Article #275
Subject: Relation of Mr. Hubbard's definition of motion to Aristotle's and Galileo
Author: Andrew W. Harrell
Posted: 2/12/2016 09:32:12 AM

Discussion of the importance of Galileo’s life and work to modern science and philosophy and
theology, as part of a review of the overall Church’s (Catholic, Protestant, Jewish, Hindu)
perspective on his life 700 years later.

References:
Galileo by J.L.Heibron Oxford U. Press
(See the May 2015 issue of the American Mathematical Society (AMS) Notices for a review by
mathematicians...not necessarily theologians...of this recently published book. Unfortunately
not many of our prominent mathematicians today believe it is possible to be both a
mathematician and a theologian like Galileo was. Last year after being asked to donate a brick
to the Mathematical Association of America (MAA) I sent in some money and the following
inscription to be placed on the brick "When God is One, His Truth is One, YHWH Christ". Some
weeks later I received a letter from the MAA board saying they had voted and that inscription
would not be acceptable for a commemorative brick to be placed at the headquarters.)
see also
The Trial of Galileo, Aristotelianism, the “New Cosmology,” and the Catholic Church, 1616-1633
by Michael S. Pettersen, Frederick Purnell,Mark Carnes

Lectures on Thought and Effort by L. Ron Hubbard, 1953

Galileo, along with Aristotle, was and still is, one of the most important thinkers in the area of
mathematics, theology, and physics the human race has produced, He is responsible for not
only helping us get rid of an earth centered view of the solar system and an over dependence
and acceptance of science and religion upon unchallenged tradition ideas, but also reframing
the actual ways and methods science and religion helps us to improve itself by knowing new
ideas and ideas about ourselves and these ideas themselves. .
Just 15 years ago or so Pope John Paul II ordered a review of the Christian Church whole
discussions with and about Galileo. Although, not a Catholic, but a Protestant I take this as an
opportunity for the whole Church of believers in Christ [Catholic, Protestant, Jewish to
reconsider things together about these important subjects. And, also to encourage us to
perhaps try and understand motion somewhat better than Galileo did. Godel's incompleteness
theorem proved that there are logical boundaries to what we as humans and computers can
understand or create. But, the more important truth is that there are no logical limits to what
computers and the human mind can understand or create, when we put our computers and
minds and the world together under the control of God.
When Galileo was a professor of mathematics and physics at Pisa much of the the way we
understand mathematics and physics now did not exist. Real numbers [roughly speaking limits
of rational and irrational numbers] which are the key to the way we understand how to use
Calculus to study physics weren’t defined yet. Decimal numbers had already been introduced as
a way of improving on the abacus and Roman numerals. Fibonacci, one of Galileo’s
predecessors at Pisa, had explained how to add and subtract using large decimal numbers. But
no one understood how to use a measure of time to compute moving velocities and
accelerations more than by using approximately geometrical values. Parmendides and Plato
and the methods of using limits of areas to exhaust calculations of the areas had been
discussed in the past. For, Archimedes had already discovered the philosophy of limits of
numbers and volumes of objects.
Aristotle had defined motion as “any kind of change” and he defined local motion as “change of
position or locution”. Galileo did not change our understanding of the broader definition but he
did change it of what Aristotle called local motion. Nowadays, in addition to reviewing and
evaluating the correctness of Galileo's theological arguments we should benefit by reviewing
again how he understood then and what we can understand now what 'motion' is.
Mr. L. R. Hubbard*, for instance, defines motion as "change of attitude in place, or from place to
place." This is an interesting refinement and extension in definition from Arisotle's distinction
between local and general motion.

We define motion in terms of functions from the real line [or complex or quaternions spaces
which are made up of axes or vector bundles of real continua or real spaces] to the some similar
"type" of real lines or continua. Of course, since he, like [Plato, Aristotle, Parmenides and the
ancient Greeks, didn't yet understand what a continua was and how it is defined
mathematically] we should be able now to define what we want to call motion better than he
did. A robot can use the monomial equations of algebraic geometry as data structures in order
to calculate using functions or mappings where to go. While thinking about this, one thought I
had was that we knowing what we know now about computer science and expert systems [see
some of my papers on this at the website] could define a concept of "psychological motion"
[emotion] for a robot. The 'places' as Dr. Grothendeick has taught us on a manifold or topos
defined algebraic geometrically are different than those that we define through Euclidean metric
geometry and spatial Newtonian knowledge given to us by assuming certain axioms considering
Space to be an absolute flat [uncurved] Newtonian manifold.
All movement in space and time occurs in what the Buddhists call the "form" realms. But, we
know[or at least i believe] that we can represent movement in the "formless realms" by
represent objects that don't occur in space and time [are eternal] in our consciousness. If you
believe philosophically and theologically , as I do, and a lot of recent scientific studies have
confirmed that mind [intentional consciousness] having intentions existing both inside of our
own minds and outside of them, and matter [ not intentional consciousness] can both be
represented mentally, conceptually, them we should be able to move "formless" objects in our
mind thereby affecting "form" that exists outside of it. After all, when we remove knowledge of
forms from our minds there is always a little of it left inside of us all, because in order to create
the knowledge you have to represent it in us. Consider and thinking deeply about all of this
perhaps we can mathematically represent the movement of both object and mental functions of
them in something that mathematicians now call "categories" of thinking mathematically. For, a
long time in the last two centuries mathematicians tried to understand all of mathematics just in
terms of what we call "sets of objects". But, now most of us recognize we need to broaden our
thinking to include not only "sets of mathematical objects" but "categories of objects and
functions[ arrows that represent a " field" of movement of the objects from a particular point of
view [ what is called a monad having a slightly different definition in computer science and
mathematics at the present time.."]

