scholarly journals The Brain and the New Foundations of Mathematics

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1002
Author(s):  
Alexey V. Melkikh
Keyword(s):  
Directed Evolution ◽  
Mathematical Object ◽  
Quantum Effects ◽  
Foundations Of Mathematics ◽  
Arithmetic Operations ◽  
Finite Amount ◽  
New Foundations ◽  
Basic Axiom ◽  
The Axiom Of Choice ◽  
The Brain

Many concepts in mathematics are not fully defined, and their properties are implicit, which leads to paradoxes. New foundations of mathematics were formulated based on the concept of innate programs of behavior and thinking. The basic axiom of mathematics is proposed, according to which any mathematical object has a physical carrier. This carrier can store and process only a finite amount of information. As a result of the D-procedure (encoding of any mathematical objects and operations on them in the form of qubits), a mathematical object is digitized. As a consequence, the basis of mathematics is the interaction of brain qubits, which can only implement arithmetic operations on numbers. A proof in mathematics is an algorithm for finding the correct statement from a list of already-existing statements. Some mathematical paradoxes (e.g., Banach–Tarski and Russell) and Smale’s 18th problem are solved by means of the D-procedure. The axiom of choice is a consequence of the equivalence of physical states, the choice among which can be made randomly. The proposed mathematics is constructive in the sense that any mathematical object exists if it is physically realized. The consistency of mathematics is due to directed evolution, which results in effective structures. Computing with qubits is based on the nontrivial quantum effects of biologically important molecules in neurons and the brain.

scholarly journals Comparing Functional (PET) Images: The Assessment of Significant Change

1991 ◽  
Vol 11 (4) ◽  
pp. 690-699 ◽  
Author(s):  
K. J. Friston ◽  
C. D. Frith ◽  
P. F. Liddle ◽  
R. S. J. Frackowiak
Keyword(s):  
Repeated Measures ◽  
Verbal Fluency ◽  
Null Hypothesis ◽  
Mathematical Object ◽  
Normal Subjects ◽  
First Case ◽  
Threshold Adjustment ◽  
Significant Change ◽  
The Brain ◽  
Parametric Maps

Statistical parametric maps (SPMs) are potentially powerful ways of localizing differences in regional cerebral activity. This potential is limited by uncertainties in assessing the significance of these maps. In this report, we describe an approach that may partially resolve this issue. A distinction is made between using SPMs as images of change significance and using them to identify foci of significant change. In the first case, the SPM can be reported nonselectively as a single mathematical object with its omnibus significance. Alternatively, the SPM constitutes a large number of repeated measures over the brain. To reject the null hypothesis, that no change has occurred at a specific location, a threshold adjustment must be made that accounts for the large number of comparisons made. This adjustment is shown to depend on the SPM's smoothness. Smoothness can be determined empirically and be used to calculate a threshold required to identify significant foci. The approach models the SPM as a stationary stochastic process. The theory and applications are illustrated using uniform phantom images and data from a verbal fluency activation study of four normal subjects.

СВЕРХКРИТИЧЕСКИЙ МОЗГ ТЬЮРИНГА И УСИЛИТЕЛИ СВОБОДНЫХ БИТОВ: ХОРОША ЛИ ГИПОТЕЗА КВАНТОВОГО МОЗГА?

2020 ◽  
pp. 17-21
Author(s):  
Dmitri Vinnik
Keyword(s):  
Nervous Tissue ◽  
Quantum Coherence ◽  
Signal Transmission ◽  
Quantum Fluctuations ◽  
Quantum Effects ◽  
Nerve Cells ◽  
Thermodynamic Conditions ◽  
The Brain ◽  
Non Equilibrium

This article reviews arguments for the quantum brain hypothesis and against it. According to this hypothesis, quantum fluctuations within nerve cells and at synaptic clefts are able to amplify and translate their states to the brain's macrostructures level. Proponents appeal to the theory of neural avalanches, arguments about the non-equilibrium nature of cerebral dynamics and the theory of nonsynaptic signal transmission. Opponents insist that the thermodynamic conditions of nervous tissue prevent the emergence of quantum coherence and other macro-scopic quantum effects; the brain is not enough isolated from the environment to observe such effects. All quantum fluctuations have to be are averaged and their computational role have to be eliminated.

scholarly journals Quantum effects in the brain: A review

2020 ◽  
Vol 2 (2) ◽  
pp. 022901 ◽  
Author(s):  
Betony Adams ◽  
Francesco Petruccione
Keyword(s):  
Quantum Effects ◽  
The Brain
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