Yesterday John Harland and I talked about physics. How might we think
of it in terms of "ways of figuring things out" and my overview of
that? John and I were graduate students at UCSD in the math department
where we received our Ph.D's. I have a B.A. in Physics and I think John
does, too, but he certainly knows and thinks a lot more about physics
than I do.
I share my notes based on my understanding of ideas that John sparked or
stated and I tried to make sense of in my system.
Measurement. We can always start fresh with a new measurement. Each
measurement assumes a partial view, an interest in some part of the
system. We don't need a complete description, but rather we tease out
whatever part of reality that we are interested, even though it is
dubious in the big picture, yet our point of view (say, particle or
wave) can be successful, even though incomplete. Yet therefore we need
to keep working with independent measurements. Analogously, in math we
can start fresh with a new piece of paper, or in life we can give a
person a new chance.
Particle point of view. Our measurement can take place within the frame
of measurement. We have a natural frame of reference, for example, the
center of mass. That center of mass can then be considered as balancing
different masses, and integrating a system of masses, and ultimately
defining a vector space. This is a static, spatial, nontemporal point
of view. Every state has a location. We can speak of the state of a
system. Analogously, in math we have a blank sheet with a natural
frame, a center, a balance around that center, a polynomial algebra of
constructions, and ultimately, a vector space where a basis makes
explicit that every point can be the center. And in life, we can
discard the unessential, presume only God, allow for both self and
others, find harmony amongst our interests, and create a space for good
Wave point of view. Our measurement can take place outside of our
frames of measurement and thus link several such frames. This is a
dynamic point of view where there is no distinction between the future
and the past so that all is reversible. We can think of the wave in
terms of where it starts and where it ends. It includes all paths
between these two points. This is a deterministic, nonspatial point of
view, which establishes time, an ideal continuum that is beyond the
frames but thus relevant for us. Analogously, in math we may have a
sequence of sheets, as with mathematical induction, some of which may be
of ultimate importance, as with the extreme principle, thus allowing for
boxing in with greatest lower bounds and least upper bounds, leading to
limits that may transcend, go beyond what we can account for. Or in
life, we can be open to care about everything, then care about our minds
by which we care, then come up against our personal limits, then allow
for an ideal (such as Jesus) that transcends our limits.
Scientific method. We design experiments that link together, tangles
together the two incomplete outlooks of space and time, single frame and
multiple frames, particle and wave, static and dynamic, free and
deterministic. This is because each experiment presumes an experimenter
and thus takes place both within a frame of measurement and beyond it.
Each experiment includes a hypothesis, an experimental test, and an
appraisal of the results. Analogously, in math, given a constraint, we
extend its domain to include a new domain, we stitch them together by
presuming continuity, and we relate the two applications by
superimposing them, yielding a more general constraint. In life, we
take a stand, follow through and reflect.
Sets of objects exist. We can fuse the particle and wave points of view
to work with a partial reality. For example, we can talk about a
banana, an apple or an orange as well defined objects that mean
something more than a random assemblage of half of the atoms in a banana
with half of the atoms in the apple. We are then no longer talking
about the symmetry of the universe. John says: A symmetry group
commutes with the underlying symmetry of a particular phenomenon, its
spacial symmetry, as the set of possible transformations, possible
futures. Previously, we worked with the entire universe, and if we
translated it abstractly in a symmetry group and then ran things forward
in the translated frame, it was exactly isomorphic to what it would have
been if we had not translated it. But now, as we want to
compartmentalize the universe, then the price to pay is that we are not
translating by the full symmetry group, but only by some part of it.
This is analogous to having a tensor product and considering only one
component, so that we have partial symmetry. We are going to treat one
part of the universe as a compartment. This gives the reality to the
symmetry group because otherwise it couldn't be measured. Andrius: This
compartmentalization is also what allows us to define entropy and the
one-way direction of time, which says that states drift away from
deliberateness, which is expressed by the compartmentalization.
Compartmentalization also indicates the philosophical gaps or boundaries
that allow for measurement to take place, allow for objectivity, the
separation of the observer and the observed. Analogously, in math we
have symmetry groups, and in life we have meanings, the essence of what
we wish to say, which me take to be absolute, in cases where we have
Experiments and Theory. Experiments (specific instances) and theory
(general laws) are related as level and metalevel. There is a dualism.
But, actually, they are not qualitatively different. For an experiment
is never a single instance, but always a set of instances, for it must
be reproducible. In that sense, every experiment has a generality, just
as a theory does. These two levels can be conflated, which is how we
view Reality, where the facts and the laws coincide. Or the levels can
be distinct to various degrees, and completely distinct when the facts
are considered to be applications of the rules. Andrius: There are four
possible levels (Whether, What, How, Why) for relating facts and rules,
and there are six pairs of possible levels, with the wider level
reserved for the rules (the imagined observer) and the narrower level
reserved for the facts (the imagined observed). Analogously, in Math we
have the mathematical structures that describe (on paper) our problem,
and we have the mathematical structures that describe how our minds are
solving the problem. The two are conflated as Truth. They are
distinguished as Model, Implication and Variable. There are six kinds
of variables. In life, we have four ways of distinguishing the truths
of the heart and the world, given by Whether, What, How, Why we know
what we know, and there are six ways that the two truths may be related.
Causality. Rules are applied in six different ways to link states
before and after an event. In math, these are the kinds of subsystems
that Implication forms. In life, these are the ways that we visualize.
Identity. John says that the whole concept of identity is very flexible
in physics, even shaky. What is a storm? Where does it go when it no
longer exists? What is the reality of the kludge? You can't know where
things come and go in physics. Once you write about it you are not
talking about physics in the big picture. This is where there is slack
and wiggle room. Identity is what allows for eternal nature. We
acknowledge the storm and, though it comes and goes, yet its eternal
nature jumps over into us. This is eternal life. In math, there is
Context, which can change the meaning entirely, as when 10+4 turns out
to be 2'o-clock on a clock. In life, if we obey God, then we can
imagine God's point of view, and that opens up incredible freedom.
I'm excited that the above attempt at a system is fruitful. It allows
me and John to ask questions and flesh out this picture. What are the
kinds of causality? How do experiments link together space and time,
particle and wave, static and dynamic? How is entropy and
deliberateness related to compartmentalization? And it's very helpful
that we have many analogues in math, life and other domains.
I've also started to collect examples from physics, starting with
thought experiments from Wikipedia:
and I'll add real experiments, too.
Edward, thank you for your letters! They are very helpful. I ask you
also to think of examples where methods, or a kind of thinking, proved
fruitful. You mention the excluded middle. For example, the Lithuanian
semiotician Algirdas Julius Greimas developed the semiotic square
(related to Aristotle's logical square), for example: White Black
Not-Black Not-White. Where Not-White might be "colorlessness" and
Not-Black might be "grey" if I remember correctly. But for my purposes,
I want to document examples where such thinking was actually fruitful.
I don't want to confuse fruitful and nonfruitful approaches! And I also
want to relate each way of thinking with the kinds of results it yields.
I'm always wondering how I could make a living from documenting and
sharing "ways of figuring things out". Perhaps I should do that for
business and economics.
Thank you for thinking along with me!