Distinctions with and without Differences

September 24, 2016 Martin K. Jones 1 Comment

It is often asked, why is there something rather than nothing?

Instead why not ask, why is there a rich diversity of things, rather than a dull sameness? And even though the closer and the further one looks the diversity is almost without limit, one also sees the world divided into natural kinds that partition it into a differentiated but interrelated mixture.

Several ancient philosophers thought that the entire world was an indivisible whole, a solid “being”. Others thought that you can’t even step into the same river twice, thus a fluid “becoming”. The real world seems to be somewhere in-between these two poles, moving continuously back and forth to now generate difference and newness, and then returning to sameness and oldness, and next continuing on to newness again.

Why drives these generative processes? One could say evolution, but evolution merely means “change over time”. And it would need to be an evolution at all levels of the cosmos, from the physical constituents of matter to the psychological constructs of culture. What do these disparate systems have in common?

Perhaps the commonality lies in the relations between small and large ensembles of chunks of space and time. In theories of statistical thermodynamics, the associations between micro states and macro states as well as micro events and macros events may drive entropy.

Here I present a schema that divides the continuum between one and many into four: Sameness, Similarity, Distinction, and Difference.
A member of the “being” camp might say these aren’t really different, whereas one from the “becoming” camp could say there really isn’t any sameness to begin with. Here I’ve chosen neither camp but struggled to bridge the gap between them.

References:

https://en.wikipedia.org/wiki/Being

https://en.wikipedia.org/wiki/Becoming_(philosophy)

https://en.wikipedia.org/wiki/Distinction_without_a_difference

Also see:

Statistical Thermodynamics

One and Many

[*9.110]

fourfolds, Science

Statistical Thermodynamics

September 22, 2016 Martin K. Jones 1 Comment

What drives the arrow of time? How does macroscopic irreversibility arise from microscopic reversibility? What makes entropy increase for closed systems, but decrease in certain open systems?

From the viewpoint of statistical thermodynamics, one can model the evolution of any discrete system by its possible macro states and micro states.

Those macro states having more possible micro states will be more likely to occur, and the macro states having less micro states will be less likely.

Similarly, those macro events caused by more possible micro events will be more likely to obtain, and the macro events caused by less micro events will be less likely.

Therefore, the probabilities of how the past effects the future are determined by the arrangements of the parts making up the micro states and macro states, and similarly the chains of causes constituting the relations between the micro events and macro events.

Apparently time is a progression of events unfolding from the more ordered to the less ordered. However, we know that local order can increase while global order decreases, even if we are unclear as to why. Information and organization can grow; nature and biological evolution are proof of it.

So there is an arrow of time, yet one might think that time is more like a river. (Heraclitus said you could not step into the same river twice.) There is a main flow of the current that carries most everything downstream to disorganization and increasing entropy, but there are eddies here and there that actually increase information and organization.

What enables this to happen? Some say thermodynamic gradients. Some say quantum entanglement. Some say gravity. Some say by the expansion of the universe. Some say dark matter or dark energy. Some say sorting processes.

Can we think of time as being “reversed” in these eddies where information and organization increase locally? No, but it’s an interesting (unscientific) thought.

References and Further Reading:

http://www.informationphilosopher.com/problems/arrow_of_time/

https://en.wikipedia.org/wiki/Arrow_of_time

https://en.wikipedia.org/wiki/Statistical_mechanics

https://en.wikipedia.org/wiki/Entropy

https://en.wikipedia.org/wiki/Introduction_to_entropy

https://en.wikipedia.org/wiki/Entropy_(arrow_of_time)

https://en.wikipedia.org/wiki/Entropy_(statistical_thermodynamics)

https://en.wikipedia.org/wiki/Entropy_(classical_thermodynamics)

https://en.wikipedia.org/wiki/Entropy_(order_and_disorder)

https://en.wikipedia.org/wiki/Entropy_(information_theory)

https://en.wikipedia.org/wiki/Sorting

Italo Scardovi / Time and Chance: a statistical hendiadys

https://rivista-statistica.unibo.it/article/viewFile/75/71

[*7.136, *8.43]

fourfolds, logic

Laws of Form

September 19, 2016 Martin K. Jones Leave a comment

George Spencer-Brown, author of Laws of Form, recently passed away.

I’ve tried to appreciate this work in the past, but couldn’t really get started. I recently ran across the following four terms associated with the work,

Compensation
-> (())
Cancellation
(()) ->
Condensation
()() -> ()
Confirmation
() -> ()()

Compensation and Cancellation are both considered Order, and Condensation and Confirmation are both considered Number. Number and Order are distinguished by Distinction, and the pairs of the two distinctions are distinguished by Direction.

I understand Laws of Form starts with “Draw a distinction.” Perhaps I would say “Draw a distinction, then draw a distinction of that distinction.”

References:

http://www.telegraph.co.uk/obituaries/2016/09/13/george-spencer-brown-polymath-who-wrote-the-landmark-maths-book/

https://en.wikipedia.org/wiki/G._Spencer-Brown

https://en.wikipedia.org/wiki/Laws_of_Form

https://en.wikipedia.org/wiki/Distinction_(philosophy)

For my further reading: