By Germano Resconi

The publication is at the geometry of agent wisdom. the real thought studied during this publication is the sphere and its Geometric illustration. To enhance a geometrical photograph of the gravity , Einstein used Tensor Calculus yet this can be very various from the information tools used now, as for example suggestions of information mining , neural networks , formal suggestion research ,quantum computing device and different subject matters. the purpose of this e-book is to rebuild the tensor calculus with a purpose to supply a geometrical illustration of agent wisdom. by utilizing a brand new geometry of data we will be able to unify the entire subject matters which have been studied in recent times to create a bridge among the geometric illustration of the actual phenomena and the geometric illustration of the person and subjective wisdom of the brokers.

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13). w = Hz = j j ⎡ h11 ⎢h ⎢ 21 ⎢ ... ⎣⎢ hq1 h12 h22 ... hq 2 ... h ⎤ ⎡ z ⎤ 1p j ,1 ⎥ ... h ⎥ ⎢ z 2 p ⎥ ⎢ j ,2 ⎥ ... ⎥ ⎢ ... ⎥ ... 53) ⎦ or w j ⎡ h1 p ⎤ ⎡ h11 ⎤ ⎡ h12 ⎤ ⎢h ⎥ ⎢ h21 ⎥ ⎢ h22 ⎥ =z ⎢ +z + ..... + z j , p ⎢ 2 p ⎥ = j ,1 ... ⎥ j ,2 ⎢ ... ⎥ ⎢ ... ⎥ ⎢h ⎥ ⎢h ⎥ ⎢⎣ hqp ⎥⎦ ⎣⎢ q1 ⎦⎥ ⎣⎢ q 2 ⎦⎥ z H +z H + .... 45), we have y h,k ⎡ y11 ⎢y = ⎢ 21 ⎢ ... ⎢⎣ yq1 ⎡ ∑p z h ⎤ h12 ... j k . j ⎥ p ⎥ h22 ... j k . 48) ... ... ⎥ ⎢ ... ⎥ i j ⎢⎣ hq1 hq 2 ... j k . j ⎥⎦ y 12 y 22 ... y ⎤ ⎡h 1p 11 ...

We term them Agents of the Second Order. 3. 4. In a new image we show both the task and the sources by the symbols Sk and Tk. 3 where at any node of the graph the tasks and the sources with the same number are the same entity. Source 1 Source Task 4 Task 2 Action Source Task Source Source Task 3 Task Fig. 2 Network showing the Action between Different sources and the task. For example from the source 1, we can obtain two different actions tasks 2 and the task 4 S1 1 S1 Action T2 2 T1 S2 T4 4 S3 S4 T3 3 T3 Fig.

2 Field, Neural Network Geometry and Coherence 43 For dS = G −1dS C , using the language of the tensor calculus we have dS = G −1dS C In the Einstein notation we have dS i = G −1dS j = G i , j dS j Where dS i = dS are the controvariant basis (ρ,θ) and dS j = dS C are the covariant basis We will show geometric examples of the controvariant and covariant basis. Given the transformation x1 = x'1 + x'2cos(α) x2 = x'2 sin(α) Geometrically, it can be shown as follows x2 P(x1,x2) α x’2 x’1 Fig. 2 Field, Neural Network Geometry and Coherence 45 Geometrically, the basis and the conjugate basis are represented as follows: dS2C x2 P dS2 ds P’ dS1C dS1 α x1 Fig.