Why is your view restricting this to numbers? There is no reason you need to represent things with numbers.

Sounds like Early Wittgenstein's picture theory of language.

What if we did not use words, but communicated with math?
— Athena

How would that work, basically? — Lionino

Good gravy, I do not know! As I just said in another thread, there is so much I do not know and didn't even know I didn't know so much. I swear I am at a time in my life when every day I feel more and more ignorant of everything I do not know and absolutely paniced to figure out a way to reduce this ignorance.

I sure respect Socrates right now and I would bet my bank account, he did not know how much he did
not know until he got old. :lol: Remember when we were teenagers and thought we knew it all?

I can barely imagine how it is to think in terms of mathical code. To see H2O and know that means water, is special. To think "water" and immediately think where does it come from and where does it go and why is it important and is it clean and safe to drink, etc., etc. is absolutely amazing! No other animal on the planet has this capability. Yes, animals can communicate but they do not come close to the mental activity of which we are capable.

How many books have you read about why math is deemed a very important thinking tool? What justifies us taking you seriously as an authority on communication or math?

Interesting idea. Logicians might be able to do this, but math people use words and symbols. I have never heard of a math research paper written in math symbols only. Thinking in mathematical terms is common amongst my colleagues, but even there one talks to oneself with words. — jgill

Perfect! I wish I could know what you know through experience with those who think mathematically. I am quite sure some things can not be communicated with math, but I am not sure exactly what divides the world of math and human language, but I suspect AI does not get high scores for comprehending being human. Being human is an experience and that is outside of logic. We are not predictable machines. Are barely inside the laws of nature, compared to the rest of the animal kingdom.

"The exciting thing about mathematics and science and music and literature is what they can tell us about the workings of the human mind. For these disciplines are literally models (extensions) of at least certain parts of the mind. Just as the knife cuts but does not chew, while the lens does only a portion of what the eye can do, extensions are reductionist in their capability. No matter how hard it tries, the human race can never fully replace what was left out of extensions in the first place. Also, it is just as important to know what is left out of a given extension system as it is to know what the system will do. Yet the extension-omissions side is frequently overlooked.”
― Edward T. Hall

Did you communicate this message with numbers?

As she sent it with a computer, absolutely.

But the information isn't numbers, the symbols are not numbers.

The whole point of my op is that information and numbers are the same thing

Yeah but how would you answer the point that you don't need numbers to represent something?

So a string of bits or the numberline exist in the happy world where we can just take this paradoxical division between the continuous and the discrete for granted. Continuums are constructible. Don't ask further questions. Get on with counting your numbers and bits. — apokrisis

This makes me think about the distinction, particularly in quantum mechanics, between the unmeasured and the measured.

Numbers are just scribbles (2 and two refer to the same thing. it's just easier to do math with the condensed version using numbers instead of words) that refer to certain quantities. They are causally connected - the scribble and the quantity of objects within a category, whether it be cows or photons.

Information is the relationship between the scribble (the effect) and the quantity (the cause).

It is easy to assume things are just what they are. But that depends on them being in fact not what they are not. — apokrisis

Maybe I'm misunderstanding but this seems counter-intuitive considering that we must categorize objects by their similarities, not their differences or what they are not. Objects that are similar fall into some category and it is only then that we can assert that there is a quantity of similar objects. If everything was unique and there are no categories of similar objects then what use are quantities? If there is only one of everything what use is math?

Why does 2+2=4? Some may say that this is logically sound statement, but why? What makes some string of scribbles true? It seems to me that you have to have made some observation, and categorizing your observations, prior to making this statement. Are they just scribbles on this page or are they about something that I can experience and make predictions from?

Similarly, numbers in themselves are not information, because they do not encode any message - they are just there. — SophistiCat

Where are the numbers and how did they get there?

Objects that are similar fall into some category and it is only then that we can assert that there is a quantity of similar objects. — Harry Hindu

Object recognition thus parallels an entropic view of information. An equilibrium system like an ideal gas is defined by its macro properties - temperature and pressure - and not its micro properties. The actual position of a bunch of particles is an ensemble of differences that becomes merely the sameness of a statistical blur. And the global state of the ensemble is a sameness that can be now treated as a difference when comparing one thermal system to some other in terms of a pressure and temperature.

If I asked you to count the number of crows in a tree, the fact that some were rooks, some ravens, some magpies, would be differences you are being asked to ignore. They are all varieties of crow, but that is being treated as a difference that doesn’t make a difference for the purpose of counting crows.

