[xenotolerance]

Thread inspired by this recent post from the good doctor Tommy B:

Astronomy, Geometry, Physics, many more fields; the foundation of which is all built on a house of cards at a fundamental level.

I challenge the author and other Pyrrhonic believers to use this thread to identify specific problems with the foundations of those three fields, astronomy, geometry, and physics, and thereby knock down the house of cards that is mainstream science.

[Tom Bishop]

Aren't the flaws obvious? Geometry predicts things like the concept of a "circle". Pi, etc, are thrown out to calculate attributes of those "circles."

But who has ever actually seen a perfect circle, such that is required by Pi? A geometric circle assumes that the universe is continuous rather than discrete. When did the Ancient Greeks ever demonstrate that?

[Rama Set]

Aren't the flaws obvious? Geometry predicts things like the concept of a "circle". Pi, etc, are thrown out to calculate attributes of those "circles."

But who has ever seen a perfect circle? A perfect circle assumes that the universe is continuous rather than discrete. When did the Ancient Greeks ever demonstrate that?

Scientific theories are only supposed to describe the world to degrees of accuracy, not to perfection.  Why should the lack of perfection mean that science can never describe something accurately?

[inquisitive]

Aren't the flaws obvious? Geometry predicts things like the concept of a "circle". Pi, etc, are thrown out to calculate attributes of those "circles."

But who has ever actually seen a perfect circle, such that is required by Pi? A geometric circle assumes that the universe is continuous rather than discrete. When did the Ancient Greeks ever demonstrate that?

Most of us are clear what a circle is.

[Tom Bishop]

Aren't the flaws obvious? Geometry predicts things like the concept of a "circle". Pi, etc, are thrown out to calculate attributes of those "circles."

But who has ever seen a perfect circle? A perfect circle assumes that the universe is continuous rather than discrete. When did the Ancient Greeks ever demonstrate that?

Scientific theories are only supposed to describe the world to degrees of accuracy, not to perfection.  Why should the lack of perfection mean that science can never describe something accurately?

It is more that the Ancient Greek concept of a circle makes a fundamental assumption that the universe is continuous. The Ancient Greeks also describe length in space as a number line which is infinitely divisible and continuous.

You guys use all of this theory to try and explain what would happen to a sun setting over a plane, predicting that the sun would continuously approach, but never reach, the horizon. The sun could not reach the horizon no matter how far away it is, and would descend infinitesimally. But this prediction is made assuming the unfounded continuous models of the Ancient Greeks.

Where have the Ancient Greeks shown that two perspective lines would never be seen to intersect? What experiments have they performed before coming up with those theories of perspective?

The concept of a continuous universe needs clear and compelling evidence before we accept it as true.

[inquisitive]

Aren't the flaws obvious? Geometry predicts things like the concept of a "circle". Pi, etc, are thrown out to calculate attributes of those "circles."

But who has ever seen a perfect circle? A perfect circle assumes that the universe is continuous rather than discrete. When did the Ancient Greeks ever demonstrate that?

Scientific theories are only supposed to describe the world to degrees of accuracy, not to perfection.  Why should the lack of perfection mean that science can never describe something accurately?

It is more that the Ancient Greek concept of a circle makes a fundamental assumption that the universe is continuous. The Ancient Greeks also describe length in space as a number line which is infinitely divisible and continuous.

You guys use all of this theory to try and explain what would happen to a sun setting over a plane, predicting that the sun would continuously approach, but never reach, the horizon. The sun could not reach the horizon no matter how far away it is. But this prediction is made assuming the unfounded continuous models of the Ancient Greeks.

Where have the Ancient Greeks Shown that two perspective lines would never be seen to intersect? What experiments have they performed before coming up with those theories of perspective?

A declaration can't be made that the universe is continuous without clear and compelling evidence.

None of that is relevant to the relatively small size of the earth and how we view the sun at different times from different locations.  timeanddate.com is a good, accurate, source of information.

[Rama Set]

Aren't the flaws obvious? Geometry predicts things like the concept of a "circle". Pi, etc, are thrown out to calculate attributes of those "circles."

But who has ever seen a perfect circle? A perfect circle assumes that the universe is continuous rather than discrete. When did the Ancient Greeks ever demonstrate that?

Scientific theories are only supposed to describe the world to degrees of accuracy, not to perfection.  Why should the lack of perfection mean that science can never describe something accurately?

