Do Mathematical Entities Really Exist?

[nimzov]

Would pi apply to tree rings if we did not know of it? I don't think so.

I don't think that geological stratas are put in place randomly and that they come into order because some nervous system makes an observation.

Order and sequences are there in the geological stratas even if an intelligence has not yet defined the concept of order and sequences ?

Previous, successor and order are there in stratas and in nature. In my opinion, whether there is an observer or not.

I find your arguments are interesting and so are Zygar's. But I lean on Zygar's side.

nimzo

 

[Soapy Sam]

Not sure I follow you, Nimzov.
We may be misunderstanding each other .
(My own background is geology, by the way).

I don't think there is a tree ring equation involving pi , which is required for tree rings to form.
I think tree rings form by accretion of cells, for solidly biological reasons and pi is something we use to model their shape, just as beauty is something we might use to describe their shape.
I have seen many examples of fossilised wood containing tree rings very like modern ones, formed long before humans existed, so I don't doubt that trees grew back then in much they way they do now.

 

[nimzov]

Not sure I follow you, Nimzov.
We may be misunderstanding each other .

The reason that I do not participate actively in this discussion is because of my poor writing skill in english. So I am not surprise that my writing leads to a misunderstanding. I take the blame.

Let me try again.

Geology was just an example to show that mathematical concepts like : "successor', "previous", "order", "first" or "last" that we find in mathematics (or numbers), do exist in nature and have been there for millions of years irrelevant of the presence of an intelligence or an observer.

In my opinion, the ordering (first, successor, last, previous) that we find in stratas is an example of such mathematical concepts in action in nature.

nimzo

 

[Zygar]

Is the op not analogous to the famous tree falling in the forest question?
If humanity was eaten by a giant planet eater tomorrow, would pi still exist?
I'd say "no" to both questions.
Noises are artifacts of nervous systems, not trees.
pi is an artifact of minds.

So ants, squirrels, and deer do not hear?

Last I heard, ants, deer and squirrels all had nervous systems.

Sorry. I merged the statements and ended up with humanity in the noise question.

The way the zen question is phrased always makes it seem (to me) that it confuses the physics of molecular displacement with the operation of nervous systems. This is an easy error to make as we routinely think of the cause and the resulting sensation as aspects of the same thing. Which they are. But they are not THE SAME thing. The tree falls, shaking the ground and displacing air molecules. But if there is no nervous system there to hear it, there is no noise. The noise is an artifact of brains responding to pressure changes. It's a question of definitions.
(If there was no observer, could there be surprise? I see surprise and noise as equally artifacts of the observer).

I still see this as a arrogant and naive view of the issue. Humans hear through an entirely seperate mechanism from ants, sharks, and many other creatures. Also their nervous systems are often completely different from our own. They most likely do not percieve sound as we do. But just because an observer with ears is not present, doesn't mean the noise is not present.

I feel we make a similar error when we confuse number with quantity.
"Two" and "Two pianos" are very different things.

Agreed, they are different. But "two pianos" are a specific form of two which require the existance of the mathematical entity "two". The number doesn't have to be understood to be present.

Would pi apply to tree rings if we did not know of it? I don't think so.
Would beauty apply to trees in the absence of observers? I don't think so.

Beauty and pi are unrelated. Beauty is relative, pi is absolute. Two people cannot agree on what is beautiful, so aliens are guaranteed to never agree. On the other hand pi can be agreed upon by any two individuals on earth, even without speaking a similar language. Aliens will also agree on the value of pi, even if it is in a different base. If the value can be arrived at independently by any intelligent race, is it not real?

Would tree rings be the same shape? The rings in fossil trees are certainly evidence that they would be.

I support nimzov's take on this.

 

[Soapy Sam]

The reason that I do not participate actively in this discussion is because of my poor writing skill in english. So I am not surprise that my writing leads to a misunderstanding. I take the blame.

Let me try again.

Geology was just an example to show that mathematical concepts like : "successor', "previous", "order", "first" or "last" that we find in mathematics (or numbers), do exist in nature and have been there for millions of years irrelevant of the presence of an intelligence or an observer.

