Comments about the book "The Laboratory of the Mind" by James Robert Brown

This document contains comments about the book: "The Laboratory of the Mind" by James Robert Brown. 1991
To read this book select this link: http://www.course.sdu.edu.cn/G2S/eWebEditor/uploadfile/20121224165049418.pdf
The book can also be download via this link: https://www.researchgate.net/publication/243782944_The_Laboratory_of_the_Mind_Thought_Experiments_in_the_Natural_Sciences In the last paragraph I explain my own opinion.

Contents

Reflection

Chapter 0.

Preface and Acknowledgements - page viii

Like most philosophers, I encountered a bit of rationalism (Plato and Descartes) and a bit of empiricism (Hume) in my first formal introduction to the subject.
From this sentence it becomes clear that the writer is a philosopher. There is nothing wrong with that.
It seemed obvious to me, as it does to most, that all our knowledge is based upon sensory experience.
A lot of our knowledge becomes of what we observe. However the physical reality can be more complicated. But more important is what we learn by performing experiments.
Then one day I heard about Galileo’s thought experiment showing that all bodies must fall at the same rate—I almost fell out of my chair.
That is the why question. How it is possible that only by using our brain, we can unravel,explain the details of certain processes.
The first chapter introduces the subject by giving several examples of thought experiments.
Okay.
A multitude of cases is necessary since I have no definition of thought experiment to work with; we need a variety of paradigm instances.
It is impossible to study thought experiments if you have no clear definition what is involved in any thought experiment. Specific what the rules are.

page ix

Chapter three is a defence of platonism in mathematics.
Most physical processes in the universe can not be described by mathematics. A typical case is human behaviour.
So the point of the third chapter is to carry empiricist-, naturalist-, and physicalistminded readers as gently as possible into chapter four which contends that we really do have some a priori knowledge of nature.
We humans don't have a priori knowledge.
If someone made an invention means, that a scientist discovered something new based on previous inventions or experiments, which in turn are based on previous inventions or experiments of an earlier scientist. None of these previous inventions or experiments can be called a priori knowledge of an earlier scientist. Other wise it is called fraud.

Chapter 1.

1. ILLUSTRATIONS FROM THE LABORATORY OF THE MIND - page 1

Thought experiments are performed in the laboratory of the mind
Thought experiments are created in the mind solely based on text.
They are diferent from real experiments which are performed in a laboratory using chemical material, elements involving chemical reactions.
We recognize them when we see them: they are visualizable; they involve mental manipulations; they are not the mere consequence of a theory-based calculation; they are often (but not always) impossible to implement as real experiments either because we lack the relevant technology or because they are simply impossible in principle.
If they are impossible in principle than the results of the exercise can not be validated. I agree that such discussions are important to discuss outside limits.
If we are ever lucky enough to come up with a sharp definition of thought experiment, it is likely to be at the end of a long investigation.

1.1 GALILEO ON FALLING BODIES - page 1

This is Galileo’s wonderful argument in the Discorsi to show that all bodies, regardless of their weight, fall at the same speed
Reasoning in the Aristotelian manner leads to an absurd conclusion.
Okay.
First, the light ball will slow up the heavy one (acting as a kind of drag), so the speed of the combined system would be slower than the speed of the heavy ball falling alone (H > H+L)
How do you know that? How do you that drag is involved? What is drag.?
The only way to answer these questions is by performing different experiments, but that is not allowed.
If the light ball has the shape of a parachute it will slow down the heavy object, but the first is not the case.
On the other hand, the combined system is heavier than the heavy ball alone, so it should fall faster (H+L > H).
This is the basic assumption by Galileo.

page 2

But the question remains, ‘Which falls fastest?’ The right answer is now plain as day. The paradox is resolved by making them equal; they all fall at the same speed.
The problem is, is this paradox the real solution to claim that they both fall at the same speed. The reasoning can be wrong.
’ Salviati replies, ‘Without experiment, I am sure that the effect will happen as I tell you, because it must happen that way’.
But that does not mean that the reasoning is correct.

