Help attempting to form concept: dimensionality

[stabu]

Hi,

I wonder if anybody can help me in conceptualising an idea for teaching students (16+).

I call it dimensionality thought probably that's a bad name. It concerns the fact that we llive and are active at a certain scale - at a certain mass - that distances us both from activities of biomolecules at nanoscale and also in terms of planetary dimensions.

Many phenomena only matter when you are able to affect them or record them at a relevant scale. Many students (and non-science people too) read the media, and this is aspect often escapes them. Very many things are possible, but often it is interacting at the required scale, at the required timeframe which causes the obstacles.

Sorry for those who don't understand what I'm driving at. Ask me more questions and I'll try and refine.

Cheers.

 

[lisab]

I think I understand what you're saying. Perhaps a graph showing scale would help...I mean, a visual aid showing the effect of resolution?

 

[robphy]

http://www.powersof10.com/
http://powersof10.com/index.php?mod=education (see "Space", "Time", ... )
http://en.wikipedia.org/wiki/Powers_of_Ten

http://video.google.com/videosearch?q=powers+of+ten (video)

en.wikipedia.org/wiki/Orders_of_magnitude_(length)

 

[Ivan Seeking]

Here is one thing that I've seen done: Use objects like a basketball, baseball, marble, ball bearing, spot on a piece of paper, etc., at scale, to represent the solar system - planet sizes and distances. Then throw in the distance to the nearest star. I saw where some guy did this in the midwest somewhere. You had to drive from one planet to the next.

Then turn it around: Use the same objects to represent nuclear particles, atoms, etc. Compare the relative sizses to something like a grain of sand.

The resolution of the Hubble and other telescopes comes to mind. I'm sure you've heard the comparisons. For example, someone in California could tell if someone in New York was holding a egg by its major or minor axis; or if one is holding one or two matches... And there is one that I heard about detecting distant planets. I think it was in regards to the wobble in stars measured - the size of the wobble in arc seconds. There is an interesting number in regards to the relative brightness of distant stars as compared to their orbiting planets. It is like trying to detect a firefly next to a spot light, or something similar to that.

One of my favorites was to consider the velocity required for a basketball to refract while passing through a doorway. It turns out the ball would have to be moving so slowly that, IIRC, the universe isn't old enough for this to have happened yet [given the size of the ball].

btw, I think you want the word "scale", not dimension.

 

[tiny-tim]

From http://www.imdb.com/title/tt0371724/quotes" …

… the two opposing battle fleets decided to settle their few remaining differences in order to launch a joint attack on our galaxy, now positively identified as the source of the offending remark. For thousands of years the mighty starships tore across the empty wastes of space and finally dived screaming on to the planet Earth - where, due to a terrible miscalculation of scale, the entire battle fleet was accidentally swallowed by a small dog.

 

[robphy]

The notion of "relative scales" (i.e. scales relative to some "characteristic scale" in the problem) is probably what you seek. ("Dimensional analysis" and "order of magnitude" are useful concepts.)

For example, what approximations are used so that we can think of a given volume of water as a continuous fluid? How small a volume can I use before I have to consider the fact that water is composed of molecules? Of course, these answers depend on what I wish to do with the water.



Possibly useful starting points:

en.wikipedia.org/wiki/How_Long_Is_the_Coast_of_Britain%3F_Statistical_Self-Similarity_and_Fractional_Dimension

http://dx.doi.org/10.1119/1.12326 (Man's size in terms of fundamental constants)

https://www.amazon.com/dp/0521447712/?tag=pfamazon01-20 (Mr Tompkins in Paperback)

http://ocw2.mit.edu/OcwWeb/Electrical-Engineering-and-Computer-Science/6-055JSpring-2008/CourseHome/index.htm (The Art of Approximation in Science and Engineering - Sanjoy Mahajan)
http://www.inference.phy.cam.ac.uk/sanjoy/mit/

http://web.mit.edu/Edgerton/
http://www.engr.colostate.edu/~dga/high_speed_video/
http://video.google.com/videosearch?q=EX-F1

 

[stabu]

thank you one and all for that ... give me some stuff to go on.

as well as distance, the impact of scale in time is also of interest. It would be cool to have a look at that IBM video while traveling through scales of time, instead of distance, as well.

 

[robphy]

thank you one and all for that ... give me some stuff to go on.

as well as distance, the impact of scale in time is also of interest. It would be cool to have a look at that IBM video while traveling through scales of time, instead of distance, as well.

I recall a discussion about a TIME-based version of the Powers of Ten
but I see no trace of it.
However, there is
http://powersof10.com/index.php?mod=strand&id=TIME
which was one of the links that I suggested above
http://powersof10.com/index.php?mod=education (see "Space", "Time", ...)