Does mathematics really exist in nature or not?

[cladking]

 

For instance the receiving nerve cells don't understand the information they receive, they just pass it along according to a chemically mechanistic process. It'd be like forming a line of people to pass a bucket of water or sand, or stuff in general. You never look at the bucket, you don't think about it, you just pass it to the next guy in line.

 

 

This can't be the reality.

 

If it were true there would be no free will. We'd be automatons processing whatever stray signal crossed our paths. Even individual differences would be more subtle.

 

At some point in this bucket brigade there has to arise a change in the signal. This is caused by the way the brain processes these signals. I believe this is where the formatting of language applies. Groups of signals are processed in this formatting. It's not entirely dissimilar to the operation of a computer and the computer language. Brain cells are either on or off.

 

Also, many species reproduce asexually, arguably a lot more than those that do so sexually, also most animals don't mate for life, that's pretty rare. In general you're presenting us with fallacious reasoning, even "perfect" hives do nothing to prove your claims about language, it's not even evidence really, or an argument, it's a question and the answer for most of those questions has nothing to do with language.

 

 

I stand corrected on sexual reproduction.

 

But the fact remains that sexual reproduction requires communication. Perhaps all those simple species don't use sexual reproduction simply because they lack the ability to communicate sufficiently. Do you really believe these animals aren't communicating?

 

https://vimeo.com/31158841

 

 

 

It is hard because (a) there obviously is such a thing as intelligence;

 

 

 

 

But this is exactly my point. You are mistaking 40,000 years of human progress and language for intelligence. Those murmurating birds are showing as much intelligence as the average human shows most of the time.

 

It's not so much that "intelligence" doesn't exist at all as it is that it is grossly overestimated. I prefer to use the word "cleverness" and "cleverness" is an event and not a condition. It is an event that all animals show.

 

And why do you claim that "they understand everything they see"? I don't know anyone that that applies to. So yet another in your endless series of untrue assertions.

 

 

Each individual sees things in the terms they understand. An electrician looking at a skyscraper sees an entirely different thing than a structural engineer or a doctor. An elevator repairman sees something different altogether. Each of these people believe that between all the people in the world that pretty much everything possible is known about skyscrapers. Each believe they have a good understanding of their own spectrum of the reality of skyscrapers.

 

They each see things in terms of the concepts and language we learned on our parents' knees.

 

They're all wrong.

[Strange]

This can't be the reality.

 

Why? Because you say so?

 

If it were true there would be no free will.

 

Maybe there isn't.

Or maybe you don't understand how the brain works.

(Both could be true, of course.)

 

Brain cells are either on or off.

 

Yep, that'll be it. You don't know how the brain works. Thanks for confirming it.

 

But the fact remains that sexual reproduction requires communication.

 

But not necessarily language.

 

Do you really believe these animals aren't communicating?

 

Oh look: another strawman. How pretty.

[cladking]

 

 

 

Oh look: another strawman. How pretty.

 

 

Perhaps you don't understand that we are talking about a subject no one knows anything about. I'm merely trying to present an hypothesis based on logic and observation. Of course you don't believe math can be misapplied, logic can be essential to nature, or that language can reflect nature just like the wiring of the brain can reflect it. I understand your position probably far better than you understand mine, probably. I see this from an entirely different perspective than you and am reporting what I think I see.

 

I could be wrong and your results may vary.

 

Or are you just suggesting murmurating birds mustta seen a scarecrow?

[Strange]

Perhaps you don't understand that we are talking about a subject no one knows anything about.

 

There are plenty of people who know a lot about how animals communicate. Just because you don't, there is no need to project your ignorance on to everyone else.

 

I'm merely trying to present an hypothesis based on logic and observation.

 

Then don't present it as fact. And show us the evidence that supports this hypothesis.

 

Of course you don't believe math can be misapplied

 

Why would you say that? Have I or anyone else ever said that? Is this just yet another strawman?

Edited November 22, 2015 by Strange

[studiot]

Rather than continuing this squabble here is something on topic to ponder.

 

Consider the set of all humans who are alive (or dead if you prefer).

 

Now at present all (known humans) are concentrated on one planet so the relativity of simultaneity is not an issue.

 

But

 

Consider a set of transientobjects such that they have substantial relative velocity.