1.2 STEVIN ON THE INCLINED PLANE - page 3

Consider a prism-like pair of inclined (frictionless) planes with linked weights such as a chain draped over it.
The assumption that the surface of the planes are frictionless, makes this experiment physical impossible.
There are three possibilities: It will remain at rest; it will move to the left, perhaps because there is more mass on that side; it will move to the right, perhaps because the slope is steeper on that side.
Okay.
Stevin’s answer is the first: it will remain in static equilibrium.
The main reason is why.
The second diagram below clearly indicates why. By adding the links at the bottom we make a closed loop which would rotate if the force on the left were not balanced by the force on the right.
Such an action can not be done in a thought experiment.
Thus, we would have made a perpetual motion machine, which is presumably impossible.
How do we know that a perpetual motion machine is impossible.? The only way is to perform an experiment which demonstrates that such a machine exist. The reality is that this was never demonstrated.
(The grand condusion for mechanics drawn from this thought experiment is that when we have inclined planes of equal height then equal weights will act inversely proportional to the lengths of the planes.)
Such a conclusion can only be drawn from a real experiment.
Unquestionably in the assumption from which Stevin starts,that the endless chain does not move, there is contained primarily only a purely instinctive cognition.
To perform science can never be based on your instinct. You need observable evidence.

1.3 NEWTON ON CENTRIPETAL FORCE AND PLANETARY MOTION - page 6

page 2

As thought experiments go, this one probably doesn’t do any work from a physics point of view; that is, Newton already had derived the motion of a body under a central force, a derivation which applied equally to apples and the moon.
All what Newton did cannot be derived based on a thought experiment. His idea's starts from the observation that an apple falls from a tree.

1.4 NEWTON’S BUCKET AND ABSOLUTE SPACE - page 8

1.5 EUCLIDEAN GEOMETRY - page 10

1.6 POINCARÉ AND REICHENBACH ON GEOMETRY- page 11

1.7 NON-EXAMPLES - page 14

1.8 EINSTEIN CHASES A LIGHT BEAM - page 15
Maxwell’s great discovery was that the wave travelling through the electromagnetic field with velocity c is light.
/ That is physics
When he was only sixteen Einstein wondered what it would be like to run so fast as to be able to catch up to the front of a beam of light.
Perhaps it would be like running toward the shore from the end of a pier stretched out into the ocean with a wave coming in: there would be a hump in the water that is stationary with respect to the runner.
That is the situation when you run as fast as the waterwave.

1.9 SEEING AND MANIPULATING - page 17

1.10 EINSTEIN’S ELEVATOR - page 17

1.11 HEISENBERG’S γ-RAY MICROSCOPE - page 20

1.12 SCHRÖDINGER’S CAT - page 23

Many of the great thought experiments associated with quantum mechanics are attempts to undermine the uncertainty principle, or more generally, the orthodox interpretation of the quantum formalism known as the Copenhagen interpretation.
Understanding this sentence requires the understanding of the uncertainty principle and the Copenhagen interpretation. The understanding of these concepts can not be explained as a thought experiment.
Measurement outcomes are always eigenvalues, magnitudes which are associated with eigenstates, not with superpositions. So a very natural question is, what is the physical meaning of a superposition, and what happens when a measurement changes a superposition to an eigenstate?
Why is the concept of superposition important?

1.13 EPR - page 25

1.14 PHILOSOPHICAL THOUGHT EXPERIMENTS - page 27

1.15 THE STATUS OF PHILOSOPHICAL EXAMPLES - page 28

1.16 OTHER FIELDS - page 31

Thought experiments flourish in physics and in philosophy; to some extent they are to be found in mathematics as well (see Lakatos 1976). But they seem to be rather scarce in the other sciences. In chemistry, for example, I can’t find any at all.
That is not so amasing. It is impossiple (?) in your mind to predict what element 50 in the periodic table is.
Even in physics thought experiments are rare (You can even claim that there are none). How can you predict that an apple will fall from a tree?
In biology how can you predict that there are trees in the first place?
Biology, on the other hand, is quite rich. Darwin in The Origin of Species imagined giraffes with necks of different lengths
At the same the whole concept of the evolution theory has nothing to do with any thought experiment. He based the evidence of for this theory based on careful collecting of historical items, while showing that for example, identical birds changed in time.

