But I think animals have a sense of number — Janus

That is only awareness of quantity. It is nothing like recognizing numbers as a code and bits of information that can help us understand the universe. It is not like the ability to use origami to understand how nature works.

That comes from a video about a father and son, both mathematicians, discovering how much we have to learn of nature by studying origami. And the ability of work with that kind of information can be transferred in genes. That is, the ability to do math or play the piano can come in our genes. That is true for dogs and humans. :lol: I did not get the gene.

That is only awareness of quantity. — Athena

Yes, it is only a basis, not linguistically elaborated obviously.

I agree that many dogs are very smart. It's hard for us, an animal capable of abstracting and reflecting on our experiences, an ability which seems to be reliant on symbolic language, to understand animal intelligence on its own terms, and not to underestimate it. No doubt we have it there somewhere.

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. — Athena

Of course I don't really know you and you should consider the following a matter of speculation on my part. If there is something that resonates with you it might be worthwhile to consider it more, if not I won't be offended if you tell me you can't relate to what I say. That said...

I don't think IQ works the way you think. We all have different constellations of cognitive strengths and weaknesses, with the consequence that learning some things may be harder or easier for us than for others. It seems plausible to me that math just doesn't come as easy for you as it does for some or even most. There is no failure on your part in that. Furthermore, it sound to me like the results of what you have learned are beautiful, and I hope you can be less hard on yourself.

Of course I don't really know you and you should consider the following a matter of speculation on my part. If there is something that resonates with you it might be worthwhile to consider it more, if not I won't be offended if you tell me you can't relate to what I say. That said...

I don't think IQ works the way you think. We all have different constellations of cognitive strengths and weaknesses, with the consequence that learning some things may be harder or easier for us than for others. It seems plausible to me that math just doesn't come as easy for you as it does for some or even most. There is no failure on your part in that. Furthermore, it sound to me like the results of what you have learned are beautiful, and I hope you can be less hard on yourself. — wonderer1

Thank you so much for your concern about my feelings. That is something lacking in forums and yet science is making us aware of how important our emotions are and that we are healthier and happier when we reach out to others. And your nice words make me want to try even harder. I have math games I can put in my computer and I can give some time to using them. If we kept a running thread about math, the social aspect might help me stay motivated.

The weird thing is I am fascinated by math. I have books and DVD's about math. I want to learn the language of math and I understand learning a language is one way to keep our mental powers as we age. And oh shit, I am in trouble. Your encouragement led to looking for books and I have to have at least 2 of them. These are some thrift books offerings...

The Language of Mathematics: Making the Invisible Visible
by Keith Devlin
"The great book of nature," said Galileo, "can be read only by those who know the language in which it was written. And this language is mathematics." In The Language of Mathematics, award-winning author Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden...

The Math Instinct: Why You're a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs)
by Keith Devlin

There are two kinds of math: the hard kind and the easy kind. The easy kind, practiced by ants, shrimp, Welsh corgis -- and us -- is innate. What innate calculating skills do we humans have? Leaving aside built-in mathematics, such as the visual system, ordinary people do just fine when faced with mathematical tasks in the course of the day. Yet when they are confronted with the same tasks presented as "math," their accuracy often drops. But if we have innate mathematical ability, why do we have to teach math and why do most of us find it so hard to learn? Are there tricks or strategies that the ordinary person can do to improve mathematical ability? Can we improve our math skills by learning from dogs, cats, and other creatures that "do math"? The answer to each of these questions is a qualified yes. All these examples of animal math suggest that if we want to do better in the formal kind of math, we should see how it arises from natural mathematics. From NPR's "Math Guy" -- The Math Instinct will provide even the most number-phobic among us with confidence in our own mathematical abilities. This description may be from another edition of this product.

In one of my sets of college lectures, the professor can talk about knots for at least an hour. This is using math to understand the unseen, such as to explore DNA with math.

I agree that many dogs are very smart. It's hard for us, an animal capable of abstracting and reflecting on our experiences, an ability which seems to be reliant on symbolic language, to understand animal intelligence on its own terms, and not to underestimate it. No doubt we have it there somewhere. — Janus

I just order a book that explains math and animals. If I could get to understanding math at least as well as a dog I will have achieved something while I sit at home with COVID.

