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Thought Experiments http://www.thoughtexperiments.net Famous Thought Experiments Explained Mon, 14 Jan 2019 14:52:07 +0000 en-US hourly 1 https://wordpress.org/?v=5.4 https://i2.wp.com/www.thoughtexperiments.net/wp-content/uploads/2016/03/cropped-te.png?fit=32%2C32 Thought Experiments http://www.thoughtexperiments.net 32 32 108905062 Many Minds http://www.thoughtexperiments.net/many-minds/ http://www.thoughtexperiments.net/many-minds/#respond Tue, 06 Dec 2016 14:31:05 +0000 http://thoughtexperiments.net/?p=48528 This post builds on two ideas we explored in previous posts: Quantum Suicide and Personal Identity. You should definitely read those […]

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This post builds on two ideas we explored in previous posts: Quantum Suicide and Personal Identity. You should definitely read those posts first if you’d like the full picture.

Hugh Everett was an American physicist known for his radical interpretation of Quantum Mechanics called the Many-Worlds interpretation. Everett challenged the validity of leading interpretations of Quantum Mechanics at the time, first and foremost the Copenhagen Interpretation. Under the Copenhagen Interpretation, the true behavior of a quantum system can be inferred by an observer independently of its own state. Everett’s big idea was that observers are part of the quantum system. Both are entangled such that one cannot be defined without the other. The false notion that observations are independent of the observer leads to one of the thorniest issues in Quantum Mechanics, a conundrum known as the measurement problem.

The Many-Worlds interpretation, published in 1957, holds that the probabilistic equations used to predict quantum phenomena continue to hold after an observation is made — it is just that every time a measurement is made, all the possible outcomes actually occur in different branches of reality, creating a multitude of parallel worlds, or a “multiverse.”

The notion of the world continually splitting at every quantum decision point across a multiverse of parallel universes has significant implications for personal identity. This is because individuals are deemed to be in continual superposition with themselves because they exist in many parallel universes simultaneously. In his dissertation, Everett summarizes the implication of this contention as follows:

“The price, however, is the abandonment of the concept of the uniqueness of the observer, with its somewhat disconcerting philosophical implications.”

Everett proposed a thought experiment to better illustrate the state of the observer:

“As an analogy one can imagine an intelligent amoeba with a good memory. As time progresses the amoeba is constantly splitting, each time the resulting amoebas having the same memories as the parent. Our amoeba hence does not have a life line, but a life tree. The question of identity or non-identity of two amoebas at a later time must be rephrased. At any time we can consider two of them, and they will have common memories up to a point (common parent) after which they will diverge according to their separate lives after this point. It becomes simply a matter of terminology as to whether they should be thought of as the same amoeba or not, or whether the phrase “the amoeba” should be reserved for the whole ensemble.”

Everett’s experiment is astonishingly similar to another thought experiment titled People Who Divide Like an Amoeba by british philosopher Derek Parfit, which we have discussed in a previous post. Everett then suggests a closer analogy:

“If we were to take one of these intelligent amoebas, erase his past memories, and render him unconscious while he underwent fission, placing the two resulting amoebas in separate tanks, and repeating this process for all succeeding generations, so that none of the amoebas would be aware of their splitting. After awhile we would have a large number of individuals, sharing some memories with one another, differing in others, each of which is completely unaware of his “other selves” and under the impression that he is a unique individual. It would be difficult indeed to convince such an amoeba of the true situation short of confronting him with his ‘other selves’.”

Everett claims that the same is true for our own existential state under the Many-Worlds approach to quantum mechanics. Thus, he contends:

“The same is true [if] one accepts the hypothesis of the universal wave function. Each time an individual splits he is unaware of it, and any single individual is at all times unaware of his “other selves” with which he has no interaction from the time of splitting.”

The term Wave Function refers to the equation used by quantum theory to predict the probability of possible outcomes in a quantum system. Everett suggested the term Universal Wave Function to describe the equation governing the totality of existence.

The Many Minds interpretations examines the consequences of the Everett Many-Worlds interpretation from the perspective of the mind. Rather than many worlds branching at each quantum decision point, it is the observer’s mind that is branching. It was first introduced in 1970 by H. Dieter Zeh as a variant of the Everett interpretation and explicitly termed “Many Worlds” by American philosophers David Albert and Barry Loewer in 1988. It was re-formulated again by the British Philosopher Michael Lockwood (Many-Minds Interpretations of Quantum Mechanics, 1996).

According to Lockwood, the significance of the Many-Minds interpretation is that it is the first scientific theory to recognize the necessity of subjective experiences. This is because Many-Minds leads directly to the following scenario:

“[a view] of the world as, in some sense, a sum of perspectives…the inevitable selectivity involved in a point of view is automatically accommodated, via the idea that consciousness is tied to one amongst a potential infinity of what, in the context of quantum mechanics, are known as representations.”

Here is Lockwood’s account of the Many-Minds interpretation:

“A many minds theory, like a many worlds theory, supposes that, associated with a sentient being at any given time, there is a multiplicity of distinct conscious points of view. But a many minds theory holds that it is these conscious points of view or ‘minds,’ rather than ‘worlds,’ that are to be conceived as literally dividing or differentiating over time.”

When an observer interacts with a quantum system, they become a part of a larger quantum system. Each possible outcome predicted by the equations of quantum mechanics has a corresponding mental state, or mind, in the brain of the observer. Ultimately, only one mind is experienced. The minds corresponding to outcomes which did not occur simply become inaccessible. This leads to a scenario under which every conscious being is endowed with a large number of minds, corresponding to all possible outcomes. As an observer interacts with a quantum system, the probabilities of realizing specific outcomes directly correlates to the number of minds they have.

