Does mathematics really exist in nature or is math just a human construct?

my only point is two plus two is the same to an animal as it is for a human. If a dog has two bones and you give him two more he has four not five or six or seven. c'mon man, work with me here.

 

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I must admit, the world would be a better place if everyone lived like Thoreau at Walden Pond.
But alas, we like loud electric guitar sounds over the whispered symphony of the forest

But on topic. Rhesus monkeys can count just as fast as humans. Some even better.
Understanding mathematical relationships in the abstract in other organisms is in no way inferior to understanding mathematics in human symbolic language.

The *brainless* slime-mold solves mazes through a mathematical procedure!!!!

 

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Classical electromagnetism, quantum mechanics, special relativity, general relativity, quantum field theory, the standard model of particle physics and statistical mechanics cannot really be studied pictorially.

So isn't the fact that physics isn't pictorial proof enough that mathematics actually exists?

 

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There is no external force being applied to our nature. All the forces of nature are internally generated. Nature follows a self-balancing principle. Any incremental change happening to our nature follows from this self-balancing principle. Mathematics also follows a balancing principle. So we can say that mathematics is there in the Nature.

 

Ecellent question. While we may see a horse tapping it's foot the correct number of times to a maths question, others may know the owner is simply holding out a certain number of fingers and the horse has been trained to tap that many times. I would say it is a human construct.

 

Then you don't understand the question.

 

IMO, all we can say that the dog knows which is "more" rather than "less", which is a mathematical function, albeit rudimentary. See my post #102, the Rhesus monkey experiments (thousands) clearly show that they can tell the difference between more or less of something and make decisions on that cognitive ability. IOW, they can and do practice mathematics at some fundamental level.

 

And how does a horse recognize how many fingers the owner displays? Training is not the issue, cognition is. We train people in mathematics and its applications also.

 

Personally I think the argument that mathematics is something other than phenomena that exists in this universe is really boring and counterproductive. It seems I look at plenty of graphs that help me understand the physics when I'm reading text. Other than that your argument has some validity in my estimation. Very difficult to base your entire arguments on pictures.

 

You assume that at a minimum that the horse is keeping track of how many times it has tapped regardless of whether it knows that matches the signal given to it by the human. Thus you have assumed the horse has some knowledge of number.

If you have assumed the horse is mapping the number of taps to the number of fingers shown then you have assumed the horse has generalized the concept of numbers in than it is relating the number of concrete objects (fingers) to the number of actions (taps).

Neither hidden assumption is a good way to convince someone that number is a solely human concept.

 

IMO, there are two sides to this problem.

a) The Universe works in orderly functions, based on physical values and properties which interact in consistent and predictable predictable ways. This is a reasonable assumption based on direct observation, which has given us our understanding of these Universal functions and values. "Function based on Values".

b) Human observation and understanding of these mathematical functions based on physical values of the Universe allowed us to translate those values and functions by means of mathematical symbols and equations. "Mathematics".

Perhaps the following may be related to the mystery of a *mathematical Universe*
I recently ran across this intriguing definition of *Simultaneous necessity and Sufficiency

http://en.wikipedia.org/wiki/Necessity_and_sufficiency

IMO, this equivalence holds on an immaterial (metaphysical) level as well.
Fundamentally the Universe, the singularity with infinite Potential, functions as a duality, the absolute minimum material or immaterial equivalence of Necessity and Sufficiency.

 

No; it moves through mazes via immediate responses to immediate stimuli, nothing more (it detects remnants of its own slime trail).

We draw mathematical algorithms to model what it is doing (just like we model planetary motion over time, even though the planet responds only to its local, immediate gravitational environment).

 

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That argument does not negate the mathematical nature of the actions of the Mold or the Planet.
A thing does not need to be sentient at all to be subject to the mathematical function.

Daisies follow the Fibonacci Sequence. It seems that the natural mathematical function has *selected* this sequence as the most efficient growth configuration for Daisies and many other things, including the spiral configurations of some Galaxies.

IMO, one has to separate *human* symbolic mathematical calculus and mathematical modeling from *Universal mathematical functions*. Why else would *mathematicians* say that they always have a sense of *discovery* of Universal mathematical functions, which existed long before life itself existed and humans invented mathematics as the symbolic language to explain these functions?

IMO, the Universal Constant of the Mathematical Function was causal to the formation of the very first elements from the chaotic "inflationary epoch". Everything in the Universe follows the mathematical function, with an occasional and temporary chaotic symmetry breaking, such as when a star goes Nova. But the *cause* for a star going Nova is a mathematical function; the *result* is a temporary state of chaos, which eventually orders itself again through the Universal Mathematical Function.

 

I'm sure animals know the difference between more or less (they know how much to eat or at least when to stop eating), but is this a grasp of mathematical concept? Surely animals are aware of how many mouths they have to feed? However this cannot be true for ALL creatures: fish that lay eggs do not remain to see them hatch (do they?) Despite my previous post I imagine they are aware they are one above all else? But then not all humans are aware of this anyway...

 

As explained before *knowledge* (awareness) of the natural mathematical funcion is completely irrelevant. Non-sentient organism still must follow the universal constant of the mathematical function.

 

But not every function is available! Some sequences simply are without pattern (which I CAN prove.)

 

Do you even read my posts? I am the one who stated that occasional *symmetry breaking* occurs which results in chaos.
But if you can show an example of a persistent non-pattern, give me an example.

 

Since a sequence is a pattern, the meaning of Waiter's claim is far from clear.

Perhaps he means that no amount of output of a sequence with unrevealed origin can let you know the values yet to come.

-2089, 271, 1329, 1583, 924, 784, -268, 929, 785, -3709, 1726, -4642, -4206, 8683, 13187, 2893, -12280, 14700, -2474, 5929

Can you know that the next value is even an integer?

 

Many species of fish guard their eggs until they are hatched. Seahorse comes to mind immediately.

https://en.wikipedia.org/wiki/List_of_fish_species_that_protect_their_young

p.s. edit of post 118 to read: One example of a non-repeating pattern can be found in Pi.