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Discovery versus invention and why mathematics is just another language

October 31, 2021

Languages are invented, and words are invented. We can assign whatever meaning we can commonly agree on, to any word. Discovery and invention are such words and are labels, placeholders, for some intended meaning. Confusion with words arise because the nuances of meaning associated with a word may not be as common as we think. This post is about mathematics being a language, but I need to start by what I understand to be discovery and how it differs from invention.

Discoveries and inventions

I do not quite understand the uncertainty sometimes expressed about whether things are inventions or discoveries. I find no ambiguity between “discovery” and “invention”. It is not as if everything in the world must be either discovered or invented. There is no need for any epistemological issues here. Discovery consists of the first finding of that which exists but is unknown. It includes what may be newly inferred either by deduction or by induction. What has been discovered by others can still be discovered by someone else as new knowledge. The discoverer, however, does not impact what is discovered. Discovery is always about finding. Invention, on the other hand, is always about creation. It creates something (material or immaterial) that did not exist before. The act of invention requires purpose and always results in a construct. The inventor defines and creates the invention. Once invented by someone, something may be discovered by others. An invention may be so complex that even its inventor has to discover some of its detailed characteristics or workings. It may be rediscovered if it has been forgotten (if immaterial) or has fallen into disuse (if material). Creation is not necessarily or always invention. A copy or even an improvement of an invention by someone else may involve creation but is neither a discovery nor an invention. Both finding and creation imply a doer, though it is not necessary for the doer to be human.

Of course everything discovered to exist must – so our logic tells us – have had a beginning. Whether such a beginning was a creation event (an invention), or random happenchance, or something else, lies at the heart of the most intractable philosophical question of all – the mystery of existence. I take the view that existence encompasses both material and immaterial things, and that the immaterial does not necessarily require a mind within which it is perceived to exist. The flow of time, causality and the laws of nature are, to my mind, examples of such immaterial existence. Thoughts, however, are also immaterial and exist but they need a mind within which to reside.

  • we discover our existence, we invent our names
  • emotions are discovered, their descriptive names are invented
  • hate is discovered, war is invented
  • a thought is discovered, a story is invented
  • the laws of nature are discovered, the laws of man are invented
  • knowledge is discovered, the Koran and the Bible are invented
  • human capabilities are discovered, actual behaviour can often be invented
  • the cognitive ability to relate and recognise patterns in sound is discovered, a piece of music is invented
  • language ability is discovered, languages are invented
  • new individual experiences (emotions, colours, feelings) are discovered, naming them may be inventions
  • individual learning of what is knowable but not known is discovery, creating a new word is invention
  • (Pooh learning about elephants was an invented discovery, naming them heffalumps was invention by Milne)
  • the cognitive ability to tell lies is discovered, fiction is invented
  • the human need to seek explanations is discovered, gods are invented
  • the emotional, human need for spiritualism is discovered, religions are invented
  • logic is discovered, argument is invented
  • relationships and patterns in the universe are discovered, languages to describe these are invented
  • where no man has gone before leads to discovery, naming or mapping the where is invention
  • my need for coffee is a discovery, my mug of coffee is a creation but is no invention
  • human behaviour may be discovered, “social science” is always invention
  • new geography is usually discovery and no geography can ever be invented
  • the past is immutable, history is a patchwork of discovered islands in a sea of invented narrative
  • news is discovered, fake news is invented

As a generalisation there is scientific discovery and there is artistic invention. The process of science is one of discovery and there is little ambiguity about that. The search for knowledge is about discovery and never about the invention of knowledge. That tools and instruments used for this process of discovery are often inventions is also apparent. Some ambiguity can be introduced – though I think unnecessarily – by treating postulates and hypotheses and theories as inventions in their own right. Thoughts are discovered, never invented. Any hypothesis or theory – before being put to the test – is a discovered thought, whether based on observations or not. Theories are discovered thoughts, but a conspiracy is always invented. Of course, observation (empiricism) may lead to conjecture, which may then take the form of a postulate or a theory. But there is no need for such conjectural thought to be equated with invention (though it often is).  Science discovers, engineering often invents. A good scientist discovers and uses inventions to further his discoveries. A good scientist may also be, and often is, an inventor. (Of course a great many calling themselves scientists are just bean counters and neither discover nor invent). Composers and authors and lawyers often invent. Doctors discover a patient’s ailments, a quack invents them. Most pharmaceutical companies invent drugs to suit discovered illnesses, some less ethical ones invent illnesses to suit their discovered compounds. Talent is discovered, a celebrity is invented.