In the end, Lockwood concludes that it is senseless to ask which, of the many possible minds, are “yours” following a specific quantum interaction. His conclusion is similar to the one arrived at by Parfit, as we saw in the post about Personal Identity. Parfit was not concerned with Quantum Mechanics, but rather with a series of thought experiments under which a person’s mind is duplicated or split either by surgery or some other means. These experiments demonstrate that, following such a split, questions such as “which person will I become?” are senseless. His conclusion is that we should discard the notion of personal identity. There is no determinate answer to these questions, even if we know everything there is to know. In a way, I will become none of them and, in a way, I will become all of them.

I find it fascinating that two thinkers from two unrelated disciplines arrive at such similar conclusions. It is even more fascinating that both lines of thought suggest that it is the way we speak about something as seemingly trivial as our own identity which ought to change.

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People Who Divide Like an Amoeba http://www.thoughtexperiments.net/people-who-divide-like-an-amoeba/ http://www.thoughtexperiments.net/people-who-divide-like-an-amoeba/#respond Sat, 08 Oct 2016 16:11:48 +0000 http://thoughtexperiments.net/?p=48510 The notion of identity or “sameness” is fundamental to our understanding of the world. The debate about its nature is […]

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The notion of identity or “sameness” is fundamental to our understanding of the world. The debate about its nature is as old as philosophy itself. The law of identity is the first of the three basic laws of classical logic, on which mathematics and the rest of scientific knowledge rests. It states that “each thing is the same with itself and different from another,” or more formally, that “X is X” for any variable X.

The law of identity may sound trivial, but the philosophical discussion about identity is very lengthy. What follows is my attempt to unpack a single thread of  this discussion involving several interesting thought experiments and some unexpected conclusions.

One of the earliest thought experiments relating to identity is called “The Ship of Theseus,” described by Plutarch, the ancient Greek historian, in Life of Theseus (75 CE):

“The ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.“

Plutarch questions whether Theseus’s ship would remain the same ship if it were to be replaced piece by piece until none of the original planks of wood remained. To the Sophists of Athens, the totally retrofitted vessel would still very much be Theseus’s ship, because such an identity is consistent with a Platonistic, idealistic world view rather than a materialistic one. A millenia and a half later, the philosopher Thomas Hobbes introduced an interesting twist to the thought experiment in his book De Corpore (On the Body, 1655):

“Two bodies existing both at once would be one and the same numerical body. For if, for example, that ship of Theseus, concerning the difference whereof made by continued reparation in taking out the old planks and putting in new, the sophisters of Athens were wont to dispute, were, after all the planks were changed, the same numerical ship it was at the beginning; and if some man had kept the old planks as they were taken out, and by putting them afterwards together in the same order, had again made a ship of them, this, without doubt, had also been the same numerical ship with that which was at the beginning; and so there would have been two ships numerically the same, which is absurd.”

Hobbes concedes that the ship remains the same if all its planks were replaced, but asks an interesting question. What if someone were to have gathered all the old planks only to reassemble a ship out of them? Surely, he argues, this other ship must also be the ship of Theseus. This leads to a seemingly absurd situation in which we now have two ships which are both Theseus’s Ship. There are many variations and further elaborations of this thought experiment, which merit an in depth look, but I would now like to turn to the more interesting discussion about a particular type of identity, namely that of personal identity.

The discussion of personal identity address such issues as, “what makes an individual be the same person over time?” The discussion of personal identity is more interesting than the one about general object identity because we seem to hold personal identity to a higher standard. Whilst it is easy to conceive of a change to the identity of, say, a ship or a nation-state (e.g., “is England the same nation after 1066?”), we would rarely accept a case where a person has changed their identity.

There are four common definitions of personal identity:

  • Who we are is determined by our body; we are the sum of our physical parts. As long as there is a continuation of our body, we remain the same.
  • Who we are is determined by our brain. Only the brain is core to our identity and everything else is transient.
  • Who we are is determined by our mind, or our soul. It is not the physical but rather the mental which is core.
  • Who we are is determined by our memories. It is our memory which provides a sense of continuity.

The American philosopher Sydney Shoemaker describes the following thought experiment in his 1958 book Self Knowledge and Self-Identity:

“Suppose that medical science has developed a technique whereby a surgeon can completely remove a person’s brain from his head, examine or operate on it, and then put it back in his skull (regrafting the nerves, blood-vessels, and so forth) without causing death or permanent injury …. One day a surgeon discovers that an assistant has made a horrible mistake. Two men, a Mr. Brown and a Mr. Robinson, had been operated on for brain tumors, and brain extractions had been performed on both of them. At the end of the operations, however, the assistant inadvertently put Brown’s brain in Robinson’s head, and Robinson’s brain in Brown’s head.

One of these men immediately dies, but the other, the one with Robinson’s body and Brown’s brain, eventually regains consciousness. Let us call the latter ‘Brownson’ …. He recognizes Brown’s wife and family (whom Robinson had never met), and is able to describe in detail events in Brown’s life, always describing them as events in his own life. Of Robinson’s past life he evidences no knowledge at all. Over a period of time, he is observed to display all of the personality traits, mannerisms, interests, likes and dislikes, and so on that had previously characterized Brown, and to act and talk in ways completely alien to the old Robinson.

What would we say if such a thing happened? There is little question that many of us would be inclined, and rather strongly inclined, to say that while Brownson has Robinson’s body he is actually Brown. But if we did say this we certainly would not be using bodily identity as our criterion of personal identity. To be sure, we are supposing Brownson to have part of Brown’s body, namely his brain. But it would be absurd to suggest that brain identity is our criterion of personal identity.”

Shoemaker’s analysis of the experiment is based around common usage – the way by which most people would describe the unfortunate Mr. Brownson. He concludes that such use, “to say that while Brownson has Robinson’s body he is actually Brown”, contradicts the bodily definition of identity.

