Does mathematics really exist in nature or not?

[cladking]

No evidence then.

 

 

Of course there's no evidence.

 

From the current perspective, the perspective generated by the brain's operating system call language, only our consciousness is set in stone and even it can't be clearly defined, measured, or understood (except when considering itself). It's little better from the perspective where reality is taken as a given however things fit together differently and some things are more easily seen.

 

People want answers to the big questions but the reality is we can't have these answers at the current time so all we can do is better understand the questions.

 

To each his own?

[Klaynos]

 

 

Of course there's no evidence.

 

Then how can you be quite so definitive?

 

It's a really interesting topic, I just don't think you can state a well evidenced answer either way.

[ThinkingMind]

I searched everywhere on the Internet but couldn't find a conclusive answer.

 

My question is: Do mathematical entities (like numbers or probability distributions for example) really exist in the universe or are mathematical entities just a human invention?

 

In other words, is mathematics really out there in the universe or is mathematics just a tool that humans invented in order to describe the universe?

Some have argued Math is simply a language we made up to understand things. That Math does not exsist with out us, we simply invented it to explain things to each other. Kind of how a rock exsist but in nature its not called a rock, its called a rock since we decided it needed a name.

[arc]

Considering the pace of advancing developments in artificial intelligence and CGI technology, I cannot help but think it will be possible in the distant future to generate individually conscious CGI characters that will contemplate whether their mathematics is something they created or is instead intrinsic to their natural world, of which it would undoubtedly be.

[cladking]

Then how can you be quite so definitive?

 

It's a really interesting topic, I just don't think you can state a well evidenced answer either way.

 

There are not really any answers to any questions. The concept that "I think therefore I am" is simply ludicrous. One doesn't think outside of language so a more realistic perspective is "I am therefore I think".

 

And this is the heart of every question, all communication, and all knowledge; perspective. I simply prefer a perspective from which an axiomatic reality is most easily visible. Yes, I invented "reality" as being axiomatic and assuming it is exactly what people perceive and as defined by scientific results as seemn through the definitions, processes, and rules of the science that produced those results.

 

My perspective yields no more knowledge than any other but some of the connections between various aspects of reality are more easily seen. Of course, some are harder to see as well. Bouncing around the different perspectives is what I call generalism and was very similar to what I believe ancient science was. Rather than experimental results it used observation and the natural logic of a sort of mathematically based language.

 

Most of understanding reality is independent of perspective and this applies especially to scientific knowledge but I believe there are some deviations between theory and reality caused by perspective. While specialization and the ability to use a great deal of knowledge at narrow focus is of immense value to individuals and society there is a huge need for people trained to see other perspectives. The current trends are all unsustainable and apparently getting worse. Debt in a broad spectrum of meaning is increasing geometrically while ever more resources are being wasted to combat it. Meanwhile ever more highly leveraged bets on the future are a weight on any eventuality. Eventually one individual will have all the money and it will have no value at all.

 

Math works because it is logical and logic is an aspect of nature. It just does it. Area is equal to lenght times width or width times lenght because it is. This isn't apparent from the perspective of the mind using modern language as its operating system. If you think that you exist because you are conscious then you can't see that it is language in which you think. If you think 1 + 1 = 2 because this is the right answer or this usually seems to agree with reality then you can't see that these are constructs and a shorthand way of thinking rather than reality itself. It is a reality where 1 + 1 doesn't really = 2. It's merely the logic of nature which we never did see directly but are now removed another step away by language.

[Klaynos]

That's a lot of assertions with no evidence.

 

Let's concentrate on "maths works because it is logical". Can you define your use of the word logic here, as logic is a subset of maths, not the other way around which is what you impy.

[DevilSolution]

Then how can you be quite so definitive?

 

It's a really interesting topic, I just don't think you can state a well evidenced answer either way.

 

Mathematics relies on logic as its fundamental corner stone, every branch relies on basic logic to give it plausibility. HOWEVER logic needs no such thing from mathematics, therefor we can discern them. To say logic is a branch of mathematics is the same as defining the brain as part of the body, although this is true, its only through the brain that were able to even comprehend the rest of the body, or what a body is, or what a brain is.