Then there is the question of whether mathematics is discovered or invented. But before that we must define what it is that we are considering.

What mathematics is

(more…)

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Always mish before the mash and never the tock before the tick

July 18, 2021

Mish-mash, tick tock, ping pong, King Kong, chit-chat and clip-clop trip off the tongue. But reverse the order and the tongue protests. Bing bong is fine but bong bing just does not work. English is replete with examples. Tip top, flip flop, shilly shally, hip hop, pitter patter, sing song and flim flam among many others. It is even acceptable to create such duplications for rhetorical effect even if the meanings are not defined as long as the unwritten rule is followed. You could write kling klang but not klang kling. Frippery-frappery, hee haw, pish posh, tip tap, Kit Kat, or flik flak would all be okay but none of the reverse. Invent new and unusual combinations and the unwritten rule still applies. Mish-mosh not mosh mish. Clip clap but not clap clip.

Reduplication is the label for creating new words by the repeating of some or all of a word for rhetorical effect. Almost all languages use reduplication. The simplest form of reduplication is with just an exact repetition of a sound which has its origins, I would guess, in the babble of infants. It creates rhythm. The rhythm of language would seem to be a cognitive trait. Mama, papa, dada, tata, and nana all originate in infancy and have all become words with specific meanings. There are three kinds of reduplication:

  1. Exact reduplication, (ma ma, pa pa, bang bang, …)
  2. Rhyming reduplication (super-duper, hoity-toity, hanky-panky, ….), and
  3. Ablaut reduplication

The pattern by which vowels change in reduplication to form a new word or phrase with a specific meaning is called ablaut reduplication. In English the discovered rule is i before a or o. It is not a a rule which has been imposed but is one created by usage and discovered to hold. There are almost no examples in English of ablaut reduplication where the first vowel is not an i. The second word is nearly always with a or o. There are a very few examples of usage with three words in sequence, but where they do occur the i before a before o still applies (bing bang bong, sing sang sung). 

It is not just a simple matter of following vowel classification. Vowels are usually classified according to the position of the tongue in the mouth from high to low and from front to back. High to low gives (i, u, e, o and a) while front to back gives us (a, e, i, o and u). 

Brittanica:

Vowel, in human speech, sound in which the flow of air from the lungs passes through the mouth, which functions as a resonance chamber, with minimal obstruction and without audible friction; e.g., the i in “fit,” and the a in “pack.” Although usually produced with vibrating vocal cords, vowels may be pronounced without such vibration, resulting in a voiceless, or whispered, sound. From the viewpoint of articulatory phonetics, vowels are classified according to the position of the tongue and lips and, sometimes, according to whether or not the air is released through the nose.

A high vowel (such as i in “machine” and u in “rule”) is pronounced with the tongue arched toward the roof of the mouth. A low vowel (such as a in “father” or “had”) is produced with the tongue relatively flat and low in the mouth and with the mouth open a little wider than for high vowels. Midvowels (such as e in “bed” and o in “pole”) have a tongue position between the extremes of high and low.

High, middle, and low vowels are also classified according to a front-to-back dimension. A front vowel is pronounced with the highest part of the tongue pushed forward in the mouth and somewhat arched. The a in “had,” the e in “bed,” and the i in “fit” are front vowels. A back vowel—e.g., the u in “rule” and the o in “pole”—is produced with the back part of the tongue raised toward the soft palate (velum).

Ablaut theory has an explanation (sort of) for why the i, a, o rule applies.

How does Ablaut reduplication work?