The British philosopher Derek Parfit takes the experiment a step further (basing his argument on that of yet another British philosopher, David Wiggins), and giving it the colorful name “People who divide like an amoeba” (Personal Identity, 1971):

“My brain is divided, and each half is housed in a new body. Both resulting people have my character and apparent memories of my life. What happens to me?”

Parfit makes several non-trivial assumptions: brain transplant is possible, and that transplanting the two halves of the brain produces healthy individuals with the same personality and memories. However, the point of the scenario is not to determine the actual feasibility of such an operation but rather the implications it would have if it could be performed. The surgery has 3 possible outcomes:

  1. I do not survive
  2. I survive as one of the two people
  3. I survive as both people

The third option is an actual possibility because we know of people who have in fact survived with half of their brain destroyed; there is therefore no theoretical reason why both halves of a brain should not produce two conscious individuals. Parfit describes two ways by which we can explain this awkward situation. He then demonstrate why both lead to absurdities and suggests a third alternative.

The first explanation attempts to treat the two resulting individuals as one person:

“What we have called ‘the two resulting people’ are not two people. They are one person. I do survive Wiggins’ operation. Its effect is to give me two bodies and a divided mind.”

Initially the two individuals share the same set of memories. The problem is that as time goes by, and the two individuals live their lives accumulating a distinct set of experiences, it makes less and less sense to speak about them as one person. The second description treats the two individuals as two distinct people:

“I do survive the operation as two people. They can be different people, and yet be me, in just the way in which the Pope’s three crowns are one crown.”

Parfit claims this explanation seems plausible, at least initially, because we can imagine that  person with two disconnected hemispheres would experience two disjoint personalities, in which case we would still be inclined to say it is one person we are referring to. The problem with the second explanation, he notes, is that it involves two bodies and thus alters the meaning of “person” far beyond the common usage.

It seems that no matter how hard we try, a coherent explanation of personal identity for the situation described in this experiment eludes us. Parfit claims that this difficulty is the hallmark of the debate about personal identity. Although we’d like to think otherwise, the way we conceive of personal identity is riddled with holes.

In his book Reasons and Persons (1984), Parfit describes a further thought experiment involving  a “Teletransporter,” a device similar to the one we know from Star Trek, which illustrates a similar dilemma:

“I enter the Teletransporter. I have been to Mars before, but only by the old method, a spaceship journey taking several weeks. This machine will send me at the speed of light. I merely have to press the green button. Like others, I am nervous. Will it work? I remind myself what I have been told to expect. When I press the button, I shall lose consciousness, and then wake up at what seems a moment later. In fact I shall have been unconscious for about an hour. The Scanner here on Earth will destroy my brain and body, while recording the exact states of all of my cells. It will then transmit this information by radio. Travelling at the speed of light, the message will take three minutes to reach the Replicator on Mars. This will then create, out of new matter, a brain and body exactly like mine. It will be in this body that I shall wake up.

Though I believe that this is what will happen, I still hesitate. But then I remember seeing my wife grin when, at breakfast today, I revealed my nervousness. As she reminded me, she has been often teletransported, and there is nothing wrong with her. I press the button. As predicted, I lose and seem at once to regain consciousness, but in a different cubicle. Examining my new body, I find no change at all. Even the cut on my upper lip, from this morning’s shave, is still there.

Several years pass, during which I am often Teletransported. I am now back in the cubicle, ready for another trip to Mars. But this time, when I press the green button, I do not lose consciousness. There is a whirring sound, then silence. I leave the cubicle, and say to the attendant: ‘It’s not working. What did I do wrong?’ ‘It’s working’, he replies, handing me a printed card. This reads: ‘The New Scanner records your blueprint without destroying your brain and body. We hope that you will welcome the opportunities which this technical advance offers.’ The attendant tells me that I am one of the first people to use the New Scanner. He adds that, if I stay for an hour, I can use the Intercom to see and talk to myself on Mars. ‘Wait a minute’, I reply, ‘If I’m here I can’t also be on Mars’.

Someone politely coughs, a white-coated man who asks to speak to me in private. We go to his office, where he tells me to sit down, and pauses. Then he says: ‘I’m afraid that we’re having problems with the New Scanner. It records your blueprint just as accurately, as you will see when you talk to yourself on Mars. But it seems to be damaging the cardiac systems which it scans. Judging from the results so far, though you will be quite healthy on Mars, here on Earth you must expect cardiac failure within the next few days.

The attendant later calls me to the Intercom. On the screen I myself just as I do in the mirror every morning. But there are two differences. On the screen I am not left-right reversed. And, while I stand here speechless, I can see and hear myself, in the studio on Mars starting to speak.”

The careful way by which Parfit decides to unravel events in this thought experiment makes it extremely hard to speak about identity as something equivalent to survival. It also undermines the idea that identity is related to a common set of memories. As long as the teletransporter operates seamlessly, destroying one body while creating another, the notion of identity is preserved  (I’m the same person before and after the teletransportation). Once a gap is introduced between creation and destruction, it no longer seems appropriate to speak of survival. Part of the problem is the gap allows the two resulting individuals to develop distinct sets of memories; even if only for an hour.

Parfit argues that the only sensible solution is to entirely give up on the notion of personal identity. We can suggest, he argues, that in both experiments I survive as two people without suggesting that I am these two people. Parfit describes two commonly held beliefs which are at the heart of the debate:

  1. Any question about personal identity, in any describable case, must have a true answer.
  2. Important questions rest on the notion of personal identity.

The experiments challenge both beliefs. They directly challenge the first by demonstrating cases where there is no one correct answer to the question of personal identity. The effect is that our notion of personal identity is demoted to that of object identity, for which we’ve already agreed, there sometimes are no clear resolutions.

