All posts by Hans Rudolf Straub

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Resonance and Octave

6. January 2021 Hans Rudolf Straub Leave a comment

This is a post about the theory of the three worlds and continues the post about the octave.

We generate a resonance

If you regard resonance as an abstract phenomenon – or as a musical phenomenon that you have not yet experienced – I recommend that you should conduct the following simple experiment: look for a piano (not a digital one) and for a tone on that piano that you can sing well. Press the key of this note and sing it. Of course, this already requires the resonance in your inner ear, otherwise you would not hit the tone. Then press the piano key again, but in such a manner that no sound is produced, and keep the mute key depressed. In this way, the string can vibrate freely. Now sing the tone again. If you have struck the pitch of the key, then the tone will sound in the piano without you pressing the key again. This works best when the piano is open; possibly, you may merely have to sing a bit louder. Now you can sing various tones, for instance a short melody, and you will see that the tone will sound in the piano whenever your voice has the same pitch as the key.

This experiment gives you a sensuous (= physico-mental) impression of the phenomenon of resonance. If you find it difficult to hit the note, there is a simpler way. Depress the piano pedal on the right. Now all the strings can vibrate freely. Now shout at the piano, preferably with the lid open. Again, you will hear how the strings vibrate as an echo of your voice.

Simple resonance

The “long-distance effect” in the above experiment is not magic but produced by sound waves. These waves resonate with the strings. The typical feature of this is the fact that resonance does not occur with any frequency but precisely when the sound wave hits the string’s natural frequency. Natural frequencies are properties of many physical systems; for example, a bridge can have its natural frequency, as can a glass, a piece of wood or a pot. String and wind instruments are perfected in such a way as to resonate particularly well, i.e. to ensure that their natural frequencies are particularly strong and sonorous.

Higher-level resonances

Again I propose a small experiment, and again you will need a piano, which should be tuned this time.

Fig. 1: Two Cs on the piano at the distance of an octave

Now depress the higher C key on the piano (the one on the right). Of course there are many such Cs on the piano; it would be best to take two neighbouring Cs in the middle of the keyboard, where the experiment can be heard most clearly. You can also take tones other than C; the experiment works with all tones, provided that the distance between the two tones is precisely an octave. You will now also realise why the octave is so called: the higher C is at a distance of eight (Latin octo) tones from the lower one (when you count the musical intervals, the starting tone is always counted as well).

Now keep the higher (right-hand) C key mutely depressed. Now hit the lower C key briefly and strongly. You will again hear a “long-distance effect”. Clearly, the string of the higher C started to vibrate when you hit the lower C. Now hit the keys immediately to the right and left of the lower C. You will not be able to get the higher C to vibrate with those keys; no resonance occurs.

Why resonance occurs precisely with an octave

Fig. 2: Possible vibrations of a string

In Fig. 2, you can see five possible vibration patterns for a stretched string. At the bottom (at 1), the string vibrates with precisely one wave peak. At 2, there are two peaks; at 5, there are five. Yellow represents the vibrating string; the black line shows the corresponding sound wave, i.e. the travelling sound wave which has the same frequency as the standing wave, which is represented by the resonant string.

State 1 in Figure 2 is the basic state, i. e. the tone which you hear when you press the piano key. State 2 is the next permitted state of the vibration. Here, the string vibrates with two peaks; at 3, there are three, etc. All states in which the string at its two fixed ends does not vibrate are states that permit the string to vibrate unimpeded. Thus it is not only the state of simple string vibration that is possible, but in principle every state that corresponds to a wavelength that fits integrally into the string length.

In state 2, the wavelength is half as long as in the basic state and thus the frequency is twice as fast/high. State 2, with its frequency twice as high, corresponds to the tone that sounds an octave higher; state 4 corresponds to the tone that sounds two octaves higher.

Now why does the higher C also resonate when you hit the lower C as in the experiment proposed above? The reason for this is the fact that the string of the lower C – like any other string – does not only generate sound in the basic state (state 1 in Fig. 2), but more or less in all the permitted vibrations. These vibrations are thus superimposed on each other. When the sound waves emitted from the lower string reach the string of the higher C, then they do not only contain the basic vibration, but a bit more faintly also the higher vibrations and therefore precisely also the vibration of the higher C string. Thus a resonance is generated.

Sine vibrations and overtones

In mathematical terms, the two black curves in Fig. 2 are sine curves. With a technical device, it is possible to generate such curves acoustically; we then speak of a sine vibration. In natural resonating bodies such as piano strings, the human voice or everywhere else in nature, such pure sine vibrations do not exist; rather, the sound waves produced by them always also contain higher vibrations (levels 2ff. in Fig. 2) in complex superimpositions. They are called overtones. The proportions of the individual overtones, i.e. the extent to which the vibrations of levels 2ff. resonate besides the fundamental tones in the sound mixture, are highly variable and are determined by the sound-producing medium. These mixtures account for the character of the sound of the individual instrument.

Interpretation of the string vibrations in the three worlds

Platonic → physical (from simple to complex)

The example of the vibrating string shows us how mathematical laws from the Platonic world determine the physical world. In the physical world, however, they manifest themselves in many different ways, and a great diversity emerges: several vibrations are simultaneously generated on the string; besides the fundamental tone, there are always many overtones at the same time. Each single one of these vibrations can be described very simply in mathematical terms. The mixture, however, is very complex.

What is very simple in the mathematical world, i.e. in the Platonic world, quickly becomes complex as soon as it takes effect in the physical world.

Penrose’s endless staircase and the “anti-Penrose” direction

In my view, the funnels in Penrose’s sketch represent only one direction of the relationships. Penrose emphasises in his explanation that a description of physics does not require the whole of mathematics and thus arrives at proportions such as those represented in the sketch with the funnels and which appear to contradict logic as in the endless staircase.

In my view, however, the funnels can also be seen in the opposite direction when we focus on the volume of information. This is larger in the physical world than in the Platonic one. When mathematics enters physics, new things emerge, namely the complex diversity of the mixing ratios. This concrete diversity in the physical world constitutes a piece of information which far exceeds the information of the original mathematical world. The volume of information increases in the direction from Platonic to physical. In terms of volume, this represents a countermovement to Penrose’s funnel. Thus when we take a closer look, the endless staircase of the three worlds loses some of its paradoxical terror.

Platonic → mental

Presumably you have heard technically generated sine vibrations. They were the beginning of electronic music and had the charm of something new and technical at the time. It was precisely their naked purity that was impressive. However, these tones also become very boring very quickly. The purity and the sterile banality of these technical sounds is caused by the lacking resonance of the overtones. As listeners, we perceive the rich information of these additional vibrations, and they account for the wealth of natural sounds. I wouldn’t want to have to do without them.

In the next post, I would like to explain why the octave is so important in the mental world and what contributes to the fact that musical scales in all cultures are always based on the octave.

This is a post about the theory of the three worlds.

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The Octave

10. December 2020 Hans Rudolf Straub Leave a comment

A remarkable common feature

All the musical scales known to me encompass an octave. Even scales which tones unusual to us Europeans – Arabic, Indian, Japanese and African ones – encompass precisely an octave, i.e. the deepest and highest tones have a distance of precisely an octave, whatever scale this may be.

I find this extremely remarkable. This is as if all the world’s languages, which after all have very different words, used the same word for a certain concept, had always done so, and done so independently of each other. What is the reason for this?

The theory of the three worlds is capable of providing a plausible explanation of the unusual common feature of the musical scales of all human cultures.

The octave in Platonic terms

If you pluck a string on a violin, you will produce a tone. If you press a finger onto the fingerboard exactly in the middle of the string, the tone will be one octave higher. The same applies to pipes. A pipe that is half as long as another one sounds an octave higher. Obviously, the octave is based on a ratio of 1:2. This is the Platonic, i.e. mathematical side of the octave. Simple mathematical ratios (= fractions) also play a part in connection with other intervals, which will be discussed later.

These mathematical ratios of the relationships between the tones – i.e. the intervals – have long been known and were taught by the Greek Pythagoras, who founded an influential school in southern Italy before Socrates and Plato.

Fig. 1: A vibrating string. In the upper graph, the string is attached on the left and on the right (0 and 1) and is consequently incapable of vibrating there. The farther away it is from the attachment points, the more strongly it vibrates, most strongly in the middle. In the lower graph, a finger has been pressed onto the string, and it now vibrates in half its length and an octave higher. (With these descriptions, however, we have already left the Platonic world and entered the physical world.)