So reality is like this. There are always further distinctions to be had. Even two electrons might be identical in every way, except they are in different places. But equally, the differences can cease to matter from a higher level that sees instead the sameness of a statistical regularity. Sameness and difference are connected by the third thing of where in scale we choose to stand in measuring the properties of a system.

Are we interested in the distinctions between types of crow. Or if it is birds we are counting, is a crow any different from an ostrich?

Why does 2+2=4? Some may say that this is logically sound statement, but why? What makes some string of scribbles true? — Harry Hindu

So reality is divided into sameness and difference by its hierarchical scale. There really is something to talk about at the level of statistical mechanics. But then our talking about it is done in a way that claims to talk past the third thing of a viewpoint where either the sameness or the difference is being ignored. Information and numbers are our means to talk about reality as if from some completely objective nowhere.

It matters in language whether I think I am being asked to count birds or ravens. I have to place myself at a certain interpretive level that matches your understanding about what you were asking. But then the number line is its own abstract thing where there is no physical scale involved. Space, time and energy are all generalised as differences to be ignored. Three ravens is equivalent to three birds, three apples or three spaghetti monsters. The focus is now on the arithmetic or algebraic operations that can be performed on an abstract number system.

We have shifted ourselves into a Platonia so far as reality is concerned. And that new mathematical level of semiosis or reality modelling offers a huge entropic payback for us humans in terms of technology, engineering, computation, and other ways of mechanistically controlling the world.

It makes the whole of reality look the same in our eyes. A mechanical device. A system of particles regulated by differential equations. A sameness of physical laws with a difference in initial conditions.

So numbers and information are part of a new way of speaking about the world that is very useful in proportion to the degree that it is also unreal. It is a language of atomised reductionism that places itself outside even space, time and energy as those are the physical generalities it now aspires to take algorithmic control over.

A modelling relation with the world coming from the God’s eye view. Just equations and variables. Absolute sameness coupled to absolute difference now.

Forms are ideas, not in the sense of concepts or abstractions, but in that they are realities apprehended by thought rather than by sense. — Perl, Thinking Being

Rational thought or the cognition, the apprehension of pattern, it is grounded in? Animals obviously recognize forms. Should we say they are rational?

Were you addressing me? :chin:

Animals obviously recognize forms. Should we say they are rational? — Janus

But anyway, animals obviously have good object recognition. The recognise pragmatic forms. But are they apprehending form at a rational level? Or is that level of abstraction how we humans learn to view the world for our own new purpose of seeing reality in general as one giant rational machine?

Semiosis would say that animals are rational at the level of genetic and neural encoding. They see the world in terms of a regulated metabolism and a patterned environment.

Humans have linguistic semiosis which gets us to a level of seeing the world in terms of a pattern of interaction between intentional agents. The play of viewpoints captured by being able to speak of me and you, before and after, good and bad.

And the OP concerns mathematical semiosis. Pattern abstracted to the point of a mechanical generality. The ability to construct forms in algorithmic fashion. What seems to us the ultimate level of rationalised structure.

Semiosis would say that animals are rational at the level of genetic and neural encoding. — apokrisis

This seems a useful clarification. Information is encoded meaning. Genetic information encodes for constraints on chemical actions. Neural information encodes for constraints on environmental actions. Verbal information encodes for constraints on intentional actions. And numeric information encodes for constraints on mathematical actions.

So information is about the pragmatic encoding of meanings. It is how an organism regulates its world by having the kind of memory that acts as a store for data and algorithms – to put it rather computationally. An organism can construct states of constraint because a meaningful relation with the world has been atomised into a system of syntax acting on semantics. Habits or routines that can be run. Behaviours which can be switched on or off.

Numbers are then just the form that information takes at the level of a complete semiotic abstraction in terms of the self that is aiming to regulate its world by the business of constructing states of constraint. A numberline gives both the data points and the algorithmic logic that are needed to encode an absolutely general – but also perfectly mechanistic – modelling relation with the world.

So four levels of information or mechanistic regulation. With maths and logic at the end of this trail as the most evolved form of pragmatic rationality. The ultimate way that an organism could think about the world. If also then, the least actually "organic". :razz:

I was addressing the quoted text from Perl. I haven't read his work but have received the impression that "apprehending form via the rational intellect" was the thought in play there. I guess it depends on whether you think "apprehending form" means recognizing it or reflecting on it. I would agree with you that the latter requires symbolic language and I don't think that is at all controversial.