With regards to the second belief, Parfit claims that yes, there are important questions that do presuppose a question about personal identity. Because these questions are important, the thought experiment does represent a problem. The only way to resolve the difficulty is to drop the presuppositions about personal identity.

Parfit suggests that we change the way we speak about this and similar cases. This is not merely a cosmetic change, but one that has implications on how we behave:

“”Will I survive?” seems, I said, equivalent to “Will there be some person alive who is the same person as me?” If we treat these questions as equivalent, then the least unsatisfactory description of Wiggins’ case is, I think, that I survive with two bodies and a divided mind. Several writers have chosen to say that I am neither of the resulting people. Given our equivalence, this implies that I do not survive, and hence, presumably, that even if Wiggins’ operation is not literally death, I ought, since I will not survive it, to regard it as death. But this seemed absurd.”

The situation is particularly absurd because we would not consider a related case, one in which we “survive” a brain transplant to only one other person, as death. Surly a brain transplant to two individuals is at least as satisfying.

The cases described in both thought experiments are imaginary, but their purpose is to serve as a warning that our notion of personal identity has problematic metaphysical baggage. Although we routinely make consistent use of personal identity in our day to day lives, it does prove problematic in certain real situations, such as that of amnesia or of brain damage.

Parfit’s applies Ockham’s razor to the notion of personal identity. Since it seems to be possible to describe our experiences without presupposing personal identity, the notion must be discarded. People do not exist apart from their components. Parfit describes the change he underwent personally as a result of discarding the notion of personal identity:

“My life seemed like a glass tunnel, through which I was moving faster every year, and at the end of which there was darkness… When I changed my view, the walls of my glass tunnel disappeared. I now live in the open air. There is still a difference between my life and the lives of other people. But the difference is less. Other people are closer. I am less concerned about the rest of my own life, and more concerned about the lives of others.”

If you find the topic of personal identity interesting you should definitely check out a follow up post on the Many Minds interpretation of Quantum Mechanics, and thought experiment. It arrives at a very similar conclusion to the one arrived by Parfit, but from a completely different perspective.

Follow the discussion on this post on Reddit and Hacker News.

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Alexander at Waterloo http://www.thoughtexperiments.net/alexander-at-waterloo/ http://www.thoughtexperiments.net/alexander-at-waterloo/#comments Sat, 08 Oct 2016 11:26:27 +0000 http://thoughtexperiments.net/?p=48505 Alexander the third of Macedon, better known as Alexander the Great, was the architect of one of the world’s largest […]

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Alexander the third of Macedon, better known as Alexander the Great, was the architect of one of the world’s largest empires, an empire he created by leading an undefeated army to victories across Persia, Syria and Egypt. By the age of 25, he had accumulated the titles of King of Macedonia, Leader of the Greeks, Pharaoh of Egypt, and “great king” of Persia. Alexander then led his army a further 11,000 miles, founding over 70 cities and creating an empire that stretched across three continents, covering an area that extended from Greece in the west, to the Danube in the north, Egypt in the south, and as far east as the Indian Punjab.

Of all his achievements, Alexander’s most notable contribution was probably the way in which he revolutionized the art of war. Consider the following from the wikipedia entry on Alexander the Great:

“He never lost a battle, despite typically being outnumbered. This was due to use of terrain, phalanx and cavalry tactics, bold strategy, and the fierce loyalty of his troops. The Macedonian phalanx, armed with the sarissa, a spear 6 metres (20 ft) long, had been developed and perfected by Philip II [Alexander’s father] through rigorous training, and Alexander used its speed and maneuverability to great effect against larger but more disparate Persian forces. Alexander also recognized the potential for disunity among his diverse army, which employed various languages and weapons. He overcame this by being personally involved in battle, in the manner of a Macedonian king.”

In his book The Origins of War, military historian Arther Ferrill comments about Alexander’s military achievements as follows:

“After Alexander warfare would never be the same. He had carried the art to a level of sophistication that would rarely be equalled and even more rarely excelled for more than 2,000 years from his own day to the age of Napoleon.”

Alexander’s main contributions, which to a  large degree built on the achievements of his father, Philip, included four main components. The first was the creation of the integrated army, which has been referred to as the integration of  ”the infantry of the West” with “the cavalry of the East”. The second development was the logistical support of such an army, which is challenging due to differences in the speed of travel and attack of infantry and cavalry units. The third major development was the  formation of an engineering corps, which enabled a much more effective form of siege than had previously been possible. The final major innovation consisted of experimentation with and improvements on an infantry formation known as the phalanx.

Ferrill has proposed an interesting thought experiment to illustrate the far-reaching influence of Alexander’s tactics over the following two millennia. He suggests that we compare the achievements of the Macedonians of Alexander with those of Napoleon’s Grand Army in the battle of Waterloo against the British army of the Duke of Wellington. According to Ferrill, the purpose of the experiment is as follows:

“The best way to appreciate the qualities of Alexander’s generalship (and of his army) is to compare him in some detail with another well known general. For this purpose I have selected Napoleon – not arbitrarily, but because the comparison has often been made, in passing, by military historians. The comparison between the two generals is not far-fetched. By the Age of Napoleon the practice of war had obviously changed in many ways since the time of Alexander, but closer examination will reveal that the changes were not as great as one might imagine, and it will also illustrate the enormous contribution of Alexander to the art of war.”

Another military historian, E.W. Marsden, notes that both commanders faced similar strategic challenges as one prepared to invade Persia and the other, Russia. In both cases, conquest of vast territories controlled by a rival empire was involved. Ultimately, Napoleon failed while Alexander succeeded.