The simple ratio doesn’t yet explain the uniqueness of the common feature, the octave, across all human cultures. Why does the ratio play a part in musical scales at all?

To explain this, we’ll have to have a look at the other two worlds, namely the physical, in which the tones are produced, and the mental, in which we perceive them.

The octave in physical terms

Tones

Tones are material vibrations in a transmission medium such as air. As a rule, a tone contains a superimposition of several vibrations (fundamental tone plus overtones). At this moment, however, we are only looking at the fundamental vibration, which determines the recognisable pitch.

This fundamental vibration is a sine wave, and the pitch is indicated as a frequency, for instance 440 Hz. This frequency means that the sine wave vibrates at a rate of 440 movements per second. The same is done by the string.

When the string vibrates in a fixed place, we speak of a standing wave (cf. Fig. 1 above). Conversely, the vibration in the air moves away from this fixed place (travelling wave). The string is able to move the air by means of its stationary vibration and thus produces a vibration in the air, a sound wave. The string transmits the properties of its vibration, particularly its frequency, to the sound wave.

The wavelength in a travelling wave, i.e. a sound wave, but also a wave on a water surface, for example, is the distance between the antinodes (or wave peaks). In a standing wave such as the string in Fig. 1, the wavelength equals the (double) length of the vibrating string.

If the speed of a travelling wave is constant, then more antinodes must follow each other, the shorter the distances between them are. The distances between the wave peaks represent the wavelength, the number of peaks per time unit represent the frequency of the wave. The more peaks pass a specific place, the smaller their distances.

Thus there is an inversely proportionate ratio between wavelength and frequency, i.e. the shorter the wavelength, the higher the frequency must be. This is why the string that is half as long vibrates at twice the speed. This is the physical origin of the octave.

Tone generation

How does the vibration get into the string? This is the consequence of the fact that a stretched string has a tendency towards natural oscillation. The tension in the string leads to a situation whereby a stimulus, for instance the plucking of a string, triggers off a movement which does not stop at either end of the string but is pushed back. In this way, the standing wave is produced. The wavelength, i.e. the distance between the antinodes, is determined by the length of the string. The reason for this is the fact that no motion is possible any longer at either end of the string since it is attached there. The wave can only vibrate in between. The wavelength must therefore fit precisely into the length of the string.

The octave in mental terms

The inner ear

We perceive sound with our two inner ears. These are organs of an extremely refined design with the structure of a snail, which is why they are called cochlea (Greek for snail). The sound wave comes from outside and travels into the cochlea, which is filled with liquid, and by means of resonance generates a vibration in the so-called basilar membrane, which runs through the entire cochlea. Along the basilar membrane, so-called hair cells receive the vibrations of the basilar membrane and transmit them into the brain as electrical signals. The complex and refined structure of the cochlea, which is only cursorily described here, enables the acoustic signals to be analytically separated so that depending on the frequency, different hair cells are stimulated: the higher the frequency, the closer to the entrance of the cochlea; the lower the frequency, the deeper inside the cochlea.

Mental tone perception

Up to this point, tone perception through the inner ear has nothing to do with the mental world as yet; these are merely the anatomical requirements, i.e. the physical apparatus which specifically prepares the physical signals (the sound waves) for actual perception. This latter takes place in the brain and is a subjective process.

Subjective processes are characterised by the fact that they cannot be understood from the outside. I don’t know how you hear or feel something; this is entirely your own world. However, we have so many common properties as human beings that I may assume that you will experience many things very similarly to me. We have the same anatomy and the same living conditions. Why do many people perceive the same music as beautiful? If we are moved by the same music and apprehend it as cheerful, sad, comforting, rousing, etc. like other people, this demonstrates that our mental worlds are strongly connected to each other despite their subjectivity.

In this context, cultural aspects – learned habits – play a very important role. Ultimately, culture is also part of the mental world; it is the spirit, i.e. the subjectivity, that we share.

This individual and collective subjectivity, our mental world, is not least also based on the physical preconditions, i.e. the physical world.

Thus we are back with our topic: why do all human cultures have the octave in their musical scales, which are so different in other respects? The reason for this can now be explained in terms of physics and lies in resonance.

Resonance

Resonance is required for tones to arrive in the inner ear at all, for the basilar membrane in the inner ear receives the vibrations of the sound waves in a very specific manner. Not all the frequencies find the same resonance in the basilar membrane. The inner ear is structured in such a way that the basilar membrane resonates with high frequencies at its entry and with low frequencies in its depth. In this way, the ear analyses the various pitches. But resonance is responsible for much more, inter alia also for the fact that the octave is always present in the thousands of different musical scales.

This conspicuous observation will be the subject of the next post.

In a further post, I will then deal with the perception of the octave in the mental world, i.e. our subjective world.

This is a post about the theory of the three worlds.

The next post will deal with resonance in the three worlds.

Translation: Tony Häfliger and Vivien Blandford

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The bit has no meaning

29. November 2020 Hans Rudolf Straub Leave a comment

The bit is the basis of IT

Our information technology is based on the bit. Everything that happens in our computers is based on this smallest basic element of information. If someone asks you what a single bit means, you may well answer that the bit can assume two states, of which one means 0 and the other means 1. As is generally known, this enables us to write numbers of any size; all we have to do is to line up a sufficient number of bits.

But is this really true? Does the one state in the bit really mean 0 and the other 1? Can these two states not also assume completely different meanings?

A bit can be attributed arbitrary meanings

In fact, the two states of the bit can assume any meaning. Besides 0/1, true/false, yes/no and positive/negative are also popular; but in principle and in practice, a bit can be attributed any meanings from the outside. Of course, inversions are also possible, i.e. 0/1 and 1/0.

The attribution of the meaning of the bit comes from the outside

Whether the specific bit in the computer programme means 0/1 or 1/0 or something else, does of course play a crucial part. However, the meaning is not in the bit itself, for the bit is a most radical abstraction. It only says that two states exist and which is currently active. What the two mean, however, is a completely different story, which goes far beyond the single bit. In a computer program, it can be declared, for instance, that the bit corresponds to the TRUE/FALSE pair of values; but the same bit, together with another bit, can also be interpreted as part of a number or a letter code – very different meanings, then, depending on the program context.

Digital and analogue context

The software program is the digital context, and of course it consists of further bits. The bits from the surroundings can be used to determine the meaning of a bit. Let’s assume that our bit and other bits are involved in defining the letter ‘f’. Our program is also organised in such a manner that this letter will appear in a table, in a column which is headed ‘Gender’. All this is clearly set out in the software. Now, does the software determine the meaning of the bit? You will doubtless not be surprised if the ‘f’ means ‘female” and the table probably lists various people who can be male (m) or female (f). But what do male and female mean? It is only in the analogue world that these expressions receive a meaning.

The bit, the perfect abstraction

In fact, the bit represents the final point of a radical abstraction of information. In a single bit, information is reduced to what is absolutely elementary in that the information about the meaning has been completely removed from the bit. The bit merely says that two states exist that have been described outside it and which of the two is active at a specific point in time.

This radical abstraction is intentional and makes a great deal of sense in a software, for in this way, the same physical bit in the chip of the computer can be put to a new use again and again, once as a TRUE/FALSE pair, once as 0/1, once as YES/NO, etc. This is very practical and enables the computer to solve any task whatsoever. The perfect abstraction that has thus been achieved, however, simultaneously deprives the single bit of its individual meaning, which can and must be attributed to it anew for every application.

The endless regress

When the meaning of the bit is given from the outside, then of course other bits can take on this task and define the meaning of a bit. For this purpose, however, these outside bits must have the necessary effective power, which of course they cannot have without their own meaning. And naturally, the meanings of the bits of this outer circle are not in these bits themselves – for the same reason as above – but have to be given from the outside, i.e. by a further circle of bits. The bits of this second outer circle must be explained in a further circle, and the meanings of the bits of this further circle in another outer circle… Of course this process of attributing meanings never reaches an end in a world of bits: the regress is endless.

The endless regress only ends in the analogue world

Only when we step out of the program into the real world are we really able to attribute a meaning to the information from the computer.

Selective and descriptive information content

If we recapitulate the above, we can make the following distinction in the bit:

The descriptive information content says what the bit means; it describes the two states of the bit but does not say which state has currently been selected. The selective information content says which of the two states is currently active but does not know anything about the properties of the two states and thus about their individual meanings.

