Fractal Food: Self-Similarity on the Supermarket Shelf (2005)
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Re: Fractal Food: Self-Similarity on the Supermarket Shelf (2005)
#2How do those holding opposing views of mathematical realism account for the presence of such plants and similar computed natural phenomena?
Re: Fractal Food: Self-Similarity on the Supermarket Shelf (2005)
#3Chou 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 :)
Re: Fractal Food: Self-Similarity on the Supermarket Shelf (2005)
#4How do those holding opposing views of mathematical realism account for the presence of such plants and similar computed natural phenomena?
What phenomenon is NOT computed i.e. following a set of exact rules that play out over time?
Re: Fractal Food: Self-Similarity on the Supermarket Shelf (2005)
#5How do those holding opposing views of mathematical realism account for the presence of such plants and similar computed natural phenomena?
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.
Re: Fractal Food: Self-Similarity on the Supermarket Shelf (2005)
#6How do those holding opposing views of mathematical realism account for the presence of such plants and similar computed natural phenomena?
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 throug…
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".
Re: Fractal Food: Self-Similarity on the Supermarket Shelf (2005)
#7How do those holding opposing views of mathematical realism account for the presence of such plants and similar computed natural phenomena?
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 throug…
it was difficult to frame this question
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
Re: Fractal Food: Self-Similarity on the Supermarket Shelf (2005)
#8Earlier quoted context omitted.
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 throug…
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".
but this is more about definitions right?
culture 1 : 2+2=4
culture 2 : 2+2=5
translation between culture 1 and 2:
2==2
4==5
180==360
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
Re: Fractal Food: Self-Similarity on the Supermarket Shelf (2005)
#9How do those holding opposing views of mathematical realism account for the presence of such plants and similar computed natural phenomena?
What phenomenon is NOT computed i.e. following a set of exact rules that play out over time?
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?
Re: Fractal Food: Self-Similarity on the Supermarket Shelf (2005)
#10Earlier quoted context omitted.
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".
but this is more about definitions right? culture 1 : 2+2=4 culture 2 : 2+2=5 translation between culture 1 and 2: 2==2 4==5 180==360 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.