In my opinion, the ordering (first, successor, last, previous) that we find in stratas is an example of such mathematical concepts in action in nature.

nimzo

OK. I take your point.
We agree that the process of sedimentation is wholly natural and proceeded in a set order without human intervention.
We also agree that these are examples of human concepts in nature, but that the concept is not necessary for nature to operate- there would be tree rings even if humans had never existed.

If we differ at all, it's about definitions. For me, while the human concept describes a model we can understand, it may not describe the way nature works.
We could use mathematics to calculate the trajectory of a ball in order to catch it. If the mathematics involved a constant K, we might feel that K had some real existence every time a ball is caught. But I also know that I don't use K when I catch a ball- I just get in front of and below it, then hope for the best. (It usually hits me on the head).

I think the same is true of pi- it's something we use, not something intrinsic to reality.

 

[athon]

I don't think the fact that a diameter fits into a circumference 3.41 times would be called 'pi' without humans. But without humans - or indeed any form of life, this relationship would still exist in our universe.

My interest is in the basic information that creates consistency throughout time and space. While I don't envisage a three dimensional space-time in which it is kept, I do wonder on the principles of the 'mathematics' which applies to everything, and has done in the past and will do in the future. Indeed, two photons created at different moments, separated by time and space, share identical properties. The information is not a 'thing', not as we might conventionally see it, but it has to exist in some way independent of time and space.

Mathematics, as I understand it, must do too. Indeed, while mathematics isn't the same thing as physics, but rather a set of descriptors for it, they fundamentally must be preserved in some form through time and space in the same way physics must.

It might take an intelligent mind to model it, but when we refer to pi we are referring to an objective principle through the means of a model, not to the model itself.

Athon

 

[andyandy]

I don't think the fact that a diameter fits into a circumference 3.41 times would be called 'pi' without humans.
Athon

I don't think 3.41 would be called "pi" by humans either

 

[Zygar]

I don't think 3.41 would be called "pi" by humans either

OK. I take your point.
We agree that the process of sedimentation is wholly natural and proceeded in a set order without human intervention.
We also agree that these are examples of human concepts in nature, but that the concept is not necessary for nature to operate- there would be tree rings even if humans had never existed.

If we differ at all, it's about definitions. For me, while the human concept describes a model we can understand, it may not describe the way nature works.
We could use mathematics to calculate the trajectory of a ball in order to catch it. If the mathematics involved a constant K, we might feel that K had some real existence every time a ball is caught. But I also know that I don't use K when I catch a ball- I just get in front of and below it, then hope for the best. (It usually hits me on the head).

I don't think K has any significance. But the process of deriving K is a universal process that can exist for humans, dolphins, birds, etc. The value for K is a number, but the process is mathematics, and that is universal even when you don't know you are using it.

I think the same is true of pi- it's something we use, not something intrinsic to reality.

So, please define for me what you think pi represents? Since we can both agree that the symbol for pi and the number 3.14159... are meaningless to anything but humans, what is pi to you? Is it the value of pi? Is it the proper definition (circumfrence/diameter)?

 

[delphi_ote]

What would be a mathematically impossible amount of beef?

The Godel number of the Turing Machine which decides the Halting Problem ounces?

 

[nimzov]

I think the same is true of pi- it's something we use, not something intrinsic to reality.

The problem I see with this is the fact that pi is found in geometry in relation to circles but is also present in number theory where circles are not an element of the theory.

So we have pi the ratio in a circle but we also have pi that appears in such basic mathematical relation:

If pi is not intrinsic to reality as you say, then it seems to me that we have to believe that it is by pure coincidence that pi appears in this sum of the inverse of the squares of natural numbers (which has nothing to do with circles) ?

nimzo

 

[Soapy Sam]

Sorry. I merged the statements and ended up with humanity in the noise question.

Okydoky.