The distinction between the selective and descriptive information content was coined by the British radar pioneer and information scientist Donald McKay in the 1940s, practically at the same time as the first mention and description of the classic bit by the American Shannon. McKay also clearly recognised that Shannon’s bit only carries a selective information content and that the descriptive information content must be given from the outside.

Surprisingly, this insight of McKay’s has almost fallen into oblivion today.

Conclusion:

The bit supplies the selective information content.
2. The descriptive information content is not located in the bit.
3. Thus the bit on its own does not have any meaning.
4. The meaning of the bit is always given from the outside.
5. This initiates an endless regress.
6. Only in the analogue world does the endless regress end.

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Musical Scales in the Theory of the Three Worlds

20. November 2020 Hans Rudolf Straub Leave a comment

Scales are mathematical patterns

When you hear a melody, it is based on a musical scale. The scale consist of the small number of tones which are allowed and may occur in the melody. In a linear sequence, these tones constitute the musical scale. Most melodies that can be heard in our cultural area can be traced back to one single scale, the Ionian or major scale, which is made up of seven notes in very specific scale steps.

Thousands of scales

However, there are thousands of different scales. Presumably you are familiar with the minor as well as with major scale and may have heard something about pentatonic scales or about whole tone scales, Lydian and Phrygian scales, Indian ragas, Japanese and African scales. All these scales differ from each other.

As we will see, however, they have some astounding similarities. Why should people all over the world, in all cultures and with all their differences, comply voluntarily and strictly with these similarities? The reasons for this are easy to explain if we don’t merely look at one world (‘world’ in the sense of Penrose), but at the interaction of all three worlds.

In which of the three worlds do the scales exist?

Scales are part of our reality, no matter how we define reality – unless we define reality as that which we call matter. In that case, the scales are not part of matter. They may manifest themselves in the physical world, for instance if a human being sings or plays them, but they have an identity which is independent of the individual way they are performed. In this sense, scales are non-local, as is typically the case with entities of the Platonic world. Between the scale and its performance, there is thus the relationship of an abstract, i.e. Platonic pattern with its material instance. This is always a 1/n relationship, for the pattern is unique but can be the source of any number of instances.

As a pattern, scales are part of the Platonic world, even though they manifest themselves in the material world. Mathematics, in particular, has much to do with the form of scales, which can be demonstrated easily, yet you don’t need to know anything at all about this kind of mathematics in order to recognise the scales correctly or to sing them. Your mental world in which you experience these scales has no need of figures and formulae.

Scales thus exist in all three worlds:

Platonic world: here, a scale exists as an entity, i.e. as a unity and as a whole. Here, every scale exists only once.

Physical world: here, a scale exists as any number of occurrences – whenever melodies are produced on the basis of it.

Mental world: here, i.e. in your head, you recognise the melodies and the scales.

Of course, each world is organised in its very own way. Now, how do the three worlds interact?

This is a text in the series about the theory of the three worlds.

Translation: Tony Häfliger and Vivien Blandford

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The Physical World

11. November 2020 Hans Rudolf Straub Leave a comment

The world of the natural sciences

The physical world is what is explored by the natural sciences and by physics in particular. The successes of the natural science programme are obvious, both with regard to its insights into how the world works, i.e. theory, and with regard to the technologies this enables, i.e. practice. The natural sciences have changed our world fundamentally ever since Galileo Galilei.

Objectivity

The success became possible because from the Renaissance onwards, the thinkers and explorers in Europe did not solely refer to what had been handed down since ancient times, but conducted unprejudiced research and looked for results themselves. Whereas the monks in the monasteries interpreted and compiled old manuscripts (scholasticism), the free spirits dared to believe what they themselves could see in nature – even if it was in contradiction to the monastic authorities.

However, the loss of the old authorities called for a new guiding principle to prevent a situation whereby everyone would be able to claim anything. Therefore researcher’s proposition should be independently verifiable, and solely what was discernible by everybody beyond any doubt should in future be true and applicable. Thus the ideal of objectivity was born.

Measurability

But the world should not only be able to be described objectively, but also measured with the highest possible precision. This has two advantages: a) A proposition is all the more credible the more precise its predictions are. The more precisely we are able to measure things, the more significant the observations. b) Besides more precise insights, precise measurements also enable us to build increasingly precise instruments and machines.

The world from the outside

The natural sciences thus focus on what can be seen and measured from the outside. This is what Penrose describes as the physical world. Not my internal view, my feeling or my belief is what is called for, but what can be observed and measured from the outside beyond any doubt. This is the physical world.

The physical world in interaction

We could consider the physical world to be the sole true reality, but our view of the world becomes more inclusive if we add the other two worlds. How do the three worlds interact? – There are bridges from one to the other, there are crossovers, and there are effects from one world on the others. I would like to illustrate how these interactions work with examples from the field of music – a field in which obviously all three worlds are involved.

This is a text in the series about the theory of the three worlds.

Translation: Tony Häfliger and Vivien Blandford

Theory of the Three Worlds

The Platonic world

28. October 2020 Hans Rudolf Straub 2 Comments

Why “Platonic”?

Penrose calls one of the three worlds in the theory of three worlds as Platonic. Why?

Plato

The rich Athenian citizen Plato was a follower of the philosopher Socrates. He set up a school of philosophy in the 4th century B.C., which was fundamental for European philosophy and has crucially shaped philosophical discussions until the present day. If Roger Penrose thus calls one of the three worlds “Platonic”, he refers to Plato and specifically to one particular question and the discourse about it, which is still of great significance today. This question is, “Are ideas real?”

Plato’s realism of ideas

Subsequent philosophers often presented the issue as a conflict between Plato and his disciple Aristotle. Plato is ascribed the attitude that ideas were not only real but even constitute actual reality, while what we describe as reality were mere shadows of the original ideas. Penrose calls the abstract world of mathematics “Platonic”, thus referring to Plato’s thought that abstract ideas had the quality of reality.

The world of ideas as one of the three worlds

Of course the Platonic reality of ideas was also disputed, and Europe’s history of philosophy is full of pros and cons about it, which under the headings of realism, nominalism and the problem of universals have shaped the philosophers’ discourse for many centuries and exert an influence in the background even now. Like Plato, Penrose’s theory attributes a reality to the abstract Platonic world, but not an exclusive reality, as would an uncompromising Platonic realism, but as one of the three real worlds, which interact with each other. Thus the theory of the three worlds is not about which world is the real and true one – which was discussed at length as the problem of universals – but about how the interaction takes place between them.

But let’s return to the Platonic world. What distinguishes it from the other two worlds?

Characteristics of the Platonic world

Nonlocality

Where is the number “3”? Can you point your finger at it somewhere in your environment?

Of course you can point at three apples, at three pencilled lines or at three coffee cups, but this is not the number three; rather, they are apples, pencilled lines and coffee cups. The number three remains abstract. No one can point at it.

Naturally, you can also point at the word “three” or at the “3” in this text, but these are only symbols of the number and not the number itself. The number itself remains abstract; it simultaneously exists everywhere and nowhere.

Symbols are always in a certain place, they are thus localised. The number itself, however, is non-local, i.e. there is no place in the universe wh ere the number is found; rather, it can be found everywhere. It exists on earth, on the moon and equally in Andromeda. This nonlocality is a very elementary property of the objects of the Platonic world; in particular, it distinguishes them from the objects in the physical world, in which objects are locally defined, i.e. localised.

Timelessness

The Platonic world’s relationship with time is analogous to locality:

1 plus 2 is 3 – this is true now, was true yesterday and will be true tomorrow and for ever thereafter. In this sense, we can describe the Platonic world as a place of eternal truths, in stark contrast to the physical world, which is subject to constant change. If it rains today, the sun may shine tomorrow; 1 plus 2 is 3 every day and any day. This timelessness applies to all mathematical statements, but also to their objects, again in contrast to the objects of the physical world: the number 3 is timeless, whereas 3 apples are not.

This is a text in the series about the theory of the three worlds

Semantics

Semantics and Linguistics

13. October 2020 Hans Rudolf Straub Leave a comment

What is semantics?

A simple and easily understandable answer is that semantics is the meaning of signals. The signals can exist in any form: as text, as an image, etc. The most frequently studied semantics is that of words.