Chapter 2

2. THE STRUCTURE OF THOUGHT EXPERIMENTS - page 33

Chapter 3

3. MATHEMATICAL THINKING - page 49

Chapter 4

4. SEEING THE LAWS OF NATURE - page 75

Chapter 5

5. EINSTEIN’S BRAND OF VERIFICATIONISM - page 99

Chapter 6

6. QUANTUM MECHANICS: A PLATONIC INTERPRETATION - page 127

Index

light page 15
radioactivity page 74
superposition page 74

Reflection 1 - Physical experiments versus Thought experiments.

Physical experiments involve equipment, raw materials and products.
There exists a range of physical processes: chemical processes, mechanical processes, electrical processes, medical processes and financial processes. Chemical processes are reactions between chemical elements, in a reactor using special equipment to control the reaction and measurement equipment to measure the state of the reaction.
The main purpose of experiments to understand the details of existing processes or to develop something new like a new vaccin.
A very important part of any physical experiment is documentation. The main purpose of documentation is describe the whole experiment in great detail such that the same experiment can be repeated (validated) some where else with the main objective that the results are the same.

Thought experiments do not involve any equipment, raw material or product.
The purpose of a thought experiment is the same a physical experiment, but the experiment is not performed in a laboratory but in the brain of humans, based on text.
Before to go in more detail about the pros and cons of thought experiments, let us first discuss A special type of thought experiment called Brain storming .

Brain storming is performed in a team. The purpose of a Brain storming session is to evaluate what has happened and to define what the team is going to do. Brain storming is often done when an accident has happen. In that case the purpose is to prevent that the accident happens again.
A special type of brain storming are the meetings to setup a pilot plant.

The question can be raised if brain storming is realy a thought experiment, implying discussions only. The answer is no. Because as the result of a brain storming session real physical experiments can be performed, in order to define the real cause of an accident. Was it based on a human error or a mechanical failure. As such brain storming is a powerful tool to investigate the physical reality

As mentioned a thought experiments is completely performed as a mental exercise. Nothing is based on any real experiment. All is on paper. How can such an exercise result in a document describing an experiment or conclusion which when performed or used is also valid in a real experiment? My impression is that this is difficult, if not impossible.

To be continued

Reflection 2 - Definition thought experiment.

A real experiment consist of the following steps:
  1. First you have a general plan what the experiment is suppose to demonstrate.
  2. Next you make a detail plan how the experiment is designed and how the experiment is performed.
  3. Next you perform the experiment
  4. Next you describe a detailed report describing the results of the experiment
  5. Finally you describe a conclusion with possible what to do next.
A strong defintion of a thought experiment is the following:
Step 1 and step 2 are exactly the same. Step 3 is skipped. Only step 4 is performed by inviduals. In that case each individual predicts the outcome of the experiment. It is very important to give a detailed description about the reasoning behind the prediction.

2.1 GALILEO ON FALLING BODIES

Considering the real experiment:
  1. The idea behind the experiment is to demonstrate what happens with two objects of different weights when they fall simultaneous.
  2. The experiment consists of dropping two objects of different weights from the tower of Piza.
    In order to demonstrate that the objects are of different weight a balance is used.
Considering the thought experiment:
  1. The outcome of the experiment can be the following:
    1) The heavy ball will hit the ground first. 2) They will hit simultaneous. 3) The heavy ball will hit second.
    We predict that both the heavy ball and the light ball will hit the bottom simultaneous.
  2. This prediction is based on the following logical reasoning: ?
In the book, as part of the thought experiment, the heavy and the light ball are connected together with a string.
This creates a new thought experiment which answers a new question: what happens when a heavy object and a heavy + light object fall simultaneous.
This new thought experiment is almost identical as the original thought experiment, however with the extra complexity that the shapes of the two objects are different.
You could also perform a new thought experiment, with a new ball which has the same weight as the light ball + heavy ball. You can compare this new heavier ball with the two balls that are connected. The problem is this special combination does not answer the first question.

