Chou romanesco is probably a regular thing for people living in southern Europe, but coming from central Europe, it blew my mind the first time I've seen it in a grocery store :)
If you like this, then you'd almost certainly love the book "The Computational Beauty of Nature". It explores a lot of similar themes, and is very visual, too.
As I understand it, math realism says that the mathematical object (for example, a class of self-similar sequences) exists whether or not it was discovered by humans. That the mathematical object happens to model some physical phenomenon pretty well is independent of the philosophy of mathematical realism.
Are you arguing against mathematical realism by saying certain mathematical objects are only discoverable through the observation and modeling of physical phenomenon? A pure math realist would respond that the object in question stills exists, whether or not it was discovered.
Opposition to mathematical realism also tends to bring in heavy doses of mathematical+cultural relativism, i.e. believing that if a culture decided 2 + 2 = 5 or that the interior angles of a triangle sum to 360 degrees, then those statements would be just as true as "2 + 2 = 4" or "the interior angles of a triangle sum to 180 degrees".
if you could agree on specific definitions: this is a triangle, this is interior, this is an angle, and this is a degree; you would be unable to come to opposing conditions on the sum of interior angles
Not really. The relativists aren't saying "oh, your 4 translates to their 5", and in fact are trying to say that such a statement is impossible to make. Your attempt at translation assumes the existence of some culture-independent thing, and tries to say "4" and "5" are different culture-specific symbols for representing that culture-independent thing, whatever it may be. The relativist position is that no such culture-independent thing exists.
In other words, the relativist believes that:
* If a culture decides this many objects (represented by dots): ". ." combined with this many other objects: ". .", produce this many objects: ". . . . ."
* Then that decision is just as valid and just as true as our culture's decision that ". ." objects and ". ." objects make ". . . ." objects.
The fact that every culture we know of has adopted the second one instead of the first is then explained as some sort of massive coincidence, or perhaps the result of some very old "2 + 2 = 4" culture successfully imposing its norms on everyone else such that it has persisted as a cultural belief to the present day.
because the philosophy of mathematics has so many branches with even more leaves i just went with the vague 'opposing' of one branch to cover as much ground as possible
in doing so i was moreso hoping to encourage others would define their own philosophical views on mathematics
i suppose if i was 'arguing against' anything it was more against a sort of mathematical formalism that states math only exists in the mind, or the axioms defined by human minds
if one can construct fractals and then encounter a plant like this it would seem validating to infer the mathematics being utilised by both the plant and the mathematician does indeed exist outside both
i'd tend to agree with this proposition, but i was asking because i wanted to have my views challenged
i rarely get an opportunity to debate the philosophy of mathematics and i was trying to use this article about this common found mathematical
object whose form expresses that computation explicitly to open a dialogue in that capacity
with that in mind, what are you trying to say philosophically with your question?
from your question i am inferring.. perhaps incorrectly, feel free to correct me.. that you think all phenomena are computed
what are the philosophical consequence of such a view?
Realism is the correct philosophical view? Formalism? Some other?
I wasn't really looking at it from a philosophical perspective, and I'm a layman at philosophy, and don't know the difference between Realism and Formalism. And actually I don't believe EVERYTHING is following exact rules, which is why I posed my comment as a question. I do believe there is at least a subset of reality that follows rules, which is why math and science works, and most daily phenomena that surround us are subject to those rules. In fact if you believe you found something that is not, you'll be called a nut job by most scientifically minded people. That being said, I'll reveal my own belief, and that is that the layer underneath our clockwork world could be governed by a different set of rules or perhaps no rules at all. I don't have much evidence for that other than psychedelic experience and wishful thinking, but it seems odd to me that there are any rules at all in the first place, rather than an infinitely malleable canvas, so my intuition tells me that our experience is a purposeful limitation on that rule-free layer for some unknown or unknowable purpose.