This is a good reason to examine the relationship of linguistics and semantics. Can semantics be regarded as a subdiscipline of linguistics?

Linguistics and semantics

Linguistics, the science of language and languages, has always examined the structure (grammar, syntax) of languages. Once the syntax of a sentence has been understood, linguists see two further tasks, i.e. secondly to examine the semantics of the sentence and thirdly to examine its pragmatics. “Semantics” is about the meaning of sentences, “pragmatics” about the “why” of a statement.

The linguists’ three steps

In the linguists’ eyes, there are thus three steps in understanding language: syntax -> semantics -> pragmatics. These three fields are weighted very differently by linguists: a conventional textbook predominantly deals with syntax, whereas semantics and pragmatics play a marginal role – and always on the basis of the previously conducted syntactic analysis. The linguists’ syntactic analysis thus already sets the course for what is based on it, namely semantics and pragmatics.

This is not really ideal for semantics. When you deal with semantics in more detail, it becomes clear that the grammar and other properties of individual languages constitute externals which may circumscribe the core of the statements – their meaning – in an occasionally very elegant manner, but they merely circumscribe them and do not represent them completely, let alone directly. A direct formal representation of what is meant by a text, however, would be the actual objective of a scientific semantics.

Can this objective be attained? First, we will have to clarify the relationship between words and concepts – words and concepts are not the same. Concepts are the basic elements of semantics and have a special, but not entirely simple relationship with the words of a language.

Word does not equal concept

One could flippantly assume that there is a one-to-one relationship between words and concepts, i.e. that behind every word, there is a concept which summarises the meaning of the word. But this is precisely what is wrong. Words and concepts cannot unequivocally be mapped on each other. The fact that this is the case can be recognised by everybody who observes himself while reading, talking and thinking.

It is obvious that a word can have several meanings depending on the context in which it is uttered. Occasionally, a word may even have no meaning at all, for instance if it is a technical term and I don’t know the specialist field. In such a case, I may be able to utter the word, but it remains devoid of meaning for me. Yet somebody who understands the specialist field will understand it.

Meaning has much to do with the addressee

Even perfectly normal words which we all know, not always have an unequivocal meaning but can evoke slightly different ideas (meanings) depending on the listener or the context. This does not only concern abstract words or words to which various values are attached, such as happiness, democracy, truth, etc.: absolutely concrete terms like leg, house and dog are interpreted differently by different people, too. The reception of the words as meaningful concepts has much to do with the addressee, his situation and expectations. There is definitely no 1:1 relation between words and concepts.

Meanings vary

Even in ourselves, there are quite different ideas for the same word; depending on the situation, we associate different ideas with the same word, depending on the situation and the everchanging state of our momentary knowledge of words and topics.

A dynamic process

The transition from one language to another shows how the link between words and concepts is a dynamic process in time and changes the meaning of the words. The English word ‘brave’ is the same word as the word ‘bravo’ in Italian, which we use if a musical performance inspires us. But the same word also exists in German, where today it means prissy or well-behaved – certainly not exactly the same as brave, though it is the same word and once meant the same in German as in English.

Semantics examines the play of meanings

We have to accept that a word and a concept cannot be mapped on each other just like that. Although in individual cases it may seem that there is precisely one concept (one semantics) behind every word, this idea is completely inappropriate in reality. And it is this idea which prevents the play of meanings from being understood correctly. Yet it is precisely this play of meanings which, in my view, constitutes semantics as a field of knowledge. In this field, it is possible to represent concepts formally in their own proper structure – which is completely independent from the formal representation of words.

Translation: Tony Häfliger and Vivien Blandford

Uncategorised

The theory of the three worlds

29. September 2020 Hans Rudolf Straub Leave a comment

The theory of the three worlds, according to Roger Penrose connects different fields of science and philosophy.

The three worlds are:

Die platonic world contains objects that are non-local and “timeless”.
The physical world contains objects which can be examined from outside.
The mental world is how we experience things in our head.

Music in the three worlds

Musical scales are part of all three worlds

Logic, Theory of the Three Worlds

The theory of the three worlds (Penrose)

28. September 2020 Hans Rudolf Straub 1 Comment

The theory of the three worlds

There are practical questions which concern our specific lives, and there are theoretical questions which seemingly don’t. However, there are also theoretical considerations which definitely concern our practical everyday lives. One of these is the three worlds theory, which deals with questions as to which worlds we specifically live in.

On what foundation is our everyday existence based? The theory of the three worlds points to the fact that we simultaneously live in three completely different worlds. Practically, this does not constitute a problem for us; theoretically, however, the question arises as to how three worlds which are so different from each other are able to meet in reality at all.

Roger Penrose has named the three worlds as follows:
A) the Platonic world,
B) the physical world,
C) the mental world.

This is Roger Penrose’s original graph:

Platonic world: The world of ideas. Mathematics, for example, is completely located in the Platonic world.

Physical world: The real, physical world with things that are in a specific place at a specific time.

Mental world: My subjective perceptions without which I would not be able to recognise the other worlds, but also my thoughts and ideas as I experience them.

The circular relationship between the three worlds

The arrows between the spheres indicate the circular relationship that these worlds engage in together:

Platonic → physical: Behind physics, there is mathematics. Physics is inconceivable without higher mathematics. Evidently, the physical world complies with mathematical laws with a staggeringly accurate precision. Is the real world therefore determined by mathematics?

Physical → mental: My brain is part of the physical world. According to common understanding, the neurons of the brain tissue determine my brain performance with their electric switches.

Mental → Platonic: Great thinkers are capable of formulating the laws of mathematics in their thoughts (mental world); these laws “come into being” in their heads.

This, then, is the circular process: The Platonic world (mathematics) determines the physical one, which is the basis of human thought. In human thought, in turn, mathematics (and other ideas) are located. These mathematical laws … and here we come full circle.

The scope of the three worlds

What is also interesting are the opening funnels in Penrose’s sketch, which together with the arrows point from one world to the next. Penrose uses them to indicate the fact that the world that follows in the circular process merely requires part of the world from which it emerges during the generation process.

Platonic → physical: Only a small part of mathematical findings can be used in physics. Seen in this light, the physical laws only need (are?) an excerpt from mathematics.

Physical → mental: My brain is a very small part of the physical world.

Mental → Platonic: My brain deals with many things; mathematics and abstract ideas are only a part of it.

The Platonic world is then the origin of the physical world again. However, the proportions do not appear to work out properly. This resembles the famous impossible staircase:

figure: the impossible staircase

The impossible staircase

As an aside:
The impossible staircase was discovered by Roger Penrose’s father, Lionel Penrose, and is also called the Penrose steps – or the Escher-Penrose steps after the Dutch graphic artist who, inter alia, inspired Douglas Hofstadter to write his book Gödel, Escher, Bach. The endlessness with which the steps ascend can seemingly be graphically represented without any problems, but from a logical point of view it is eminently intricate (self-referential taboo).

For Penrose, there is a mystery in the three worlds. He writes that undoubtedly there are not three separate worlds in reality but only one, and at present we are not even able to divine the true nature of this world. This is therefore about three worlds in one – and thus about their differences and the form of their interlinkage.

Not an abstract theory

The three worlds are not an abstract theory but can be recognised in our own world of private experiences. They play an important part in music, for instance. The example of music also enables us to see how the three worlds interact. More about this on this website.

Translation: Tony Häfliger and Vivien Blandford

Artificial Intelligence

Artificial and natural intelligence: the difference

17. September 2020 Hans Rudolf Straub Leave a comment

What is real intelligence?

Paradoxically, the success of artificial intelligence helps us to identify essential conditions of real intelligence. If we accept that artificial intelligence has its limits and, in comparison with real intelligence, reveals clearly discernible flaws – which is precisely what we recognised and described in previous blog posts – then these descriptions do not only show what artificial intelligence lacks, but also where real intelligence is ahead of artificial intelligence. Thus we learn something crucial about natural intelligence.

What have we recognised? What are the essential differences? In my view, there are two properties which distinguish real intelligence from artificial intelligence. Real intelligence

– also works in open systems and

– is characterised by a conscious intention.

Chess and Go are closed systems

In the blog post on cards and chess, we examined the paradox that a game of cards appears to require less intelligence from us humans than chess, whereas it is precisely the other way round for artificial intelligence. In chess and Go, the computer beats us; at cards, however, we are definitely in with a chance.