 

What is in the set depends upon the time at which you enumerate the set, if the set has physical reality (even as a non material thing)

 

But this conflicts with relativity of simultaneity.

 

Some observers will include some objects, but others will exclude them since the observe the objects to have run their course at the moment of counting.

 

My head hurts.

 

[TheGeckomancer]

This is a question I think about a lot but I am by no means an expert at anything related to any subject. I think numbers are real abstract entities. We did not invent them, we discovered them, through observing the world. It's all been indirect observation and indirect testing. I can't think of a way to ever test these things directly. I think this is something we can only conclude through indirect observation. Every time we apply a mathematical forecast to the world, and watch it come true we are confirming indirectly the existence of numbers and math.

[sciwiz12]

I think a lot of mathematicians would agree with you, but I would disagree. Let's take the concept of a face for instance, faces do definitely exist in the universe right? Yet if the right part of the brain is destroyed you'll still be able to see all of the same parts, eyes, nose, chin, etc... yet you would not be able to comprehend it is a face, even if it is a face you've seen on numerous occasions. A face, as it turns out, is all in how you interpret what you're looking at.

 

You can staunchly declare that faces exist, certainly all of the cells and component features are there, but the face only exists because you interpret an otherwise meaningless collection of features as a face.

 

I suspect it is the same with math. You could argue that numbers are real because when test your suspicions by having one apple and adding another to get two apples, but if the part of your brain responsible for your inate number sense is damaged, as it is for some unfortunate individuals, then suddenly the "two" apples are just apples, no notion of the count.

 

So I feel comfortable in saying that while mathematics seems real enough upon initial examination, and could be considered real from a certain point of view, it is in fact not an abstract truth within the objective universe, but an interpretation of some parts of the universe. Most healthy brains have a number sense because numbers and the related sciences are pretty useful on balance, but just because it feels real doesn't make it so.

[studiot]

 

 

I think a lot of mathematicians would agree with you, but I would disagree. Let's take the concept of a face for instance, faces do definitely exist in the universe right? Yet if the right part of the brain is destroyed you'll still be able to see all of the same parts, eyes, nose, chin, etc... yet you would not be able to comprehend it is a face, even if it is a face you've seen on numerous occasions. A face, as it turns out, is all in how you interpret what you're looking at.

 

You can staunchly declare that faces exist, certainly all of the cells and component features are there, but the face only exists because you interpret an otherwise meaningless collection of features as a face.

 

I suspect it is the same with math. You could argue that numbers are real because when test your suspicions by having one apple and adding another to get two apples, but if the part of your brain responsible for your inate number sense is damaged, as it is for some unfortunate individuals, then suddenly the "two" apples are just apples, no notion of the count.

 

So I feel comfortable in saying that while mathematics seems real enough upon initial examination, and could be considered real from a certain point of view, it is in fact not an abstract truth within the objective universe, but an interpretation of some parts of the universe. Most healthy brains have a number sense because numbers and the related sciences are pretty useful on balance, but just because it feels real doesn't make it so.

 

 

Would this imply that the only place in Nature you think mathematics can exist is within a human brain?

[Bill Angel]

So I feel comfortable in saying that while mathematics seems real enough upon initial examination, and could be considered real from a certain point of view, it is in fact not an abstract truth within the objective universe, but an interpretation of some parts of the universe. Most healthy brains have a number sense because numbers and the related sciences are pretty useful on balance, but just because it feels real doesn't make it so.

What science considers to be the "abstract truth within an objective universe" are the conservation laws, such as the conservation of energy and the conservation of momentum.

Two observers in different reference frames won't necessarily see the same thing, especially if one reference frame is moving at close to the speed of light relative to the other reference frame. But they should both see adherence to the same conservation laws of physics in the situation or events that they are both observing.

[cladking]

It seems to me that if math is simply discovered by man and we can do differential calculus then there's no reason to suppose the brightest elephants or smart whales couldn't do algebra. Elephants can be taught to paint and we don't understand their communication but I'd wager you aren't going to even get them to do first grade math. There's no proof animals can even count.

 

Yet it's obvious to all humans that we are far more intelligent than animals.

 

Houston, there be a problem here. Maybe we're looking in the wrong direction with the wrong perspective.

