- Even better! And for delightful reasons known only to @Marta and me, … very timely. Thanks!
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- Explored Jerram’s name and was led to this:
Jerram Barrs on Harry Potter and the Deathly Hallowskquote
- Now I have to read J.K. Rowling’s series of Harry Potter books.
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- Hamlet said as much: he didn’t say “The argument’s the thing …”, he said: “The play’s the thing …”
Sure, but mathematics is not the same as those relationships, we just use mathematics to describe them.
And you think I cannot use chess to describe anything in the natural world? If I do does that mean the chess relationships were a preexisting part of reality waiting to be found? LOL
…asked the frog of the flea…
If you insist. The ratio of a circle’s circumference to its diameter was not π – it did not preexist math and we invented it.
Earth was held to be a sphere, and some recognized that the sun was a sphere, even before Erathosthenes famously calculated the diameter. There don’t have to be any perfect spheres in nature for the concept to have come from nature.
The universal constants most certainly do determine what the universe will be like. The values of the various forces plus various constants dictate very precisely how everything will work starting with what all the elements will be like including their interactions, their crystalline structures, etc.
No, the rules would have to be derivable by any observer without other input. Since your rules are totally arbitrary and not the result of nature, they are inventions. Only those which can be derived by any observer of the universe count as discoveries – to be more specific, only those which can be derived by any non-privileged observer. Your board game and its rules require a privileged observer, one who can read your rules.
How you could get the bizarre idea I just responded to from a post specifically saying otherwise baffles me.
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He’s ignoring the fact that circles and spheres and arcs and triangles and squares are derived from observing nature. Despite the claim otherwise, there are perfect circles in nature – a rainbow is one example – and other perfect shapes, e.g. hexagons and octahedrons, and many shapes close enough that a generalization from these leads to the mathematics of geometric shapes and more.
Quite so. If people had been making up the math, pi would have a value of 3.
When I first learned of i, the square root of -1, it was purely invented and deserving of the disdainful moniker “imaginary”; later I learned that while imaginary, its use in various scientific work made it entirely justified, and recent experiments have shown that there are phenomena in nature that cannot be described without it – which makes it just as “real” a number as the real numbers.
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And then there is the concept of volume. Is that independent of your mathematical axioms? No it isn’t. The volume of the earth in Euclidean geometry is not the same as the volume according to the non-Euclidean metric of general relativity.
Come to think of it, my younger brother had a friend at university who shifted from agnostic to Deist due to math; it was another “conversion” by what I think of as the argument from elegance.
How so?
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I probably misspoke. Exponential notation would be an invented tool for conciseness. And of course any glyph would be invented, but not the preexisting reality they might symbolize.
On the other hand, the additive relationships of exponents of similar terms in numerator and denominator I would say preexisted the discovery of that fact.
- Ha! I was quoting Vern Poythess’ words in his book immediately following the previous paragraph.
- I could see that. But it takes someone’s belief in Jesus’ crucifixion, resurrection, and ascension to get a Deist to become “a true believer in Jesus”.
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Historically this is not the case. The generalizations come from us, but they rest on observation of nature, and they are true not because we devised a system, they are true because they are deducible from observation by any non-privileged observer, thus indicating that they are properties of the universe.
Only in speculative mathematics can it be said that “the axioms come from us and not from the world”, and ever that is suspect given how often scientists in need of math to describe some phenomenon find the math they need already figured out by someone doing “pure research”.
Yet ultimately it is the axioms that actually rest in nature that are of most interest – and speculative math where an axiom or two gets altered has proven in the past to describe something real.
I’m not sure what that friend means. In the doctoral program in math that my older brother was in at Berkeley, as well as in the master’s program in math my younger brother did, some very foundational concepts were dealt with, including things like proving that 2 + 2 = 4 (more generally, that addition works and has the properties we associate with it [even though initially addition is just a description of the real world]).
Definitely true of crows! At least one crow who lives in my neighborhood can tell the difference between round and square as evidenced by choice of sticks to poke into holes.
It invented the tool, it discovered the relationships (probably spatial) that suggest the invention.
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You’re arguing that the converse of a statement is logically true, which is not the case. The proposition is that seeing relationship in the real world tells us rules about the real world; you’re arguing that if you can apply an arbitrary set of rules to some part of the real world, then the rules are “a preexisting part of reality”.
It’s only a preexisting part of reality if it will be found by any non-privileged observer.
It is; the idea of volume is obvious from the task of filling one large container using a smaller container: volume is what will determine how many loads from the smaller container will suffice to fill the larger container.
Anyone who’s made barrels as a cooper understands volume since coopers back in the day had barrels, half-barrel barrels, quarter-barrel barrels, and even eighth-barrel barrels: a barrel was the volume of a standard sized barrel that everyone agreed on, and actual wooden barrels were made to hold one-half, one-quarter, and one-eighth of a standard barrel (though more colorfully there’s “blood tun” and “firkin” amd “pony keg” [not ignoring the difference between a barrel and a keg and a cask…]).
So volume was originally associated with fluids but was easily extended to agricultural products and more.
A lot of questions came from observation of nature – and correspondingly, a lot of our units came from nature, e.g. the foot and the cubit.
Yes – the relationship “squared” was a discovered one about triangles and squares made with the triangle’s sides as side lengths for the squares; the notation is invented.
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No the volume of the earth is NOT independent of the mathematical axioms you choose to accept. The volume of the earth in Euclidean geometry is not the same as the volume according to the non-Euclidean metric of general relativity. Frankly you two only demonstrate that you are confusing your subjective perception with reality itself. What you think is a property of the world isn’t any such thing – it is just an idea in your own head.
Fluids including liquids are compressible and so this rough approximation doesn’t even hold on the everyday scales for some liquids. And I have already shown that your basic concept of volume isn’t even correct. It demonstrates how our mathematics is a product of the axioms we choose and that makes it a human invention.
Using such everyday common sense as a measure for absolutes is what leads to the nonsense of claiming the god Ares must be supplying the heat and light of the sun since everybody knows balls of gas don’t produce heat and light.
You can’t undermine what happened in history by appealing to esoteric science they didn’t know.
How much beer there is in a keg isn’t a matter of volume? How odd a claim.
I can’t even figure out how that is supposed to be a rational statement connected to what anyone here has been saying.
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I don’t suppose you want to talk about π and how it is not a property of a circle but rather is completely dependent on ideas in people’s heads. We could invent a new value if you like.
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Nothing could be more obvious, that this number which cannot even be specified exactly by anyone does not come from observation of the world but must be the product of human invention. Of course it is a property of this other mathematical invention in Euclidean mathematics, the perfect circle. It can be said to be a discovery in the same sense that the queen’s gambit is a discovery in chess.
You completely ignore what @St.Roymond said about non-privileged [alien] observers who can analyze circles without having to invent them and their properties.
You cannot ‘discover’ the rules of chess by looking at the board and the spilled pieces. It is in no way analogous.
I find the formula for the volume of a sphere to be distasteful. Would you please invent a new one that is more aesthetically pleasing? (I would like it better if you didn’t use π. ; - )
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