Why is this the case? – The reason is the closed nature of chess, which means that nothing happens that is not provided for. All the rules are clearly defined. The number of fields and pieces, the starting positions and the way in which the pieces may move, who plays when and who has won at what time and for what reasons: all this is unequivocally set down. And all the rules are explicit; whatever is not defined does not play a part: what the king looks like, for instance. The only important thing is that there is a king and that, in order to win the game, his opponent has to checkmate him. In an emergency, a scrap of paper with a “K” on it is enough to symbolise the king.

Such closed systems can be described with mathematical clarity, and they are deterministic. Of course, intelligence is required to win them, but this intelligence may be completely mechanical – that is, artificial intelligence.

Pattern recognition: open or closed system?

This looks different in the case of pattern recognition where, for example, certain objects and their properties have to be identified on images. Here, the system is basically open, for it is not only possible that images with completely new properties can be introduced from the outside. In addition, the decisive properties themselves that have to be recognised can vary. The matter is thus not as simple, clearly defined and closed as in chess and Go. Is it a closed system, then?

No, it isn’t. Whereas in chess, the rules place a conclusive boundary around the options and objectives, such a safety fence must be actively placed around pattern recognition. The purpose of this is to organise the diversity of the patterns in a clear order. This can only be done by human beings. They assess the learning corpus, which includes as many pattern examples as possible, and allocate each example to the appropriate category. This assessed learning corpus then assumes the role of the rules of chess and determines how new input will be interpreted. In other words: the assessed learning corpus contains the relevant knowledge, i.e. the rules according to which previously unknown input is interpreted. It corresponds to the rules of chess.

The AI system for pattern recognition is thus open as long as the learning corpus has not been integrated; with the assessed corpus, however, such a system becomes closed. In the same way that the chess program is set clear limits by the rules, expert assessment provides the clear-cut corset which ultimately defines the outcome in a deterministic way. As soon as the assessment has been made, a second and purely mechanical intelligence is capable of optimising the behaviour within the defined limits – and ultimately to a degree of perfection which I as a human being will never be able to achieve.

Who, though, specifies the content of the learning corpus which turns the pattern recognition program into a technically closed system? It is always human experts who assess the pattern inputs und who thus direct the future interpretation done by the AI system. In this way pattern recognition can be turned into a closed task like a game of chess or go which can be solved by a mechanical algorithm.

In both cases – in the initially closed game program (chess and Go) as well as in the subsequently closed pattern recognition program – the algorithm finds a closed situation, and this is the prerequisite for an artificial, i.e. mechanical intelligence to be able to work.

Conclusion 1:
AI algorithms can only work in closed spaces.

In the case of pattern recognition, the human-made learning corpus provides this closed space.

Conclusion 2:
Real intelligence also works in open situations.

Is there any intelligence without intention?

Why is artificial intelligence unable to work in an open space without assessments introduced from outside? Because it is only the assessments introduced from outside that make the results of intelligence possible. And assessments cannot be provided purely mechanically by the AI but are always linked to the assessors’ views and intentions.

Besides the differentiation between open and closed systems, our analysis of AI systems shows us still more about real intelligence, for artificial and natural intelligence also differ from each other with regard to the extent to which individual intentions play a part in their decision-making.

In chess programs, the objective is clear: to checkmate the opponent’s king. The objective which determines the assessment of the moves, namely the intention to win, does not have to be laboriously recognised by the program itself but is intrinsically given.

With pattern recognition, too, the role of the assessment intention is crucial, for what kind of patterns should be distinguished in the first place? Foreign tanks versus our own tanks? Wheeled tanks versus tracked tanks? Operational ones versus damaged ones? All these distinctions make sense, but the AI must be set, and adjusted to, a specific objective, a specific intention. Once the corpus has been assessed in a certain direction, it is impossible to suddenly derive a different property from it.

As in the chess program, the artificial intelligence is not capable of finding the objective on its own: in the chess program, the objective (checkmate) is self-evident; in pattern recognition, the assessors involved must agree on the objective (foreign/own tanks, wheeled/tracked tanks) in advance. In both cases, the objective and the intention come from the outside.

Conversely, natural intelligence has to determine itself what is important and what is unimportant, and what objectives it pursues. In my view, an active intention is an indispensable property of natural intelligence and cannot be created artificially.

Conclusion 3:
In contrast to artificial intelligence, natural intelligence is characterised by the fact that it is able to judge, and deliberately orient, its own intentions.

This is a blog post about artificial intelligence. You can find further posts through the overview page about AI.

Translation: Tony Häfliger and Vivien Blandford

Artificial Intelligence

Now where in artificial intelligence is the intelligence located?

17. September 2020 Hans Rudolf Straub Leave a comment

In a nutshell: the intelligence is always located outside.

a) Rule-based systems

The rules and algorithms of these systems are created by human beings, and no one will ascribe real intelligence to a pocket calculator. The same also applies to all other rule-based systems, however refined they may be. The rules are devised by human beings.

b) Conventional corpus-based systems (neural networks)

These systems always use an assessed corpus, i.e. a collection of data which have already been evaluated (details). This assessment decides according to what criteria each individual corpus entry is classified, and this classification then constitutes the real knowledge in the corpus.

However, the classification cannot be derived from the data of the corpus itself but is always introduced from the outside. And it is not only the allocation of a data entry to a class that can only be done from the outside; rather, the classes themselves are not determined by the data of the corpus, either, but are provided from the outside – ultimately by human beings.

The intelligence of these systems is always located in the assessment of the data pool, i.e. the allocation of the data objects to predefined classes, and this is done from the outside, by human beings. The neural network which is thus created does not know how the human brain has found the evaluations required for it.

c) Search engines

Search engines constitute a special type of corpus-based system and are based on the fact that many people use a certain search engine and decide with their clicks which internet links can be allocated to the search string. Ultimately, search engines only average the traces which the many users leave with their context knowledge and their intentions. Without the human brains of the users who have used the search engines so far, the search engines would not know where to point new queries.

d) Game programs (chess, Go, etc.) / deep learning

This is where things become interesting, for in contrast to the other corpus-based systems, such programs do not require any human beings who assess the corpus, which consists of the moves of games previously played from the outside. Does this mean, then, that such systems have an intelligence of their own?

Like the pattern recognition programs (b) and the search engines (c), the Go program has a corpus which in this case contains all the moves of the test games played before. The difference from the classic AI systems consists in the fact that the assessment of the corpus (i.e. the moves of the games) is already defined by the success in the actual game. Thus no human being is required who has to make a distinction between foreign tanks and our own tanks in order to provide the template for the neural network. The game’s success can be directly recognised by the machine, i.e. the algorithm itself; human beings are not required.

With classic AI systems, this is not the case, and a human being who assesses the individual corpus items is indispensable. Added to this, the assessment criterion is not given unequivocally, as it is with Go. Tank images can be categorised in completely different ways (wheeled/tracked tanks, damaged/undamaged tanks, tanks in towns/open country, in black and white/coloured pictures, etc.). This opens the interpretation options for the assessment at random. For all these reasons, an automatic categorisation is impossible with classic AI systems, which therefore always require an assessment of the learning corpus by human experts.

In the case of chess and Go, it is precisely this that is not required. Chess and Go are artificially designed and completely closed systems and thus indeed completely determined in advance. The board, the rules and the objective of the game – and thus also the assessment of the individual moves – are given automatically. Therefore no additional intelligence is required; instead, an automatism can play test games with itself within a predefined, closed setting and in this way attain the predefined objective better and better until it is better than any human being.

In the case of tasks which have to be solved not in an artificial game setting but in reality, however, the permitted moves and objectives are not completely defined, and there is leeway for strategy. An automatic system like deep learning cannot be applied in open, i.e. real situations.

It goes without saying that in practice, a considerable intelligence is required to program victory in Go and other games, and we may well admire the intelligence of the engineers at Google, etc., for that, yet once again it is their human intelligence which enables them to develop the programs, and not an intelligence which the programs designed by them are able to develop themselves.

Conclusion

AI systems can be very impressive and very useful, but they never have an intelligence of their own.

Logic

Static and dynamic IF-THEN, Part 2

18. June 2020 Hans Rudolf Straub Leave a comment

(This blog post continues the introduction to the dynamic IF-THEN.)