 

If we're so smart then why don't we understand the nature of gravity after 4750 years? Or are we waiting for this knowledge to become perfect?

[Acme]

... There's no proof animals can even count.

 

...

I gave a reference in post #43 giving numerous examples of animals counting. You have either missed it or chosen to ignore it.

[cladking]

I gave a reference in post #43 giving numerous examples of animals counting. You have either missed it or chosen to ignore it.

 

"Bottlenose dolphins have shown the ability to choose an array with fewer dots compared to one with more dots."

 

I'm not so much ignoring it as suggesting it is irrelevant. "Count" has a very specific meaning in modern language. It means to assign numbers randomly to members of a specific group consecutively such as there is a one to one correspondance between members of the group and the numbers where the largest number is the "count". This corresponds to nothing at all in nature or in the real world so is not done nor understood by animals. It is of no value whatsoever to animals. If birds are warning one another of multiple threats they will refer to the "first hawk", "second hawk", and "third hawk" and will treat them individually. They will not "count" hawks and I'm aware of no evidence that they do.

 

No, I can't prove how an animal thinks but I can observe them and make deductions, guesses, and hypotheses. I can perform simple experiments or stage more complex observations. I don't know anything but I'm quite confident no one can prove any animal can "count".

[Acme]

...

No, I can't prove how an animal thinks but I can observe them and make deductions, guesses, and hypotheses. I can perform simple experiments or stage more complex observations. I don't know anything but I'm quite confident no one can prove any animal can "count".

Your confidence and lack of knowledge count for little to nothing in this discussion.

[Strange]

"Count" has a very specific meaning in modern language.

 

You are just inventing a definition that allows you to ignore evidence you don't like.

 

I have lost count of the number of times you have done this.

Edited November 24, 2015 by Strange

[cladking]

Your confidence and lack of knowledge count for little to nothing in this discussion.

 

 

Indeed.

 

If you thought like I do then it would count for a great deal.

 

There are many questions that science can't really address because the question or its terms lie outside of metaphysics. The topic of this thread is just one of these.

 

You are just inventing a definition that allows you to ignore evidence you don't like.

 

I have lost count of the number of times you have done this.

 

Why don't you define it then?

 

Just define it as the number of times a horse kicks when you ask him to do it three times and you'll have it made. Assuming the conclusion always works.

 

Why not count the number of words in this post and maybe you'll understand the meaning of the word. Then count them backward and see if you get the same answer. ...Then define "count" such that even I can understand it.

[Strange]

Why don't you define it then?

 

I would suggest looking at the examples in post #43. That should give you a pretty good idea.

[cladking]

This is really a very simple point. There are an infinity of ways to make the point and they are all valid.

 

A falling object accelerates at 32 ft/s/s. This applies to every falling object. The earth accelerates toward the object and the object accelerates toward the earth and closes the distance at 32 ft/s/s. There's nothing "magical" about this number. God didn't create the earth so this would fit His devine plan. There's no conference each morning to discuss variation in the acceleration due to gravity but rather is the result of the mass of the earth affecting a much smaller body. This number was the same when caveman walked the earth and if we all stumble off the mortal coil it will be the same when we leave. It wasn't measured or defined before we got here and the same will be true if we leave. It is the reality and is the result of our definitions and terms. It wasn't created by man and for all practical puposes it wasn't really discovered by man but rather it was simply quantified. We took an observation and exzplained it in terms of "gravity" and then quantified it. This doesn't mean we understand gravity but rather that we observe it and measure it. Even things we do "understand" aren't our doing but merely comprehensible to us because of their effect on experiment.

 

We don't understand animals not because they are dumb or we are so smart but because they don't think like we do and don't use language the way we do. They need a way to see nature that is compatible with their means to manipulate nature. A bird doesn't need to know that a hawk can dive at 160 MPH. It needs to know if it can make it to the trees before the hawk gets to him. This is a complex calculation and if he gets it wrong there will be no more chicks for him.

[TheGeckomancer]

Most species of monkeys have better innate number sense than we do, can can memorize large strings of numbers better than we can.

 

Also. Humans do not make math exist. It is a real nonphysical constant of the universe. If all humanity died, but we created an AI that would sit there and just assemble things to mathematical algorithms it would continue without ANY humans even existing. Honestly, I am starting to wonder if Math shouldn't be a fundamental force lol.