Numbers are then just the form that information takes at the level of a complete semiotic abstraction in terms of the self that is aiming to regulate its world by the business of constructing states of constraint. — apokrisis

Yes, "numbers" are abstractions. But I think animals have a sense of number. The word "form" in information seems to reflect the relationship between information and form. Form and information and number all primordially rely on cognition and recognition of difference and sameness or similarity and pattern.

But I think animals have a sense of number. — Janus

Or of perceptual grouping. Human working memory famously tops out at about “7 ± 2” items. The kind of grouping in the test that Trump aced when he could recall “Person, woman, man, camera, TV.“ And probably even manage that feat in reverse order.

Animals all have working memory too. The ability to juggle a small set of particular aspects of some larger cognitive task.

But that is not the same as counting. Just the reason why we struggle with holding number strings longer than seven in our working memories.

The word "form" in information seems to reflect the relationship between information and form. — Janus

Indeed. I would call the abstracted notion of information our “atoms of form”. Form reduced to the counterfactuality of a binary switch. We can count how many distinctions it takes to arrive at something completely specific.

The game of Twenty Questions is a good example. Ideally, every question cuts the number of remaining choices in half. And that way we cut through a world of possibilities with an exponentialised efficiency.

The form I have in mind is … well you will just have to start guessing. And each guess is an atomistic act of counterfactual switching. If you are any good at this game, you will switch off half the world of possibilities as you zero in on the possibilities still left switched on.

But that is not the same as counting. Just the reason why we struggle with holding number strings longer than seven in our working memories. — apokrisis

That makes sense to me. I have come across reports that suggest some animals can learn to do basic small number counting. They may be apocryphal.

I have come across reports that suggest some animals can learn to do basic small number counting. — Janus

You know yourself that three, four or even five things can be seen as different sized collections at a single glance. And remembered as such. But the difference between seven or eight apples starts to require a method of checking if you want to be sure of your mathematical correctness. Whereas as for a hungry monkey, it becomes a difference not making a difference. It is just seen as a lot of apples.

:up:

The game of Twenty Questions is a good example. Ideally, every question cuts the number of remaining choices in half. And that way we cut through a world of possibilities with an exponentialised efficiency. — apokrisis

Nice ordinary example!

I've been thinking more about this. At first I thought I was just mistaken in my op. The set of all possible arrangements of bits is countable, so it is no wonder that we can uniquely assign a whole number to every arrangement. Just because bits are countable, doesn't establish some kind of identity between bits and numbers. — hypericin

I wouldn't be surprised if you were able to (in a manner unknown to me at the moment) topologically map out the possible logical spaces for information to represent truths in state space. Again, I am assuming that theorems and truth of theorems can be topologically mapped out in a heuristically manner in logical space.

So reality is like this. There are always further distinctions to be had. Even two electrons might be identical in every way, except they are in different places. But equally, the differences can cease to matter from a higher level that sees instead the sameness of a statistical regularity. Sameness and difference are connected by the third thing of where in scale we choose to stand in measuring the properties of a system. — apokrisis

Sure. Information is everywhere causes leave effects. What information is relevant, or attended to, depends on the goal in the mind.

So numbers and information are part of a new way of speaking about the world that is very useful in proportion to the degree that it is also unreal. It is a language of atomised reductionism that places itself outside even space, time and energy as those are the physical generalities it now aspires to take algorithmic control over. — apokrisis

I don't know if I agree with what you're saying here. What does it mean for something to be useful but not real? What does it mean for something to be useful if not having some element of being real? It seems to me that survival is the best incentive for getting things right. The environment selects traits that benefit the survival and reproductive fitness of organisms. Our highly evolved brain must have been selected for a reason and there must be a reason why humans have been so successful in spreading across the planet and out into space. Are those reasons unreal? Do your many words point to real states of reality? Am I to gain some advantage by reading your words? If not, then why read them?

It seems to me that a rational process takes time and mental space.

If I were to talk about marijuana legalization in this thread, would that be a real state of affairs of being off-topic? It seems to me that the way we perceive the world has a real effect on the world by means of our behaviors. Is Santa Claus real? As an idea Santa Claus is very real as you merely need to look at the effect the idea has had on the world.

In your example of the variety of birds we currently observe, we can point to evolution as the cause. Their differences evolved to fill different environmental niches. The variety of birds informs us of how they evolved and what their common ancestor would be like. The differences and similarities in birds indicate that they started with one common ancestor and evolved over time in different environments. We could potentially point to one common ancestor for all life with space and time being the medium in which the differences accumulate to the current state of affairs with the variety of life that we observe today.