I hope we always have a math thread to sustain my interest in math.

The weird thing is I am fascinated by math. I have books and DVD's about math. I want to learn the language of math and I understand learning a language is one way to keep our mental powers as we age — Athena

You might not be aware that the infamous western gunman, John Wesley Hardin, when in prison worked his way through an algebra textbook. He also became a lawyer.

In one of my sets of college lectures, the professor can talk about knots for at least an hour. — Athena

That would have put me to sleep. :cool:

I have no doubt that with enough passion you will get there. I hope you have a speedy recovery from Covid.

Are there tricks or strategies that the ordinary person can do to improve mathematical ability?

Devlin knows a lot more about this than me, but In all my years I haven't witnessed any kind of improvement that hasn't come from simply picking up an elementary math text and making an attempt to understand it. Or taking an elementary class. With Wikipedia as a sort of backdrop it's easier to do this these days.

Sometimes people convince themselves they have little to no math ability. Then it's really hard to make progress.

The same question arises with critical thinking. I am discouraging there also. But I would love to be shown wrong. ChatGPT disagrees with me, but its suggestions assume someone who has certain personality qualities. Can these be cultivated?

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

How would that work, basically?
— Lionino

Good gravy, I do not know! — Athena

I doubt it's possible. We communicate much more than mathematical ideas. If we tried using math to talk about any of those things, it would no longer be math. It would be numbers, equations, etc., representing things. Just another language. 1 stands for me. 27 stands for eat. 4,534 stands for apple.
1 + 27 + 4,534 = I eat apple.
There's no math in that. Yeah, I just did that in five minutes. But would we find a solution if we spent a thousand years trying? I doubt it. And I assume it's been tried by plenty of mathematicians over the centuries. I can't imagine a way of actually doing math that also means things we want to discuss.

But next time I'm in Castalia, I'll see if they've figured it out.


Is there a way to have tagged inside of the Athena quote?

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. — apokrisis

Language evolved from a theory of other minds. Animals have learned to anticipate other animals intentions by observing their behavior and learned to communicate their intentions by behaving in certain ways. Drawing scribbles and making sounds with your mouth are just more complex forms of communicating your intentions and reading into others intentions.

Words refer to things that are not words. It would be better to show you what I'm talking about than to just tell you. If words only referred to things in our heads, how would we ever be able to communicate that to others? Words refer to things that we can see and feel in the world and are only necessary to communicate to others what they were not present for.

Language evolved from a theory of other minds. — Harry Hindu

That’s been one theory favoured by cognitivists. As a biosemiotician, I would instead stress the simpler story that language proper arose when Homo sapiens evolved the modern articulate vocal tract.

Drawing scribbles and making sounds with your mouth are just more complex forms of communicating your intentions and reading into others intentions. — Harry Hindu

A capacity to generate syntactical speech is a difference in kind and not just degree. All apes are social and so have an ability to anticipate and coordinate actions in their social setting. But no ape can learn fluent grammar.

I doubt it's possible. We communicate much more than mathematical ideas. If we tried using math to talk about any of those things, it would no longer be math. It would be numbers, equations, etc., representing things. Just another language. 1 stands for me. 27 stands for eat. 4,534 stands for apple.
1 + 27 + 4,534 = I eat apple.
There's no math in that. Yeah, I just did that in five minutes. But would we find a solution if we spent a thousand years trying? I doubt it. And I assume it's been tried by plenty of mathematicians over the centuries. I can't imagine a way of actually doing math that also means things we want to discuss. — Patterner

I think this is where the op goes astray. Information is what is represented by symbols, and "mathematical" is a type of information. Mathematical symbols have corresponding with them, mathematical information. But not all symbols are mathematical symbols, nor is all information mathematical information.

"Identity" is what a particular (individual) thing is said to have. So when a symbol represents a particular thing, this is a special type of information in which identity is assumed. So the information represented with "that apple is mine", is not mathematical information.

The principal difference between these two types of information seems to be that the same mathematical information is freely applied in a wide variety of situations, in a universal way, and to a multitude of different things, while identity information is by its nature restricted in application, to particular things.

Indeed, not along the lines of the op. I just commented on a snippet of side conversation I thought was interesting. I'll stop now. :smile:

That’s been one theory favoured by cognitivists. As a biosemiotician, I would instead stress the simpler story that language proper arose when Homo sapiens evolved the modern articulate vocal tract.

