Big Sky Café

Stream History captures segments of BigSky Cogsci WeChat group in more readable form.

(Note: Currently we only post the contributions of the moderator. These include thought questions, previews, analysis etc. We are looking at how to best capture non-moderator contributions. More soon.)

Let’s start!

From time to time we will look at some of the basic physics, mathematics and structural considerations which inform how the key players in cognitive sciences develop, “grow up,” emerge and interact. We’ll start with some underlying considerations of physical objects like streams, weather systems, and work our way toward brains, nervous systems, information systems, minds, societies and … who knows! Let’s start with Surfaces and Surface Areas.

Surfaces and Surface Areas: Leonardo da Vinci, streams and ant races!

Leonardo da Vinci’s paintings and drawings of living humans where informed in part his study of what lay underneath the SURFACE of skin: the form and movements of muscles, tendons and bones. He informed his keen observation of the surface of things with an understanding of the movements and connections of the structures beneath.

We have been discussing “streams.” da Vinci, the master of observation, spent many many hours thinking about, observing and drawing streams of water.

[Thought Question] Imagine that you are a student sitting by the banks of a stream with da Vinci. What might he say about the relationships of the surface of the stream to what might lay beneath? How would you learn to understand the stream and capture its movements?

[Reply] A cool thing for me: When we observe streams, surface activity only tells us something of what is beneath WHEN the stream is IN MOTION. If the movement stops the surface information disappears (the water surface is flat). In fact the surface information is a function of the speed of the stream.

[more replies to be added]

[Note: We are about to consider our first “Zoomed-Out Definition.” These definitions purposefully “zoom-out” to include ideas that may have been dropped from view in more traditional definitions. They are recreational and exploratory.]

 Surface: Zoomed-Out definition. A surface is a transitional interface between two or more fields that are distinguishable from each other in terms of some characteristic (such as substance, state, energy, pattern, degree of complexity). These surface interfaces often reflect the influence or impingement of each field on the others – in all directions. As such It is a dynamic membrane which reflects a changing relationship between (at least) two complex systems.

Example: The surface of the stream is an interface between the underlying water and the atmosphere above. This surface is animated by (at least) the energy, movement and other properties from BOTH the air and the water. If you look at the surface from beneath – you “see” the influence wind; from above, the influence of the water and river bed.

[Preview] The concepts of  “surface” and “streams” will come into play when we consider [the biology and physics of nervous systems], [sensory perception], [complex systems], [memory], [internality], [learning], [personality], [culture], and a number of other topics! They also connect us to our first mathematics, physics and modeling concepts. …. Here comes one now….

[Concept] Let's float the concept of “Surface Area” down the Big Sky stream. This will be a key term as we develop an abstract calculus (a language) to help us describe and extend considerations of things like nervous systems, memory systems and consciousness – any space where two complex systems interact to generate a third.

[Thought Question] Consider a section of a stream. Consider the surface area between the water and the air. Imagine that this surface is still and completely flat. Then imagine it with ripples generated by movement and objects beneath the surface. Which has the greater surface area? Still or moving?

[more replies to be added]

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As all of you are pointing out in various ways – surfaces areas are everywhere. Let's dig deeper to get our heads wrapped around some of the most interesting properties of surface areas and their implications. To do this we'll need to think a little about interactions between dimensions (2D, 3D, 4D, nD).

Let's look at a thought experiment of small dimension.

[Thought Question] Imagine yourself on a beach. Take two stones and place them about 1 meter apart. Take a stick and dig a very straight channel between the stones. Then make another channel – this time with a very slight bend in it. Put two little ants at one stone, one in each channel, and give them the job of traveling to the other stone. Which ant is likely to arrive first – the one in the straight channel or the one in the bendy channel?

The obvious answer: The ant on the straight channel finishes first. Consider the Bendy Path a little more. If you redraw the bend, how much can you increase the ant’s travel time? How about if you add more bends? Is there any limit as to how much you can increase our ant friends’ travel time?

Finally, consider the edges of the Bendy Path again. In a way each side of the channel can be thought of as a surface relative to the other side. And the duration of the ants trips can be thought of as a kind of measurement of those surfaces.

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[Perspective Popper!] The inner surface area of the human lungs measures between 80 and 100 square meters, which is comparable in size to half of a tennis court.