I was addressing the quoted text from Perl. I haven't read his work but have received the impression that "apprehending form via the rational intellect" was the thought in play there. I guess it depends on whether you think "apprehending form" means recognizing it or reflecting on it. I would agree with you that the latter requires symbolic language and I don't think that is at all controversial. — Janus

How does one even learn a language without apprehending the scribbles and sounds in the present and reflecting on how those same scribbles and sounds were used before? I could argue that language use is just more complex learned behavior. Animals communicate with each other using sounds, smells and visual markings. Animals understand that there is more to the markings than just the form the marking takes. It informs them of some state of affairs, like this is another's territory, not mine and in essence has some form of self-model.

I often link this story in discussions like this:
https://vimeo.com/72072873

This man made it to an adult without having learned a language. How he eventually learned language was by reflecting on what others were doing over time to come to understand that those scribbles mean things or are about things?

I agree that numbers and information have something in common.

So, numbers physically exist as,
Brain; (numbers)
And, information physically exists as,
Brain; (information)

The general form is,
Brain; (a non-physical thing)

So as far as identity of numbers and information...they are associated with a physical location and time of a physical brain...always.
And they have the mental content consistent with what brains can do.

Numbers and information are not non-physical without support...but only exist as a physically supported non-physicals.

Any Claude Shannon reference is going to cause confusion
Is it physical, non-physical or physically supported non-physicals? I assume anything with Shannon information theory is physical only.
Entropy doesn't apply to non-physicals or physically supported non-physicals.

How does Shannon information even deal with a non physical things such as the past or future?
Our brains do it all the time, so something different is going on. More than a physical signal in our brains...

What does it mean for something to be useful but not real? — Harry Hindu

To be clear, yes of course information storage as genes or words has some entropic cost. To scratch a mark on a rock is an effort. Heat is produced. Making DNA bases or pushing out the air to say a word are all physical acts.

But the trick of a code is that it zeroes this physical cost to make it always the same and as least costly as possible. I can say raven or I can say cosmos or god. The vocal act is physical. But the degree of meaning involved is not tied to that. I can speak nonsense or wisdom and from an entropic point of view it amounts to the same thing,

As they say, infinite variety from finite means. A virtual reality can be conjured up that physical reality can no longer get at with its constraints. But then of course, whether the encoded information is nonsense or wisdom starts to matter when it is used to regulate the physics of the world. It has to cover its small running cost by its effectiveness in keeping the organism alive and intact.

I could argue that language use is just more complex learned behavior. Animals communicate with each other using sounds, smells and visual markings. — Harry Hindu

There are grades of semiosis. Indexes, icons and then symbols. So I was talking about symbols when I talk about codes. Marks that bear no physical resemblance to what they are meant to represent.

Animals communicate with signs that are genetically fixed. A peacock has a tail it can raise. But that one sign doesn’t become a complex language for talking about anything a peacock wants.

A language is a system of symbolic gestures. Articulate and syntactically structured. A machinery for producing an unlimited variety of mark combinations. Quite different in its ability to generate endless novelty.

:up: It is quite a few years since I read A Man Without Words. It seems reasonable to think people and some animals can conceptualize prelinguistically in the form of imagery.

So "apprehending forms", in the sense of prelinguistic recognition would amount to prelinguistic conceptualization.

To be clear, yes of course information storage as genes or words has some entropic cost. To scratch a mark on a rock is an effort. Heat is produced. Making DNA bases or pushing out the air to say a word are all physical acts.

But the trick of a code is that it zeroes this physical cost to make it always the same and as least costly as possible. I can say raven or I can say cosmos or god. The vocal act is physical. But the degree of meaning involved is not tied to that. I can speak nonsense or wisdom and from an entropic point of view it amounts to the same thing,

As they say, infinite variety from finite means. A virtual reality can be conjured up that physical reality can no longer get at with its constraints. But then of course, whether the encoded information is nonsense or wisdom starts to matter when it is used to regulate the physics of the world. It has to cover its small running cost by its effectiveness in keeping the organism alive and intact. — apokrisis

The entropic cost in creating the sound or scribble isn't the only part of the equation. Don't forget about the mind that is observing the mark or hearing the sound and the mental effort involved with decoding the message. It takes more mental power to get at the meaning of "philosophy" than "photograph" even though both words contain the same amount of letters. The question then becomes does the discussion about philosophy provide any survival or reproductive benefit (wisdom), or are we just playing symbol games (speaking nonsense)? For humans at least it could be argued that entering a virtual reality world can relieve stress and provide unique social interactions with others sharing the same virtual reality that strengthen social bonds in the physical world.