Drawing scribbles and making sounds with your mouth are just more complex forms of communicating your intentions and reading into others intentions.
— Harry Hindu

A capacity to generate syntactical speech is a difference in kind and not just degree. All apes are social and so have an ability to anticipate and coordinate actions in their social setting. But no ape can learn fluent grammar. — apokrisis

This seems too anthropomorphic to me. The difference you are talking about is one between the rules of representation humans have selected in the scribbles they use for efficient communication vs. the rules natural selection has selected for efficient communicating. One could argue that natural selection had a role in the former as well.

Then there's this:
https://phys.org/news/2024-08-uncovering-secret-communication-marmoset-monkeys.html

There's still a lot we do not know about animal communication. It appears to me that what you have shown is that the level of complexity in communication is based on the degree the brain has evolved to distinguish between certain symbols. It's like comparing how hominids started cooking food by throwing it on a fire and the diversity of recipes we have in the modern era. It's still cooking food.

An advanced alien species that communicates telepathically might consider our mode of communication not a language. There are many different ways to communicate, most of which we probably don't even know about.

1 + 27 + 4,534 = I eat apple. — Patterner

:heart: I absolutely love that example. :rofl: That makes as much sense as spell-check programs that obviously don't have a clue about the intended meaning. Or don't know it is a quote and not something to correct. And AI can do better why?

I am not sure if there should be a separate thread for communication because we are getting far from the identity of numbers and information and when this happens a thread loses its cohesiveness and cognizance.

I am creating a thread for communication. "From numbers and information to communication".

At the time I had this epiphany, the insight arose, 'so this is why ancient philosophy held arithmetic in high esteem. It was certain, immutable and apodictic.' These are attributes of a higher cognitive functionality, namely rational insight. Of course, I was to discover that this is Platonism 101, and I'm still drawn to the Platonist view of the matter. The philosophical point about it is that through rational thought we have insight into a kind of transcendental realm. — Wayfarer

I'm not qualified to engage in this profound thread, but your "epiphany" suggested a relationship between Numbers and Information that is not covered by Shannon's engineering theory, yet may be implicit in Plato's broader philosophical worldview.

Shannon's digital Information is defined in terms of pragmatic, physical, immutable, apodictic distinctions. But Plato's ideal Numbers*1 were non-physical, non-sensible things in a realm beyond time and space (transcendent). Ironically, the latter may be more applicable to mundane human use of Information with analog values, personal meanings, and perhaps even fractal dimensions, that don't lend themselves to yes/no digitization.

Quantum Physics has analyzed reality down, not to atoms of value & meaning, but to oceans of value (the Quantum Field) that lie, not on a simplistic linear number line, but in a "transcendent" state-of-being where "real" particles of Matter are temporary, conditional, and statistically probable. Could Plato's ideal non-sensible mathematical realm correspond to that hypothetical abstract mathematical sphere-of-Influence that physicists call "the universal quantum field"*2?

In Plato's Cave allegory, material things in the sensible world are merely shadows of an illuminated-but-unreal domain. Likewise, our social meanings and linguistic information consist of imperfect analog values that are close enough to absolute True/False to be useful for communication. Not Identical, but relative.

Conservative Physicists probably don't think of the Quantum Field as "transcendent", so exploring that possibility is left to Liberal (new-agey ; mystical energy) Metaphysicians*3. Personally, I doubt that there are any practical real-world applications of transcendental preternatural information, such as access to "unlimited knowledge". But the theoretical philosophical implications of perfection may be of interest to those who like to reason beyond immanent Materialism and utilitarian Mechanism. :smile:


*1. Mathematical Platonism :
the doctrine that there exist abstract objects—objects that are wholly nonspatiotemporal, nonphysical, and nonmental . . . . based on the postulation of unchanging and eternal realities known as forms.
https://www.britannica.com/topic/mathematical-Platonism

*2. The Universal Field Theory is not a physics theory in a classical sense. It is rather a philosophical theory explaining Why and How physical phenomena appear.
https://theuniversalfieldtheory.com/

*3. What is Quantum Transcendence? :
I just googled QT and got this hit.
https://www.1to1coachingschool.com/QEC_What_is_Quantum_Transcendence_Coaching.htm

analog values, personal meanings, and perhaps even fractal dimensions, that don't lend themselves to yes/no digitization. — Gnomon

I don't think analog values are not information, while digital values are. Of course analog values are just as representable on machines. The difference with physical values is that in a machine precision is fixed and immutable, you cannot extract more or less. Whereas precision is more fluid in natural values, you can expend more or less work to extract more or less precision. But this precision is also ultimately fixed, bound by physical limitations.