It is more that the Ancient Greek concept of a circle makes a fundamental assumption that the universe is continuous. The Ancient Greeks also describe length in space as a number line which is infinitely divisible and continuous.

You use these terms, continuous and discrete, often but I am never sure exactly what you mean. I don’t want to plunge ahead in to a rebuttal until I know what you are talking about. Can you define these terms please?

You guys use all of this theory to try and explain what would happen to a sun setting over a plane, predicting that the sun would continuously approach, but never reach, the horizon. The sun could not reach the horizon no matter how far away it is, and would descend infinitesimally. But this prediction is made assuming the unfounded continuous models of the Ancient Greeks.

Where have the Ancient Greeks shown that two perspective lines would never be seen to intersect? What experiments have they performed before coming up with those theories of perspective?

The concept of a continuous universe needs clear and compelling evidence before we accept it as true.

The ancient Greeks never treated in perspective afaik, but if you are referring to parallel lines then there is no proof required. Parallel is a definition.  Hypocritical though that your argument is based on us not being able to prove a negative.  All we can say is that no parallel lines have been observed actually meeting, they appear to meet but this has continually been shown to be a trick of the eye. Couple that with the fact that to our best measurements show the universe to be flat, then we get to a place where it is healthy to trust what we observe.

[garygreen]

The concept of a continuous universe needs clear and compelling evidence before we accept it as true.

actually it doesn't matter at all.  for example: electric charge is discrete.  electric charge is absolutely not distributed continuously in a conductor. 

but you can still use calculus to make correct predictions about electric fields/potentials/forces/whatever.  a huge portion of vector calculus was invented for the purpose of solving problems involving distributions of discrete charges.

all you're doing in this thread is demonstrating naivete of the subject you're trying to criticize.  as usual.

[Scroogie]

It is more that the Ancient Greek concept of a circle makes a fundamental assumption that the universe is continuous. The Ancient Greeks also describe length in space as a number line which is infinitely divisible and continuous.

You guys use all of this theory to try and explain what would happen to a sun setting over a plane, predicting that the sun would continuously approach, but never reach, the horizon. The sun could not reach the horizon no matter how far away it is, and would descend infinitesimally. But this prediction is made assuming the unfounded continuous models of the Ancient Greeks.

Where have the Ancient Greeks shown that two perspective lines would never be seen to intersect? What experiments have they performed before coming up with those theories of perspective?

The concept of a continuous universe needs clear and compelling evidence before we accept it as true.

I would like to rebut this, but I haven't the faintest notion what it is you are trying to say?

Are we (REers) being accused of "predicting that the sun would continuously approach, but never reach, the horizon"?

Are there REers who are trying to "explain what would happen to a sun setting over a plane"? I don't understand why any would attempt that, at the sun in the real world doesn't set over a plane. It dips below the visible horizon of a sphere.

In what manner does the "concept of a circle make a fundamental assumption that the universe is continuous"?

Did "Ancient Greeks [really] also describe length in space as a number line which is infinitely divisible and continuous"? Is this implying that a continuous line could be simultaneously discontinuous?

My head hurts.

[Tom Bishop]

Here are some of the fundamental elements the models and maths of the Ancient Greeks assume:

- That perfect circles can exist
- That one could zoom into a circle forever and see a curve
- That any length of space can be divided into infinitely smaller parts
- That the space can be infinitely long
- Time can likewise be infinitely divided, or infinitely long

This is what is meant by "continuous universe." The math further takes such elements and runs with them. Continuous this, continuous that. None of it is justified. The Ancient Greeks performed no experiments before coming up with those ideas. It is merely their idea of a "perfect" universe.

Making conclusions from this continuous universe model, such as the sun would never set on a plane, relies on many axioms of the continuous universe model being true. Since the Ancient Greeks never really performed experiments to justify their ideas, that calls any such calculation into question.

[inquisitive]

Here are some of the fundamental elements the models and maths of the Ancient Greeks assume:

- That perfect circles can exist
- That one could zoom into a circle forever and see a curve
- That any length of space can be divided into infinitely smaller parts
- That the space can be infinitely long
- Time can likewise be infinitely divided, or infinitely long

This is what is meant by "continuous universe." The math further takes such elements and runs with them. Continuous this, continuous that. None of it is justified. The Ancient Greeks performed no experiments before coming up with those ideas. It is merely their idea of a "perfect" universe.

Making conclusions from this continuous universe model, such as the sun would never set on a plane, relies on many axioms of the continuous universe model being true. Since the Ancient Greeks never really performed experiments to justify their ideas, that calls any such calculation into question.