Edited November 25, 2015 by TheGeckomancer

[sciwiz12]

Alright, I can see where this line of objective mathematical reasoning is coming from.

 

One example that was given, for instance, was the rate of the acceleration of an object falling given as 32ft/s/s. This rate of acceleration would be the same without any observer to observe it, and the argument is that if a facet of nature "exists" without observers it must be an objective part of reality.

 

There was a really good comic on Saturday morning breakfast cereal that makes a similar argument. One person argues that the beauty of math is that it is the same everywhere in the universe, and in all likelihood somewhere in the universe there is a race of aliens that has also discovered the same math we have. One example given by the first person is the counting numbers, to which the second person argues that an alien civilisation might create a new number, "splorf", that comes between 2 and 3. The first person accepts this without hesitation frustrating the second person to retaliate with a barage of mathematical questions, discovering that the first person has accepted splorf as the new three, shifting every subsequent number by one increment. The moral of the story being that the properties of mathematical concepts are unaltered by changes in name and symbology.

 

This is the crux of the mathematical objectivist argument, but here's my counter-position. Let's take an apple falling at a particular velocity, doesn't matter what in particular, just that it is moving toward the earth at a particular speed. Now whatever number is ascribed to that speed, let's also say we have that many apples. So X apples moving toward earth at a speed of Xft/s.

 

This illustrates a very fine point about the nature of mathematics, I can describe the speed at which an apple falls in the same terms by which I can describe the number of apples, two completely unrelated or at best only tangentially related facets can be described in the same terms. This is, as we all know, because numbers, and mathematics in general, is abstracted away from the physical universe. The same X that describes the speed at which an apple falls is not the X which describes the number of apples, or rather while they may share the same numerical property the number of apples is not the speed at which any individual apple falls, even though but the number of apples and the act of changing position as a function of time can both be objectively experienced and measured through the filter of mathematical understanding, the values themselves are merely abstract descriptions of real properties.

 

This is the point I'm trying to drive home here, and it's a really complicated point so I will admit I may be looking at the matter from an inaccurate perspective, but an abstraction is, by it's very nature, not objectively real.

 

It may be very well suited to the task of describing general properties of reality, and those general properties might be real, but the abstractions taken from those properties are not real.

 

Now here's the thing, one might argue that numbers are not subjective, because the properties of numbers however abstract do not change depending on the person. That is to say one might argue that 1+1=5 is not true depending on the person, and I would agree with you, even if you change the name and symbol, as long as you are abstracting from the same properties you will arrive at the same conclusion, this is a core foundational principle of mathematics.

 

That's why I brought up the point of faces earlier. We may see a pattern of shapes that taken together we can generally recognise as a face. In fact so powerful is this ability to abstract from a pattern of features in order to recognise a face that we can recognise faces in things that don't have faces. We talk about the face of the Mona Lisa, which is just paint on a canvas. We can see faces in stuffed animals, plastic toys, butterfly wings, pieces of toast, etc... Yet there is a piece of the brain which, when damaged precludes the ability to perceive faces. People suffering from this effect cannot see faces in paint, fruit, toast, nor even flesh on a human skull. The brain once could recognise a pattern in objective reality and from those patterns abstract the concept of a face. After sustaining specific damage, even though the same objectively real facets of the universe (fruit, toast, etc...) Exist and still could, if perceived by a healthy human observer, represent a face, the ability is lost to the patient, and as such the concept itself is rendered meaningless noise.

 

Such is the case with numerical abstractions. We and similarly constructed observers can perceive patterns in the fabric of objective reality which can be abstracted away to useful ends, but the pattern in reality is not objective proof of the abstraction. The object accelerating at 32ft/s/s is not expressing an objective property of 32ness, it is our brains which draw from the pattern of relationships between size and distance some abstract notion of units in feet which is further abstracted into pure mathematical representations as the notion of a single unit which can be cross-applied to any subject containing objects which can be treated as a unit.

