Mathematics, Discovered or Invented?

[Polymath257]

I happened to have found an interview with Sabine Hossenfelder (not on her own channel) where she takes the position that we've gotten far with mathematics as a useful tool for describing observations but that she doesn't think its possible to determine whether mathematics captures what reality is. She also doesn't think its ever going to become plain.

Yes, one of the biggest issues is that we will never know when or if we have a final description. There will *always* be more to test. As long as the tests agree with the model, we say it describes reality (at least approximately). It may also be that we have the 'correct math' in terms of formulas describing various phenomena, but that we cannot actually *solve* the math to get good predictions. If that happens, the utility of the math might be severely limited.

https://youtu.be/6xGwdUCYzgw?t=633
channel: The Institute of Art and Ideas
titled: Physics at the Limits of Reality

Nevertheless I am in love with the idea that the universe could not exist at all and could merely be invisible relationships, not exactly maths but analogous. To me it makes no sense for us to exist rather than not.

The universe exists, almost by definition of the term 'exists'. What its nature is, however, is to be determined experimentally. It may well only be relationships between different quantum fields (the word 'invisible' here seems to miss a lot). if so, then that is what it means to 'exist'.

 

[Brickjectivity]

Yes, one of the biggest issues is that we will never know when or if we have a final description. There will *always* be more to test. As long as the tests agree with the model, we say it describes reality (at least approximately). It may also be that we have the 'correct math' in terms of formulas describing various phenomena, but that we cannot actually *solve* the math to get good predictions. If that happens, the utility of the math might be severely limited.

Yes! That is true.

The universe exists, almost by definition of the term 'exists'. What its nature is, however, is to be determined experimentally. It may well only be relationships between different quantum fields (the word 'invisible' here seems to miss a lot). if so, then that is what it means to 'exist'.

The limitations of languages show themselves: When science studies 'Existence' it means something different then when philosophers discuss 'Existence'. Any time a Science paper tries to discuss existence its going to presume the thing in question. Philosophically existence is either an axiom or a proposition.

 

[muhammad_isa]

No, I am not interested in such. But I don't consider religion to be a serious topic for scholarship because there is no way to establish truth in the subject: it is literally all opinion with no possibility of testing.

It might appear that way to you .. but it is not so.
Like in any subject, knowledge is a great asset, and helps us to distinguish truth from falsehood.
However, without the correct intention, we can also employ knowledge for evil purpose too.

Yes, community is important because we are a social species. I think we will be much better off if we can put aside our superstitions and learn to focus on real problems instead of 'praying for solutions', which does nothing except make people feel good for doing nothing.

Sometimes, we feel helpless to do anything else.
..but religion is not limited to invocation.

Communities need ethics. They need people with clear insight into the situations they find themselves in. They need people who speak unpopular truths. They need people who aren't so caught up in their superstitions that they forget reality. Religion, as far as I can see, is exactly what we *don't* need more of.

A person can lie under oath in court, yet many people understand that it is about trust..
..and we tend to trust pious people more than others .. with good reason, I would say.

Half of faith is to have hope in G-d's Mercy, and the other half is fear of G-d's wrath.
..and lying under oath is definitely a sin.

 

[muhammad_isa]

As a good book for learning more about this, I would suggest 'Behave' by Sapolsky. he goes into some detail concerning how our brains make decisions and the complexities involved..

You are missing the point.

..but then, being a physicalist, you insist that consciousness, state of mind etc. is purely about
the material, and refuse to acknowledge non-material concept.

Sometimes, knowledge can work against us .. and I do believe that the reading of too
much classical philosophy is a case in point.

It is not a balanced view .. its roots are in disbelief.
i.e. We are nothing more than biological machines, and there is no point to our existence

This leads us to the view that this material life is the only important thing in our lives, and we see
no long-term spiritual goals.

 

[RestlessSoul]

Concepts are invented by us to help us make sense of the world. They exist, but only in our minds.

Yes, but can we say more of entities?

 

[Polymath257]

It might appear that way to you .. but it is not so.
Like in any subject, knowledge is a great asset, and helps us to distinguish truth from falsehood.
However, without the correct intention, we can also employ knowledge for evil purpose too.