But how valid is a comparison of two figures separated by 2,000 years of history? First, it is important to note that the thought experiment received the support of several other military historians. Furthermore, Ferrill asks his readers to make the following concession in order to make a meaningful comparison:

“I ask (…) to set aside the consideration of the psychological impact of exploding gunpowder on Alexander and his men. There is no way of knowing what that might have been, though I am prepared to concede that it would have been great.”

The concession Ferrill is asking for is an important one. In the experiment that follows, we will be pitching Alexander and his army, as they fought the Persians in 331 BC, against Wellington’s army of 1815 AD. Arguably the most significant military advancement between 331 BC and 1815 AD was the perfection of the use of gunpowder. Ferrill argues that Alexander’s skill more than compensates for his lack of gunpowder and all other military advancements so long as we ignore the psychological impact explosions would have had on Alexander’s men.

The Battle of Waterloo, which took place south of Brussels near the village of Waterloo, matched Napoleon and his 72,000 of troops against the British army of  68,000. The British army, which included Belgian, Dutch and German troops, was commanded by Arthur Wellesley, Duke of Wellington. Ferrill describes Napoleon’s strategic ambitions early on the day of the battle:

“Napoleon’s plan was to storm Wellington’s position in a series of frontal attacks, and Marshal Ney was given tactical command of the French army while Napoleon stayed in the rear with the Imperial Guard, which was to be thrown into the fighting at the decisive moment. As David Chandler says, The Emperor was seeking a quick victory of an unsophisticated type. Napoleon himself is supposed to have said that ‘in half an hour I shall cut them to pieces’.”

In terms of the scale of the battle, both in terms of troop strength and geography, nothing about Waterloo would have been unfamiliar to Alexander and the Macedonians. They had fought opponents more numerous than Wellington’s army along lines of about the same length (indeed, ancient battles were larger and more sophisticated than is generally appreciated). The following illustration shows Alexander’s line at the Battle of Issus against the Persians as an overlay to a map of the Battle of Waterloo:

Battle of Issus against the Persians as an overlay to a map of the Battle of Waterloo
Battle of Issus as an overlay to a map of the Battle of Waterloo

Napoleon was exceptionally confident victory was his, estimating the odds at nine to one. Plans were even made for his staff to have dinner in Brussels that evening. However, the day turned out badly for Napoleon, who had made two crucial mistakes. Ferrill explains the first mistake and why, in his view, Alexander would have been quite unlikely to mimic it:

“Napoleon’s first mistake was in delaying the initial attack against Wellington for so long, a mistake compounded by the fact that Prussians were coming to relieve the British. Everything we know about Alexander suggests that he would not have been so sluggish and indecisive. At the Granicus and at Issus [the two first major battles the Macedonians fought against the Persians] Alexander moved from line of column into line of battle and attacked his enemy without delay. In his other battles he always moved vigorously, once he was in tactical range, to close with the enemy. Furthermore Alexander would not have mounted an attack either with cavalry or with infantry unsupported by the other arm.”

Napoleon’s second mistake was to position himself at the rear of the troops alongside his Imperial Guard. As the battle ensued, Napoleon was unable to intervene and affect the outcome in time. As Ferril notes, however, Alexander always positioned himself at the front of the troops, often leading the charge:

“Alexander would not have stayed behind his line the way Napoleon did. Wellington and Ney exposed themselves to risks all day long. Ney went through five horses on the afternoon of the battle, but Napoleon was so far behind his line that he could not intervene in tactical operations. He is reported to have been angry when Ney organized the French cavalry for the initial charge, but the Emperor was too far away to prevent it. Although Napoleon’s presence on the field, according to Wellington, ‘was worth 40,000 men’ (a statement that could be made equally well of Alexander), at Waterloo he dissipated this effect by remaining too far to the rear. That is a mistake that Alexander could not conceivably have made.”

He concludes with regard to Napoleon’s mistakes:

“All military historians agree that Napoleon and Ney made several critical mistakes on the day of Waterloo, and we can safely assume, based on what we know of Alexander’s career, that he would not have made any of them. It is of course theoretically possible that he might have had a bad day too, just as Napoleon did, but, unlike Napoleon, Alexander never actually had such a day in his own experience.”

There remains one important factor which might theoretically distinguish Alexander’s hellenistic warfare from that of the Napoleonic era: the invention of gunpowder and the use of muskets and artillery. Ferrill examined the influence of gunpowder on the Battle of Waterloo, and concludes that it played little part in the British victory:

“Since the British troops were able to protect themselves behind the ridge selected by Wellington, French guns did little damage. On the whole artillery was not an important factor in the battle of Waterloo.

Gunpowder would have been new to him, but he had some experience in using catapults as field artillery, at somewhat less range and destructive power. In fact neither French nor British artillery proved decisive at Waterloo. The battle was determined when cavalry and infantry, singly or in combination, closed with the enemy. The big guns at Waterloo could not prevent that from happening.”

He adds on the effect British artillery would have had on Alexander and his army:

“…it is doubtful that Alexander’s army would otherwise have been decisively affected by British firepower. Although Napoleon’s forces attacked in even deeper formation than the Macedonian phalanx, and were therefore a more inviting object of attack for British artillerymen, artillery did not prevent the French from getting within twenty yards of the British line in the fateful final assault. Presumably Alexander’s troops might have done that also.”

And on the effect of musket fire:

“Likewise the infantry musket was not an especially formidable weapon. Useless at 100 yards, it had some effect at fifty, but the injunction to ‘wait until you see the whites of their eyes’ was widely applied in Napoleonic warfare, and the Guard had approached to within twenty yards before Wellington turned his own forces against it. At a distance of twenty yards the Macedonian phalanx with its thirteen-foot lances would have been a greater threat to Wellington than Napoleon’s Guards. It is of course possible that British firepower might have broken their ranks just as it did, in conjunction with a bayonet charge, against Napoleon’s Guard. But a bayonet charge against the Macedonians would have been futile. Since it took several seconds to reload a musket, and the British had only two lines of musketeers, Macedonians within a range of fifty yards or less, trained as they were to charge at the double when necessary, could have closed with devastating effect against the British infantry. Assuming that they could have withstood the initial barrage of fire in which, admittedly, they would have taken heavy losses.”

