Conjugation concepts in GA₃

Contents

1. Memo
2. Involutions: reversion and conjugation in GA₃
   1. Reversion
   2. Magnitude or modulus
   3. Conjugation
3. Comments

Appendix
Pauli algebra

References

1. David Hestenes, „Space–Time Algebra”
2. David Hestenes, „New Foundations for Classical Mechanics”
3. Chris Doran & Anthony Lasenby, „Geometric Algebra for Physicist”
4. Stephen Gull, Anthony Lasenby, Chris Doran, „Imaginary Numbers are not Real — the Geometric Algebra of Spacetime” http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/ImagNumbersArentReal.pdf

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Subjective and unfinished thoughts on GA dimensions

In everyday life we ordinarily use the term dimension as spatial size. In sciences, than the mathematics and physics, the term of the dimension is used in a diverse, different sense.

Contents

1. Dimension and grade in GA
2. Unit of measurement as dimension
3. Qualitative infinite as dimension

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Apropos of an ÉS’s article written by Károly Fazekas^[1]

Contents

1. On the individual's role
2. On the society's and the social groups' role
3. On the individual and the society affecting each other
   1. In peacetime
   2. In troublous time
4. Conclusion

Honor 8

I protest against it vainly, some of my friends keeps me gadget manic. I admit it, I like the new, inventive technologies for example I would like to use:

• 3D printer; I have a lot of idea for what would be good a 3D printer,

• 3D pen, to fulfill my artistic aptitude,

• drone, to take aerial photos.

But none of the above were bought by me, and I have used the same smartphone for 3 years. So I cannot be a gadget manic.

Now, however, I bought a new smartphone: Huawei Honor 8.

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With Exciting Dénouement

Contents

1. Introduction
2. Geometric Algebra of the Plane
3. The Algebra of 3-Space
4. Conclusions

Abstract by a quotation
„These considerations all indicate that our present thinking about quantum mechanics is infested with the deepest misconceptions. We believe, with David Hestenes, that geometric algebra is an essential ingredient in unravelling these misconceptions.”¹

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¹ See Stephen Gull, Anthony Lasenby, Chris Doran, „Imaginary Numbers are not Real — the Geometric Algebra of Spacetime”;
http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/ImagNumbersArentReal.pdf

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Abstract

For the present information theory is only the theory of the communication. But the main problem is about false and true. There is no differentiation between false and true information in the information theory.

Contents

1. The information
2. New experiences about the human information and manipulation
3. The genesis of information and the created information
4. The information and the probability theory
5. Conclusions

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Abstract

The geometric algebra (GA) is a Clifford algebra (CA) of a vector space over the field of real numbers. A similar concept of complex numbers can be derived from the GA. It is very instructive to compare, as the various authors deduce one of the two-element numbers from CA, or from GA.

Contents

1. David Hestenes
2. Garret Sobczyk
3. Doran-Lasenby
4. Stefan Ulrich
5. Summary

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Inappropriate Mathematical Model in the Interpretation of Bell's Inequality

A few days ago the yellow press was flooded by the news of Big Bell Test. Apropos of Big Bell Test I would like to criticize the interpretation of the Bell inequality as a general principle.

Content

1. A brief overview of the mathematics of probabilities
2. The problem of the Bell inequalities
3. Summary

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Brief thoughts – apropos of an ÉS’s article¹

Abstract by a quotation:

“In our time, the language of politics has become infected with obscurity and madness. No lie is too gross for strenuous expression, no cruelty too abject to find apologia in the verbiage of historicism. Unless we can restore to the words in our newspaper, laws, and political acts some measure of clarity and stringency of meaning, our lives will draw yet nearer to chaos. There will then come to pass a new Dark Ages.”
/ George Steiner, The retreat from the word, 1961 /

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¹ ÉS is the abbreviation of “Élet és Irodalom”, which is a literary and political weekly.

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Desiderata

Content

• The notion of number
• Desiderata to the extension of the numbers
• Summary

Abstract

Although the numbers are yet considered as the simplest abstractions of mathematics, it is increasingly taking shape is a picture in which the numbers will the most complex and exciting concept in mathematics. The geometric algebra is a probable candidate for the new number system, but desiderata of the author is unlike the criteria of the geometric algebra in three points:

• The number line of real numbers is orthogonal to the space-dimensions according to the definition of scalar product.
• As the fundamental operation of arithmetic the product is commutative.
• The space-dimensions evolve from time-dimension which is represented by number line of real numbers.

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