The motion I am talking about would take place in a 2nd level reasoning structure
superimposed as an algebraic place on the manifold. It would occur in either a 'top-down'
movement from the assumption of a 'final cause' or faith therein such as some current Prolog
language interpreters do using backward thinking unification of clauses. Or it would occur in a
'bottom-up' object oriented type of thinking or movement in knowledge instantiation. Is it
possible to combine these two types of thinking, the scientific and the theological? Yes, it you
arrange the assumptions and conclusions of the thinking rules according what is called in
computer science a topological sort algorithm and use the type of 'mixed-chaining' instantiation
that I described in my paper written for the U.S.Army Conference on Computing using an
example from the Corps of Engineers Seattle District river-bar formation rules. Since what a
function is depends on the data structures we use to define its mapping, is using such an
artificial intelligence, functional consciousness, definition of motion going to teach us new
physics like Galileo was taught new physics when he improved on Aristotle's idea of what
motion is?

Aristotle argued from logic that local motion was of three kinds: 1: linear, 2:circular, 3:mixed of
linear and circular. He said this motion occurred because of natural tendencies in the element
themselves and not because of acceleration of velocities of motion of bodies relative to each
other represented as being effected or caused by a “force field”.
Under these assumptions linear motion cannot occur naturally without some external agent
impressing itself on the elements that are moving. However, circular motion will continue to
move indefinitely. In fact it is the archetype of how we define "theologically" eternal movement
as something that has an "end"[a purpose] in a "beginning" and a "beginning"[continuation of
itself] in an "end", like circles do. And, under these assumptions because the nature of objects
vary the natural speeds at which they fall and rise should also vary.
Galileo argued from experiments that he conducted both linear and circular motion occur
because of a universal force (which Newton later defined using his universal coefficient of
attraction) occurring at all times between two bodies. He found by experiment (dropping objects
from the tower of Pisa and measuring the time it took them to reach the ground) that heavier
objects do not fall more quickly than lighter ones. From this we can conclude that the
acceleration of their velocities is a constant and it was this constant that Newton later
measured more precisely.

Newton, however, did not understand how "energy" can be represented in a formula that
connects mass and velocity in order to determine it. For Newton energy was represented as a
"momentum" or massxvelocity and not as a "vis-viva" as mass velocity squared as Leibniz
understood it [it wasn't until a hundred years later that a French aristocratic lady named
L'Chatelet explained this to us.


In Galileo's age, space itself was not represented in the calculations using coordinate axes and
vectors in space as we do now. Although the beginnings of perspective and projections were
beginning to be studied geometrically by Renaissance artists, the differences between what we
now call metric projective geometry and metric Euclidean geometry were not understood.
Space itself was considered only a place or location for objects and our sense impressions of
them. The concept of what we now call in mathematical physics of a manifold [a collection of
places for objects and our thoughts about them, not all of which are sense impressions but
which can be studied mathematically]. This requires the notion of what a collection or sets of
objects are. Also, the idea a ‘field’ of locations or places for objects and our thoughts about
them [requiring for its final definition a better understanding of what a motion is and what a
‘force’ is] was not understood. Galileo went back to Aristotle and improved on his method of
using conservation of momentum to solve problems in physics. He used a two dimensional
scheme of how vertical and horizontal axes are balanced geometrically to represent velocities
and accelerations in a geometrical wau of visualization that helped solve problems in the
displacement of water volumes by ships and trajectories of falling bodies fired from cannons.
Only later were Newton, Descartes, Riemann, Weierstrass building on their study of Galileo’s
discussions and dialogues about how these ideas are to be defined outside of a context of
theology but within one of science and logic was modern mathematics and physics able to
accomplish all it has.
Aristotle being one of the best human philosphers and logicans that has ever existed, he had
confused everybody, about the nature of space and motion (which affects how we think we can
visualize temporal and eternal spiritual beings with our souls).
We now consider Galileo and not Aristotle right as to whether bodies can move from there own
nature {they can’t}. Most people now would say that bodies do not have a separate ‘nature’
such as a consciousness. But, the answer to this question depends on how we define ‘bodies
[matter]’ and ‘nature’. If we are metaphysical ‘dualists’ and separate everything into ‘body’ and
‘mind’ and ‘spirit’, then the mind is considered separate because it is capable of having
‘consciousness’ of which is something that is capable of having ‘intentions’.
“A spirit is defined as something as not being composed of ordinary ‘material’ things and not
subject to ‘ordinary material’ laws. Ordinary matter being composed as we know of something
that has the qualities of ‘mass’, ‘volume’,’velocity’,’solidity’.
Ordinary material laws referring to the laws of physics as we currently understand them. Light,
for instance, is not composed of ordinary matter. But, its behavior does compose to ordinary
physical laws. And, we know from the laws of quantum mechanics that it can exist in different
‘states’ or ‘quantum levels’ corresponding to the frequency of how it vibrates the ‘space’ it is
existing in. It is therefore not spiritual. Neither is a magnetic field. “
Keith Campbell “Body and Mind”.

