Contents

• Introduction
  • About the concept of angle classically
  • Measurement of angles – measurement of argument on the planes of two-element numbers
  • Norm and argument on the planes of two-element numbers
• The invariance of the argument on the hyperbolic number plane
• Summary

Appendix

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Abstract
The various procedures for renormalization i.e. "abnormalization" in agreement with Feynman, suggest that current physics has serious problems with numbers, especially zero and infinity. This problem can be solved by the discovery of the relationship between two-element numbers – complex, parabolic (dual), hyperbolic numbers – with a so-called quality infinity.

Contents
Introduction
Scale-dependency
Fine-tuning and other jugglery in theoretical physics
Extra
Summary

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About a book

Six Impossible Things: The ‘Quanta of Solace’ and the Mysteries of the Subatomic World – this book like John Gribbin's previous reference books, is a demanding job. The book is a brief description of each of the six leading interpretations of quantum physics. These hypotheses are, in the true sense, science fictions, i.e. ideas that are both scientific and at the same time physicists' fantasies about our world.

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God vs. Science: A Debate between a Physicist and a Priest

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Quotes as abstract

“The idea that space may be emergent from entanglement is an old idea that's getting new traction from people like Roger Penrose. My theory is that space may be emergent, but that time is fundamental and that causality is fundamental. That's a view that a number of people would agree with, and a lot of people would disagree with.” (Lee Smolin, https://www.space.com/einsteins-unfinished-revolution-lee-smolin-interview.html )

„Quantum weirdness isn't real – we've just got space and time all wrong.” (Lee Smolin, https://www.newscientist.com/article/mg24332440-600-quantum-weirdness-isnt-real-weve-just-got-space-and-time-all-wrong/ )

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Comments on ÉS’s article¹

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¹ ÉS is the abbreviation of “Élet és Irodalom”, which is a literary and political weekly. (“Élet és Irodalom” is in English "Life and Literature")

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Review¹

Quotes as abstract

"A valuable insight into what one of the most prominent theoretical physicists of recent times makes of reality's relationship to ideas in quantum theory, standard cosmology, and theories that pretend to replace them."
Richard Webb, New Scientist)

"This gem of a book is vintage Roger Penrose: eloquently argued and deeply original on every page. His perspective on the present crisis and future promise of physics and cosmology provides an important corrective to fashionable thinking at this crucial moment in science. This book deserves the widest possible hearing among specialists and the public alike."
Lee Smolin, author of Time Reborn: From the Crisis in Physics to the Future of the Universe)

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¹Roger Penrose, Fashion, Faith, and Fantasy in the New Physics of the Universe, Princeton University Press, 2016.

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I am planning three articles on a new number system; two are about the number system itself because there are two significantly different number fields: the infinite expansion of real numbers with isotropic and anisotropic number fields. And the third article is about how these numbers can be used to model physical processes.

At the moment, the first article has been completed and the second one is going on. But the hardest task will be the third article.

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It may seem like I'm idle because there was hardly anything on my website since February. But I am working hard on a new number system. It is a big task - I can't promise to finish it within reasonable time.

I'd like to write a little about Roger Penrose's latest book, "Fashion, Faith, and Fantasy in the New Physics of the Universe". Another plan is to comment Lee Smolin’s article about the final illusion. (https://blogs.scientificamerican.com/observations/space-the-final-illusion)

An old Poem

An old poem is humming in my ears for days, Mihály Tompa, The birds to his sons*:

Silent upon a barren bough how long
Will ye remain, sad choristers and mute ?
Have ye forgotten the sweet lay and song
I taught you ? Though blithe music ill would suit
Our present lot, though wit and mirth be gone
And at the notes no merry echoes ring.
Although the song should be a mournful one
Sing, sons, I prithee sing!

A tempest has our forest refuge torn,
No leafy shelter doth receive us now.
Still silent ? Will ye vanish with the morn,
Will ye desert us when we are brought low?
Ah, in an alien grove your song would be
Strange and uncomprehended – curb your wing
And still abide with us, for sad are we :
Sing, sons, I prithee sing!

Sing of our country and her past sublime,
The golden harvest of the days of yore ;
Sing of her future, of that glorious time
When the bare earth shall laugh with flowers once more.
The music shall awake the folded seed
And o'er the quickened fields fair morning bring,
Helping with growing hope our present need:
Sing, sons, I prithee sing !

Here in this bush your ancient home behold.
Where first ye spread your wings ; will ye not rest
After a vagrant flight through cloud aisles cold
At last, and gladly, in your former nest?
Although the wind hath rent it, will ye be
Like callous men, the wreck abandoning?
Fly not to alien shores beyond the sea.
But sing, I prithee sing!

*An allegorical poem addressed by Tompa to the younger generation of poets, after the disastrous Revolution of 1848.
(Nora de Vallyi and Stuart, Dorothy)

(Source: https://www.babelmatrix.org/works/hu/Tompa_Mih%C3%A1ly/A_mad%C3%A1r_fiaihoz )