Please explain how this is relevant to the many measurements and observations we make of the earth.  Please give details of your current research and experiments on the subject.

[garygreen]

Since the Ancient Greeks never really performed experiments to justify their ideas, that calls any such calculation into question.

what controlled experiments have you performed to demonstrate that the continuous/discrete quantity distinction matters?  genuine question, not trying to be flippant.

to elaborate: if you haven't performed an experiment to justify your idea that the distinction matters, then that calls any such calculation into question.

[Scroogie]

Here are some of the fundamental elements the models and maths of the Ancient Greeks assume:

- That perfect circles can exist
- That one could zoom into a circle forever and see a curve
- That any length of space can be divided into infinitely smaller parts
- That the space can be infinitely long
- Time can likewise be infinitely divided, or infinitely long

This is what is meant by "continuous universe." The math further takes such elements and runs with them. Continuous this, continuous that. None of it is justified. The Ancient Greeks performed no experiments before coming up with those ideas. It is merely their idea of a "perfect" universe.

Making conclusions from this continuous universe model, such as the sun would never set on a plane, relies on many axioms of the continuous universe model being true. Since the Ancient Greeks never really performed experiments to justify their ideas, that calls any such calculation into question.

Could you please point me toward the text(s) from which you derived these assumptions? I would like to be on a somewhat even playing field vis a vis what the ancient Greeks actually did or didn't propose to be fact. Not being a mathematician, I'm not familiar with "Assumptions Made by the Ancient Greeks".

In the meantime, lets begin here:
"Plato believed that the entire cosmos was constructed with precision and that circles and spheres, as the most perfect objects, were the key to understanding the universe."  From https://explorable.com/greek-astronomy

That is not saying that Plato believed circles or spheres were perfect, only that they were the nearest things to perfect that he could conceive of.

[Tom Bishop]

Could you please point me toward the text(s) from which you derived these assumptions? I would like to be on a somewhat even playing field vis a vis what the ancient Greeks actually did or didn't propose to be fact. Not being a mathematician, I'm not familiar with "Assumptions Made by the Ancient Greeks".

Open a High School Geometry textbook. All of that is there, and all of it is the handed down teachings of the ancients.

Since the Ancient Greeks never really performed experiments to justify their ideas, that calls any such calculation into question.

what controlled experiments have you performed to demonstrate that the continuous/discrete quantity distinction matters?  genuine question, not trying to be flippant.

to elaborate: if you haven't performed an experiment to justify your idea that the distinction matters, then that calls any such calculation into question.

I have not made any controlled experiments regarding the continuous nature of the universe. Why would I? That may not even be possible to test. I'm not the claimant. I'm the skeptic. It is enough for the skeptic to question. It is those with the claims who need to demonstrate them. If those Euclidean Geometry proponents cannot test their own ideas because it is impossible, then that shows how strong and established those ideas are.

[Rama Set]

Here are some of the fundamental elements the models and maths of the Ancient Greeks assume:

- That perfect circles can exist
- That one could zoom into a circle forever and see a curve
- That any length of space can be divided into infinitely smaller parts
- That the space can be infinitely long
- Time can likewise be infinitely divided, or infinitely long

This is what is meant by "continuous universe." The math further takes such elements and runs with them. Continuous this, continuous that. None of it is justified. The Ancient Greeks performed no experiments before coming up with those ideas. It is merely their idea of a "perfect" universe.

Making conclusions from this continuous universe model, such as the sun would never set on a plane, relies on many axioms of the continuous universe model being true. Since the Ancient Greeks never really performed experiments to justify their ideas, that calls any such calculation into question.

So let’s say for the sake of argument you are correct with your assumptions that the Greeks made. I have never come across these in all the math I have studied, but so be it. If you are correct, how does us only possessing a tool for approximation, that we know is extremely accurate undermine modern science?

Could you please point me toward the text(s) from which you derived these assumptions? I would like to be on a somewhat even playing field vis a vis what the ancient Greeks actually did or didn't propose to be fact. Not being a mathematician, I'm not familiar with "Assumptions Made by the Ancient Greeks".

Open a High School Geometry textbook. All of that is there, and all of it is the handed down teachings of the ancients.

Since the Ancient Greeks never really performed experiments to justify their ideas, that calls any such calculation into question.

what controlled experiments have you performed to demonstrate that the continuous/discrete quantity distinction matters?  genuine question, not trying to be flippant.

to elaborate: if you haven't performed an experiment to justify your idea that the distinction matters, then that calls any such calculation into question.