In Indo-European languages, the primary, inherent vowel of most syllables is a short e. Ablaut is the name of the process whereby the core vowel, which is almost always an e as mentioned above, would either be lengthened, altered to an o, altered and lengthened, or completely removed, known as the zero grade (an example of a zero grade: does not – doesn’t). These alterations on the way e sounds are what is known as Ablaut grades. This results in five ablaut grades overall: full grade (e), altered grade (o), lengthened grade (ee), altered length grade (oo), and zero grade (nothing). The first vowel is almost always a high vowel. This is then followed by the repetition of a lower vowel in relation to the first vowel. This is why the order is I, A, O.

Ultimately it is human physiology, ease of production and our sense of rhythm (cognition) which creates the sequences our tongues follow. It is physiology first and then cognition which determine the sequences of sounds we produce. The (i, a, o) rule is a discovered rule and only describes what comes naturally. It is not a rule that is invented and imposed.

And Spike Milligan’s Ning Nang Nong (in the style of Edward Lear) complies with the rule – how not?
 
On the Ning Nang Nong
 
On the Ning Nang Nong
Where the Cows go Bong!
and the monkeys all say BOO!
There’s a Nong Nang Ning
Where the trees go Ping!
And the tea pots jibber jabber joo.
On the Nong Ning Nang
All the mice go Clang
And you just can’t catch ’em when they do!
So its Ning Nang Nong

Cows go Bong!
Nong Nang Ning
Trees go ping
Nong Ning Nang
The mice go Clang
What a noisy place to belong
is the Ning Nang Ning Nang Nong!!
 
Spike Milligan (1959)
 
 

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“Most beautiful words in English”

July 6, 2021

The beauty of a word lies both in the meaning and in the sound, the rhythm and the music of the word itself.

Re-blogged from Atkins Bookshelf

The Top Ten Most Beautiful Words in the English Language

The English language is vast, containing more than a million words and growing at a rate of several thousand words each year. However, most English speakers have a vocabulary that is substantially smaller: generally between 20,000 to 35,000. Every once in a while, through reading or conversation, you come across a word that stands out; you think to yourself “that is such a beautiful word.” Many logophiles keep lists of what they consider to be beautiful words. For example, in 1932, to publicize the publication of one of Funk & Wagnalls new dictionaries, founder Wilfred Funk published a list of what he considered, after a “thorough sifting of thousands of words” the ten most beautiful words (in his words, “beautiful in meaning and in the musical arrangement of their letter”) in the English language. (Incidentally, there is a word for that: euphonious — a euphonious word is a beautifully-sounding word; interestingly, euphonious is itself… euphonious.) Here is Funk’s list of the top ten most beautiful words in the English language:

chimes
dawn
golden
hush
lullaby
luminous
melody
mist
murmuring
tranquil

More recently, the editors of BuzzFeed cast their net into the vast ocean of the Twitterverse to find out what people considered the most beautiful words in the English words. They came up with a great list of “32 of the most beautiful words in the English language.” The list should be published with some caveats. One of the words, hiraeth, is actually Welsh. A few are actually neologisms (relatively new words that are in the process of entering common use) and will not be found in traditional dictionaries. Here are the top ten most beautiful English words from that list:

aquiver
mellifluous
ineffable
hiraeth
nefarious
somnambulist
epoch
sonorous
serendipity
limerence

To celebrate United Nations English Language Day (April 23), the editors of KBLOG, the blog of Kaplan International Languages, published their own  list of the top 10 most beautiful English words:

sequoia
euphoria
pluviophile
clinomania
idyllic
aurora
solitude
supine
petrichor
serendipity

Any list would be entirely subjective and arguing against a list makes no sense. All one can do is suggest alternatives. I have chosen a list where I like the word but where the meaning is not necessarily beautiful. They all have at least 3 syllables and I suspect that at least 3 is needed for the word itself to have an inherent rhythm.

surreptitious

sublime

liberation

salamander 

mysterious

mellifluous

palpitation

calamitous

infinity, and, of course,

forty-two.

 

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Numbers emerge from the concept of identity

December 18, 2020

Numbers are abstract. They do not have any physical existence. That much, at least, is fairly obvious and uncontroversial.