 

That being said there are aspects to mathematics (or physics atleast) that cant be described in any logical formalities i know of, such as time for example and the abstract notion of the locus and circles.

 

All that being said Logic is a tool in a mathematicians toolbox as much as it is a philosophers.

 

 

And dont forget conceptually speaking, you must walk before you run. This is what logic is to maths, it gives it the ability to run free and wild.

And although you say logic is a subset of maths, its also primary to mostly all philosophical notions, which means it belongs to philosophy as much as maths, if not more.

Edited November 15, 2015 by DevilSolution

[cladking]

That's a lot of assertions with no evidence.

 

Let's concentrate on "maths works because it is logical". Can you define your use of the word logic here, as logic is a subset of maths, not the other way around which is what you impy.

 

I'm obviously not referring to the "logic" we study in school. Frankly, I see this subject as interesting but it is far more about semantics and definitions than the logic of nature. Logic is easily twisted and tortured by words and until we create concrete definitions for words this will always be the case. Words with concrete definitions are still constructs as we use language but there's no wiggle room for twisting meaning.

 

"Logic" as I'm using the term and saying nature is inherently logical is embedded deeply in reality itself and is brutal. If you need two oars to propel a boat and you bring two types of ores you might find yourself up the creek without a paddle. Logic is every single mammal having one male and one female parent. This is the logic where one plus one equals three yet we each have two parents. We have four grandparents. This logic is wired right into the human brain and the brains of all animals. This logic is simply quantified in mathematics. One plus one is said to equal two because in reality when one thing is considered in conjunction with a similar thing there is typically about twice as much. Thus one times two is equivalent to one plus one. Of course in the real world one plus one can equal anything from a very large number to minus a very large number. The logic always holds because a man and woman are inherently different so this difference is what creates the third. This same thing applies to apples, grains of sand, and miles. Each is inherently different and each follows the logic of nature. We invent concepts and words to describe it and math to quantify it but it all still always obeys the logic of nature preferentially to the logic of man. Every thing and all of their parts bend to the will of nature and we merely strive to understand her.

Edited November 15, 2015 by cladking

[andrewcellini]

 

Logic is a branch of mathematics.

philosophy actually, at least that seems to be what it is conventionally classified under. https://en.wikipedia.org/wiki/Logic

Edited November 16, 2015 by andrewcellini

[studiot]

 

Does mathematics really exist in nature or not?

In other words, is mathematics really out there in the universe or is mathematics just a tool that humans invented in order to describe the universe?

 

 

 

It is well known in biological science that some animals can count, I'm sure one of the life sciences members could tell us which birds can count eggs and chicks.

 

So is counting mathematics and does it have to be a human invention?

[cladking]

 

 

It is well known in biological science that some animals can count, I'm sure one of the life sciences members could tell us which birds can count eggs and chicks.

 

So is counting mathematics and does it have to be a human invention?

 

You're assuming their construct is identical to the human construct.

 

It's far more likely animals 1st egg, 2nd egg, 3rd egg, etc. To the animal there is no construct. Just eggs.

Humans imagine that 1, 2, and three are entities but they are not.

 

 

 

 

[Klaynos]

 

I'm obviously not referring to the "logic" we study in school. Frankly, I see this subject as interesting but it is far more about semantics and definitions than the logic of nature. Logic is easily twisted and tortured by words and until we create concrete definitions for words this will always be the case. Words with concrete definitions are still constructs as we use language but there's no wiggle room for twisting meaning.