 

So yes, things in reality have patterns and properties which can be treated as numerical to quite a useful effect. In fact this kind of cross application through abstraction is such a useful mechanism that I would not be surprised if alien civilisations independently arrived at highly similar, if differently worded conclusions. Still, utility is not objectivity. Just because it is useful to describe a collection of a thing in numerical terms such as describing it by a property of two-ness does not mean that the useful abstract property exists objectively. I mean hopefully I've given a fairly persuasive argument of that at this point. The only object I would regard as entirely objective would be the whole of reality without regard to division or categorisation. Every other concept is just that, a concept, a pattern drawn from facets of reality with the intention of analysing reality in chunks in order to facilitate the process of intelligent understanding, but with every abstraction and with every subdivision you gain precision and weaken, even if by some infinitesimal measure, your tether to reality. Take for example the concept of a point, or the very nature of calculus. These are where we find the chinks in the armor of mathematical objectivity. There are concepts in mathematics which are useful but lose meaning and coherence when applied to reality. There are minute differences between states in reality of such an infinitesimal and or continuous nature that mathematics can only ever approximate their existence asymptotically, coming closer and closer in accuracy without ever truly mirroring it.

 

The attempt to align mathematical observations with reality is like attempting to solve a seemingly infinitely complex rubix cube. You will maybe come frustratingly close after thousands of years only to discover that there are a handful of inaccuracies, and the solution may be to undo a lot of hard work and effort to begin with a fresh perspective, or you may be a few turns from completion in the current state.

 

Mathematics as it is seems so very very close to accurately describing and predicting almost every conceivable event in reality, but it is important to remember that it is not an objective truth, because it may occasionally be useful to ask the question, what if the entirety of mathematics starts from faulty premises, could we do it better another way? If you fool yourself into thinking of mathematics as real then you preclude the possibility that it can be wrong and that there might be a better way, and you get stuck on a conceptual plateau where what you have may never be able to sufficiently answer certain questions because as good as it is, it isn't the best.

[studiot]

sciwiz

 

Are you saying that you believe two distinct objects cannot possess the same property?

 

Or perhaps that one object cannot possess more than one property?

 

 

 

With all that typing you skillfully avoided responding to my post#83.

[cladking]

This illustrates a very fine point about the nature of mathematics, I can describe the speed at which an apple falls in the same terms by which I can describe the number of apples, two completely unrelated or at best only tangentially related facets can be described in the same terms. This is, as we all know, because numbers, and mathematics in general, is abstracted away from the physical universe. The same X that describes the speed at which an apple falls is not the X which describes the number of apples, or rather while they may share the same numerical property the number of apples is not the speed at which any individual apple falls, even though but the number of apples and the act of changing position as a function of time can both be objectively experienced and measured through the filter of mathematical understanding, the values themselves are merely abstract descriptions of real properties.

 

 

You seem to grasp much if not all of my point.

 

But remember that the "reality" of "32" is as tenuous as the reality of "feet". "32" is here being defined as the unit measure of "g". Any distance the apple has fallen can simply be defined as "1" yet the acceleration is unchanged. This same thing applies to the apple as well since no two apples are identical. If you suppose a unit such that there are two in the displacement then where is the second apple? Is in in the earth's gravitational field or was it left behind at tranquility base?

 

The acceleration is real and the apple is real but a unit must be defined as well as any other "apples". Everything else is just words and models we use to understand experiment and the perspective we have from language.

[sciwiz12]

If I avoided responding to something I may apologise according to the merit of the contention in question, but as I do not know how to search a thread based on the post number I cannot assess the contention for merit, or I could but the search would seem awefully taxing, especially if the claim lacked any real substance.

 

But yes, I am arguing that any claim that a property can be shared among distinct objects is an abstraction and thus a fabrication. The redness of apple one may be similar to the redness of apple two but it is fundamentally tied to every other property of apple one, such as distinct location in space time. The same could therefore apply to any perception of oneness, to abstract is to cut away from the objective reality by removing the unnecessary, which from another perspective could also be seen as creating a property of the mind to mirror a perceived property of reality but in the process losing the tether to that which makes the property objectively real. This is in response to studiot mostly.

 

 

Here's something for cladking to consider, suppose of course that our notions of physical reality are accurate. Suppose also that there is an organism somewhere in the universe which does not sense nor perceive light, nor the sensation of touch, nor any save the sensation of gravitational and electromagnetic fields through some as of yet unimagined means.