While personal meanings are not in themselves information, but rather frameworks of interpretation. I think the conflation of information and interpretation is one of the main confusions of this topic.

Besides, I have a suspicion that the designation of 'information' as being foundational to existence, goes back to Norbert Wiener saying 'Information is information, not matter or energy. No materialism which does not admit this can survive at the present day.' I'm sure this is what leads to the prevalence of information-as-foundation in contemporary discourse.

If information is thought of as form (actuality, quiddity) then the idea of information as a "foundation" of sorts is very old indeed. In Aristotle, form (act) has primacy over matter (potency).

But often it seems that attempts to use information in a hylomorphic sense are hamstrung by being unable to jettison the modern conception of matter as having form, and so you end up with reductionist versions of information-based ontologies where things are "made of bits," which seems to badly miss the point.

I suppose this subject is also haunted by the mistake of some scholastics, particularly later ones, of turning natures, species, genera, etc. into logical objects, when they are first and foremost the principles of actual, changing being (and the principles of the change therein). Hence, the idea that evolution is a problem for essences because it shows they can change—well this presupposes thinking of them in what is probably an unhelpful manner. I think this is an area where Deely's treatment of Aristotle is particularly helpful, even if he tends to neglect the "form as intellection," side that folks like Perl bring out well.

While personal meanings are not in themselves information, but rather frameworks of interpretation. I think the conflation of information and interpretation is one of the main confusions of this topic. — hypericin

Shannon took an ancient term referring generally & loosely to meaning in a mind*1 --- or as you noted, "frameworks for interpretation --- and adapted it for use in mindless computers*2. To that end, he ignored the inconsistent variable analog concrete semantic forms of Information, and focused on the consistent absolute digital abstract mathematical (either/or ratios) that could be exactly defined as something or nothing (1 or 0).

Human meanings are subject to vague personal interpretation and mis-interpretation, while computer bits & bytes are impersonal & precise. However, those numerical values can later be translated back into human (natural language*3) meanings, but at the risk of mis-interpretation. Anything that can cause an information processor (computer or brain) to create meaningful internal Forms (images ; configurations) is a source of Information. :smile:


*1. Information :
Knowledge and the ability to know. Technically, it's the ratio of order to disorder, of positive to negative, of knowledge to ignorance. It's measured in degrees of uncertainty. Those ratios are also called "differences". So Gregory Bateson defined Information as "the difference that makes a difference". The latter distinction refers to "value" or "meaning". Babbage called his prototype computer a "difference engine". Difference is the cause or agent of Change. In Physics it’s called "Thermodynamics" or "Energy". In Sociology it’s called "Conflict".
https://blog-glossary.enformationism.info/page11.html

*2. Information is an abstract concept that refers to something which has the power to inform. At the most fundamental level, it pertains to the interpretation of that which may be sensed, or their abstractions. . . . Information is not knowledge itself, but the meaning that may be derived from a representation through interpretation ____Wikipedia

*3. Natural Language :
a language that has developed naturally in use (as contrasted with an artificial language or computer code). ____ Oxford Languages

To that end, he [Shannon] ignored the inconsistent variable analog... — Gnomon

Gnonsense. Shannon worked on analog computers before essentially inventing digital logic. His communication theory was very much about communicating uncorrupted digital data through the noisy analog world. So no, he didn't ignore the analog.

What is with your obsessive need to propagate misinformation?