I still see this as a arrogant and naive view of the issue. Humans hear through an entirely seperate mechanism from ants, sharks, and many other creatures. Also their nervous systems are often completely different from our own. They most likely do not percieve sound as we do. But just because an observer with ears is not present, doesn't mean the noise is not present.

I see it as a question of definition. Sound is something heard, whatever the nature of the hearing mechanism. Sound waves are pressure variations in air , water or the ground, which make it possible for nervous systems to register a sound. If the sound is not sensed, in what way is it actually there?

Agreed, they are different. But "two pianos" are a specific form of two which require the existance of the mathematical entity "two". The number doesn't have to be understood to be present.

I'm not sure I follow this.
You mean there is an essential "twoness," which would still be there even if the pianos were not?

1.Beauty and pi are unrelated.
2.Beauty is relative, pi is absolute

You think 1 follows from 2?
I am male. My mother is female. Because we do not share the same sex, would you say we are unrelated?

Two people cannot agree on what is beautiful, ...

Oh I think they often can.

...so aliens are guaranteed to never agree.

Guaranteed? You seem very sure. You know a lot about alien nervous systems?

On the other hand pi can be agreed upon by any two individuals on earth, even without speaking a similar language. Aliens will also agree on the value of pi, even if it is in a different base. If the value can be arrived at independently by any intelligent race, is it not real?

We're back to defining real. What if both we and the aliens are wrong? Two people may have the same answer to a question and both be mistaken. But I really think we are talking past one another. If your aliens had similar senses and thought processes to ours, they might well come up with a similar idea - that circles have a constant ratio of circumference to diameter. And if they think it valid to measure curves they might well come up with the same value to a given accuracy, but so what? How does this make pi real? If they divide 6 by 3 they will likewise always get the same answer, does that mean that 6/3 is also "real"? But that means any number is equally real. So what's special about pi?

I support nimzov's take on this.

As he does yours. I forgive you both.

 

[Zygar]

Okydoky.


I see it as a question of definition. Sound is something heard, whatever the nature of the hearing mechanism. Sound waves are pressure variations in air , water or the ground, which make it possible for nervous systems to register a sound. If the sound is not sensed, in what way is it actually there?

Defining it as something sensed means that it is not anywhere except where it is sensed. In other words it is only internal in living creatures capable of sensing it. It does not exist in the air, or in computers, or on CDs. Which makes this not a philosophical question, but a simple question of location.

I'm not sure I follow this.
You mean there is an essential "twoness," which would still be there even if the pianos were not?

If there are two oranges, and two pianos, they both carry a quality of twoness. So yes.

You think 1 follows from 2?
I am male. My mother is female. Because we do not share the same sex, would you say we are unrelated?

Different definition of related. You are obfuscating.

Oh I think they often can.
Guaranteed? You seem very sure. You know a lot about alien nervous systems?

Nothing. I maintain that beauty is too relative for any two humans to agree 100% of the time. And if we cannot, then it is a logical impossibility for aliens to agree with humans on what is beautiful, even if we agree on the concept of beauty.

We're back to defining real. What if both we and the aliens are wrong? Two people may have the same answer to a question and both be mistaken. But I really think we are talking past one another. If your aliens had similar senses and thought processes to ours, they might well come up with a similar idea - that circles have a constant ratio of circumference to diameter. And if they think it valid to measure curves they might well come up with the same value to a given accuracy, but so what? How does this make pi real? If they divide 6 by 3 they will likewise always get the same answer, does that mean that 6/3 is also "real"? But that means any number is equally real. So what's special about pi?

Nothing. It is a number. And I don't think you've proven that numbers are not real. And since numbers are a mathematical entity, we're stuck with me saying that mathematical entities are real.

As he does yours. I forgive you both.

Thanks. I forgive you back.

 

[William Meegan]

Yes, what you call mathematical (first nine digits) entities actually do exist though they are not visable via the five senses. They are abstractions and the only proof that man has that God does exist: that is it you see God as a priciple such as divine law the is unchangeable.