It 'appears' that way to me because I have looked at the history of the subject of religion. There is *never* actual agreement except for those points that are dangerous to question (as in, losing a job to being put to death). On no single point is there agreement that lasts *unless* all those who disagree are cowered in some way.

Sometimes, we feel helpless to do anything else.
..but religion is not limited to invocation.

Yes, religion *claims* to set morality. But, in practice, that is very far from the case. Instead, people decide what is right or wrong and *then* argue that God agrees with them.

A person can lie under oath in court, yet many people understand that it is about trust..
..and we tend to trust pious people more than others .. with good reason, I would say.

And I would disagree. I would be far more likely to trust an atheist than most theists.

Half of faith is to have hope in G-d's Mercy, and the other half is fear of G-d's wrath.
..and lying under oath is definitely a sin.

Sounds like a typical hustle

Yes! That is true.

The limitations of languages show themselves: When science studies 'Existence' it means something different then when philosophers discuss 'Existence'. Any time a Science paper tries to discuss existence its going to presume the thing in question. Philosophically existence is either an axiom or a proposition.

to me: you get all you could possibly want, but only after death and only if you follow what I say.

 

[Polymath257]

Yes, but can we say more of entities?

I don't know what it technically means to be an 'entity'.

 

[RestlessSoul]

I don't know what it technically means to be an 'entity'.

Entities are observable, terms and concepts are not.

But how do we distinguish between those things which exist in the mind of the observer, and those things which exist independently thereof?

 

[muhammad_isa]

to me: you get all you could possibly want, but only after death and only if you follow what I say.

Who is 'I' ?

 

[wellwisher]

We live in space-time, which is connected to matter and the law of physics. In general relativity, space-time reference is mass dependent. It is a function of substance and gravity. Space-time is where space and time are connected, and have to work together similar to two people in a three legged race. Even if both people can run faster untethered, once they are tethered, like space-time, they need to coordinate together, which can slow both down. In terms of space-time and reality, the tether sets limits of what is materially possible. It would be impossible for the two fastest sprinters in the world, to set a new work record, for 100 meters, while tethered together; speed of light limit.

Say we were to separate space-time into separated space and separate time. Now the limits of the three legged race would be gone. Both 100 meter sprinters, can now run full speed. They are no longer co-dependent on each other, within the limitations of the three legged race of space-time. This would theoretically allow the laws of the physics to be exceeded; both can break the world record on the same day. If I could move in space untethered to time I could be omnipresent. Being in one location in space-time, only happens when we tether space and time, as space-time.

If you look at engineering, things are built, all the time, that would not form naturally, under the natural laws of space-time. For example, what are the odds the Empire State Building, formed naturally in place, without any human or alien involvement? In this scenario, it would need to somehow come together by just natural laws, apart from human or higher consciousness interaction. Let us amplify this impossible scenario with just the natural laws of space-time. What are odds that all the buildings in the New York City skyline would appear, spontaneously, by only natural laws, tethered as space-time? There is another variable connected to consciousness.

An argument can be made that the human mind and brain can simulate or express separated space and separated time. This intellectual and consciousness platform would not theoretically be constrained, by the just natural laws and odds within tethered space-time. Such as this could predict and cause the Empire State Building to appear, even with zero natural odds in natural space-time.

My guess is math, since it can be used to express the natural sciences; space-time, as well as the applied sciences; separates space and time, came from the human brain's ability to see nature via the prism of space-time, as well as via the prism of the transcendent view of separated spaced and separated time. Math is a bridge between the two; NYC sky line; is space-time extrapolated via separated space and time. Nothing in the NYC skyline is beyond space-time accept the integration of the parts, which themselves are modified natural.

Religion played an important role in developing this consciousness platform of separated space and separated time, since divine ideas are not explainable by space-time; alone. They very often exceed the laws of physics. They are more in line with the more flexible and expansive platform of separated space and separated time.

I no longer see a wall between science and religion, since this space-time and separated space and time bridge ,allows me to go back and forth. This is the realm of what may be possible in space-time, superimposed on the natural limits of space-time. I do not use math, per se, since the brain has its own separated space and time math; what is and what can be. I suppose this natural brain math could be expressed with equations. It evolved from the brain compiling natural, and man made data, and trying to form bridge expressions to merge these and make both more practical. Some has to do with 3-D thinking; z-axis beyond the 2-D cause and effect (x and y) of logic and reason.