With the threat of artillery and musket fire out of the way and a leveled battlefield, the Macedonian Phalanx left to its own devices would likely to have wreaked havoc on the British troops:

“Macedonian phalangites would have been vastly superior to British infantrymen in hand-to-hand combat. Alexander’s skirmishers would have been more effective at Waterloo than they were in antiquity. Bows and slings had a longer effective range than muskets, and, since warriors of the early nineteenth century wore little armour, arrows and slingstones would have done relatively more damage. The likely performance of Macedonian cavalry against British stirrups is perhaps more debatable, but the quality of Macedonian horsemanship was high, and the Macedonian cavalry lance was a fearsome weapon, French lancers caused the British so much trouble on the field at Waterloo that in the following year the British organised their own lancer units.”

Ferrill concludes his thought experiment with the following statement:

“Whatever Alexander’s performance on the field of Waterloo might have been, he had brought warfare 2,000 years earlier to a high water mark. The Romans later made improvements in the organization of infantry, but no other ancient general made as many basic contributions to warfare as Alexander the Great.”

Whether you agree with Ferrill’s conclusion or not, the very fact that a sensible comparison of a battle fought by Alexander’s army to one fought by Napoleon’s is at all possible is a testimony to the former’s remarkable achievements. Fast forward only 100 years, and a similar comparison to battles fought during World War I seem too absurd to consider.

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Quantum Suicide http://www.thoughtexperiments.net/quantum-suicide/ http://www.thoughtexperiments.net/quantum-suicide/#comments Sat, 08 Oct 2016 01:22:44 +0000 http://thoughtexperiments.net/?p=6 Quantum Mechanics is a strange and counterintuitive theory. Dealing with the behaviour of subatomic particles, it is extremely difficult to […]

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Quantum Mechanics is a strange and counterintuitive theory. Dealing with the behaviour of subatomic particles, it is extremely difficult to reconcile with our experience of everyday life. Niels Bohr, one of the theory’s father figures, famously said, “Anyone who is not shocked by quantum theory has not understood it.”

The inherent counterintuitiveness of Quantum Mechanics has led some scientists to adopt an approach termed “shut up and calculate;” intentionally resisting the urge to attribute meaning and interpretation to the predictions of  the mathematical equations behind the theory. Others have attempted to ascribe meaning to Quantum Theory, attempts which have resulted in the multitude of interpretations prevalent today.

Quantum Suicide is a fun, quirky thought experiment that I particularly like because it makes an introspective argument, rather than an observational one, casting us, the readers, as both experimenter and experimentee.

Published independently by Hans Moravec in 1987 and Bruno Marchal in 1988, and developed further by Max Tegmark in 1998, it is the only practical experiment capable of distinguishing between the two leading interpretations of quantum mechanics: the Copenhagen (and a host of similar interpretations) and the Many-Worlds interpretations. The distinction is accomplished by means of a variation on Schrödinger’s cat thought experiment, this time from the cat’s point of view.

In classical physics, the solutions to mathematical equations that describe physical systems are specific, discrete values. For example, a planet orbiting a star has a specific measurable direction and angular momentum. On the other hand, the equations that govern quantum physics assign probabilities to the set of possible outcomes. It is only when we attempt to measure the actual state of a system that it reverts to a classical behaviour, and we obtain a discrete value. For example, a fundamental particle can spin clockwise and counterclockwise at the same time – until you look at it, at which point it definitely becomes one or the other. More precisely a quark, a fundamental particle with a property called spin, which can have values of both up and down at the same time until a measurement is made, after which it can only be one or the other, up or down. When a measurement is made and the system shifts from indeterminism to determinism it is said that the function used to describe the set of possible outcomes collapses.

This odd property of Quantum Mechanics is called Quantum Indeterminacy, which both the Copenhagen and the Many-Worlds interpretations attempt to explain.

The Copenhagen Interpretation of Quantum Mechanics (developed by Niels Bohr, Werner Heisenberg and collaborators in the 1920s) claims that observed indeterminacy (in our example, particles spinning both ways at the same time) is a statement not about the limits of measurement, but about the nature of reality — that is to say, that determined positions and velocities simply do not exist for fundamental particles before a measurement is made. Measurements select from the many possibilities and narrow them down to one. The theory claims that observing reality fundamentally changes it. Several additional interpretations are similar to the Copenhagen interpretation in that they also create a link between observervations and reality.

The Many-Worlds Interpretation (Hugh Everett, 1957), ignored for years after its appearance, states that the equations used to predict quantum phenomena continue to hold after observation is made. Every time a measurement is made, all of the possible outcomes actually occur in different branches of reality, creating a multitude of parallel worlds (one world where the particle is spinning clockwise and another where it is spinning counterclockwise).

The Many-Worlds interpretation presents a more elegant alternative to the Copenhagen Interpretation in terms of its underlying assumptions because it does not assert a relation between observer’s consciousness and reality.

A more intuitive explanation of the Many-Worlds Interpretation is provided by Andrew Zimmerman Jones and Daniel Robbins:

“The universe is continually splitting apart as every quantum question is resolved in every possible way across an immense multiverse of parallel universes.

This is one of the most unusual concepts to come out of quantum physics, but it has its own merit. Like the work of Einstein, Everett arrived at this theory in part by taking the mathematics of quantum theory and assuming it could be taken literally. If the equation shows that there are two possibilities, then why not assume that there are two possibilities?

