Local and overall differences between emergence and morphology

(x,0)---m*n*k---(1,0)(0,1)

(x,8)---m*n*k---(1,0)(0,1)

use x and 0 classification , And then use x and 8 classification , Under the same convergence error , Is it because 8 There are two circles so that the number of iterations is 0 Twice as many ？ The answer is No .

	3	0	8	2	9	6	5	4	7
X：1	35671.24	23558.45	16861	11792.54	10721.14	10241.39	10137.68	9577.513	9568.94
	3	4	9	7	1	6	0	8	5
2	33389.61	19984.86	13772.15	12555.62	11792.54	9360.106	8358.603	7658.015	7100.643
	1	2	9	7	8	4	0	5	6
3	35671.24	33389.61	19919.65	17331.39	17015.68	15199.52	12572.23	11703.08	8136.266
	2	9	3	0	1	6	7	8	5
4	19984.86	18523.66	15199.52	11983.15	9577.513	9020.96	7572.704	6106.347	5689.266
	3	1	7	2	9	8	4	0	6
5	11703.08	10137.68	8617.161	7100.643	6794.688	6116.397	5689.266	5402.955	5362.608
	0	1	2	9	4	7	8	3	5
6	25605.5	10241.39	9360.106	9044.211	9020.96	8983.447	8626.678	8136.266	5362.608
	9	3	2	1	6	5	0	4	8
7	20211.46	17331.39	12555.62	9568.94	8983.447	8617.161	7822.01	7572.704	7073.432
	0	3	1	6	2	7	9	5	4
8	27905.07	17015.68	16861	8626.678	7658.015	7073.432	6966.322	6116.397	6106.347
	7	3	4	2	0	1	6	8	5
9	20211.46	19919.65	18523.66	13772.15	13346.79	10721.14	9044.211	6966.322	6794.688

Give Way x Respectively equal to 1,2,3,4,5,6,7,9 Respectively and 0 and 8 classification , The number of iterations obtained has no multiple relationship , If you think about 0 Circular ratio of 8 The circle of is bigger , The size relationship should always be consistent . But in fact, the size relationship is also inconsistent ,1,2,4,6,7,9 Iterations of 8 Than 0 Big . and 3 and 5 The number of iterations is 0 Than 8 Big .

Consider the assumption that the number of iterations is inversely proportional to entropy , The larger the number of iterations, the more similar the two classified objects are , The smaller the entropy . And think of form 0 It's form 8 A part of , This means that it cannot be used x and 0 To estimate the number of iterations x and 8 Iterations of , It shows that there is no simple additive relationship between local morphological differences and overall morphological differences . The relationship between local differences and overall differences depends on the classification environment x,x The relationship between the two may be different .

This is a group 4*4 Pictures of the

This is a group 2*2 Pictures of the . hold 2*2 The picture of is regarded as 4*4 Part of the picture , It's obviously hard to use 2*2 Different pictures to predict 4*4 Picture differences .

Like a blind man touching an elephant , In the world of form, we can't simply push the whole from the part , But the material world is not always like this . such as 2-1=1, Again 102-101=1,1 To 10 Add law and 100-110 And the law is the same , For the whole number axis . This means that as long as you know 1-10 This 10 The function relationship of number can be deduced to the whole , In the field of number, it is possible to deduce the whole from the part . This law has no difference between local and overall .

Or for example, the spectrum of hydrogen atoms on earth is the same as that in extrasolar systems , There is no difference . The laws of physics on earth should be the same as those in a corner of the universe . Physical experiments on earth can be used to predict the phenomenon in a corner of the universe . Therefore, there is no difference between local and overall laws of Physics .

Although there is a smallest unit of energy , But because it is very small, for macro objects, it is assumed that the energy is continuous , The atom is regarded as a material embodiment of one-dimensional real number continuity . Therefore, the laws of physics have a strict mathematical expression , Therefore, whether for matter or real numbers, we can deduce the whole from the part . This classification method, which can be deduced from part to whole, is a classification method of elements . Because the relative position between particles does not affect classification , Therefore, it is a one-dimensional continuous internal progressive classification .

Now, an hourglass leaks sand from high down , When there is less sand , Morphological characteristics can be ignored , We can use element classification to approximate . It can clearly predict the overall behavior from the local . But when there is more sand , At this time, the behavior of this pile of sand becomes unpredictable , Its overall characteristics become very different from local characteristics . So this transition can be explained as when there is more sand , Its morphological characteristics become no longer negligible , What should be considered at this time is the overall difference of form , Not its components . Its overall morphological differences can no longer be predicted by local characteristics .

Therefore, it is reasonable to think that emergence behavior can be explained by morphological classification , This is a kind of two-dimensional non progressive considering the relative position of particles , A taxonomy that recognizes global and local differences . This classification is equivalent to thinking that every form is indivisible , It can only be viewed as a whole , Every classification behavior is an atomic behavior . And the emerging strange phenomenon is a manifestation of the non progressive phenomenon inside the form .