 

"Logic" as I'm using the term and saying nature is inherently logical is embedded deeply in reality itself and is brutal. If you need two oars to propel a boat and you bring two types of ores you might find yourself up the creek without a paddle. Logic is every single mammal having one male and one female parent. This is the logic where one plus one equals three yet we each have two parents. We have four grandparents. This logic is wired right into the human brain and the brains of all animals. This logic is simply quantified in mathematics. One plus one is said to equal two because in reality when one thing is considered in conjunction with a similar thing there is typically about twice as much. Thus one times two is equivalent to one plus one. Of course in the real world one plus one can equal anything from a very large number to minus a very large number. The logic always holds because a man and woman are inherently different so this difference is what creates the third. This same thing applies to apples, grains of sand, and miles. Each is inherently different and each follows the logic of nature. We invent concepts and words to describe it and math to quantify it but it all still always obeys the logic of nature preferentially to the logic of man. Every thing and all of their parts bend to the will of nature and we merely strive to understand her.

This seems to be closest to the definition of logic of "it makes sense to me". But we know the universe doesn't work like that (and why should it).

 

 

I strongly agree we need some fourth definitions here. English isn't really suited to that though.

[studiot]

 

 

You're assuming their construct is identical to the human construct.

 

It's far more likely animals 1st egg, 2nd egg, 3rd egg, etc. To the animal there is no construct. Just eggs.

Humans imagine that 1, 2, and three are entities but they are not.

 

 

 

 

 

 

From your response I assume that you regard counting as mathematics, although you didn't specifically answer that part of my question.

 

In respect of your comment, as far as I can tell, it is only humans who compare counting methods. Animals are not that advanced.

But were the earliest human counters that advanced either?

[Strange]

Humans imagine that 1, 2, and three are entities but they are not.

 

Some do, some don't. Isn't that basically the question asked at the start of this thread.

 

What arguments and evidence would you provide for your claim that numbers do not have an independent existence?

[cladking]

 

From your response I assume that you regard counting as mathematics, although you didn't specifically answer that part of my question.

 

In respect of your comment, as far as I can tell, it is only humans who compare counting methods. Animals are not that advanced.

But were the earliest human counters that advanced either?

 

Counting isn't natural logic/ natural math. It is a human construct founded on modern language but employing terms that mirror natural logic. Numbers are part of language moreso than math. They are constructs. just as all operators in our math are constructs.

 

Animals can't understand human math or counting. Counting is simple enough an individual monkey or other "intelligent" animal might be able to "get it" but then the individual couldn't describe how our system differs from its. Even if it had the words we wouldn't understand them. I doubt any coulds have the words because animal language is geared toward more immediate needs and they lack the ability to build on past learning generationally so they lack the complex knowledge to frame such thoughts.

 

At the risk of going off-topic, early humans were animals. They used a complex language for 40,000 years but this was a natural language with natural logic. When complex language arose the language became increasingly complex to contain all the new learning which accumulated generationally. The language became too complex and failed leaving us modern language where words are constructs with many meanings which become apparent through context. I don't believe these early "coiunters" counted at all but rather they used animal math. ie- the first egg plus the second egg is the sum total of the eggs. The second egg is half the first and second egg. In a set of the first and second eggs, two eggs exist. I don't think this is even "math" in our terms but rather a way of seeing the world by use of natural logic. There is a one to one correspondance between the set of eggs and the set of myself and my mate. Hence breakfast is served. The ability to manipulate this logic became so complex that we still haven't figured it out. Some operations are rather clumsy using this "math", of course.

 

We count. It makes perfect sense to us. When we apply the rules of math and nature correctly we are often capable of great things.

...but this doiesn't mean we understand the laws of reality or gravvity better than a goat.

[studiot]

 

Animals can't understand human math or counting.........................

 

......................animal math. ie- the first egg plus the second egg is the sum total of the eggs. The second egg is half the first and second egg. In a set of the first and second eggs, two eggs exist. I don't think this is even "math" in our terms but rather a way of seeing the world by use of natural logic. There is a one to one correspondance between the set of eggs and the set of myself and my mate. Hence breakfast is served. The ability to manipulate this logic became so complex that we still haven't figured it out. Some operations are rather clumsy using this "math", of course.

 

 

Is that so?

 

I wonder how you deduce this ?

 

Or is it one of the many claims you are going to make without evidence.

 

Have you ever heard of the cuckoo?