Are numbers even real? The concept of numbers is real but reason flounders when considering the reality of any particular number. All “rational” numbers (positive or negative) are considered “real numbers”. But in this usage, “real” is a label not an adjective. “Rational” and “irrational” are also labels when attached to the word number and are not adjectives describing the abstractions involved. The phrase “imaginary numbers” is not a comment about reality. “Imaginary” is again a label for a particular class of the concept that is numbers. Linguistically we use the words for numbers both as nouns and as adjectives. When used as a noun, meaning is imparted to the word only because of an attached context – implied or explicit. “A ten” has no meaning unless the context tells us it is a “ten of something” or as a “count of some things” or as a “measurement in some units” or a “position on some scale”. As nouns, numbers are not very pliable nouns; they cannot be modified by adjectives. There is a mathematical abstraction for “three” but there is no conceptual, mathematical difference between a “fat three” and a “hungry three”. They are not very good as adjectives either. “Three apples” says nothing about the apple. “60” minutes or “3,600” seconds do not describe the minutes or the seconds.

The number of apples on a tree or the number of atoms in the universe are not dependent upon the observer. But number is dependent upon a brain in which the concept of number has some meaning. All of number theory, and therefore all of mathematics, builds on the concept and the definition of one.  And one depends, existentially, on the concept of identity.

From Croutons in the soup of existence

The properties of one are prescribed by the assumptions (the “grammar”) of the language. One (1,unity), by this “grammar” of mathematics is the first non-zero natural number. It is the integer which follows zero. It precedes the number two by the same “mathematical distance” by which it follows zero. It is the “purest” number. Any number multiplied by one or divided by one remains that number. It is its own factorial. It is its own square or square root; cube or cube root; ad infinitum. One is enabled by existence and identity but thereafter its properties are defined, not discovered. 

The question of identity is a philosophical and a metaphysical quicksand. Identity is the relation everything has to itself and nothing else. But what does that mean? Identity confers uniqueness. (Identical implies sameness but identity requires uniqueness). The concept of one of anything requires that the concept of identity already be in place and emerges from it. It is the uniqueness of identity which enables the concept of a one.

Things exist. A class of similar things can be called apples. Every apple though is unique and has its own identity within that class of things. Now, and only now, can you count the apples. First comes existence, then comes identity along with uniqueness and from that emerges the concept of one. Only then can the concept of numbers appear; where a two is the distance of one away from one, and a three is a distance of one away from two. It is also only then that a negative can be defined as distance away in the other direction. Zero cannot exist without one being first defined. It only appears as a movement of one away from one in the opposite direction to that needed to reach two. Negative numbers were once thought to be unreal. But the concept of negative numbers is just as real as the concept for numbers themselves. The negative sign is merely a commentary about relative direction. Borrowing (+) and lending (-) are just a commentary about direction. 

But identity comes first and numbers are a concept which emerges from identity.

image from personality-psychology.com/

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What the brain cannot undo

December 6, 2020

2020 comes close to being annus horribilis.

There is much I wish I had not seen or heard or smelled or learnt. But to unsee or unhear or unlearn or unremember or unknow are not permitted, by reality or by language.

  • There is much more unseen than seen.
  • But what has been seen cannot be unseen.
  • To unsee is not an action permitted by reality or by language.
  • What has been seen may not be remembered.
  • What is remembered is only a decaying image of what was seen.
  • What is remembered may be forgotten but cannot be erased selectively or voluntarily
  • To unremember is not an action in reality or in language.
  • What is known is a tiny part of what is knowable. 
  • The size of the unknowable is unknowable.
  • To learn is to convert some of what is unknown (but knowable) to be known.
  • To convert knowledge to ignorance by unknowing is unreal.
  • Forgetting is real and ignorance is common, but how to unknow is unknown.
  • To unlearn is not an action permitted by reality or language.
  • To not hear many things is normal and to forget what has been heard is common.
  • But to unhear what has been heard is not permitted.

Doing is a temporal activity. Undoing in time is fundamentally impossible.