In the case of the Schrödinger’s cat experiment, when you look inside the box, instead of something odd happening to the quantum system, you actually become part of the quantum system. You now exist in two states — one state that has found a dead cat and one state that has found a living cat.”

But how are we to determine which of the two interpretations accurately describes the world we live in? This is where the Quantum Suicide thought experiment steps in. It attempts to offer an empirical way distinguishing between the two types of interpretations.

Tegmark describes the ”Quantum Suicide Experiment” as follows:

note that this is a simplified version of the text without the mathematical proofs

“The apparatus is a “quantum gun” which each time its trigger is pulled measures the spin of a particle (particles can be spin up or spin down, seemingly at random). It is connected to a machine gun that fires a single bullet if the result is “down” and merely makes an audible click if the result is “up”.

The experimenter first places a sandbag in front of the gun and tells her assistant to pull the trigger ten times. All Quantum Mechanics interpretations predict that she will hear a seemingly random sequence of shots and duds such as “bang-click-bang-bang-bang-click-click-bang-click-click”.

She now instructs her assistant to pull the trigger ten more times and places her head in front of the barrel. This time the non Multiple World interpretations have no meaning for an observer in the dead state… and they will differ in their predictions. In interpretations where there is an explicit collapse, she will be either dead or alive after the first trigger event, so she should expect to perceive perhaps a click or two (if she is moderately lucky), then “game over”, nothing at all.

In the Multiple World Interpretation, on the other hand, the prediction is that the experimenter will hear “click” with 100% certainty. When her assistant has completed this unenviable assignment, she will have heard ten clicks, and concluded that the collapse interpretations of quantum mechanics (all but the Multiple World Interpretation) are ruled out to a confidence level of 1-0.5n ˜ 99.9% .

Note, however, that almost all instances will have her assistant perceiving that he has killed his boss.”

The experiment really only works from the point of view of the experimenter. In most worlds, there is one less experimenter, but the experimenter herself does not experience death.

In other words, the two interpretations differ in how they view the interaction between quantum phenomena and human consciousness. In the experiment above, the machine gun is triggered by a quantum phenomena, whilst the bullet hitting the experimenter’s head is equivalent to an observation made by a continuous being.

According the the Copenhagen Interpretation; when the trigger is pulled and a measurement is made, the machine gun enters a state where it is has both fired and not fired, reflecting the two possible spin value measurements, each with 50% probability (the technical term for this state is “superposition”). But because the experimenter’s head is in the flightpath of the bullet, it is in a way conducting a measurement, admittedly not in the most elegant fashion. This results in a deterministic outcome where the machine gun either has or has not fired, and the experimenter is either dead or alive. The quantum behaviour of the system is hidden from everyone, including the experimenter. All observers see a classical system in which each round results in either a live or a dead experimenter.

The Many-World interpretation differs from the point of view of the experimenter. When the trigger is pulled and a measurement is made the universe splits into two, reflecting the two possible spin value measurements, each with 50% probability. In one universe the machine gun has fired and the experimenter has died, whilst in the other she is still alive. Of course, the experimenter only lives to experience the second universe.

By repeating the experiment 10 times, the experimenter can conclude with 99.9% confidence that, since she is still alive, the Many-Worlds interpretation is true: she can repeat the experiment a greater number of times to improve her confidence. The experimenter is privileged over all other observers since only she has direct access to her own consciousness.

An interesting implication of the experiment is the notion of Quantum Immortality:

“Quantum immortality, which posits that no one ever dies, they only appear to. Whenever I might die, there will be another universe in which I still live, some quantum event (however remotely unlikely) which saves me from death. Hence, it is argued, I will never actually experience my own death, but from my own perspective will live forever, even as countless others will witness me die countless times. Life however will get very lonely, since everyone I know will eventually die (from my perspective), and it will seem I am the only one who is living forever — in fact, everyone else is living forever also, but in different universes from me.”

Another related concept is that of the Doomsday Device, described in Hans Moravec’s book Mind Children – The Future of Robot and Human Intelligence:

“Two builders of a future super (immensely expensive) particle accelerator have a problem. The machine has been completed for months, but so far has failed on each attempt to use it. The problem is not in the design but seemingly just in the designer’s bad luck. Lightning caused a power outage just at turn on, or a fuse blew, or a janitor tripped over a cable, or a little earthquake triggered an emergency cutoff; each incident was different, and apparently unrelated to the others.

But perhaps the failures are an enormous stroke of luck. New calculations suggest that the machine is powerful enough to trigger a collapse of the vacuum to a lower energy state. A cosmic explosion might radiate out at the speed of light from the accelerator’s collision point, eventually destroying the entire universe. What a close call!

Or was it? If the universe had been destroyed, there would be no one left to lament the fact. What if the many-worlds idea were correct? In some universes the machine would have worked. For all practical purposes those worlds would have ceased to exist. Only in the remainder would a pair of puzzled physicists be scratching their heads, wondering what had gone wrong this time.

Given so many nearly identical universes, the destruction of a few seams of small consequence. An idea strikes them. Why not reinforce the weak points in the machine so that a random failure within it is extremely unlikely, then wire it to a detector of a nuclear attack, like the doomsday machine in Stanley Kubrick’s film Dr. Strangelove? An attack would be met by the destruction of the offending universe. Only those universes in which the attack had not happened, for some reason (the commanding general had a heart attack, the missile launch system failed, the premier had a fit of compassion…), would live to wonder about yet another close call.