Both the cuckoo and the target bird can count to at least 5.

It is really quite sophisticated, but not as sophisticated as the fractions you seem to claim animals can cope with.

[cladking]

 

 

Both the cuckoo and the target bird can count to at least 5.

 

 

How do you know the bird isn't simply creatin a one to one correspondance between its responses and the number of objects.

 

If a horse kicks three times in response to three fingers it might simply be kicking once for each finger rather than counting fingers and kicks.

 

We'll need another thread for the extensive evidence an animal human language once existed.

[Acme]

Animal Cognition

 

...

Numeracy

 

Some animals are capable of distinguishing between different amounts and rudimentary counting. Elephants have been known to perform simple arithmetic, and rhesus monkeys and pigeons, in some sense, can count.[90][91][92] Ants are able to use quantitative values and transmit this information.[93][94] For instance, ants of several species are able to estimate quite precisely numbers of encounters with members of other colonies on their feeding territories.[95][96] Numeracy has been described in the yellow mealworm beetle (Tenebrio molitor)[97] and the honeybee.[98]

 

Western lowland gorillas given the choice between two food trays demonstrated the ability to choose the tray with more food items at a rate higher than chance after training.[99] In a similar task, chimpanzees chose the option with larger amount of food.[100] Salamanders given a choice between two displays with differing amounts of fruit flies, used as a food reward, reliably choose the display with more flies, as shown in a particular experiment.[101]

 

Other experiments have been conducted that show animals' abilities to differentiate between non-food quantities. American black bears demonstrated quantity differentiation abilities in a task with a computer screen. The bears were trained to touch a computer monitor with a paw or nose to choose a quantity of dots in one of two boxes on the screen. Each bear was trained with reinforcement to pick a larger or smaller amount. During training, the bears were rewarded with food for a correct response. All bears performed better than what random error predicted on the trials with static, non-moving dots, indicating that they could differentiate between the two quantities. The bears choosing correctly in congruent (number of dots coincided with area of the dots) and incongruent (number of dots did not coincide with area of the dots) trials suggests that they were indeed choosing between quantities that appeared on the screen, not just a larger or smaller retinal image, which would indicate they are only judging size.[102]

 

Bottlenose dolphins have shown the ability to choose an array with fewer dots compared to one with more dots. Experimenters set up two boards showing various numbers of dots in a poolside setup. The dolphins were initially trained to choose the board with the fewer number of dots. This was done by rewarding the dolphin when it chose the board with the fewer number of dots. In the experimental trials, two boards were set up, and the dolphin would emerge from the water and point to one board. The dolphins chose the arrays with fewer dots at a rate much larger than chance, indicating they can differentiate between quantities.[103] A particular grey parrot, after training, has shown the ability to differentiate between the numbers zero through six using vocalizations. After number and vocalization training, this was done by asking the parrot how many objects there were in a display. The parrot was able to identify the correct amount at a rate higher than chance.[104] Angelfish, when put in an unfamiliar environment will group together with conspecifics, an action named shoaling. Given the choice between two groups of differing size, the angelfish will choose the larger of the two groups. This can be seen with a discrimination ratio of 2:1 or greater, such that, as long as one group has at least twice the fish as another group, it will join the larger one.[105]

 

Monitor lizards have been shown to be capable of numeracy, and some species can distinguish among numbers up to six.[106]

...

[studiot]

 

How do you know the bird isn't simply creatin a one to one correspondance between its responses and the number of objects.

 

Isn't that a definition of counting?

 

 

Anyway, do you know what the responses are that I am referring to and why I chose the cuckoo and mentioned a 'target bird'?

[andrewcellini]

If a horse kicks three times in response to three fingers it might simply be kicking once for each finger rather than counting fingers and kicks.

that is counting

 

to count to three, you have to start at 1 and add 1 twice - > 1 + 1 + 1 = 3

 

i'm not sure what you're getting at when you say "extensive evidence an animal human language once existed," or why that is relevant.

Edited November 16, 2015 by andrewcellini

[cladking]

 

Isn't that a definition of counting?