Several IF-THENs next to each other

Let’s have a look at the following situation:

IF A, THEN B
IF A, THEN C

If a conclusion B and, at the same time, a conclusion C can be drawn from a premise A, then which conclusion is drawn first?

Static and dynamic logic

In terms of classical logic, this does not matter since A, B and C always exist simultaneously in a static system and do not change their truthfulness. Therefore it does not matter whether one or the other conclusion is drawn first.

This is completely different in dynamic logic – i.e. in a real situation. If I opt for B, it may be that I “lose sight” of option C. After all, the statement B is usually related to further other statements, and these options may continue to occupy my processor, which means that the processor does not have any time at all for statement C.

Dealing with contradictions

There is an additional factor: further conclusions drawn from statements B and C lead to further statements D, E, F, etc. In a static system, all the statements resulting from further valid conclusions must be compatible with each other. This absolute certainty does not exist in the case of real statements. Therefore it cannot be ruled out that, say, statements D and E contradict each other. And in this situation, it does matter whether we reach D or E first.

A dynamic system must be able to deal with this situation. It must be able to actively hold the contradictory statements D and E and “weigh them up against each other”, i.e. analyse their relevance and plausibility while taking their individual contexts into consideration – if you like, this is the normal way of thinking.

In this process, it matters whether I “weigh up” B or C first. Depending on the option I choose, I will end up in a totally different “field” of statements. It is certain that occasionally, statements from the two fields contradict each other. For static logic, this would be tantamount to the collapse of the system. For dynamic logic, however, this is perfectly normal – indeed, a contradiction is the reason for having a closer look at the system of statements from this position. It is the tension that drives the system and keeps the thought process active – until the contradictions are resolved.

Describing this dynamism of thinking is the objective of logodynamics.

Truth – a search process

The fact that the truthfulness of the statements is not determined from the start may be regarded as a weakness of the dynamic system. Then again, this is exactly our own human situation: we do NOT know from the start what is true and what isn’t, and we first have to develop our system of statements. Static logic is unable to tell us how this development works – it is precisely for this that we need a dynamic logic.

Thinking and time

In real thinking, time plays a part. It matters which conclusion is drawn first. Admittedly, this makes things in dynamic logic slightly more difficult. However, if we want to track down the processes in a real situation, we have to accept that real processes always take place in time. We cannot remove time from thinking – nor can we remove it from our logic.

Yet static logic does so. This is why it is only capable of describing one result of thinking, the final point of a process in time. What happens during thinking is the subject of logodynamics.

Determinism – a cherished habit

If I can conclude both B and C from A and if, depending on which conclusion I draw first, the thought process evolves in a different direction, then I will have to face another disagreeable fact: namely that I am unable to derive from the initial situation (i.e. the set of statements A that I accept as being truthful) what direction I will pursue. In other words: my thought process is not determined – at any rate not by the set of what I have already recognised.

On the one hand, this is regrettable, for I can never be quite sure whether I draw the right conclusions since I simply have too many options. On the other hand, this also provides me with freedom. At the moment when I must decide to follow the path through B or C first – and that without already seeing through the system as a whole, i.e. in my real situation – at this moment I also gain the freedom to make the decision myself.

Freedom – there is no certainty

Logodynamics thus explores the thought process for systems which still have to find truth. These systems, too, are not in a position to examine an unlimited number of conclusions at the same time. This is the real situation. This means that these systems have a certain arbitrariness in that they are capable of making decisions at their own discretion. The thought structures that emerge in the process, the advantages and disadvantages they have and what may be taken for granted, is explored by logodynamics.

It is clear that derivability cannot be taken for granted. This is regrettable, and we would prefer to be on the safe side. Yet it is only this uncertainty that enables us to think freely.

The dynamic IF-THEN is necessary

In terms of practical thinking, the point is that static logic is not equal to the process of finding truth. Static logic merely describes the found consistent system. The preceding discussion of whether the system resolves the contradictions and how it does so, will only become apparent through a logodynamic description.

In other words: static logic is incomplete. To examine the real thought process, the somewhat trickier dynamic logic is indispensable. It deprives us of certainty but provides us with a more realistic tool.

This is a blog post about dynamic logic. The preceding post made a distinction between dynamic and static logic IF-THEN.

Artificial Intelligence

Games and Intelligence (2): Deep Learning

8. May 2020 Hans Rudolf Straub Leave a comment

Go and chess

The Asian game of Go shares many similarities with chess while being simpler and more sophisticated at the same time.

The same as in chess:
– Board game → clearly defined playing field
– Two players (more would immediately increase complexity)
– Unequivocally defined possibilities of playing the stones (clear rules)
– The players place stones alternately (clear timeline).
– No hidden information (as, for instance, in cards)
– Clear objective (the player who has surrounded the larger territory wins)

Simpler in Go:
– Only one type of piece: the stone (unlike in chess: king, queen, etc.)

More complex/requires more effort:
– Go has a slightly larger playing field.
– The higher number of fields and stones require more computation.
– Despite its very simple rules, Go is a highly sophisticated game.

Summary

Compared with their common features, the differences between Go and chess are minimal. In particular, Go satisfies the strongly limiting preconditions a) to d), which enable an algorithm to tackle the job:

a) a clearly defined playing field,
b) clearly defined rules,
c) a clearly defined course of play,
d) a clear objective.(Cf. also preceding blog post)

Go and deep learning

Google has beaten the best human Go players. This victory was achieved by means of a type of AI which is called deep learning. Many people think that this proves that a computer – i.e. a machine – can be genuinely intelligent. Let us therefore have a closer look at how Google managed to do this.

Rule- or corpus-based, or a new, third system?

The strategies of the known AI programs are either rule-based or corpus-based. In previous posts, we asked ourselves where the intelligence in these two strategies comes from, and we realised that the intelligence in rule-based AI is injected into the system by the human experts who establish the rules. Corpus-based AI also requires human beings, since all the inputs into the corpus must be assessed (e.g. friendly/hostile tanks), and these assessments can always be traced back to people even if this is not immediately obvious.

However, what does this look like in the case of deep learning? Obviously, it does not require any human beings any longer in order to provide specific assessments – in Go, with regard to the individual moves’ chances of winning; rather, it is sufficient for the program to play against itself and find out on its own which moves have proved most successful. In this, deep learning does NOT depend on human intelligence and – in chess and Go – even turns out to be superior to human intelligence.

Deep learning is corpus-based

Google’s engineers undoubtedly did a fantastic job. Whereas in conventional corpus-based applications, the data for the corpus have to be compiled laboriously, this is quite simple in the case of the Go program: the engineers simply have the computer play against itself, and every game is an input into the corpus. No one has to take the trouble to trawl the internet or any other source for data; instead, the computer is able to generate a corpus of any size very simply and quickly. Although like the programs for pattern recognition, deep learning for Go continues to depend on a corpus, this corpus can be compiled in a much simpler way – and automatically at that.

Yet it gets even better for deep learning. Not only is the compilation of the corpus much simpler, but the assessment of the single moves in the corpus is also very easy: Finding out the best move from among all the moves that are possible at any given time no longer requires any human experts. How does this work? How is deep learning capable of drawing intelligent conclusions without any human intelligence at all? This may be astonishing, but if we look at it in more detail, it becomes clear why this is indeed the case.

The assessment of corpus inputs

The difference is the assessment of the corpus inputs. To illustrate this, let’s have another look at the tank example. Its corpus consists of tank images, and a human expert has to assess each picture according to whether it shows one of our own tanks or a foreign tank. As explained, this requires human experts. In our second example, the search engine, it is also human beings, namely the users, who assess whether the link to a website suggested in the corpus fits the input search string. Both types of AI cannot do without human intelligence.

With deep learning, however, this is really different. The assessment of the corpus, i.e. the individual moves that make up the many different Go test games, does not require any additional intelligence. The assessment automatically results from the games themselves, since the only criterion is whether the game has been won or lost. This, however, is known to the corpus itself since it has registered the entire course of every game right to the end. Therefore the way in which every game has proceeded, automatically contains its own assessment – assessments by human beings are no longer required.

The natural limits of deep learning

The above, however, also reveals the conditions in which deep learning is possible at all: for the course of the game and the assessment to be clear-cut, there must not be any surprises. Ambiguous situations and uncontrollable outside influences are not allowed. For everything to be flawlessly calculable, the following is indispensable:

1. A closed system

This is given by the properties a) to c) (cf. preceding post), which games like chess and Go possess, namely

a) a clearly defined playing field,
b) clearly defined rules,
c) a clearly defined course of play.

