Given the two following patterns: the left or the right, which one is more beautiful than another?
In my opinion, the left one is more clear, if the left one is enough to get the conclusion, you can use this one.
Bin,
the right one gives more detail, but the pattern is too 'busy'. The left one gives a clearer spatial pattern and is much more pleasing to the eye. For that reason it is the one most people would turn to for interpretation.
George
I would say that as busy as the right one may look, it is more "balanced". What I mean by balanced is that there are red points in vary in sizes in a progressive manner, and an even distribution of the color all around. Also seeing them side by side, the eye automatically goes to the one where there is more red, as the color red is the one that stands out the most in the image.
Hello Bin Jiang,
Just to acknowledge earlier commentators. All clever responses! Please permit to ask if this really is a puzzle. If not, a few basic clarifications are imperative before any rational and honest attempt can be made to answer your question. Do the two patterns relate to real and same cities? What the symbols represent (the red circles of different sizes, yellow lines and green patches)? And what are illustrations meant for and what do you really intend to achieve? Finally, what is your criteria for defining 'more beautiful' as "beauty is in the eyes of the beholder". Thanks in anticipation!
@Victor Udemezue Onyebueke you asked very good questions, and many thanks to all those who answered this question, actually a kind of mirror of the self test. This test is NOT to seek inter-subjective agreement, but get into human feeling that comes from the wholeness. Please note that the beauty is NOT in the eyes of the beholder, but in the deep structure. Or put it differently, our sense of beauty is mainly shaped by the deep structure, while our subjective factors play some trivial role. This deep structure is called wholeness that is defined mathematically, exists in space and matter physically, and reflects in our mind and cognition psychologically. I must say both patterns are beautiful, which human eyes are hard to differentiate, because they are almost at a same level with very slight difference. To use an analogue, two cups of waters one with 50 degrees and the other with 45 degrees, and I ask you to judge which cup of water is hotter using your hand (instead of thermometer). Very hard to judge indeed! For details about the data, what city, what different color lines etc., please refer to this paper which is to appear in Geographical Analysis:
https://www.researchgate.net/publication/305638074_A_Topological_Representation_for_Taking_Cities_as_a_Coherent_Whole
I will be preaching on the kind of beauty in the upcoming COSIT 2017:
https://www.researchgate.net/publication/316845391_Why_Topology_Matters_in_Spatial_Cognition_and_Analysis
Article A Topological Representation for Taking Cities as a Coherent Whole
Poster Why Topology Matters in Spatial Cognition and Analysis?
Many thanks, Jiang, for not just opening my eyes but also my heart to the real story. I also truly appreciate your deep insight about human likes, preferences, or love in reality emanating from the deep recesses of their being. I consider it an unassailable truth substantiated not just by Mathematics (I've just learnt) but also by divine evidence. For one, take this particular phrase in the Christian Bible "deep calls to deep" (Psalm 42:7). I'd read the above interesting publications of yours and follow your work as well. Thanks!
@Victor Udemezue Onyebueke Many thanks for sharing your thoughts! Christopher Alexander, in particular his life's work The Nature of Order is the source of my inspirations. I like your word "not just opening my eyes but also my heart" very much, and the similar phrases Alexander used again and again in his works. Beautiful things can be clearly and convincingly explained by science and divine evidence. The topological representation I developed in the above cited paper can be applied to any city, building, artifact, and even a tiny ornament to objectively assess (1) why it is beautiful, and (2) how much beauty it has. For more details, refer to this beautimeter paper:
https://www.researchgate.net/publication/272159333_Wholeness_as_a_Hierarchical_Graph_to_Capture_the_Nature_of_Space
Article Wholeness as a Hierarchical Graph to Capture the Nature of Space
Many thanks, Prof Bin. Altogether very interesting and brilliant. I'd also read it.
@Victor Udemezue Onyebueke
Built on the legacy of Alexander and his life's work pursuing beauty: https://www.researchgate.net/publication/299337109_A_Mathematical_Model_of_Beauty_for_Sustainable_Urban_Design
A new master program of architecture http://buildingbeauty.net/ has been established in Italy. I am of the teaching faculty, preaching on the wholeness and its measures.
The program aims for wholeness-oriented design, beginning with construction rather than paper based design as most architecture schools do. It intends to create buildings or cities with a high degree of wholeness, instead of slick buildings as most modernist architects do. Bear it in mind that the beauty is defined mathematically, exists in space and matter physically, and reflects in our minds and cognition psychologically. Please help diffuse this program message among those interested. Thanks!
Presentation A Mathematical Model of Beauty for Sustainable Urban Design
I am re-reading part of The Nature of Order, herewith some texts that explain the nature of mirror-of-the-self experiment in general, in particular its objectively measuring inner state of ourselves, rather than inter-subjective agreement of many psychological or cognitive tests. "The essence of the idea of measurement is the following. The degree of life of any given center, relative to others, is, as I have said, objective. But in order to measure this degree of life, it is difficult, to use what, in present-day science, are conventionally regarded as "objective" methods. Instead, to get practical results, we must use ourselves as measuring instruments, in a new form of measuring process which relies (necessarily) on the human observer and that observer's observation of his or her inner state. Nevertheless, the measurement that is to be made this way is objective in the normal scientific sense." (p354, Book 1) Note that the term life can be replaced by beauty or wholeness.
Sounds really interesting! I'm all ears. Sort of reminiscence of Basarab Nicolescu's idea of transdisciplinarity. Have you ever read him?
My COSIT talk is put online now: https://www.researchgate.net/publication/319527592_Why_Topology_Matters_in_Spatial_Cognition_and_Analysis
The key message is that beauty or cognition arises out of the wholeness.
Presentation Why Topology Matters in Spatial Cognition and Analysis?
The Left, as indicated by George J. Strachan . However, whatever reason I don't know but I am moved by this. Many many thanks!!! for ,
Right one has more detail.but the pattern is very busy. left one is very clear than right one.
Dinusha is correct. The one on the right has more detail, but the one on the left has greater clarity. The main question then is ‘not which one is more beautiful’ but ‘which pattern has classified the data best and provides a better basis for interpretation of that data’. The one on the left provides that best. Beauty is after all in the eye of the beholder; the final analysis depends on good interpretation.
George
Though the image in right one seems to be complex that character has influenced the quality on it.It depict a system within itself.so right one is best.
Some of the bubbles is map number two hiding the background syntax map. But comparatively the first one have more details the user can identify. second one also have information; but complexity kills the simple idea of the map.
I recommend first one
Spatial Efficiency metric (SPAEF) is proven to be robust when comparing two raster maps. Python and Matlab codes are available at: http://space.geus.dk/tools_products/index.html
Two papers on the metric:
https://www.hydrol-earth-syst-sci.net/22/1299/2018/hess-22-1299-2018-assets.html
https://www.geosci-model-dev-discuss.net/gmd-2017-238/
I'd vote for the right one: it looks more realistic and vivid, has more kernel centres.
Many thanks for all your involvement!
It is extremely hard for a person to judge which is more living or beautiful. It is somehow like given two glasses of water (one with temperature 36.5, and the other with temperature 37), and you are asked to tell which is warmer. However, using computation based on our mathematical model of beauty, the right pattern tends to be a big more beautiful (but both are beautiful indeed):
Article Wholeness as a Hierarchical Graph to Capture the Nature of Space
I would prefer the polycentric form rather the monocentric form which indicates the left one. Right side gives more accessibility to each nodes and reduced the spatial isolation. Hence, Right one is more Connected.
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