To answer all these question by pure reasoning is a riddle.

2.2 STEVIN ON THE INCLINED PLANE

Considering the real experiment:
  1. The idea behind the experiment is to demonstrate what happens when a string with a set of balls or a rope of a certain length is placed above two inclined planes.
  2. The experiment consists of the following examples: 
             o
       o . o
     o .   . o
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   .           .
 .               .
         1

             o
       o . o
     o .   . o
   o .       . o
   .           . o
 .               .
         2

        o
  o . o
  o . o
  o . o
    .
    .  
    3

        o
  o . o
  o . o
  o . o
    . o
    .  
    4

      oooooo
  ...... o
       . o
       .
       .
       .               
       5

      oooooo
  ...... o
       . o
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       6
Considering the thought experiment.
  1. In the book the thought experiment is considerd frictionless. When you know that there is no friction the whole thought experiment becomes almost useless. To understand friction the only way is by performing experiments. As such we include friction.
  2. With friction the outcome of thought experiment 1 can be guessed as stable. For experiment 2 the outcome is undecided.
    For thought experiment 3 and 4 the results are the same.
    In thought experiments 5 and 6 the string is part horizontal and part vertical. The difference is in the length vertical. The result is undecided.
    If there is no friction in both cases the string will drop on the floor.
  3. In the book a perpetual motion machine is constructed by connecting both ends together, by adding an extra string with balls and making it a closed strings. Such a closed string will not move by itself. The problem is that that can only be demonstrated by a real experiment and not by a thought experiment. However adding such an extra string invalidates the original experiment.

2.4 NEWTON’S BUCKET AND ABSOLUTE SPACE - page 8

Considering the real experiment:
  1. Connect a rope to the ceiling. Connect a bucket, half filled with water at the other end. Turn the bucket 10 times around. This terminates the initialization of the experiment.
  2. Release the bucket. Observe what will happen. This terminates the experiment
Considering the thought experiment.
  1. The bucket will start turning.
  2. The final state will be the same as the original state.
  3. May be some one will predict that there will be an overshoot.
  4. The shape of the water level will not be predicted.
Considering the whole experiment:
  1. The whole experiment can physical described as a relation
    First, between the force of gravity and friction between the outerlayer of the water in the bucket and the bucket. Secondly, between different layers of the water inside the bucket, going from outwards to inwards.

2.12 SCHRÖDINGER’S CAT - page 23

Considering the real experiment:
  1. In this experiment (Considering the most simple experiment)
    1. A cat is placed in a box. 2. The box is closed. 3 The cat stays in the box for 30 minutes. 4. Before the box is opened the state of the cat is declared as both in a superposition state of both alive and dead. 5. The box is opened and the state of the cat is observed.
Considering the thought experiment.
  1. The state of the cat cannot be predicted
Considering the whole experiment:
  1. The fact if the cat, anywhere, during the whole experiment was in a superposition state could not be established or tested.
  2. In the book also radioactivity is involved. That means if there is radioactivity the cat will die. The chance that this will happen, which can only be established by performing real experiments, is much higher compared that the cat will die based on natural causes. But that does not mean that the cat was or is in a superposition state.
    The fact is, if you perform the same experiment 1000 times, the average outcome will be the same, if you claim before opening the box, that the cat is in a superposition or not.

Reflection 3 - Evaluation of Thought experiments

If you want to do science you can not use thought experiments. The only way to do science is to real perform experiments.
It is impossible to predict the outcome of the schrödinger cat experiment. See: Reflection 2.1

Tests are the main tools to investigate the details of all types of processes. For example if you want to use the half life time of a radiaoactive element the only way is to test the material used. No thought experiment can be used.

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