 

Say that such a being by it's nature weaves these sensations into a perception of it's world not as distinct and divisible parts but as a continuous field which exists everywhere at higher or lower strengths.

 

Say that such a being evolves over many generations into an intelligent race of beings capable of devising formal systems. Now consider how such a being would create a formal system. Our concept of numerical abstractions is useful to us as a formal notation because our photon receptors and the perceptions built from that experience paint the world as one with distinct and divisible units. Even our conception of a field is defined by distinction and unitisation. Such a being would instead likely take a reversed approach. In developing a formal system it may initially take nothing as distinct. It might, as we have, start by making observations and abstracting from those observations, but the entire philosophy, the notation, everything would be born from this sense that there is no distinction, the universe is an indivisible whole with variations as a function of space and time but entirely continuous, a complete fabric. Assuming they ever formed a conception of arithmetic it would be an inversion of our own based on an intuition from continuation rather than distinction among bounded forms.

 

Such a race might spiral into entirely different means of calculation but arrive at accurate conclusions as we have by recursive modification from observation. In fact their system might trump our own as their system might require fewer procedures or fewer divisions of the subject while arriving at results with a greater degree of precision leading to better engineering practice's and far more advanced technology in a shorter span of time. Of course such a conclusion is not necessitated, but I offer the supposition to make this point abundantly transparent: Math may very well be subjective. This notion that observation however removed from abstract conclusion ties the conclusion to objective reality is misguided.

 

If you perceive an apple as a distinct object, if you perceive it as moving rather than perceiving simultaneous state changes in the fabric of reality, or you experience time linearly, if you experience the world as a human experiences the world and you are capable of formulating a formal system of mathematics then it will of course be akin to human mathematics, but if your perceptions are radically altered, or if you are even capable of entertaining the thought that things could be observed in radically different ways, then you can easily suppose that just because a property is seemingly observed doesn't mean that any abstractions from the seeming property are objective nor entirely accurate.

 

You must entertain the notion that reality and mathematical descriptions of reality are only really tied by our ability to revise initial conclusions to better fit the data, and that such revisions may be crutches to keep a system built on a faulty premise functional viable despite its flaws.

 

 

The ultimate implication is this: math is not real, it is a tool whose purpose is to manipulate the real through abstract imagination and calculation, but it isn't a part of reality so much as a photograph taken through an unreliable camera lens. To entertain the notion that math is objective is tantamount to declaring the infallibility of human perceptions despite being consciously aware of deep fallibilities and areas of incompatibility with reason.It is dangerous to hold that seeing makes it so.

[Bill Angel]

But yes, I am arguing that any claim that a property can be shared among distinct objects is an abstraction and thus a fabrication. The redness of apple one may be similar to the redness of apple two but it is fundamentally tied to every other property of apple one, such as distinct location in space time.

 

I believe that most physicists would disagree with you on this point. There are particles called fermions, which are particles with half integer spin. See https://en.wikipedia.org/wiki/Fermion

All fermions obey Fermi Dirac statistics, irrespective of their locations in space time. Fermions also obey the Pauli exclusion principle, irrespective of their individual locations in space time

[Acme]

...

The ultimate implication is this: math is not real, it is a tool whose purpose is to manipulate the real through abstract imagination and calculation, but it isn't a part of reality so much as a photograph taken through an unreliable camera lens. To entertain the notion that math is objective is tantamount to declaring the infallibility of human perceptions despite being consciously aware of deep fallibilities and areas of incompatibility with reason.It is dangerous to hold that seeing makes it so.

You sure spend a lot of time delineating the characteristics of something that isn't real. Just because our perception has limitations does not mean we have no perceptions nor is a blurry photograph any less a photograph because of its shortcomings.

[TheGeckomancer]

I propose the exact oppposite. Declaring that math is subjective is tantamount to declaring the infallibility of human perceptions. My problem with the idea that math isn't objective is the fact that we don't get to determine any of it's rules. Some people want to claim we invented math, but if we did we had NO SAY in how it happened, including the inventors. Inventors decide how their inventions come together and work. No one ever had that choice with math. We didn't get to decide right answers. Math would objectively tell us we are wrong. So the idea that it's a man made system that functions perfectly and describes the universe anywhere equally well seems absolutely ludicrous.

Edited November 26, 2015 by TheGeckomancer