 

 

Anyway, do you know what the responses are that I am referring to and why I chose the cuckoo and mentioned a 'target bird'?

 

I'm not familiar with the bird referent so I changed horses in mid-stream.

 

"Counting" as I'm using the term is arriving at a sum. We create a construct to represent the number of an item.

 

The horse doesn't know anything about "three". It can't tell three of something from two because it never needs to know. But it can't differentiate between objects and will understand the difference between an apple and a cube of sugar. It can differentiate between the first apple, second apple, and third apple. If you holds up three fingers it might be able to kick one time for each with training. If it needs to go to the third corral to be fed it will go to the third. But it does all this without having a referent for numbers. It doesn't know you held up three fingers or that it kicked three times because animals don't count.

 

If we count to three normally the number two has no meaning. We are merely determining the total number of objects but the horse has a distinct understanding of the three apples. The first apple remains the first apple even after it's eaten and only two apples "remain". To the horse the second and third apples remain. We see two apples. Obviously though this assumes there are identifiable differences and they were noted which isn't necessarily the case with humans or horses.

 

 

i'm not sure what you're getting at when you say "extensive evidence an animal human language once existed," or why that is relevant.

 

It was relevant for the accuracy of the statement and perspective. It's relevant because the human mind is still wired the same way even though it employs a new operating system.

 

The evidence to support this is irrelevant in this thread.

[Strange]

 

Counting isn't natural logic/ natural math. It is a human construct founded on modern language but employing terms that mirror natural logic.

 

Some animals can count so that is obviously false.

 

 

They used a complex language for 40,000 years but this was a natural language with natural logic.

 

Please don't drag this nonsense up here. You have at least one thread devoted to it. As you know nothing of historical linguistics and have no evidence for these ideas, it clearly belongs in the Speculations forum.

"Counting" as I'm using the term is arriving at a sum.

 

So you are redefining common words to try and make it seem as if you are making sense.

 

You are "correct".

"Correct" as I am using the term, means making false and unsupportable claims.

[studiot]

 

I'm not familiar with the bird referent so I changed horses in mid-stream.

 

"Counting" as I'm using the term is arriving at a sum. We create a construct to represent the number of an item.

.......Horses...........

 

I believe I introduced counting to this thread in post38 and enquired if it was considered mathematics.

 

If you wish to use a different definition please, at least, make it clear that your definition is/maybe different.

 

With regard to the cuckoo, I'm suprised you didn't look it up, it's quite a story.

 

The target bird is usually a blackbird or a thrush, but may be a smaller bird such as a sparrow or robin.

The blackbird builds a nest and lays on average 2 to 4 eggs.

Whilst the blackbird is out feeding etc the cuckoo comes along and lays 1 or two eggs in the blackbird's nest.

The blackbird knows (can count) how many eggs it laid and will reject the foreign egg(s) so the cuckoo throws out 1 or 2 blackbird eggs from the nest before it leaves.

When the blackbird returns it counts the same number of eggs (birds fuss around if the number is different) and eventually hatches and raises the cuckoo(s) as well as its own remaining chicks.

 

Quite a sophisticated setup n'est pas?

Edited November 16, 2015 by studiot

[cladking]

 

I believe I introduced counting to this thread in post38 and enquired if it was considered mathematics.

 

If you wish to use a different definition please, at least, make it clear that your definition is/maybe different.

 

 

 

I thought I was clear. Counting is mathematics which is based on natural logic which is inherent in the wiring of all brains. However animals don't use any sort of math at all. Math and numbers are human constructs which don't exist in the real world. Animals use natural logic directly without intermediary words and definitions. Their "words" hence are mathematical in nature. They have a concept of first, second, and third, but they lack the constructs of one, two, and three.

 

 

 

You are "correct".

 

 

I certainly appreciate the "support" but with neither logic nor evidence to support it I can simply ignore it.

[sciwiz12]

This one went to some really strange places rather quickly, I think the only definitive answer here is... Depends on how you look at it.