There is not one major religion on earth today that does not see this as fact. Now contemporary theologians of those religions may well be ignorant of the genesis of their faith. I personally been working on this problem for 32-years and I demonstrate in my writing that the Judeao Christian Scriptures is a mathematical and grammatical masterpiece: the integration of the Seven Liberal Arts: Arithemetic, Music/Harmony, Geometry, Astronomy/Astrology, Grammar, Rhetoric and Logic/Dialectic. When average reader reads the text he or she is reading a translation which is essentially worthless. To read the original indigenous languages of the text one actually is only reading the Grammar. Behind the grammatical text is the other six liberal arts. The mathematical sciences: Quadriviusm need the grammatical arts: Triviusm, to cloth them so the message of the trasendental reality can be convey to the masses.

Break down the text to their constituent components of the Seven Liberal Arts and you can read the message worth reading. The surface text is basically a bedtime story.

I have recently published a paper on the next through the ROSE CROIX JOURNAL called THE SISTINE CHAPEL: A Study in Celestial Cartography where I outline the science I am speaking of. I demonstrate that the Sistine Chapel is a commentary on the first letter, first word, first sentence, first chapter of Genesis.

Numbers have no meaning in an of themselves but I demonstrate that the first nine numbers actually come together to form what I call THE UNIVERSAL MATHEMATICAL MATRIX. This matrix born out of nothing but the multiplication table actually was used to structure Dante Alighieri's La Divina Commedia and the first chapter of Genesis. The mere fact that numbers can colesce into a unified matrix and used by the ancients to write the text of their religions demonstrate that they also believe that numbers were divine. This matrix I talk about even Pythagorus is said to have invented it. But goes back into the dawn of every other relgion on earth.

Are they real, you bet they are, it is the only proof that we have that there is something beyond us.

 

[athon]

I don't think 3.41 would be called "pi" by humans either

Since when did it change? Next I suppose you're going to tell me that C is not 3.1 kilometres per hour.

Athon
(bastards...)

 

[Zygar]

Since when did it change? Next I suppose you're going to tell me that C is not 3.1 kilometres per hour.

I walk faster than lightspeed!

 

[Zygar]

Ramblings

Huh?

 

[athon]

I walk faster than lightspeed!

I've just called the police. Breaking the laws of physics is a felony, mate.

Athon

 

[l0rca]

Newton's Laws have not been changed. They still apply, and are used as the basis for understanding physics. The history of science is certainly filled with examples of science finding a better/more appropriate model of the universe, but the old work has rarely if ever been thrown out the window. As a general rule the new work is based upon the old, and to my knowledge the mathematics used to describe these facts have never been changed simply because the models were wrong.

What do you mean based upon? If you mean refined, or added to, you're wrong here. However if you simply mean reflected upon as new theories were developed, you're right. But this latter truth is does nothing to help an argument that Newton's Law's have a real view of the universe.

Newton's laws of gravity, and the theory behind how gravity works, were thrown away by General Relativity.

Consequently these days, General Relativity is also having trouble fitting into the Standard Model in any way other than the science interested in prediction.

Yes, it is a tool. But thinking of it as a tool implies that mathematics are a concrete set of entities which apply to the universe. And we have never had to throw these entities out.

This is not true. Mathematical concepts have been created following the logic of math that have never been used. For instance, mathematically, we can calculate a universe with 100 spacial dimensions, and a number of time dimensions, if we wanted to. This may or may not relate to reality, but it probably does not.

And I don't think "tool" was meant in a manner relating to concrete things. Just because a word implies something in some of the ways it can be used doesn't mean it was meant so. I think you know what he meant. It's sort of just forcing a person to constantly reiterate themselves. It makes arguing a droll thing, and questions how willing an arguer is to resort to artistic dodging. That might be why he didn't reply to you yet.

It is very true that the idealized triangle in one's head is simply an approximation of reality.

No, this is not very true. Have you ever heard of nominalism? Ideas and symbols in a person's head; "approximations," are debatably resembling anything objective.

I fail to see how the difference between our internal pictures of the world built through shortcuts of mathematical approximation have anything to do with whether or not mathematical entities are real.