A closed system is necessary for deep learning to work. Such a system can only be an artificially constructed system, for there are no closed systems in nature. It is no accident that chess and Go are particularly suitable for AI since games always have this aspect of being consciously designed. Games which integrate chance as part of the system, such as cards in the preceding post, are not absolutely closed systems any longer and therefore less suitable for artificial intelligence.

2. A clearly defined objective

A clearly defined objective – point d) in the preceding post – is also necessary for the assessment of the corpus to take place without any human interference, because the objective of the process under investigation and the assessment of the corpus inputs are closely connected. We must understand that the target of the corpus assessment is not given by the corpus data. Data and assessment are two different things. We have already discussed this in the example of the tanks, where we saw that a corpus input, i.e. the pixels of a tank photograph, did not automatically contain its own assessment (hostile/friendly). The assessment is a piece of information which is not intrinsic to the individual data (pixels) of an image; rather, it has to be fed into the corpus from the outside (by an interpreting intelligence). Therefore the same corpus input can also be assessed in very different ways: if the corpus is told whether an individual image is one of our own tanks or a foreign tank, it still does not know whether it is a tracked tank or a wheeled tank. With all such images, assessments can go in very different directions – unlike with chess and Go, where a move in a game (which is known to the corpus) is solely assessed according to the criterion of whether it is conducive to winning the game.

Thus chess and Go pursue a simple, clearly defined objective. In contrast to these two games, however, tank pictures allow for a wide variety of assessment objectives. This is typical of real situations. Real situations are always open, and in such situations, various and differing assessements can make sense and are absolutely appropriate. For the purpose of assessment, an instance (intelligence) outside the data has to establish the connection between the data and the assessment objective. This function is always linked to an instance with a certain intention.

Machine intelligence, however, lacks this intention and therefore depends on being provided with it by an objective from the outside. If the objective is as self-evident as it is in chess and Go, this is not a problem, and the assessment of the corpus can indeed be conducted by the machine itself without any human intelligence. In such unequivocal situations, machine deep learning is genuinely capable of working – indeed, even of beating human intelligence.

However, this only applies if the rules and the objective of a game are clearly defined. In all other cases, it is not an algorithm that is required but “real” intelligence, i.e. intelligence with a deliberate intention.

Conclusion

Deep learning (DL) works.
DL uses a corpus-based system.
DL is capable of beating human intelligence in certain applications.
However, DL only works in a closed system.
DL only works if the objective is clear and unequivocal.

Ad 4) Closed systems are not real but are either obvious constructs (like games) or idealisations of real circumstances (= models). Such idealisations are invariably simplification with reduced information content. They are therefore incapable of mapping reality completely.

Ad 5) The objective, i.e. the “intention”, corresponds to a subjective momentum. This subjective momentum distinguishes natural from machine intelligence. The machine must be provided with it in advance.

This is a blog post about artificial intelligence.

Translation: Tony Häfliger and Vivien Blandford

Artificial Intelligence

Overview of the AI systems

5. May 2020 Hans Rudolf Straub Leave a comment

All the systems we have examined so far, including deep learning, can in essence be traced back to two methods: the rule-based method and the corpus-based method. This also applies to the systems we have not discussed to date, namely simple automata and hybrid systems, which combine the two above approaches. If we integrate these variants, we will arrive at the following overview:

A: Rule-based systems

Rule-based systems are based on calculation rules. These rules are invariably IF-THEN commands, i.e. instructions which assign a certain result to a certain input. These systems are always deterministic, i.e. a certain input always leads to the same result. Also, they are always explicit, i.e. they involve no processes that cannot be made visible, and the system is always completely transparent – at least in principle. However, rule-based systems can become fairly complex.

A1: Simple automaton (pocket calculator type)

Fig. 1: Simple automaton

Rules are also called algorithms (“Algo”) in Fig. 1. Input and outputs (results) need not be figures. The simple automaton distinguishes itself from other systems in that it does not require any special knowledge base, but works with a few calculation rules. Nevertheless, simple automata can be used to make highly complex calculations, too.

Perhaps you would not describe a pocket calculator as an AI system, but the differences between a pocket calculator and the more highly developed systems right up to deep learning are merely gradual in nature – i.e. precisely of the kind that is being described on this page. Complex calculations soon strike us as intelligent, particularly if we are unable to reproduce them that easily with our own brains. This is already the case with simple arithmetic operations such as divisions or root extraction, where we quickly reach our limits. Conversely, we regard face recognition as comparatively simple because we are usually able to recognise faces quite well without a computer. Incidentally, nine men’s morris is also part of the A1 category: playing it requires a certain amount of intelligence, but it is complete in itself and easily controllable with an AI program of the A1 type.

A2: Knowledge-based system

Fig. 2: Compiling a knowledge base (IE=Inference Engine)

These systems distinguish themselves from simple automata in that part of their rules have been outsourced to a knowledge base. Fig. 2 indicates that this knowledge base has been compiled by a human being, and Fig. 3 shows how it is applied. The intelligence is located in the rules; it originates from human beings – in the application, however, the knowledge base is capable of working on its own.

Fig. 3: Application of a knowledge-based system

The inference machine (“IE” in Figs. 2 and 3) corresponds to the algorithms of the simple automaton in Fig. 1. In principle, algorithms, the inference engine and the rules of the knowledge bases are always rules, i.e. explicit IF-THEN commands. However, these can be interwoven and nested in a variety of different ways. They can refer to figures or concepts. Everything is made by human experts.

The rules in the knowledge base are subordinate to the rules of the inference engine. The latter control the flow of the interpretation, i.e. they decide what rules of the knowledge base are to be applied and how they are to be implemented. The rules of the inference engine are the actual program that is read and executed by the computer. The rules of the knowledge base, however, are not directly executed by the computer, but indirectly through the instructions provided by the inference engine. This is nesting – which is typical of commands, i.e. software in computers; after all, the rules of the inference engine are not implemented directly but read by deeper rules right down to the machine language at the core (in the kernel) of a computer. In principle, however, the rules of the knowledge base are calculation rules just like the rules of the inference machine, but in a “higher” programming language. It is an advantage if the human domain experts, i.e. the human specialists, find this programming language particularly easy and safe to read and use.

With regard to the logic system used in inference machines, we distinguish between rule-based systems

– with a static logic (ontologies type / semantic web type),
– with a dynamic logic (concept molecules type).

For this, cf. the blog post on the three innovations of rule-based AI.

B: Corpus-based systems

Corpus-based systems are compiled in three steps (Fig. 4). In the first step, as large as possible a corpus is collected. The collection does not contain any rules, only data. Rules would be instructions; however, the data of the corpus are not instructions: they are pure data collections, texts, images, game processes, etc.

Fig. 4: Compiling a corpus-based system

These data must now be assessed. As a rule, this is done by a human being. In the third step, a so-called neural network is trained on the basis of the assessed corpus. In contrast to the data corpus, the neural network is again a collection of rules like the knowledge base of the rule-based systems A. Unlike those, however, the neural network is not constructed by a human being but built and trained by the assessed corpus. Unlike the knowledge base, the neural network is not explicit, i.e. it is not readily accessible.

Fig. 5: Application of a corpus-based system

In their applications, both neural networks and the rule-based systems are fully capable of working without human beings. Even the corpus is no longer necessary. All the knowledge is located in the algorithms of the neural network. In addition, neural networks are also quite capable of interpreting poorly structured contents such as a mess of pixels (i.e. images), where rule-based systems (B type) very quickly reach their limits. In contrast to these, however, corpus-based systems are less successful with complex outputs, i.e. the number of possible output results must not be too large since if it is, the accuracy rate will suffer. What are best suited here are binary outputs of the “our tank – foreign tank” type (cf. preceding post) or of “male author – female author” in the assessment of Twitter texts. For such tasks, corpus-based systems are vastly superior to rule-based ones. This superiority quickly declines, however, when it comes to finely differentiated outputs.

Three subtypes of corpus-based AI

The three subtypes differ from each other with regard to who or what assesses the corpus.

Fig. 6: The three types of corpus-based system and how they assess their corpus

B1: Pattern recognition type

I described this type (top in Fig. 6) in the tank example. The corpus is assessed by a human expert.

B2: Search engine type

Cf. middle diagram in Fig. 6: in this type, the corpus is assessed by the customers. I described such a system in the search engine post.