What the brain receives as sensory input cannot be undone.

To forget is human but to undo is divine.

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“Random” is indistinguishable from Divine

November 2, 2020

“Why is there something rather than nothing?” is considered by some to be the most fundamental question in metaphysics, and by others to be an invalid question. The Big Bang, quantum mechanics, time, consciousness, and God are all attempts to answer this question. They all invoke randomness or chance or probabilistic universes to escape the First Cause Problem. Physics and mathematics cannot address the question. An implied God of Randomness is the cop-out for all atheists.

Stanford Encyclopedia of Philosophy

The Commonplace Thesis, and the close connection between randomness and chance it proposes, appears also to be endorsed in the scientific literature, as in this example from a popular textbook on evolution (which also throws in the notion of unpredictability for good measure):

scientists use chance, or randomness, to mean that when physical causes can result in any of several outcomes, we cannot predict what the outcome will be in any particular case. (Futuyma 2005: 225)

Some philosophers are, no doubt, equally subject to this unthinking elision, but others connect chance and randomness deliberately. Suppes approvingly introduces

the view that the universe is essentially probabilistic in character, or, to put it in more colloquial language, that the world is full of random happenings. (Suppes 1984: 27)

The scientific method is forced to introduce random into stories about the origin of time and causality and the universe and life and everything. Often the invocation of random is used to avoid any questions of Divine Origins. But random and chance and probability are all just commentaries about a state of knowledge. They are silent about causality or about Divinity. Random ought to be causeless. But that is pretense for such a random is outside our experience. The flip of a coin produces only one outcome. Multiple outcomes are not possible. The probability of one of several possible outcomes is only a measure of lack of knowledge. Particles with a probability of being in one place or another are also an expression of ignorance. However when it is claimed that a particle may be in two places simultaneously we encounter a challenge to our notion of identity for particle and for place. Is that just ignorance about location in time or do we have two particles or two places? Random collisions at the start of time are merely labels for ignorance. Invoking singularities which appear randomly and cause Big Bangs is also just an expression of ignorance.

Whenever science or the scientific method requires, or invokes, randomness or probability, it is about what we do not know. It says nothing about why existence must be. The fundamental question remains unaddressed “Why is there something rather than nothing?”

And every determinist or atheist, whether admitted to or not, believes in the God of Randomness. Everything Random is Unknown (which includes the Divine).

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Why did we start to count?

October 12, 2020

Counting and the invention of numbers and the abstractions enabling mathematics are surely cognitive abilities. Counting itself involves an abstract ability. The simple act of raising two fingers to denote the number of stones or lions or stars implies first, the abstract ability to describe an observed quality and second, the desire to communicate that observation.

What led humans to counting and when?

Before an intelligence can turn to counting it must first have some concept of numbers. When and how did our ancient ancestors  first develop a concept of numbers and then start counting? …….. 

It seems clear that many animals do distinguish – in a primitive and elementary way – between “more” and “less, and “few” and “many”,and “bigger” and “smaller”, and even manage to distinguish between simple number counts. They show a sophisticated use of hierarchy and precedence.

Some primates show some primitive abilities when tested by humans

…..  Rhesus monkeys appear to understand that 1 + 1 = 2. They also seem to understand that 2 + 1 = 3, 2 – 1 = 1, and 3 – 1 = 2—but fail, however, to understand that 2 + 2 = 4. ……

But even chimpanzees and monkeys rarely, if ever, use counts or counting in interactions among themselves. The abilities for language and counting are not necessarily connected genetically (though it is probable), but they are both certainly abilities which appear gradually as cognition increases. Mathematics is, of course, just another language for describing the world around us. Number systems, as all invented languages, need that a system and its rules be shared before any communication is feasible. It is very likely that the expressions of the abilities to count and to have language follow much the same timeline. The invention of specific sounds or gestures to signify words surely coincided with the invention of gestures or sounds to signify numbers. The step change in the size of brains along the evolutionary path of humans is very likely closely connected with the expressions of the language and the counting abilities.