I agree with this, but I would also agree with a culled version of this statement:

I fail to see how the difference between our internal pictures of the world have anything to do with whether or not mathematical entities are real.

In short, as I try to hint above with nominalism, there is no empirical way to identify central mathematical roles in our universe. That we can only observe matter through matter, and there is a limit to our accuracy. It seems we can only get down to a certain smallness. I'm thinking of the Uncertainly Principle here.

 

[Zygar]

What do you mean based upon? If you mean refined, or added to, you're wrong here. However if you simply mean reflected upon as new theories were developed, you're right. But this latter truth is does nothing to help an argument that Newton's Law's have a real view of the universe.

Newton's laws of gravity, and the theory behind how gravity works, were thrown away by General Relativity.

Consequently these days, General Relativity is also having trouble fitting into the Standard Model in any way other than the science interested in prediction.

Fine. His theory of gravity was wrong. What about thermodynamics? What about F=Ma? Newton having a couple imperfect theories has nothing to do with whether or not the laws of physics are real, let alone accurate.

This is not true. Mathematical concepts have been created following the logic of math that have never been used. For instance, mathematically, we can calculate a universe with 100 spacial dimensions, and a number of time dimensions, if we wanted to. This may or may not relate to reality, but it probably does not.

Whether or not it does doesn't enter into whether or not the mathematical entities which allow you to calculate such a thing exist. Just because we can calculate the basic properties of an atom of Ununoctium, but we cannot create one and are pretty sure they don't occur naturally, does that make Chemistry and Quantum Physics completely wrong and made up?

And I don't think "tool" was meant in a manner relating to concrete things. Just because a word implies something in some of the ways it can be used doesn't mean it was meant so. I think you know what he meant. It's sort of just forcing a person to constantly reiterate themselves. It makes arguing a droll thing, and questions how willing an arguer is to resort to artistic dodging. That might be why he didn't reply to you yet.

So I potentially misused his statement against him. I used it because I thought it was a vaid point, not because I am nefarious and underhanded. And instead of coming up with some facts you just whine. Nice job debating.

No, this is not very true. Have you ever heard of nominalism? Ideas and symbols in a person's head; "approximations," are debatably resembling anything objective.

Nominalism ends the debate. If nominalism is accurate, then mathematics are quite forcibly not real. But I'm not willing to shift to a philosophical debate about the nature of reality. I entered this debate assuming that an abstract entity that interfaces with the universe is plausibly real. If that assumption is false then we are compelled to end this debate altogether.

I agree with this, but I would also agree with a culled version of this statement:

I fail to see how the difference between our internal pictures of the world have anything to do with whether or not mathematical entities are real.

In short, as I try to hint above with nominalism, there is no empirical way to identify central mathematical roles in our universe. That we can only observe matter through matter, and there is a limit to our accuracy. It seems we can only get down to a certain smallness. I'm thinking of the Uncertainly Principle here.

If you want to bring uncertainty into the picture, then we're mincing over whether or not all mathematical entities are both real and discovered. I would hesitate to guarantee that even a reasonable percentage of the possible mathematical entities have been uncovered. But I also don't see how our failure to find them all proves that they are not real.

 

[Zygar]

What do you mean based upon? If you mean refined, or added to, you're wrong here. However if you simply mean reflected upon as new theories were developed, you're right. But this latter truth is does nothing to help an argument that Newton's Law's have a real view of the universe.

Newton's laws of gravity, and the theory behind how gravity works, were thrown away by General Relativity.

Consequently these days, General Relativity is also having trouble fitting into the Standard Model in any way other than the science interested in prediction.

Upon giving more thought to this I disagree. Newton's gravity was a primary basis for Relativity. Relativity just modified it from instantaneous to lightspeed, and modified time to keep lightspeed constant. Yes, this was a dramatic paradigm shift, but no this was not throwing out Newton.

And General Relativity is on the block due to Dark Matter and Dark Energy, which are simply our inability to understand part of our universe. Not surprising given our puny brains and technology. I seriously doubt this will throw out Relativity, but it may tweak it a bit.