To that end, he [Shannon] ignored the inconsistent variable analog . . . concrete semantic forms of Information. (bolded words were omitted in your misinterpretation)

Gnonsense. Shannon worked on analog computers before essentially inventing digital logic. His communication theory was very much about communicating uncorrupted digital data through the noisy analog world. So no, he didn't ignore the analog.
What is with your obsessive need to propagate misinformation? — wonderer1

Please note that I wasn't talking about analog Computers (continuous vs digital values), but analog Information*1 (semantic meaning expressed by figurative analogies). Shannon found a way to reduce the Uncertainty of "noisy" Analog Computers, including human brains*2, by using Digital Information in which the Natural Language meaning is converted into synthetic Mathematical symbols. In that process, the real world meanings (analogies ; metaphors ; similes ; nuances) are ignored in favor of abstract numerical values, and must be reconstructed later, opening the possibility of misconstrual.

Ironically, cutting edge computers are now learning to communicate with human programmers in natural language instead of artificial codes*3. How do you think the programmers will deal with the inherent Uncertainties of human language? Your misinterpretation of my human language post is a prime example of self-misinformation. :smile:

*1. Analog Information :
information processing called analog-form information, or simply analog information. Until the development of the digital computer, cognitive information was stored and processed only in analog form, basically through the technologies of printing, photography, and telephony.
https://www.britannica.com/topic/analog-information

*2. Analog Brain
The mammalian brain, comprised of neuronal networks, functions as an analog device and has given rise to artificial neural networks that are implemented as digital algorithms but function as analog models would.
https://www.frontiersin.org/journals/ecology-and-evolution/articles/10.3389/fevo.2022.796413/full

*3. Why Natural Language is the New Language of the Digital Era
The days of writing lines of code to achieve tasks are gradually giving way to the era of conversation. Natural language processing (NLP) and machine learning have reached a point where machines can not only understand what we say but also grasp the context and nuances of our conversations.
https://www.linkedin.com/pulse/why-natural-language-new-digital-era-anuya-kamat

You didn't answer my question. Do you want to hear my best guess at what the answer is?

If information is thought of as form (actuality, quiddity) then the idea of information as a "foundation" of sorts is very old indeed. In Aristotle, form (act) has primacy over matter (potency). — Count Timothy von Icarus

The computer chip industry understands hylomorphism very well. Why? Because there's the chip designers, and the chip fabricators, and nowadays they're usually different companies. This is called 'fabless manufacture' and is the standard model in current chip design. NVidia, for instance, deals entirely with design ('form'), while TSMC is one of the leading companies which fabricate the chips using fiendishly complex machines ('matter') - about which, see this mind-blowing documentary on ASML's EUV lithography machines.

often it seems that attempts to use information in a hylomorphic sense are hamstrung by being unable to jettison the modern conception of matter as having form — Count Timothy von Icarus

It is because of reification, the 'thingifying' tendency deeply embedded in modern thought, which believes that only things are real.

It is because of reification, the 'thingifying' tendency deeply embedded in modern thought, which believes that only things are real. — Wayfarer

Rather the opposite of reification. Instead of treating abstractions as real, it excludes parts of the real from the category "real".

often it seems that attempts to use information in a hylomorphic sense are hamstrung — Count Timothy von Icarus

Why hamstring? If matter has or coexists with form, matter has or coexists with information. What is the problem?

Why hamstring? If matter has or coexists with form, matter has or coexists with information. What is the problem?

Ha, I am now seeing that the way I wrote that is extremely unclear. Of course matter has form in hylomorphism!

What I meant to say was that in modern, particularly early modern, thought form is packaged intrinsically with matter into fundamental "building blocks"—atomism, reductionism, smallism—"wholes are the sum of their parts." There is no "prime matter," as an abstraction, sheer potency, but rather matter as actual bits of stuff with definite form and definite/actual attributes (eliminating potency).

On such a view, the form of composite objects is just reducible to arrangements of various building blocks. The relationality and processual elements of the information theoretic view get lost. Things "are what they are made of," a view which loses sight of how information is defined by context.

If you maintain this sort of thinking you end up with "stuff made out of 1s and 0s," the sort of thing the original digital physics was taken over the coals for.

Form doesn't seem particularly equivalent to information. Just as the same information might "reside" in different material substrates, it can reside in different forms of the same substrate. (i.e black or white text, small or big) Though form does seem "closer" to information than matter (the shape of text is closer to the message than whatever material the glyphs are composed of).

Information seems more like number, something that doesn't exist at all without interpretation, that almost seems to reside in a platonic realm of its own.