 

If a thing has a property that it is quantifiable, is that proof that numbers exist? What is the property of quantifiability? Something surely is quantifiable if it can be counted, but what can be counted?

 

Let's take the example of a spoon. With even a rudimentary level of human understanding I can discern a difference between one spoon and two spoons, but the problem here is that there aren't really any spoons. If you take the principals of chemistry and modern physics on good faith given the evidence and research available on both subjects then all spoons are really collections of atoms.

 

"Aha!" You might say, "the atoms then are quantifiable, if hard to count." But really there are no atoms, only collections of quarks, discreet packets of energy. Going further and accepting particular well regarded models of the subatomic universe it would seem that particles are in fact excitations of continuous fields that have approximate values at various points in spacetime, or perhaps vibrations of superstring which themselves aren't very discrete.

 

So any property of oneness or twoness observed so far is an emergent property of collections or excitations of stuff. To take it a step further the likelihood that one spoon is exactly identical in mass to any other spoon down to even just the atomic level is absurdly low. So really there aren't likely two be two of a spoon anywhere, because each spoon is more or less unique.

 

So if your question is, "is math a property of the objective universe such that math could exist without the mathematician?" I would argue that it is not more than a useful fiction of the observer, a construct utilized in order to process the world in a more organised fashion. Going further one could even argue that the universe could be an illusion in which case math is definitely not a property of things that don't exist.

 

However if you asked, "does math exist?" I would argue that it does, in fact, exist. If our brains exist then our brains have seemingly simulated consciousness which has itself constructed all of the basic philosophical components to create a sense of math, which then exists as a function of the brains of the people that perform mathematical operations. Somewhere in the array of discharging neurons, in the processes of sending neurotransmitters across synaptic gaps, math exists and is being performed, and in that way it exists in the same way this website exists, as an emergent property of neurons forming the human brain.

 

If our brains don't exist then it is even more difficult to pin down the architecture and mechanics of our thinking, because in that case we clearly do not have easy access to accurate information concerning how we exist, but I would still argue that if I exist, then my thoughts exist as properties of me.

 

So to recap, are numbers a component of objective reality? Probably not, but I'll get back to you when I know everything there is to know about the whole of reality with 100% undeniable certainty. Does math exist? As long as you hold it... In your heart... (Sparkles and magic rainbows) but seriously, yes, as a incidental product of consciousness, not verifiably necessary to consciousness, but in this particular case an apparent effect of certain consciousnesses.

I still think it's worth considering the physical argument, though. Some argue that math is real because things in apparent reality seem to behave in definite and easily predicted patterns and the best way we've discovered to understand the apparent patterns in the universe is math.

 

I don't think this makes math not a useful fiction, but the merit of the argument comes from the idea that math is more or less discovered rather than simply created. It's not like the works of Shakespeare because it came about through observation and isn't subject to change by the will of man as far as we can tell so much as by further and deeper observation of the universe.

 

In order to understand this concept it's useful to have a notion of abstraction. Math, and even the physical sciences to a lesser extent, contain ideas that are distinct from imagination because they serve as descriptions of what we have observed through our senses, with math only being slightly more abstracted than chemistry for instance.

 

So it's not pure fiction but I also wouldn't say it exists in the physical universe because while physics demands empirical experimentation for verification (a process of constant reaffirmation of its object existence) math is unique because I can discover new "laws" of mathematics while sitting in my room writing in my private journal without ever testing my ideas in the physical world, and offer up the proof in the same stroke.

 

So assuming the universe is real and science is mostly accurate up to this point, that puts math somewhere between fiction and physical science. The best word I can think of is useful fiction. Math presents with a model of the universe that is demonstrably insufficient for many tasks and at times leads us to identify conjectures which can be described by mathematics which are also unprovable and seemingly unsolvable by mathematics, but the model is so practical we can use it to put a man on the moon and create virtual realities. In other words it is so close to accurately describing so much of reality in such great detail and is so deeply intertwined with the objective and empirical that it might as well be a part of objective reality, even if it maybe technically isn't.