Up early, to Kroger’s for milk. Breakfast, paper and iPad news. Nap. Mowed the grass. Last night Doug G. sent you a note about the Properties of a Möbius strip, here they are:
Dick, I have been thinking about your 4D object in 3D space. How about a 2D object in 3D space? This one is a 3D object with a surface that has only one side.. Below is a fascinating article about it.. Read the properties section for sure.
Doug
Properties (from Wikipedia)
The Möbius strip has several curious properties. A line drawn starting from the seam down the middle will meet back at the seam but at the "other side".
If continued the line will meet the starting point and will be double the length of the original strip.
This single continuous curve demonstrates that the Möbius strip has only one boundary.
Cutting a Möbius strip along the center line yields one long strip with two full twists in it, rather than two separate strips; the result is not a Möbius strip.
This happens because the original strip only has one edge which is twice as long as the original strip.
Cutting creates a second independent edge, half of which was on each side of the scissors.
Cutting this new, longer, strip down the middle creates two strips wound around each other, each with two full twists.
If the strip is cut along about a third of the way in from the edge, it creates two strips:
One is a thinner Möbius strip — it is the center third of the original strip, comprising 1/3 of the width and the same length as the original strip.
The other is a longer but thin strip with two full twists in it — this is a neighborhood of the edge of the original strip, and it comprises 1/3 of the width and twice the length of the original strip.
Other analogous strips can be obtained by similarly joining strips with two or more half-twists in them instead of one.
For example, a strip with three half-twists, when divided lengthwise, becomes a strip tied in a trefoil knot.
(If this knot is unravelled, the strip is made with eight half-twists in addition to an overhand knot.)
The equation for the numbers of twists after cutting a Mobius strip is 2N+2=M, where N is the number of twists before and M, the number after.
Cutting a Möbius strip, giving it extra twists, and reconnecting the ends produces figures called paradromic rings.
A strip with an odd-number of half-twists, such as the Möbius strip, will have only one surface and one boundary.
A strip twisted an even number of times will have two surfaces and two boundaries.
If a strip with a given odd number of half-twists is cut in half lengthwise, it will result in a longer strip, with the same number of loops as there are half-twists in the original.
Alternatively, if a strip with a given even number of half-twists is cut in half lengthwise, it will result in two conjoined strips, each with the same number of twists as the original.
**
You do not understand this to the point you “know” it. And, you subdivided the paragraphs mostly into separate sentences hoping that you would have better comprehension. Then you Googled ‘mathworld.wolfram.com’ and found two more representations that you thought would help you.
Alas, the illustrations of the Möbius strip look good (Wikipedia), but I cannot discover the dimensional connection in my head. I ‘know’ what a Möbius strip is but I do not comprehend ‘how’ it is. I am reminded here of how Doug, as my lab partner, helped me with (did) the equations in high school chemistry. This is the same feeling in my head dealing with this strip. I do not understand these things but I have faith in math and physics. I understand the strength of bridge framework and the principle of lift when it comes to airplanes.
This also reminds me of how I would have students from time to time who couldn’t get basic English grammar for the life of them. I always had empathy. It makes me angry because this is a problem with all the public school testing. It does not appear to allow for weaknesses in humanity. People who think education should be run solely like a business are inhuman to some children.
You were about to apologize for getting off track, however you have learned not to do so even though it still comes to mind. Maybe you’ll learn something with today’s lesson, orndorff, maybe not. – Amorella.
I am reminded of several of my weaknesses. This is a good thing almost always.
Post for now. You have afternoon errands to run. – Amorella.
After twenty-one hundred hours. Last Friday, 8 October 10, you asked a question about the five dimensional apple to your friends and some replied. You asked permission to post the results in your blog and no one denied permission, so this is a good place to post their results.
Your Facebook Question of 8 October 2010
How would a five dimensional apple appear to three dimensional humans in four dimensional space (time as a dimension)? A visual, let's say of a five dimensional apple. Would we see a red color, for instance. Would it appear as a small red floating ball? Or, would we 'see' anything? Any takers? I'm curious. Thanks, rho :-)
Aaron Pence see nothing cause we don't see in three dimensions? Just a guess Mr. Orndorff!
Friday at 1:57pm
Christie Wilt Riggsby Do you watch "The Big Bang Theory"? Your question sounds like a game they were playing this week.
Friday at 2:13pm
Laura Schamore would we not taste the apple
Friday at 2:24pm
Laura Schamore go on have a bite
Friday at 2:25pm
Laura Schamore or is that byte?
Friday at 2:25pm
Christie Wilt Riggsby I've been puzzling over this and I find that the only thing I can come up with at the moment is that the song, "Let The Sunshine In" (by the 5th Dimension) is now stuck in my head. Will have to puzzle on this when I'm less distracted.
Friday at 2:30pm
Robert Fronk A point moves thru space creating a line, length A Line moves thru space creates a plane, length x width, 2D. A plane moves thru space creating volume, L x W x Height, 3D, represented as a cube. So, ...4D, would be a volume moving in every direction. So a human,...exploding atoms in every direction. Not pretty. But if you can draw a cube on paper, representing 3D in 2D. It follows you can represent 4D w/ 3D, the idea is called a Teseract (sp). String theory is over my head. But ,.. so 5D would infinity moving in an infinite direction?!?.....ok, now I'm lite-headed....
Friday at 2:42pm
Kris Mason My guess would be that we would see the 3 dimensions, length, width, height - space plus the instance in time (4th dimension) that we perceive at a specific 4th dimensional moment plus the perceptions of our limited minds to guess at the past and future of the specific apple from our learned experiences. The 5th or more dimensions that would exist would not be able to be perceived by our minds and bodies due to our limitations.
