing") was presented. This paper is a brief summary
of that mechanism.
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