The ability to have language surely preceded the invention of languages just as the ability to count preceded the expressions of counting and numbering. It is not implausible that the first member of a homo erectus descendant who used his fingers to indicate one of something, or four of something else, to one of his peers, made a far, far greater discovery – relatively – than Newton or Einstein ever did.

We must have started counting and using counts (using gestures) long before we invented words to represent counts. Of course, it is the desire to communicate which is the driving force which takes us from having abilities to expressions of those abilities. The “cooperation gene” goes back to before the development of bipedalism and before the split with chimpanzees or even gorillas (at least 9 million years ago).

The simple answer to the question “Why did we start to count?” is because we could conceive of a count, observed it and wished to communicate it. But this presupposes the ability to count. Just as with language, the ability and the expression of the ability, are a consequence of the rapid increase in brain size which happened between 3 m and 1 m years ago.

I am persuaded that that rapid change was due to the control of fire and the change to eating cooked food and especially cooked meat. The digestion of many nutrients becomes possible only with cooked food and is the most plausible driver for the rapid increase in brain size.

Raw Food not enough to feed big brains

………. our brains would still be the size of an ape’s if H. erectus hadn’t played with fire: “Gorillas are stuck with this limitation of how much they can eat in a day; orangutans are stuck there; H. erectus would be stuck there if they had not invented cooking,” she says. “The more I think about it, the more I bow to my kitchen. It’s the reason we are here.”

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Part 2 – The brain and our senses enable language but physiology limits languages

September 22, 2020

Part 1 –  “Language” is discovered but “languages” are invented

Part 2 – The brain and our senses enable language but physiology limits languages

The capability for language is an evolved ability and clearly a species-specific, cognitive attribute. This capability is not digital (On/Off) but varies first along the axis of cognition and second, the ability (both cognitive and physiological) to generate and receive signals. The capability for language, discovered within ourselves, together with the need and desire to communicate meanings, has led to humans inventing specific systems of language (Khoisan clicks, proto-Indo-European, Egyptian, Sanskrit, English, Braille, mathematics, ….). There are those who claim that humans are the only species having language and while it is true that only humans have all the characteristics of language (as defined by humans), the claim reduces to that “only humans have human language”.

Language exists not because humans exist, but because entities with brains, having the cognitive capability for language and desirous of communicating, exist.

(I take communication to be the intentional transfer of information, where information consists of facts or knowledge. Defining meaning leads either to circular logic (a meaning is what is conveyed by language and language communicates meanings) or to metaphysics. For this post I take meaning to simply be any coherent thought).

Brain 1>>meaning >>encoding>>output signal>>detection>>decoding>>meaning 2>>Brain 2

There is no doubt that most animal species have communication. Whether dogs or tigers or horses or even bees or ants, individuals of many species do communicate with each other. Individuals of some few species communicate in ways which suggest they may have a rudimentary capacity for language. Within some communities of monkeys and elephants and dolphins, for example, specific, repeatable sounds are used, voluntarily and with intent, to communicate specific meanings. The sounds and their meanings are learned and shared within particular communities. Monkeys within a troop are known to use different sounds to distinguish between snakes and lions, and then to communicate warnings about their approach. Even prairie dogs make different warning sounds for different kinds of predator. They even have a specific sound to sound an “All Clear”. However monkeys are not capable of forming or communicating more complex meanings such as “The lion is closer than the snake”. Only humans, it seems, even attempt to communicate abstract meanings, including any related to time or numbers. Animals may deceive but cannot, it seems, create false meanings (lies).

In the main, animals use sound and gestures for communication. Ants may communicate by the pheromones they emit, by sounds and even by touch. However, much of this is probably involuntary. Animals generally use their olfactory sense to garner information about the world around them. They even produce smells to mark territory and generate mating information, but it does not seem that they can produce different smells, at will, for communication purposes. Elephants use infra-sound to communicate over long distances. Bats use ultra-sound not only for echo-location but also, it seems, for communication. Even tigers, it is thought, produce infra-sounds at mating time. No animal system of communication remotely approaches the sophistication of human language, but that is not to say that their capability for language is zero. The capability for language exists when any entity having a brain

  1. desires to communicate with another similar entity, and
  2. shares a code with that entity wherein a meaning (including information) is represented by a particular signal, and
  3. can generate such a signal at will, and
  4. which signal can then be detected and interpreted as the intended meaning by the other entity.