B3: Deep learning type

In contrast to the above types, this one (bottom in Fig. 6) does not require a human being to train or assess the neural network. The assessment results solely from the way in which the games proceed. The fact that deep learning is only possible in very restricted conditions is explained in the post on games and intelligence.

C: Hybrid systems

Of course the above-mentioned methods (A1-A2, B1-B3) can also be combined in practice.

Thus a face identification system, for instance, may work in such a way that in the images provided by a surveillance camera, a corpus-based system B1 is capable of recognising faces as such, and in the faces the crucial shapes of eyes, mouth, etc. Subsequently, a rule-based system A2 uses the points marked by B1 to calculate the proportions of eyes, nose, mouth, etc., which characterise an individual face. Such a combination of corpus- and rule-based systems allows for individual faces to be recognised in images. The first step would not be possible for an A2 system, the second step would be far too complicated and inaccurate for a B1 system. A hybrid system makes it possible.

In the following blog post, I will answer the question as to where the intelligence is located in all these systems. But you have probably long found the answer yourself.

This is a blog post about artificial intelligence.

Translation: Tony Häfliger and Vivien Blandford

Artificial Intelligence

Games and intelligence (1)

27. April 2020 Hans Rudolf Straub Leave a comment

Chess or jass: what requires more intelligence?

(Jass is a very popular Swiss card game of the same family as whist and bridge, though more homespun than the latter.)

Generally, it is assumed that chess requires more intelligence, for obviously less intelligent players definitely stand a chance of winning at cards while they don’t in chess. If we consider, however, what a computer program must be able to do in order to win, the picture soon looks different: chess is clearly simpler for a machine.

This may surprise you, but it is worth looking at the features the two games have in common, as well as their differences – and of course, both have a great deal to do with our topic of artificial intelligence.

Common features

a) Clearly defined playing field

The chessboard has 64 black and white fields; only the pieces that are situated on these fields play a part. At cards, the bridge table could be regarded as a playing field, as could the so-called square “jass carpet” that is placed on a restaurant table; it is the material playing field in the same way that the material chessboard is for chess. If we are interested in successful playing behaviour, however, the colour of the jass carpet or the make of the chess board are immaterial; what counts is solely the abstract, i.e. “IT-type” of playing field: where can our chess pieces and playing cards move in a more mathematical way? And in this respect, the situation is completely clear at cards, too: the cards are in a clearly defined place at any given time, either in a player’s hand ready to be played, or in front of a player as a trick already won, or on the table as a face-up card to be seen by everyone. Both chess and cards can therefore be said to have a clearly defined playing field.

b) Clear rules

Here, too, there is hardly any difference between the two games. Although there are all sorts of variants of whist and bridge, and although jass rules differ from village to village and even from restaurant to restaurant (which may occasionally lead to heated discussions), as soon as a set of rules has been agreed upon, the situation is clear. As in chess, it is clear what goes and what doesn’t, and the players’ possible activities are clearly defined.

c) Clear course of play

Here again, the games do not differ from each other. At any point in time, there is precisely one player who is permitted to act, and his or her options are clearly defined.

d) Clear objective

Chess is about beating the opponent’s king; card games are about scoring points or tricks, depending on the variant. Games do not last an eternity. A card game is over when all the cards have been played; in chess, the draw and stalemate rules prevent a game from going on indefinitely. There is always one clear winner, there are always clear losers, and if need be there is a definitive tie.

Differences

e) Clear starting situation?

In chess, the starting situation is identical in every game; all pieces start at their appointed place. At cards, however, the pack of cards is shuffled before every game. Whereas in chess, we always start from precisely the same situation, we have to envisage a new one before every card game. Chance thus plays an important role in cards; in chess, it has been deliberately excluded. This is bound to have consequences. Since I have to factor in chance at cards, I cannot rely on certainties like in chess, but have to rely on probabilities.

f) Hidden information?

A lack of knowledge remains a challenge for card players throughout the game. Whereas in chess, everything is openly recognisable for each player on the board, card games literally thrive on players NOT knowing where the cards are. Therefore they must guess – i.e. rely on probabilities – and run certain risks. There is no guessing in chess; the situation is always clear, open and evident. Of course, this makes it substantially easier to describe the situation in chess; at cards, however, this lack of knowledge makes a description of the situation difficult.

g) Probabilities and emotions (psychology)

If I do not know everything, I have to rely on probabilities. Experience shows that this is something that we human beings are comprehensively very bad at. We let ourselves be guided by emotions much more strongly than we care to admit. Fears and hopes determine our expectations, and we often grossly misjudge probabilities. An AI program naturally has an edge over us in this respect since it does not have to cope with emotions and is much better at computing probabilities. Yet the machine wants to beat its opponent and will therefore have to assess its opponent’s reactions correctly. The AI program would therefore do well to take its opponent’s flawed handling of probabilities into its considerations, but this is not very easy in terms of algorithms. How does it recognise an optimist? Human players try to read their opponents while trying to mislead them about their own emotions at the same time. This is part of the game. It is no use to the program if it makes computations without any emotions while being incapable of recognising and assessing its opponent’s emotions.

h) Communication

Chess is played by one player against the other. Card games usually involve four players playing each other in pairs. This aspect, i.e. that two individuals have to coordinate their actions, makes the game interesting, and it would be fatal for a card game program to neglect this aspect. But how should we program this? What has to be taken into account here, too, is point f) above, namely the fact that I cannot see my partner’s cards; I neither know my partner’s cards nor my opponents’. Of course my partner and I are interested in coordinating our game, and part of this is that we communicate our options (hidden cards) and our strategies (intentions for driving the game forward) to each other. If, for instance, I hold the ace of hearts, I would like my partner to lead hearts to enable me to win the trick. However, I am not allowed to tell him that openly – yet an experienced card player would not find this a problem. First of all, the run of the game often reveals who holds the ace of hearts. Of course it is not easy to discover this because both the cards that have already been played and possible tactics and strategies have to be taken into consideration. The number of options, the computation of the probabilities and the psychology of the players all come into play here, which can result in very exciting conflict situations – which ultimately also makes the game attractive. In chess, however, with its constantly very explicit situation, circumstances are a great deal simpler in this respect.

But this is not all:

i) The legal grey area

Is it really true that my partner and I are unable to exchange communication about our cards and strategies? Officially, of course, this is prohibited – but can this ban really be implemented in practice?

Of course it can’t. Whereas in chess, it is practically solely the explicit moves that play a part, there is a great deal of additional information at cards which a practised player must be able to read. How am I smiling when I’m playing a card? If I hold the ace of hearts, which can win the next trick, I obviously want my partner to help me and lead hearts. One possibility of achieving this in a jass game is to play a minor heart and place it on the table with distinctive emphasis. A practised partner will easily read this as a signal for him to lead hearts next time rather than diamonds to enable me to win the trick with my ace. No one will really be able to ban anyone from leading a card in a certain way, provided that this is done with sufficient discretion. Partners who are well attuned to each other do not only know the completely legal signals which they automatically emit through the selection of the cards they play, but also some signals from the grey area with which they coordinate their game.

These signals constitute information which an ambitious AI will have to be able to identify and process. The volume of information which it has to process for this purpose is not only much larger than the volume of information in chess, it is not limited by any manner of means either. My AI plays two human opponents, and those two also communicate with each other. The AI should be able to recognise their communication in order not to be hopelessly beaten. The signals agreed upon by the opponents may of course vary and be of any degree of sophistication. How can my AI discover what arrangements the two made prior to the game?

Conclusion

Card games are much more difficult to program than chess

If we want to develop a program for a card game, we will have to take into consideration aspects e) to i), which hardly play any part in chess. In terms of algorithms, however, aspects e) to i) constitute a difficult challenge owing to the imponderabilities.

In comparison with card games, chess is substantially less difficult for a computer because

– there is always the same starting situation,
– there is no hidden information,
– no probabilities need to be taken into account,
– human emotions play a small part,
– there is no legal grey area because no exchange of information between partners is possible.

For an AI program, chess is therefore the simpler game. It is completely defined, i.e. the volume of information that is in the game is very small, clearly disclosed and clearly limited. This is not the case with card games.

This is a blog post about artificial intelligence. In the second part about games and intelligence, I will deal with Go and deep learning .

Translation: Tony Häfliger and Vivien Blandford