 

[wellwisher]

Neurons are very different from the semiconductor memory that is used in computers. These differences allow for the unique math platforms of the human brain, that has allowed natural math to be discovered and invented; inside reflects the outside.

Neurons are different in that neurons expend lots of metabolic energy pumping and exchanging sodium and potassium ions. They are rolling a large "rock" up an energy hill. The "rest neuron, which is misnomer, is actually the state when the neuron is at the highest potential, and the" rock" is at the top. Computer memory is designed to be stable; lowest energy states. Neurons are designed to be an high energy accident waiting to happen.

The firing of neurons is predestined to fire; Story of Sisyphus, since this is the way to lower potential; brain waves. Sisyphus was a god who was destined to roll a large rock up a hill. When he reaches the top, the rock rolls down. Like Sisyphus, the neuron then works, feverishly, to push the rock, back up the energy hill. Sisyphus may have been an internal projection way before microscopes.

The firing of neurons and the release of the free energy is less about programmer logic paths, and more about the best way to move all that potential, stored in many connected neurons, down millions of energy hills; the best firing cascade. This logic is based on natural thermodynamics and physical chemistry and not any form of man made logic. Consciousness is composed on natural events within space-time, extrapolating; space-time and separated space and time. This deals with the large global needs.

If we wanted computers to be much more human, the semi-conductor memory would need to better mimmic neural memory. We would have to design computer memory to be deliberately unstable. If we placed such unstable memory into storage; like lots of water behind a dam, it would try to lower its potential, in natural ways, that will rearrange the data. This self changing memory will be based on physical chemical laws; free energy as entropy and enthalpy changes.

In the test lab, you would need two clone hard drives; long and short term. One stays stable, while the other is made to be chemically unstable. We allow the unstable memory to find lowest free energy potential; self rearrangement. Then we compare to this to stable memory and note the changes. We then rewrite the unstable, adding any useful content, that was based on natural physical chemical logic. Then do another cycle. This is how we learn; learning potential.

The trick to develop the math would be to alter the initial human logic logic, until the spontaneous change is easily translated by the new logic, to the free energy movement; very smart computer who can learn without any background; reinvent as needed.

 

[Polymath257]

You are missing the point.

What point? You said that the science of color is irrelevant to the color green. That seems just false to me.

..but then, being a physicalist, you insist that consciousness, state of mind etc. is purely about
the material, and refuse to acknowledge non-material concept.

What do you mean when you talk about a 'non-material concept'? Can we extend it to be a 'non-physical concept'? if so, what does *that* mean?

Sometimes, knowledge can work against us .. and I do believe that the reading of too
much classical philosophy is a case in point.

As is reading too much about religious views. Both should be done only after learning some basics about how the world around us works so we can dispense with obviously wrong ideas.

It is not a balanced view .. its roots are in disbelief.
i.e. We are nothing more than biological machines, and there is no point to our existence

No, that is not the origin of the belief. The origin is that we should be able to *test* any idea we want to accept and discard ideas that are untestable even in theory. The roots are in *skepticism*, which is different than disbelief. The difference is simply the requirement that beliefs be justified by evidence.

This leads us to the view that this material life is the only important thing in our lives, and we see
no long-term spiritual goals.

I don't even know what a 'spiritual goal' is outside of the goals to better ourselves and help those around us. And those goals don't require the belief in a supernatural.

To get back to the topic of the thread: what do you mean when you say that the number 2 exists outside of our minds? In what sense does it 'exist'? How should I even make sense of the claim that the number '2' exists?

Remember that there is a difference between being able to count to 2 and thinking that there is an object '2' that exists independently of our thoughts. Counting is a way of organizing our thoughts about the world around us. It does NOT require that there be separate objects corresponding to each number. Many other animals know how to count (at least to smaller values), but it is not at all clear that any other htan humans have come up with the concept of 'number' independent of the process of counting.

 

[Polymath257]

Entities are observable, terms and concepts are not.

But how do we distinguish between those things which exist in the mind of the observer, and those things which exist independently thereof?

Well, you seem to have given a good criterion: observability and testability.

For example, is the number '2' observable? No. Can we test its prpoerties? No. So that would suggest it only exists inside of our minds.

