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

Spirit.

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

fundamental agreement.

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:

http://www.selflearners.net/ways/#846

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!

Andrius

Andrius Kulikauskas

http://www.selflearners.net

ms@...

(773) 306-3807

Twitter: @selflearners