And, to our friend, professor Einstein and Michael Faraday, and James Clerk Maxwell we owe
the idea that the "vis-viva" formula for energy, the mass of an object [possibly atomic like a light
photon], and its speed can be connected all together in the wonderful expression E = m x c^2.
Is there some way that a generalized understanding of what "motion" is can also be generalized
to a better understanding of what the other two concepts, that of mass, and that of velocity
squared, are in the above equation? Modern day mathematicians and physicists are nowadays
trying to do this using an idea of expressing the formula for this in terms of what is called a
"Lagrangian" on a "vector bundle" [or some other algebraic geometric type of space]. All this is
still very much up in the air and subject to change because we don't understand what the
concept of "dark energy" or "dark matter" is that we are trying to find in order to make our
astronomical observations come up right. And, if you add the possibly that the type of mental
"psychic" motion we are discussing might require a new definition of what "mass" is we are
really confused. Such a space that we have been talking about algebraically would probably
have what we call non-commutative motion. And, geometrically, to have to have some "metric"
structure would entail having attached to it what we call a "quadratic form" [possibly a form
calculated over not just the real numbers, but the complex, or quaternions, or octernions], or
Cayley numbers". But, we would also need a way of reducing the number of possibilities of
such forms [either by experiment or considerations of combinatorial symmetry of space
translations and tilings] in order to determine which unique solution among the many
possibilities God had to choose.

For one interesting method to combine the algebra, the geometry, of the space translations and
tilings of quadratic forms see my 1974 UC Berkeley Mathematics Thesis " VoronoiReduction of
Quadratic Forms".


God, of course, assuming He exists, as we do, because He is omnipresent has the qualities of
both existing in space [being a body] and because He is omnipotent, of having consciousness
and intentions [having a mind.], and not being composed of ordinary ‘material’ things and not
subject to ‘ordinary material’ laws [ He is omnipotent, being a Spirit even a self-existing One
composed of the nature of ‘Oneness’ or so we believe through faith].


As our friend Dante, as discussed in this blog above, has explained because we have ‘Hope’ in
God we have the ‘Certain expectation of future glory’. We have a ‘Certain’ sense of Hope in this
in the sense that I have discussed how our friend Pascal defined Hope more precisely for this a
century later when he created the mathematical area of what we now call Probability Theory. In
these realms we are dwelling as a result of our own free will and His saving, redeeming,
sanctifying, justifiy grace with Him. We are dwelling in different levels in these realms of
Heaven, Earth, Heaven or Earth, Heaven and Earth in some sense which we can have visions of
like Dante but it very hard to define using the laws of science. The realm of ‘Earth’ is the realm
of material Oneness, the realm of One substance which our bodies which occupy ‘one’ material
space live and realize our hopes and dreams in the past, present, and future with God’s help.

* Lectures on Thought and Effort, 1953

Article #290
Subject: further comments on Mr. Hubbard's ideas
Author: Andrew W. Harrell
Posted: 7/15/2016 10:20:02 AM

cf: Lectures on Advanced Procedures and Axioms

Definition of Motion [re "We must give Definition to the Defined" B. Pascal"]

"Motion is defined as change of viewpoint of [Dimension]* in Space.

"All motion [in order to be healing]* should be upward toward Divine Goodness and the simplicity of
Itself and God [Oneness in the order of
1) The Light of the One increasing, 2) The Light of the One without a second, 3)The Light of the One
which transforms us toward Oneness and healing...Jesus Christ, 4)The Light of the Discrimination of
the Oneness inside of humanity from that of God]*not downward toward confusion in complexity and
the lack of self and Divine goodness in Satan and evil .