61–70 of 322 posts
Could the same be said about just about everything? Like Music. Is a Song just a combination of notes, beats, intervals, voice etc. waiting to be discovered? Or is it something that a musician invents in her brain through talent, experience, practice and trail and error. Or for that matter, a startup idea? A product/service that would bring immense value to its consumers, but it is not there yet, waiting to be discov…
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It's just as silly to think of the "real numbers" as being discovered. They don't exist in the real world, after all.
Don't they, though? The path of an orbit in vacuum should follow pi, unless coordinates are discrete (which they might be, I suppose)
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Ridiculous hubris, to claim to speak on their behalf, to claim to know the opinion of so many and diverse minds, and in such a crude misdirection to boot.
Good thing they wrote volumes about it which have debated and summarized to the hilt.
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Ridiculous hubris, to claim to speak on their behalf, to claim to know the opinion of so many and diverse minds, and in such a crude misdirection to boot.
Good thing they wrote volumes about it which have debated and summarized to the hilt.
I'll never understand how someone otherwise so apparently intelligent can be so religious. Weird, the systems that we spent massive amounts of energy designing to precisely describe reality do that better than all the ones that we threw out along the way!
Why not? Religious people believe that God is the Most Wise. Mathematics in nature attest to that attribute of God (as well as to other attributes of Him). An intelligent and religious person would recognize that, knowing it is God who came up with all the rules that keep the universe in balance.
I'll never understand why some people believe science and creationism can't go hand in hand.
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You think logic, the art of making distinctions, the study of critical thinking and the foundation of mathematics only matter in the same way art does?
I’d say they don’t matter nearly so much as art. The most cosmically significant export of humanity to date is Voyager’s golden record.
And if you believe art is about creativity, you can find beauty and art in in mathematics and other sciences.
Many great mathematicians were also art lovers, they appreciated music, they appreciated paintings and other forms of art.
I don't think there's a dichotomy between art and sciences.
Intuitionist mathematics claims that mathematics is purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles existing in an objective reality. [0] In intuitionist mathematics there is only potential infinity, no actual infinity. Constructive set theory differs from Zermelo set theory. That has many consequences in practice. Applying intuitionist mathematics t…
Though I'd like to think that most species would come up with some version of calculus, even though the notation will be obviously different. Afterall, two of our own species did so independently.
The expression is invented but the underlying relationships are discovered. It's silly to think that the sqaure root of negative one is something real to be discovered. It's just a stand-in to express complex relationships more succinctly. The same for negative numbers, for that matter. It would be equally silly to think that the underlying relationships are invented. Nobody invented prime numbers, they were discover…
The personal expression can get very far too, further than perhaps an advanced alien race may know. Supposing an alien race never discovered category theory, their mathematics could still be more advanced than ours, but perhaps more verbose, longer to write down or otherwise bulky and inelegant. The question of whether elegant mathematics is more advanced I guess becomes tricky to answer. But pedagogically and for pr…
The expression is invented but the underlying relationships are discovered. It's silly to think that the sqaure root of negative one is something real to be discovered. It's just a stand-in to express complex relationships more succinctly. The same for negative numbers, for that matter. It would be equally silly to think that the underlying relationships are invented. Nobody invented prime numbers, they were discover…
>The same for negative numbers Are you sure negative numbers are not "real" in the same way natural numbers are? That would mean particles like electrons with a negative charge are not "real", too. And someone can argue that his negative bank balance is not "real". As for complex numbers, I fail to see how they are less real than real numbers. Real numbers are points on the real axis, while complex numbers are points…
We could easily call them 'black' and 'white' particles and the system itself would stay the same