Language: A shared system whereby two or more brains can communicate by the encoding of meanings into signals, which signals can then be transmitted and received and decoded back into their meanings.

All human attempts to communicate with animals are, in fact, a tacit acknowledgement that dogs and cats and dolphins and elephants and horses do have a rudimentary capability for language. They all seem to be able to generate specific signals to communicate specific meanings to others of their species. None have speech, but they can all make the cognitive leap that a particular human signal represents a particular meaning. Sometimes they generate their own particular signals (a certain bark or a rumble or a gesture) which humans are able to interpret as representing a particular meaning. It is apparent that the capability for language of a pet dog is greater than that of sheep, but it is also clear that neither is zero. The capability for language is often conflated with the ability for speech, but it is more likely that while speech enabled and allowed for an unprecedented sophistication in the human invention and use of languages, the capability for language had already appeared long before humans came down from the trees.

When our human ancestors achieved bipedalism they had brains about the size of current day chimpanzees. Australopithecus lived in Africa between 4 and 2 million years ago and had an average cranial capacity of about 450 cc, which is comparable to that of chimpanzees. By 1.5 million years ago the homo habilis brain had grown to a size of about 600 cc. Between 1.5 million and 300,000 years ago, homo erectus had a brain volume of between 800 and 1000 cc. Modern humans have a cranial volume of about 1350 cc but this can vary in individuals from as little as 900 and up to as much as 2,000 cc. (Neanderthals, Denisovans and even homo sapiens of their time are thought to have had slightly larger cranial capacities averaging about 1400 cc). The combination of physiological wherewithal and the associated brain control needed for speech as we know it today, was probably in place during the latter stages of homo erectus. Some form of speech was then probably available for Neanderthals, Denisovans and the earliest homo sapiens. Mammals first appeared some 200 million years ago. A plausible evolutionary time-line is that the capacity for language first began to appear with creatures at least several tens of million years ago. However, the invention of well codified languages, coincident with the arrival of speech, only came within the last million years, and perhaps only within the last 100,000 years.

In any species the emergence of the capability for language must precede the invention of communication codes. The inputs to, and the outputs from, a brain are limited by the physiology available to the brain through the body it controls. Strictly, cognition, as the ability to comprehend, is not just of the brain but of a brain together with the sensory abilities it has access to for getting inputs. An entity with a brain, even in isolation, may develop cognition as long as it has access to sensory inputs. The capability for language is thus dependent on, and constrained by, the cognition available which in turn is a composite of the brain and its associated senses. This capability must then be different for brains having access to different senses. Communication is undefined without there existing more than one brain. Communication becomes possible only when one brain can generate output signals which can be detected as input by a different brain. (In theory an entity could generate signals that it could not, itself, detect). For all living creatures the band of available sensory inputs is much broader than the range of output signals that can be intentionally generated. For example all mammals can hear a much wider range of frequencies than they can generate. Our vision can differentiate shapes to a greater precision than our hands can draw. The bottleneck for the invention of languages is thus the ability to generate coded signals which can be detected and interpreted. We do not use smell or taste or even touch (except for Braille as a proxy for sight) for language because we cannot generate unique signals at will. Touch was probably discarded as a primary means for signals because communication at a distance – but within hearing distance – was preferred.

Of all the senses available to us, human languages use only sight and hearing for inputs (again excepting Braille where touch is a proxy for sight). The underlying reason is that we are unable to generate unique, coded, repeatable signals detectable by our other senses. The predominance of speech in the languages we invent is of necessity. The languages we invent are constrained primarily by the signals we can generate. An entity with a brain capable of language but a different physiology would inevitably invent languages constrained by the signals it can generate.

 

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An Eternal Second is 6.5 Zettayears (Zy) in an eternity of eternities

September 11, 2020

Alexander Atkins has an interesting post up at his blog about the literary treatment of “eternity”.