Terms and concepts are 'objects of thought' in the sense that they only exist in a living mind that is active on a physical substrate. There *is* a sense in which they activity of the brain while thinking those thoughts might be observable to the point we know that the brain is thinking those thoughts (we are getting closer to this every day).

 

[Polymath257]

Who is 'I' ?

In this context, the religious authorities.

 

[Polymath257]

Yes! That is true.

The limitations of languages show themselves: When science studies 'Existence' it means something different then when philosophers discuss 'Existence'. Any time a Science paper tries to discuss existence its going to presume the thing in question. Philosophically existence is either an axiom or a proposition.

I'm not sure you have this correct. For example, Peter Higg's suggested the existence of a particle. The existence of that particle was considered provisional until it was actually discovered 40 years after he proposed it as a possibility. There are many subatomic particles that have been proposed, but for which no evidence is currently available. Their existence is NOT accepted because of that lack of evidence.

One big issue I see in philosophy is that it never actually defines the concept of 'existence'. What does it mean for something to exist? How can we go about determining the existence of something? How can we know that something does NOT exist? Other than logical contradiction, which is a very, very minimal criterion, how do we know when something exists or not?

In particular, to stay on topic, what does it mean to say the number 2 exists? At the very least, it is a very different sort of existence than, say, the sun or a table. For those, we have observability and testing to use as criteria for existence. What is a criterion for the existence of a number?

And, to get back to my example, in what sense does the game of chess 'exist'? Was it invented or discovered? Does it exist independent of our minds? In what sense does the solution of a chess problem 'exist'? In what sense does it exist independent of our minds? is it invented or discovered?

And, perhaps, the dichotomy of 'invented or discovered' is a false one. Language, for example, was not invented by any single person, but is also not discovered in any sense I can fathom. Instead, it grows by successive additions allowing greater expressiveness. Sort of like mathematics.

 

[muhammad_isa]

..Remember that there is a difference between being able to count to 2 and thinking that there is an object '2' that exists independently of our thoughts.

Object? No.
Concept? Yes.

If the concept did not exist, we would not be able to communicate about what 2 items represents.
We would not understand each other.

 

[muhammad_isa]

In this context, the religious authorities.

..but it really isn't !
That type of authority is only human authority.

The ultimate authority is G-d. We don't need priests or imams to believe in G-d.
We are free to believe anything we like about G-d.

 

[Ostronomos]

I have seen your threads. Sorry, but your claims of superiority don’t go very far when you show you don’t understand the basics in many cases.

Quantum science, for example, says nothing about consciousness and you would know this if you read something other than popular accounts. But without the understanding of math, you can’t do that and your math skills are, shall we say, lacking. Maybe, if you put in some work, you could start to understand some of the basics.

The thing is, I have an illustrated encyclopedia on Quantum Mechanics called the Quantum Physics Bible. It gives bite-sized explanations on Quantum Mechanics. By its complexity and detail I have determined its validity. Have you ever personally witnessed the double slit experiment? If so you would know that single photons build up a wave pattern on the detection screen and this wavefunction collapses when they are being observed or detected. As exemplified by the title "Look and it goes away".

It 'appears' that way to me because I have looked at the history of the subject of religion. There is *never* actual agreement except for those points that are dangerous to question (as in, losing a job to being put to death). On no single point is there agreement that lasts *unless* all those who disagree are cowered in some way.

Yes, religion *claims* to set morality. But, in practice, that is very far from the case. Instead, people decide what is right or wrong and *then* argue that God agrees with them.

And I would disagree. I would be far more likely to trust an atheist than most theists.

Sounds like a typical hustle


to me: you get all you could possibly want, but only after death and only if you follow what I say.

The atheist falls prey to a type of logic that resides in reality and believes all is physical.

Please do not be deceived by the world around you. It is an illusion. Although it appears genuine. Only the spiritual realm is the real one. I can speak with authority on this as I have had a number of spiritual experiences as well as I have written a number of logical proofs to back up my claims.

Death is an illusion of change.

 

[Ostronomos]

My logic is undefeated by anyone before me.

 

[Mock Turtle]

My logic is undefeated by anyone before me.

I'm sure it is our loss, and especially so for being unworthy pupils.