Archive for the ‘Language’ Category

A square is rounder than a rectangle

July 2, 2022

Sometimes (for example after imbibing my third whiskey) I am both intrigued and frustrated by the nature of shapes. Do shapes exist at all? Except, perhaps, as a property of a thing?

Without dimensions there can be no shapes. A point has no shape. In one dimension, shape is almost, but not quite, trivial. A one-dimensional shape is just a line. Both a point and a line are abstract things and do not exist physically. We perceive three physical dimensions but we are also constrained to experience nothing but 3 dimensions. We can imagine them but there are no 1-D or 2-D things. Even a surface, which is always two-dimensional, is abstract. We talk about circular things but the concept of a circle is also an abstraction in an abstract two dimensions. Look as much as you like in the physical world but you can never find any 2-D circles in this 3-D world. Most shapes are two-dimensional. So how, I wonder, can some 3-D thing be described in terms of a 2-D circularity. If you rotate the abstract two-dimensional object called a circle in 3 dimensions you can generate an abstract 3-D object called a sphere. It pre-supposes, of course that 3-D space exists within which rotation can occur. But what is a sphere? How do you rotate an abstract object? A square rotated gives a cylinder – not a cuboid. A point stretched into two dimensions or twirled in three remains a point and still imaginary. A line rotated gives just a line.

I find the word shape is diffusely defined in dictionaries – possibly because it is itself philosophically diffuse.

shape (n):

  • the external form, contours, or outline of someone or something;
  • a geometric figure such as a square, triangle, or rectangle;
  • the graphical representation of an object or its external boundary, outline, or external surface.

Shape, it seems to me, has a connection  with identity. Things without identity have no shape. All countable, physical things have shape as an attribute. But uncountable things – rain, mist, water, … – are devoid of shape. But any shape is also an abstraction which can be taken separate from the physical things. Abstract things and uncountable things can also be invested with shape as a descriptor, but this is both figurative and subjective. We can refer to the shape of an idea, or the shape of a history, or of a culture, but the meaning conveyed depends upon the physical things normally connected with such shapes. Even when we use word shapeless we usually do not mean that it is devoid of shape but that the shape is not a standard recognised form. Shape emerges from existence though not necessarily from the existence of things. It is here that the distinction between form and substance originates. Shape needs existence but it is not difficult to imagine the concept of shapes existing in even a formless universe without substance.

In philosophy, shape is an ontological issue. There have been many attempts in philosophy to classify shapes. For example:

The shape of shapes

An important distinction to keep in mind is that between ideal, perfect and abstract geometric shapes on the one hand, and imperfect, physical or organic mind-external shapes on the other. Call the former “geometric shapes” and the latter “physical shapes” or “organic shapes”. This distinction can be understood as being parallel to types (classes, universals, general entities) and instances (individuals or particulars in the world). Geometric shapes typically have precise mathematical formalizations. Their exact physical manifestations are not, so far as I am aware, observed in mind-external reality, only approximated by entities exhibiting a similar shape. In this sense geometric shapes are idealizations or abstractions. This makes geometric shapes similar to types or universals. Their instances are inexact replicas of the shape type in question, but have similar attributes or properties in common, properties characterizing the type. By contrast, organic or physical shapes are irregular or uneven shapes of mind-external objects or things in the world. A planet is not perfectly spherical, and the branches of a tree are not perfectly cylindrical, for example. “Perfectly” is used here in the sense of coinciding with or physically manifesting the exact mathematical definitions, or precise symmetrical relations, of geometric shapes. Objects and physical phenomena in the world, rarely if ever, manifest or exhibit any concretization of geometric shapes, but this is not to say that it is not possible or that it does not obtain at times. Objects are not precisely symmetrical about a given axis, cube-shaped things do not have faces of exactly the same area, for example, and there is no concretization of a perfect sphere. ……………

With respect to the mind-external world, notice that if shapes are properties (of things), then we may have a situation in which properties have properties. At first glance this seems true because we predicate shape of objects in the world; we say that objects have a certain shape. We also describe types of shapes as having specific properties. If a shape is defined as having a particular number of sides (as with polygons), a particular curvature (as with curved shapes, such as the circle and the ellipse), specific relations between sides, or otherwise, then it should be apparent that we are describing properties of properties of things. We might be inclined to say that it is the shape that has a certain amount of angles and sides, rather than the object bearing the shape in question, but this is not entirely accurate. Shapes, conceived as objects in their own right (in geometric space), have sides, but in our spatiotemporal world, objects have sides, and surfaces, as well. When we divorce the shape from that which has the shape via abstraction, we use ‗side‘ for the former as much as we do for the latter. The distinction between geometric and physical space, between ideas and ideal or cognitive constructions and material mind-external particulars is significant.