How long is eternity

……. The first to address this question, were two brothers, Jacob and Wilhelm Grimm (better known as the Brothers Grimm), German cultural researchers, philologists, and lexicographers that wrote a seminal collection of folktales titled Children’s and Household Tales (Kinder- und Hausmärchen), first published in 1812; a second volume was published in 1815. ……. But what interests us today, in discerning the length of eternity, is a lesser known story — the insightful, charming and timeless tale of the Shepherd Boy. A king summons a shepherd, who is famous for his tremendous wisdom, and challenges him to answer three questions.

The third question is: “how many seconds of time are there in eternity?” He answers: “In Lower Pomerania [northern Poland, at the southern tip of the Baltic Sea] is the Diamond Mountain, which is two miles and a half high, two miles and a half wide, and two miles and a half in depth; every hundred years a little bird comes and sharpens its beak on it, and when the whole mountain is worn away by this, then the first second of eternity will be over.”

Even shepherds are subject to arithmetic.

In Grimms’ story the mountain would have a volume of 15.625 miles3 or about 65 x 109 cubic meters. Assuming a density of 2000 kg/ m3 (or 2 x 106 g/m3), the mountain would weigh about 130 x 1015 g. Assuming further that the bird pecked 2 mg each time, the mountain would disappear after 65 x 1018 visits. Since each visit would occur every 100 years, the mountain would last 65 x 1020 years. And since 1 Zettayear is 1 x 1021 years the mountain would last 6.5 Zettayears (Zy). And that would then be one second of Eternal Time. The curious thing is that one Eternal Year would have to consist of 31.55 million Eternal Seconds and thus

1 Eternal Year = 205,124 Yottayears where a Yottayear (Yy) is 1 x 1024 years

Eternity itself is, of course, endless even if an Eternal Year is bounded by the Diamond Mountain.

But we must not forget that for the word “eternity” plurals are allowed, and the deeper truth is that many eternities, each endless, are possible. In fact, there may well be an eternity of eternities.

 

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What’s so bad about bias?

August 13, 2020

The dictionary definition usually goes like this:

bias: n. inclination or prejudice for or against someone or something (a person or group, or an opinion, or a theory, ……). v. incline, or cause to be inclined, in favour of someone or something

Unbiased brain image johnnycullen.net

A preference for anything is a bias. A preference for a particular food, or person, or pet, or idea is a bias.  Animals too exhibit behaviour which humans would interpret as bias. A bias is clearly a cognitive state based on the knowledge, memories and values stored in that brain at that time. It is also clearly a dynamic state and changes as the state of the brain changes. Consider a brain fully capable of thinking but empty of all memory, all values, and all knowledge. A brain with no preferences for anything! Such a brain would begin as truly unbiased when required to form an opinion. An impossible state, of course, but useful as a thought experiment for defining a zero bias condition.

A preference for anything is, in fact, the result of a cognitive judgement made by a brain based on the knowledge and memories it has and on the internal value scales it uses. Our empty, thinking brain could not form an opinion about anything without first having some knowledge and some value scale to apply. Forming an opinion, is itself, the creation of a preference and a bias. Expressing an opinion is an expression of bias. All knowledge is bias. The greater the knowledge held by a brain, the greater the bias it has. The clearer the set of values held by a brain, the greater its bias. An unbiased mind is an empty mind.

Bias, itself, is not a value. It is, I think, a description of a cognitive state. A knowledgeable person, a person with opinions, is a biased person.

A learned judge is a biased judge. An unbiased music critic with no prior opinions is a useless critic. A food critic without taste preferences would be unbiased but would also be worthless as a critic. Unbiased parents would show no preference for their own children. Without bias, “good” and “bad” start with equal value. I am incurably biased against what I consider “bad” and against people I don’t like. Bias is merely the current state of a functioning brain.

Yet, bias is considered “bad” and to be unbiased is considered “good”. I suspect it is because we conflate the state of bias with the value scale of fairness.

But bias and fairness are entirely different things.

 

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