Hans Rudolf Straub, Author at Hansruedi Straub

Paradoxes and Logic (Part 2)

continues Paradoxes and Logic (part 1) "Draw a Distinction" Spencer-Brown introduces the elementary building block of his formal logic with the words ‘Draw a Distinction’. Figure 1 shows this very simple formal element: Fig 1: The form of Spencer-Brown A Radical Abstraction In fact, his logic consists exclusively of this building block. Spencer-Brown has thus achieved an extreme abstraction that is more abstract than anything mathematicians and logicians have found so far. What is the meaning of this form? Spencer-Brown is aiming at an elementary process, namely the ‘drawing of a distinction’. This elementary process now divides the world into

By Hans Rudolf Straub|2025-11-25T18:26:54+00:0022. August 2024|Categories: Information, Logic, Paradoxes|Tags: Barber paradox, Distinction, paradoxes, Re-Entry|0 Comments

Paradoxes and Logic (Part 1)

Logic in Practice and Theory Computer programs consist of algorithms. Algorithms are instructions on how and in what order an input is to be processed. Algorithms are nothing more than applied logic and a programmer is a practising logician. But logic is a broad field. In a very narrow sense, logic is a part of mathematics; in a broad sense, logic is everything that has to do with thinking. These two poles show a clear contrast: The logic of mathematics is closed and well-defined, whereas the logic of thought tends to elude precise observation: How do I come to a

By Hans Rudolf Straub|2025-12-03T14:55:02+00:0021. August 2024|Categories: Information, Logic, Paradoxes|Tags: Barber paradox, Kurt Gödel, Laws of Form, Logic, mathematics, Paradox|0 Comments

Five Preconceptions about Entropy

Which of these Preconceptions do you Share? Entropy is for nerds Entropy is incomprehensible Entropy is thermodynamics Entropy is noise Entropy is absolute Details 1. Entropy is the Basis of our Daily Lives Nerds like to be interested in complex topics and entropy fits in well, doesn't it? It helps them to portray themselves as superior intellectuals. This is not your game and you might not see any practical reasons to occupy yourself with entropy. This attitude is very common and quite wrong. Entropy is not a nerdy topic, but has a fundamental impact on our lives, from elementary physics

By Hans Rudolf Straub|2025-11-25T18:15:57+00:0016. August 2024|Categories: Information, Entropy|Tags: Bit, Chaos, entropy|0 Comments

LDC – The logodynamic Zettelkasten

LDC (Logodynamic cards) LDC is the new project of my team. It combines a digital slip box (Zettelkasten) for your personal collection of ideas, notes and internet-links with a safe exchangebility of personally selected zettels (cards). As a surplus we have added a novel deliniation of logic, especially convenient for the dynamics in reflections and discussions. LDC is freeware and publicly available at ld-cards.com. Thank you for your interest.

By Hans Rudolf Straub|2025-12-03T14:55:38+00:0016. November 2023|Categories: Unkategorisiert|0 Comments

The mental world

What is the mental world? The mental world is the world in our heads. It is the way in which we perceive the world; it consists of our sensations, feelings and thoughts. It is a completely subjective world. In the theory of the three worlds, the mental world is the third world besides the physical and the Platonic worlds. Difference from the physical world Whereas the physical world is objectively comprehensible, the mental world remains subjective. In other words: whereas we can observe the objects of the physical world from the outside, this is impossible with the objects of the

By Hans Rudolf Straub|2025-11-15T12:37:39+00:0028. March 2022|Categories: music, Semantics, Theory of the Three Worlds|Tags: Mental World, physical world, Qualia, Three worlds|0 Comments

What are the advantages of the equal temperament?

The equal temperament has prevailed in our occidental music culture – despite the obvious shortcoming that its intervals are not pure any longer. This was only possible because some substantial advantages offset the flaw of impurity: 1. One single tuning serves all keys: the fundamental tone is freely selectable. In pure intonation, instruments basically have to be retuned for each key and each fundamental tone. With a harpsichord, this concerns a few strings, but with an organ, this is really a great undertaking in view of the vast number of registers and pipes. The further the keys are apart from

By Hans Rudolf Straub|2025-11-15T12:38:31+00:0017. March 2022|Categories: music, Theory of the Three Worlds, Music scales|Tags: musical scales, Three worlds|0 Comments

Why resonance also works with imprecision

When does resonance occur? Resonance between two physical media depends on the frequency ratio of their natural vibrations. When the two frequencies constitute a simple fraction such as 2/1 or 3/2, resonance can occur. In an earlier post, I explained how the ten simplest frequency ratios lead with mathematical necessity to the ten tones which appear in our musical scales, no matter whether they are major scales, the various minor scales, the ecclesiastical modes, the major pentatonic scales, the minor pentatonic scales, the blues scale, etc. Ten tones are sufficient to build all these different scales. Pure intonation and temperament

By Hans Rudolf Straub|2025-11-15T13:05:58+00:0022. February 2022|Categories: music, Resonance|Tags: frequency ratio, impure temperament, pure temperament, resonance|0 Comments

The equal temperament

Initial wish: changing the fundamental tone during a piece of music In the preceding post, we saw that the just intonation is not pure any more when the fundamental tone is changed since certain intervals change. The further removed the key, the more tones fail to accord with the calculated, i.e. resonant tones. If the frequencies of the scale tones are very slightly shifted – i.e. tempered – then we can also change over into neighbouring keys, i.e. we can modulate. In the equal temperament, we can actually change over to any fundamental tone whatever, and this temperament has successfully

By Hans Rudolf Straub|2025-11-15T13:06:47+00:0014. February 2022|Categories: music, Theory of the Three Worlds|Tags: equal temperament, musical scales, resonance|0 Comments

How the tempered scales came into being

Musical scales before tempering Natural musical scales The musical scales of human cultures developed naturally, i.e. without any conscious mathematical considerations whatsoever, in the course of millennia. The fact that there is a great deal of mathematics behind them nonetheless has something to do with the resonances between the scale tones and the fundamental tone. These resonances strike us as attractive, and music that is based on such resonances is capable of uniting human communities. Mathematically, resonances can be traced back to fractions with as low numbers as possible, and we were able to deduce mathematically which nine intervals have

By Hans Rudolf Straub|2025-11-15T13:07:43+00:001. February 2022|Categories: music, Theory of the Three Worlds, Music scales|Tags: Tempering, Three worlds|0 Comments

Two Less Resonant Intervals for the Gaps

Starting point: two gaps In the previous post, we saw that in the sequence of the ten scales tones found so far, there are two gaps. Can we find resonant tones there, too? We already know the following: We already know the ten most resonant intervals in the octave. These ten intervals serve to constitute the five standard pentatonic scales and our major and minor scales. There, the gaps are not obtrusive; they are only conspicuous in the distribution of all the ten potential scale tones. Intervals do not occur on their own, either in a chord or in a melody. Thus