My preferred definition of shape is:

shape is an abstract identity of form devoid of any substance

I take shapes to be forms both in two dimensions and in three. So by this definition I include spheres and cylinders and cuboids and pyramids to be shapes. Shape is about form – whether or not there is a thing it is attached to. We can have regular shapes where the regularity is abstract. We can have irregular shapes which cannot be described by any mathematical expression. And we can have shapeless shapes. We can compare shapes and discover the concept of similarity. We can even compare dissimilar shapes. I can conceive of the quality of form and talk about circularity or squareness or sphericality or even shapelessness.

I can have curvy shapes and I can have jagged shapes. My ping-pong ball is more spherical than my dimpled golf ball. They are both rounder than an orange but I have no doubt that an orange is rounder than a cucumber. Just as an apple is squarer than an orange. A fat person is rounder than a thin person. I know one cannot square a circle yet I have no difficulty – in my reason – to attributing and comparing levels of squareness and roundness of things. Circular logic is not a good thing.

And any square is rounder than a rectangle.


A strategy for Wordle 7

May 12, 2022

I am very new to Wordle and only started playing last week. The greatest challenges I found with Wordle 5 and 6 were the use of American spellings and the seemingly arbitrary conjoining of two words to create “words” which I would not consider to be single words.

Wordle 5 and 6 did not seem too taxing and soon got boring. Wordle 7 is now keeping me engaged for longer than 5 or 6 did. The “strategy” I have evolved is to use the same 3 starting words (entirely by trial and error) to cover as many letters of the alphabet as possible. The last 3 attempts seem to then be sufficient to find the hidden word in most cases. But I am still not happy with two word combinations being elevated to be taken as single words. (website, manhole ….). Smacks of cheating.

I only started with Wordle 7 this week. I am sure there must be better words but the three I have ended up using – again by trial and error – are:

THREADS

LOUNGER or LOUNGES

PRIVACY

So far so good. The success rate has come up to about 75% 95% (and most failures are on my unfamiliarity with American usage and Americanisms).

My three chosen words cover 17 letters. I now need to find three better starting words perhaps covering 18 or 19 letters of the alphabet. 


When the tree falls in the forest, the sound is only due to language

May 1, 2022

The classic, cliched question goes:

“If a tree falls in a forest and no one is around to hear it, does it make a sound?”

The non-philosophical part of question is easily answered.

  • If a tree falls within an extant medium, and
  • there is consequent vibration within that medium, and
  • there is an organ which can detect such vibrations, and
  • the organ generates impulses, and
  • it sends these impulses to a brain, and
  • that brain interprets the impulses as something the brain itself labels as sound, then
  • there will be sound.

If the tree fell in a vacuum there would be no vibration of anything. No medium, no sound. No ear, no sound. No brain. no sound. In fact, if we did not have ears connected to our brains our language would be unable to come up with words for ears, hearing or sound. If we had no word for sound then there might well be vibrations when the tree fell, but there would be no sound. The non-philosophical answer then becomes that if we had no word in language for sound then there would be no sound. When a dog or a bat detects vibrations at frequencies that our ears cannot detect then such signals never reach our brains to ever be classified in our language as sound. What an animal might interpret in its brain when its ears detect signals is whatever that animal interprets it or labels it to be.  Only if we define the word sound to loosely mean what any brain may interpret on receiving signals from any ear-like organ, could we say that the animal discerns sound.

The philosophical part of the question, however, which considers perception, observation and existence is much more interesting. There are many things we cannot directly experience with our limited senses. But we can infer and/or deduce that they exist by their interactions with other things giving changes which we can observe directly. We extend our senses by creating wonderful instruments which then produce changes observable directly by our traditional senses. We “see” in the ultraviolet or the infra-red only because our cameras convert these UV or IR signals into images that do fall within our visible range.

But what of all that we cannot observe, directly or indirectly, by our limited senses and our finite brains? Is it so that if something cannot be observed, cannot be perceived, cannot be inferred to exist by any interaction it has with anything else in this universe, then it does not exist? Or is it merely that we are ignorant of its existence? Philosophy is, of course, about asking unanswerable questions. Once a question can be answered it leaves the field of philosophy.

Take bongism for example. We cannot observe it, perceive it, infer it or deduce it. It has no known interactions with anything else in this universe. But it is the imbalance in bongism which caused all existence in the first place. It is the answer to the question “Why do things exist at all?”.

Does bongism exist?

It must do, since I have a word for it.


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…)

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
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)
 
 

“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.

 


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.


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.


“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).


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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