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Main
T-Bit Project
About TAPe
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Contacts
Demo
Video Reverse Search
Ru
T-Bit Project
What's actually wrong with the concept of AI
Biology and artificial intelligence
Cognitive science: a beginning without an end
Holism and brain studies
TAPe is a new way of processing information
Why perception is necessary for modeling human-like thinking
What's actually wrong with the concept of AI
Evolution of ideas underlying AI: Brief Description
Biology does not understand how the brain works
Why AI does need biology after all
How far artificial neurons are from the real ones
Creating something really similar to how the brain works
Cognitive science: a beginning without an end
Cognitive science has never produced anything practical
Consciousness is not amenable to science
No one knows what consciousness is, everyone keeps talking about it
A sudden idea — the quantum nature of consciousness
Orchestrated objective reduction: what it is and what for
Another theory of consciousness: the integrated information theory
Global workspace theory
Conscious and unconscious thinking. Questions to an academic
Questions for Theories of Consciousness
Ultimate ways to study consciousness without cutting into the brain
Albert Einstein suspected something
Why has psychoanalysis progressed more than science without scientific methods
Insights from intuition and deep observation are not exhausted and are as good as AI
There is no computation in the brain as we all know it. What kind is there?
Why it’s unreasonable to use word Learning in relation to AI
There is a different calculability: what Hilbert and Gödel discovered
Why the brain should be studied as a whole
TAPe models the workings of the mechanisms of perception
Language is a complete system, it’s how it should be studied
The principles by which the Language of Thought functions
The isomorphism of Chinese characters and TAPe
T-Bit: a unit of information 1000x of times more efficient
There is a different calculability: what Hilbert and Gödel discovered
In the XX century, the German mathematician David Hilbert was giving a lot of focus on the question of calculability, attempting to axiomise the entire mathematics. He believed that in order to achieve this goal, it was necessary to prove the consistency and logical completeness of the arithmetic of natural numbers.
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Hilbert introduced several mandatory requirements for an ideal axiomatic theory: completeness, consistency, independence of axioms. He gave it all the collective title of logical computability, implying that if concepts were properly introduced and explained, all mathematics could be proven consistently.
As a result, Hilbert was never able to completely bring calculations down to logical explanations and formulations of all terms and values used in calculations. Hilbert was "halted" by another brilliant logician, mathematician and philosopher of mathematics, Kurt Gödel. In contrast to Hilbert’s problems, he developed incompleteness theorems that demonstrated the impossibility of realizing Hilbert’s problems — and the latter accepted this.
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Science offers its own principles of calculation. AI uses a combination of methods and principles to train its models and solve a range of problems, but without a coherent "scientific" explanation of how this occurs. However, neither scientific principles nor AI principles can solve truly complex problems with the efficiency the human brain demonstrates when doing it.
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The process of creating an ideal axiomatic theory was called "Hilbert's formalism." Other mathematicians saw it as pointless playing with formulas that wasn’t rooted in natural science, that is, in the real world.
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Incompleteness theorems speak about the fundamental limitations of formal arithmetic, and, therefore, also of the limitations of any formal system in which basic arithmetic concepts can be defined: natural numbers, including 0 and 1, addition and multiplication.
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Gödel explained that the principles, the foundations of mathematics, raised numerous questions, as well as the very concept of calculation did. Calculation in the broad sense of the word is not finite. It cannot be argued that the calculations that are used today, describe everything completely, accurately, and in the only way possible. It turned out that different ways of calculation existed, as well as different principles of calculations.