Kris Mason Similar to the visual difference between us and some insects. Insects can see ultraviolet light, we do not. Just because we can't perceive UV doesn't mean that UV doesn't exist (thus we get sunburned), but a flower - at least in terms of color and pattern) looks very different to us and the insect. Much could be said the same about smells, texture etc. Our perception of the world is different from other life creatures, even though we all function in 3/4 dimensions. maybe we function in 5/6/7 dimensions but don't know it because we aren't equip to detect them.
Friday at 2:49pm
Richard H. Orndorff I am appreciating your comments. I think I will wait until tomorrow to comment beyond this. Thank you! Cool beans! I love this stuff!! ;-)
Friday at 3:06pm
Scott Woodside Purple ,yellow, orange, red, green....all flowing together and changing with dimensional space.....puff....puff
Friday at 3:10pm
Valerie VanDervort Reed I'm confused!
Friday at 5:15pm
Michael Ilyinsky I think it all depends on how hungry the viewer is...
Friday at 11:13pm
Mary Ridgway Perhaps it could be experienced through a different sense we've not yet acknowledged. There are ranges of light outside of our visual abilities. Maybe other creatures can experience the 5D apple on our behalf. Sort of how a dog can smell things to help us find things that we can not detect through our own sense of smell.
Aaron Ball go and look at an apple. Get it in front of you. ... It looks like that! We exist in all dimensions, that truly are, simultaneously . However because we are organic beings we are limited in our conceptual senses. Therefore an apple looks apple like. Sorry.
Saturday at 11:29am (9 October)
Richard H. Orndorff Thank you all for the comments. Back in the 80's Carl Sagan had a program in which he illustrated a three dimensional red apple falling through two dimensional space as seen by a two dimensional being. First the 2D person would see a red spot in the air. The spot would lengthen to a thin horizontal red line that would become progressively wider as the apple passed through, then it would become less wide, until, as the top of the apple passed through it would end with a small red dot and then disappear. That was Sagan's science of the eighties.
I am wondering if some UFO sightings over the years (centuries) have been natural anomalies caused by extra dimensional objects falling into and through four dimensional space. I have enjoyed your comments -- each gives me something to consider on a variety of levels. Thank you. I may conceptual use some of these responses (with your permissions at that time) in book six (if I ever finish four and then five).
Peg Elfers Rich, I have tried (for 3 minutes) and just cannot visualize this doggone apple. My head hurts.
Saturday at 9:01pm
Richard H. Orndorff Peg, I think this is because a five dimensional apple may have a shape that includes something beyond a combination of straight and/or curved lines. Our brains are not built to 'see' any other shape combinations (at least I don't believe so). A dot being the end of a straight line. Hmm. I hope this is correct. ;-) Now my head hurts. ;-)
Yesterday at 11:38am (Sunday, 10 October)
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Richard H. Orndorff Hello, all! I have made a copy of all the comments and cleaned up the typos. I would like to put these in my blog for safekeeping. Does anyone mind? If so, let me know. Some of your responses were in humor, but they give me a perspective a character in the story may respond to, not exactly of course, but in context. It is interesting that thinking on the subject made three of us comment on 'light-headedness'. To me when that happens good stuff is going on upstairs. ;-)
2 minutes ago · (Monday, 11 October)
Richard H. Orndorff Also, I have a friend not on FB - but a physicist and here is what Doug Goss replied: I think that one would see a red circle. The size may change from time to time. If the object were not spherical, then the shape seen would not only depend on the height above the plain but the angle it makes to the plain. Thus one object could make a huge number of shapes. My thoughts.
**
What people say is important to me and to my writing. When I began the earlier books in the late eighties (Stuck, Home and On Earth) I asked faculty and staff for the questions they would ask a ‘real’ extraterrestrial being if sheorhe had a chance. I received a lot of good questions and it helped me broaden my thinking on what one intelligent being would as another under such circumstances. I still have those responses and used them in developing the first of the novels, Stuck, which focused on the human-like marsupial species who act more maturely human than our species.
I remember one of the most interesting questions at the time was “Who is your God?” and I went through all the questions and attempted to respond as my alien characters would have. To that question I remember responding that the God across the Milky Way Galaxy is a similar God as found in the basic tradition of Judeo, Christian and Moslem religions, throwing in aspects of Hindu and Buddhist in the process. That is one of the main reasons my marsupial are interested in Earth, both species come to similar conclusions on spiritual values. The humor is that the economic system of the marsupials is based on ‘forgiving the three-world debt’ of the species ‘family’ once a year. Bottom line economics for the individual but the greater group welfare and education funds are forgiven. I thought it was good humored in that they practice Christ’s words on their three world system but it is not a religion it is a spiritual value of the group. The primary focus is always on making their three worlds a better place to raise their children, but then they have twenty thousands years on the human species.
I don’t think we would enjoy the fact that they are more civilized than we are. Again, more humor, better than battling some kind of insects. Just like real life – native Americans meeting the Europeans. Ha! Only the modern world is the Native Americans struck by the kindness and civilization of the Marsupial humanoids, who while not perfect had a system of personal responsibility for the group that worked for them. I had a good time planning that first book, Stuck.
You have the tendency to get carried away by the mind’s moment. This is enough for you to reflect on later, especially when it comes to book six where the extraterrestrial marsupial humanoids in the first three books play a greater part than you may now consider in the second Rebellion of the Dead in your lifetime. Post. – Amorella.
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