I think I just now understood what you meant by coloring. When I say 5 colors, I mean those particular 5 colors; say (red, green, blue, yellow, orange).
Suppose we have a scanning device that walks across the map and is programmed such that it will beep when it finds a region of the map...
You can give me any map with any number of regions, but I think when 5 colors can not satisfy the minimum requirement mentioned above at any subgraph then this is equivalent to the 4 colors theorem.
Or put it in this way; there is no subgraph that requires 5 colors across the entire graph.
If...
I will try here to put it in a semiformal way;
The map of regions n is isomorphic to a graph of vertices n where each region of distinct colour is represented by a vertex of a different colour.
Adjcaney: two regions in the map are adjacent if there is an edge connecting the corresponding 2...
Do I need to prove that colouring a map requires local rule?
What I am trying to say is if the 4-colours theorem is false, then the maximum number of required colours should be at least 5. But the picture shows that can not be the case, therefore the theorem must be true.
Because colouring a map requires only local rules, I believe. When this set of 4-nodes becomes part of a larger graph, one can treat each local set of 4-nodes separately without affecting other remote parts of the graph.
The 4-colour theorem states that the maximum number of colours required to paint a map is 4.
The proof requires exhaustive computation with a help of a computer.
But I thought that one can visually prove the theorem in the following way;
If one replaces the map with a graph where each region...
I am not familiar with Quantum Decoherence, but I find it difficult to treat macroscopic states like; alive and deal on the same footing as quantum states that describes position, time, momentum and energy.
Like in a recent paper published by Frauchiger and Renner, they described states like...
But still, no matter what frame you choose to ride with any time order of the events you get, the physical theory must explain the quantum correlation between the measurement outcomes.
In other words, the problem of understanding the quantum entanglement is not because the time order of the...
Exactly, ##1 = \sum_{k =1}^N (\frac{ \overrightarrow{v_k} \cdot \overrightarrow{q_j}}{ |\overrightarrow{v_k}||\overrightarrow{q_j}|})^2##
I discovered this fact by coincidence but it turns out that it may have a nice link to the quantum mechanics.
For example, if the cosine of the angle...
That was not my assumption anyway.
I have also reached to the same conclusion; that is the pole is assigned to the larger face of the magnet too.
This solves the first problem of the thread but does not solve the second problem mentioned in the thread no.1 and explained in no.5.
If the same...
Thank you for the reply.
Here is the experiment in action.
The first picture shows the broken pieces put together side by side. I stick a small yellow paper in one side and a blue paper on the opposite side (the color does not imply the polarity of the magnet). I assume that this should be the...