The machine in Strangelove was ineffective as a deterrent unless the other side was aware of it. Not so the many-worlds version. No attack (that anyone will notice) can occur so long as it operates, no matter how secret its existence.“

In the movie Dr. Strangelove, the Russians create a doomsday device which will render the world uninhabitable for many years if a nuclear attack is launched against them. It is an absurd yet effective deterrent, mocking the stockpiles of nuclear weapons held by the US and Russia with the aim of achieving roughly the same goals. Much like these aging stockpiles, the doomsday device only works as an effective deterrent if the other side knows it exists. The advantage of the device described in the above experiment, which destroys the known universe upon an attacked, is that the enemy does not need to know about it’s existence for it to work. Although destroying the known universe might sound like a bad idea if our objective is to survive, if the universe indeed splits into many universes at every quantum decision point, and we stay alive in at least one of them, then who cares? That’s the beauty of Quantum Indeterminacy.

A note on consciousness

Several readers pointed out on reddit and in the comments below that that the Copenhagen interpretation does not make an explicit connection between consciousness and reality. Reddit user Quoggle commented:

“People really need to stop saying that the Copenhagen interpretation implies that consciousness causes wave function collapse.”

ForgetfulPotato elaborated:

“What “observe” means is more or less “interacts with.” Does the electron hit a piece of paper? That’s an “observation” because the electron is interacting with the paper. It’s not clearly defined what requires the wavefunction to collapse (there are plenty of things that don’t cause it to collapse), but it certainly doesn’t require “consciousness.” If a photon hits film, the wavefunction collapses. It doesn’t matter if there’s any consciousness there to “observe” it, the “observation” in the QM sense is the interaction with the film.

tl/dr: observe in this case means interacts with another object in a certain way, not be watched by a person.”

Both have a point, and I should have been far more careful before stepping into the consciousness trap. But there’s a good argument that the role of consciousness in Quantum Indeterminism is far from decided. What constitutes an “observer” or an “observation” is not directly specified by the Copenhagen interpretation. Reddit user person594 replies to the above comment:

“It’s not nearly as simple as that though, and while the Copenhagen doesn’t necessarily say anything about consciousness, it certainly leaves the notion of observation much vaguer than you make it seem. You mentioned that observation is just interaction, but most interactions don’t cause quantum states to collapse. […] It seems only certain kinds of interactions cause quantum states to collapse — generally ones that would involve the state becoming entangled with a macroscopic system. The Copenhagen interpretation calls these sort of interactions measurements, but there is definitely a gap to be filled in explaining why a photon hitting a piece of film is a measurement, while a qubit entangling with its neighbor isn’t.”

PM_ME_UR_Definitions added:

“And the reason people think that consciousness causes collapse has nothing to do with a misinterpretation. There’s two good reasons to think that it’s possible that conscious observation causes collapse:

  • There’s no clear end point for what counts as an observation. One electron interacts with a proton, that’s the most basic form of an observation, but that doesn’t cause a collapse. What about a bunch of protons and neutrons and other electrons? At what number does it count as an “observation”? If there is a number/amount it should be fairly easy to determine experimentally. If an electron hits a photosensor, what’s to stop the entire photo sensor from being in superposition? Afterall, it’s just made up of particles interacting with each other.
  • Complex QM experiments. Take a delayed choice quantum eraser. Pairs of photons are interacting with a dozen or more pieces of apparatus (mirrors, beam splitters, detectors, etc.) and yet an interference pattern still shows up, which means that the photons must be in superposition will being “observed” by several non-conscious things that interact with them.”

If you find this debate interesting, or feel strongly about either position then I strongly suggest reading through the discussion on Reddit. I was amazed by the wealth of information and points of view contributed. Thanks for everyone who pointed out the oversight on my part.

There is however one perspective I’d like to add to the debate, namely the historical one. It is true that consciousness might be far to strong of an assumption regarding the nature of observers as prescribed by the Copenhagen Interpretation in light of the current understanding of Quantum Mechanics. But that may not have been the case for the scientists who first conceived that interpretation.

Heisenberg explicitly claimed that the collapse of the wavefunction takes place when the result of a measurement is registered in the mind of an observer (Physics and Philosophy, 1958):

“The transition from the ‘possible’ to the ‘actual’ takes place as soon as the interaction of the object with the measuring device, and thereby the rest of the world, has come into play; it is not connected with the act of registration of the result by the mind of the observer. The discontinuous change in the probability function, however, takes place with the act of registration, because it is the discontinuous change of our knowledge in the instant of registration that has its image in the discontinuous change of the probability function.”

Bohr on the other hand believed that it was not a question of physics, but one of philosophy or convenience (The Quantum Postulate and the Recent Development of Atomic Theory, 1928):

“Ultimately, every observation can, of course, be reduced to our sense perceptions. The circumstance, however, that in interpreting observations use has always to be made of theoretical notions entails that for every particular case it is a question of convenience at which point the concept of observation involving the quantum postulate with its inherent “irrationality” is brought in.”

The Von Neumann–Wigner interpretation explicitly claims that the consciousness of an observer is the demarcation line which precipitates collapse of the wave function. Interestingly, Hugh Everett took mathematical physics classes with the same Eugene Wigner, and was himself greatly concerned by the role consciousness played in the theory. He proposed that the problem of “conscious observers” can be simplified by noting that the most important element in an observation is the recorded information about the measurement outcome in the memory of the observer. He even proposed that human observers could be replaced by automatic measurement equipment that would achieve the same result. A measurement would occur when information is recorded by the measuring instrument (“Relative State” Formulation of Quantum Mechanics, 1957):

“As models for observers we can, if we wish, consider automatically functioning machines, possessing sensory apparatus and coupled to recording devices capable of registering past sensory data and machine configurations.”

It’s worth noting that both of the terms “Observer” and “Consciousness” are far from having a precise definition. It is therefore unlikely that the question will be decided one way or another anytime soon.

In a follow up post I discuss the Many Worlds interpretation of Quantum Mechanics, which examines the consequences of the Everett Many Worlds from the perspective of the mind. It is based on a thought experiment suggested by Everett, which again opens up the question of consciousness.

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