owleye wrote:So the question devolves not to the mathematical objects themselves, but rather to the rules and procedures that are set up to finding them. Are these invented or discovered?
Whut wrote:the inner workings of math we dicovered, but there's no 1+1 without our existence.

Dave_Oblad » September 14th, 2017, 1:53 am wrote:Hi All,
That which is invented has freedom.. such as language, art, music, laws, morality.. etc.
Math has no such freedom.. it is composed of Rules, Rules that have been discovered over time.
We may discover many ways to approach a single math problem, but we can't make up our own rules.
Regards,
Dave :^)
Mitch wrote:The difference between Euclidean and nonEuclidean geometry demonstrates this.
Dave_Oblad » September 28th, 2017, 12:34 pm wrote:Sorry Mitch, but while we may have the freedom to invent the symbols that represent various math functions, we can't make up or invent those functions.. as they represent absolute truths.
Dave_Oblad » September 28th, 2017, 12:34 pm wrote:Mitch wrote:The difference between Euclidean and nonEuclidean geometry demonstrates this.
Are you kidding? That is absolutely worthless as a defense against invention. Both types of Geometry are based on very strict absolute rules that we most definitely had no choice in their invention.
You do understand that invention implies freedom of choice? Again, we may have such freedom in choosing the symbols that represent absolute truths but we can not invent the truths themselves.
Must one have a concept of mass, for example, to do Newtonian mechanics? We might at first think so, since that is the way it was taught to most of us. We have been taught that there were, at its outset, three ‘fundamental’ concepts of Newtonian mechanics: mass, length, and time. (A fourth, electric charge, was added in the nineteenth century.) But it is far from clear that there is anything sacrosanct, privileged, necessary, or inevitable about this particular starting point. Some physicists in the nineteenth century ‘revised’ the conceptual basis of Newtonian mechanics and ‘defined’ mass itself in terms of length alone (the French system), and others in terms of length together with time (the astronomical system).8 The more important point is that it is by no means obvious that we would recognize an alien’s version of ‘Newtonian mechanics’. It is entirely conceivable that aliens should have hit upon a radically different man ner of calculating the acceleration of falling bodies, of calculating the path of projectiles, of calculating the orbits of planets, etc., without using our concepts of mass, length, and time, indeed without using any, or very many, concepts we ourselves use.
Their mathematics, too, may be unrecognizable. In the 1920s, two versions of quantum mechanics appeared: Schro ̈dinger’s wave me chanics and Heisenberg’s matrix mechanics. These theories were each possible only because mathematicians had in previous generations invented algebras for dealing with wave equations and with matrices. But it is entirely possible that advanced civilizations on different planets might not invent both algebras: one might invent only an algebra for wave equations, the other only a matrix algebra. Were they to try to communicate their respective physics, one to the other, they would meet with incomprehension: the receiving civilization would not understand the mathematics, or even for that matter understand that it was mathematics which was being transmitted. (Remember, the plan in S E T I is to send mathematical and physical information before the communicating parties attempt to establish conversation through natural language.) Among our own intellectual accomplishments, we happen to find an actual example of two different algebras. Their very existence, however, points up the possibility of radically different ways of doing mathematics, and suggests (although does not of course prove) that there may be other ways, even countless other ways, of doing mathematics, ways which we have not even begun to imagine, which are at least as different as are wave mechanics and matrix mechanics.
JustAsking » October 17th, 2018, 10:34 am
I thought I'd revive this thread because it discusses something I've been pondering lately. But let me ask it a different way. Why does 1 + 1 = 2?
JustAsking » October 19th, 2018, 10:04 am
But we don't have to get fancy talking about other worlds, etc. Just think of my simple example. Two raindrops hit the ground in the same spot and form a single larger raindrop. (Or in the air as they fall.) If + refers to counting, then 1+1=1 in this case. If it refers to measuring volume, then 1+1=2. So it depends on the context. We could form a mini mathematical law about raindrops using only + . So if we were developing a theory of raindrops, and we did experiments, we could "model" the results to get 1+1=1 or 1+1=2 depending on how we define +. I.e. we could fudge the math the get the results we want. And that's what I'm wondering if theoretical physicists are doing, only with math that's so complex they actually miss the contexts. If you read Sabine's book you see how hundreds of papers come out positing all kinds of ways that this complex math seems to lead them to just about any conclusion they want. And even saying there has to be a tie in to experimental results doesn't seem to be enough.
hyksos » October 19th, 2018, 7:59 pm wrote:Six years later, and it's still a 11/10 near exact split on votes.
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