The speaker or writer must have some sense of empathy for the listener and reader. They have to put things in a way that they know they will understand with the least amount of mental effort (efficiently) if they actually want to be understood without having to re-phrase or repeat themselves.

This is why, for me at least, I get irritated at people that waste my time with word salad, mental gymnastics and intellectual dishonesty, which ends with me not putting much weight into what they write or say in the future.

There are grades of semiosis. Indexes, icons and then symbols. So I was talking about symbols when I talk about codes. Marks that bear no physical resemblance to what they are meant to represent.

Animals communicate with signs that are genetically fixed. A peacock has a tail it can raise. But that one sign doesn’t become a complex language for talking about anything a peacock wants.

A language is a system of symbolic gestures. Articulate and syntactically structured. A machinery for producing an unlimited variety of mark combinations. Quite different in its ability to generate endless novelty. — apokrisis

I would argue that when a peacock raises its tail it wants to mate. It also communicates to female peacocks the fitness of the male. There is complexity there in the causes that lead to some effect, like a male peacock showing off its tail. I could argue that the display of the peacock's tail says something about the Big Bang, as there would not be a peacocks if there wasn't a Big Bang. Of course the immediate effects say more about their immediate causes than some effect billions of years later, but my point is that all effects carry information about their causes.

In reading your words I can get at what you intended to say, the idea you intend to convey, but can get at your level of understanding of English as well. The information is there whether we look or not. Where we look, or what information we attend to, at any given moment is dependent upon the goal in the mind.

It's really just a difference in degrees. More complex brains can use more complex representations and get at more complex causal relations. The question then becomes at what point does the complexity cease to be useful? Are we overcomplicating things with our language, especially in philosophical discussions?

It takes more mental power to get at the meaning of "philosophy" than "photograph" even though both words contain the same amount of letters. — Harry Hindu

Sure. But then our brain is an expensive organ to run. It uses glucose at the rate of working muscle. On the other hand, that is a constant metabolic cost. There is little change when we daydream or go to sleep.

And the goal of the brain is also to reduce all thoughts to learnt habits. It we figure things out, then our mind can just shortcut to our routine definitions of those words. So what you call mental power is the effort of attending to novelty. But once we have reduced some thing to a habit of thought, it can simply be unthinkingly emitted. It becomes so remembered formula that just needs to be triggered. The metabolic cost of rewiring the brain has been paid.

I could argue that the display of the peacock's tail says something about the Big Bang, as there would not be a peacocks if there wasn't a Big Bang. — Harry Hindu

You could read that into a peacock tail. But two peacocks just have their one instinctual understanding.

You have actual language and that makes a huge difference. Peacocks only have their genes and neurology informing their behaviour. No virtual social level of communication.

It's really just a difference in degrees. More complex brains can use more complex representations and get at more complex causal relations. — Harry Hindu

Your own argument says it isn’t if humans have language and a virtual mentality that comes with that.

Did you communicate this message with numbers? — Apustimelogist

Can we learn more by using math than by using words? I have not communicated anything with math but computers do not use words to compute. And I am sure my failure to understand math keeps my IQ relatively low.

Rational thought or the cognition, the apprehension of pattern, it is grounded in? Animals obviously recognize forms. Should we say they are rational? — Janus

Here is an explanation of rational

Rational behavior is used to describe a decision-making process that results in the optimal level of benefit, or alternatively, the maximum amount of utility. https://corporatefinanceinstitute.com/resources/career-map/sell-side/capital-markets/rational-behavior/#:~:text=What%20is%20Rational%20Behavior%3F,highest%20amount%20of%20personal%20satisfaction

.

Animals can problem solve. Some do it better than others. Dogs are amazing. They are the only animal that recognizes we point at something, it should go see what we are pointing at. This is one of the reasons they are good hunting partners. However, not all dogs get it. Wolves do not pick up the cue to check out what we are pointing it. Dogs that come from a line of domesticated dogs can be brilliant in figuring out human behavior and how to play the human for all the human is worth. That ability can make the difference between being a street dog or attaching to a human who provides food and shelter.

That information comes from shows about dogs.