But I think animals have a sense of number — Janus
That is only awareness of quantity. — Athena
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. — wonderer1
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.
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
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
In one of my sets of college lectures, the professor can talk about knots for at least an hour. — Athena
Are there tricks or strategies that the ordinary person can do to improve mathematical ability?
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.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
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.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. — Harry Hindu
Drawing scribbles and making sounds with your mouth are just more complex forms of communicating your intentions and reading into others intentions. — Harry Hindu
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
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.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
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.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
analog values, personal meanings, and perhaps even fractal dimensions, that don't lend themselves to yes/no digitization. — Gnomon
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.