I have not made any controlled experiments regarding the continuous nature of the universe. Why would I? That may not even be possible to test. I'm not the claimant. I'm the skeptic. It is enough for the skeptic to question. It is those with the claims who need to demonstrate them. If those Euclidean Geometry proponents cannot test their own ideas because it is impossible, then that shows how strong and established those ideas are.

You are not just a skeptic, you have claimed that the current state of mathematics undermines modern science. This is a positive claim and you will need to substantiate it.

[Scroogie]

Open a High School Geometry textbook. All of that is there, and all of it is the handed down teachings of the ancients.

Give me time - I'm working on it - see my above post.

No, sorry, I nearly fell into the "Bishop Trap".

You made the following assertions:

Here are some of the fundamental elements the models and maths of the Ancient Greeks assume:

- That perfect circles can exist
- That one could zoom into a circle forever and see a curve
- That any length of space can be divided into infinitely smaller parts
- That the space can be infinitely long
- Time can likewise be infinitely divided, or infinitely long

Now back them up with corroborating texts.

And, while you're at it, it would be greatly appreciated if you could supply the data requested in the nearby "Vanishing Point" thread. I am assuming that if anyone is privy to such information, it would be you.

[garygreen]

I'm not the claimant. I'm the skeptic. It is enough for the skeptic to question. It is those with the claims who need to demonstrate them.

you are the claimant.  you claim that it matters whether or not a quantity is discrete or continuous.  that's your argument.  "Since the Ancient Greeks never really performed experiments to justify their ideas, that calls any such calculation into question."

the notion that such a distinction "calls any such calculation into question" is a positive claim.

[Buran]

The idea that we base reality off of what ancient's thought of the world is... perplexing. When the Greeks talk about dividing space on a number line, that's mathematical theory, not physics. Right now, the smallest unit, as I'm sure you all know, is the plank length. As far as an imaginary numberline, I can divide it infinitely. Literally, no one can stop me from dividing it. And you can mathematically make a perfect circle. Again, real world it is impossible to be that precise. But I cut holes on a daily basis that measure within a few thousandths of an inch of being perfect.

I guess I'm lost on what the point here is?

[AATW]

Making conclusions from this continuous universe model, such as the sun would never set on a plane, relies on many axioms of the continuous universe model being true.

Actually, all it relies on is some common sense.
How do I see something? Photons hit my eye. If that is from a light source then the photons leave the light source and travel to my eye along a straight path.
Or, the light travels from the light source, reflects off an object and travels from that in a straight line into my eye.
Either way if there is an unobstructed line of sight in between me and the light source/object then I will be able to see it. The only limitations to that are:
1) My visual acuity
2) Atmospheric conditions

So on a plane:



Clear line of sight, I can see the whole person.

On a curve:



The bottom of the person (or ship or sun) is occluded behind the hill so I can only see the top part.

And I see you have still ignored my thread about long shadows at sunset which prove conclusively that either
1) The sun is physically low in the sky or
2) The light is bending so it appears to be.

There are no other options but feel free to do some experiments and show how you can cast a long shadow of an object on the ground without the light source being physically close to the ground.

[JohnAdams1145]

Here are some of the fundamental elements the models and maths of the Ancient Greeks assume:

- That perfect circles can exist
- That one could zoom into a circle forever and see a curve
- That any length of space can be divided into infinitely smaller parts
- That the space can be infinitely long
- Time can likewise be infinitely divided, or infinitely long

This is what is meant by "continuous universe." The math further takes such elements and runs with them. Continuous this, continuous that. None of it is justified. The Ancient Greeks performed no experiments before coming up with those ideas. It is merely their idea of a "perfect" universe.

Making conclusions from this continuous universe model, such as the sun would never set on a plane, relies on many axioms of the continuous universe model being true. Since the Ancient Greeks never really performed experiments to justify their ideas, that calls any such calculation into question.

Tom, do you understand that even though we know the universe to be discrete, we know it to be discrete on so small of a level that mathematics tells us we can approximate it continuously and see virtually no difference? Or did this just completely go over your head? All of our everyday observations suggest a continuous universe. Some scientific measurements suggest that it's actually finely discretized. Is there a real difference here? No. You're making one up because you've been slammed into a corner. You clearly don't even understand basic calculus (Riemann sums are a good start).