... been put to hard trial in the past with you. ..... flask, it is the rule, ⦠at the clause N° ⦠ehm ⦠Socrates: Dont ..... mechanical horse very, very speedy. Can you.
Socratic Dialogue (aporetic) Franco Pavese V. 1.0 Reductio ad unum I Miles: Hey you, … visitors. Socrates: What a pleasant surprise, I was just annoyed to death. Simplicius: Master, why are you here in jail? Socrates: They always find an excuse to send me to jail: one day or another I will be in real danger. Sapiens: Bad guys ! Socrates: However, not all evil comes to harm. While trying to pass the time, I got an idea about a beautiful problem. If you like, I can tell you the subject matter. Simplicius: Absolutely, we are all ears., me and my friend Mercator who came with me. Mercator: For sure, and, Master, you can be certain that we will not spread around gossips against you. Sapiens: Me too I am quite interested, even if my scientific competence has already been put to hard trial in the past with you.
Miles: Hey guys, cut short … the visit time is almost expired. Socrates: Stay quiet, and listen you too, you will not get damaged by that. Today I will only illustrate the issue, so you will become interested to come again to visit me. Soon, I hope! As you certainly know, there is people stating that in our world space and time are strictly connected with each other, so much that, in order to describe the most fundamental physical phenomena completely the space tri-dimensionality is not sufficient, and time has to be added as a fourth dimension of reality, and talk about space-time.. This link is said to be estalished by the fact that the speed of light cannot be indefinitely fast. The faster is the speed of the bodies, and approaching the speed of light, the more one has to take into account space-time. In the frame of natural philosophy called mechanics, the time arrow can be directed in both directions, either toward the future or toward the past, without change of the laws of mechanics. Sapiens: That is not the case of the other branch of natural philosophy dealing with the kind of energy called heat. Socrates: Exact. Furthermore, people normally think that the natural laws are the same since the beginning of th world and will remain unchanged forever. Long since natural philosophy argues on the fascinating entity that time is, but I will not attempt any citation since, as you know, I do not like to use any. Here the issue I like to raise is our everyday experience, which seems to keep time and space definitely distinct. But, is that actually true?
Sapiens: Well, you have cited speed: this quantity places a relationship between space and time. Socrates: … and this is exactly the point: it places a relationship between two entities considered as independent with each other. We observe a space surrounding us and we notice that the time is passing independently on our will, like the grains of sand in a clessidra. If I extend my arm in that space by keeping a clessidra in my hand, I can count how many grains are falling while I sm walking, so I could get a measure of my speed in walking. However, no properties of the space depend on the elapsing of time, nor time elapses differently from yesterday, nor elapses differently here or in my home—actually here I am feeling it elapsing quite slower, but this is my sensation that, for example, our valid soldier does not share. Miles: … ah, now I understand why you have been jailed! Do not hope to confound me --- and as soon the time of the visiti will expire I will kick all you visitors off instantly. Socrates: But how you understand that the time has expired ? Miles: Simple. When the shadow of the door jamb reaches this stone it is six o’ clock, and we are almost there … Socrates: Ok, so our bald young fellow knows the secret for measuring time! Miles: well … me … ugh … Socrates: Simply, for measuring time, we need a moving object—the sun in this case— whose position in the space is measured.
Sapiens: True! It was the same with the grains of sand in the clessidra, and it would be the same for the length of a burning candle. Socrates: That is because for us life is movement or, at least, change in time of something that we can observe. Can the concept of space be more straighforward? Mercator: Sorry, Master, I need to leave you shortly for closing my shop … Socrates: I apologise, but listen, you are a merchant. When you must go to another city for business, are you interested about the specific route to follow? Mercator: Very little, it is enough that is the shortest. Socrates: This means the one requiring less time. How do you do for calculating it? Mercator: Well, I know how much time I need to reach a certain tavern on the road, and then to get the first crossroad on the way to the sea side, and so on I get the total time estimate. Socrates: So you are using in between some reference places, and you are only interested to evaluate the time you need to travel the road. But, should you sail far from the coast, or should you travel in a endless desert, how could you estimate time? Mercator: That is terrible. One counts night and hope to reach as soon as possible the end of the journey. Socrates: That means that, without reference, except the start and the end of the trip, a travel is only time.
That situation is bringing me to ask myself: would it be possible that the space is only a measure of the time elapsed, being the latter the only ingredient of the reality for the human? Sapiens: Damn, Master, this time you are hitting really hard. I have no idea from where to start thinking, and even if it is wise to do it! Simplicius: I have an instant headache in simply thinking to have to think to that! Socrates: Come on, friends, be valiant. I assume that the next time of your visit you will be able to collaborate with me for a reply. Miles: You guy will have all the time you wish in jail. You others instead please get out immediately, as I do not want to have any hassle with my officer. II Sapiens: Here we are, again empty-handed. I believe that you, Master, will have to squeeze a lot our empty heads if you hope to obtain any blood from turnips. Socrates: I appreciate that you visited me during the air time in this jail, so we will have more time for discussing together. Do you have a problemi if I am walking while talking? Simplicius: No, but not too fast, adding us strain to strain. Miles: … and do not raise dust … Socrates: Be quiet, I am not of the kind of people looking for stress without need. The previous time I have perhaps been too much vague. If I remember well, I said that, if the time
flowing outside us (and inside us) looks a mistery, also the concept of space is not made less ambiguous by the fact that we see it extending around us. First, the dimension of objects looks arbitrary, I mean the relative dimension of two objects. If you come enough close to me you are so big that I can detect the enlarged pores of you skin—not a good look! If instead you go at the bottom of this courtyeard, … yes there, I see your figure very very small and you are only tall like a dog or less than my little finger, and if you would move farer you would become like a indistiguishible stain dot. But, in future the invented telescope would allow me to make you again so big that I could count the hairs of your bear, but you could not be recognised, since neither a dot or the hairs will allow me to recognise you. When instead the microscope will be invented, each of us will become a countless—and indistinct—field of the atoms that our colleagues philosophers are telling us we are made of. Sapiens: You are right, but this is the same that everybody can see, so there is no room for mistakes or confusion. Socrates: My dear friend, surely you are convinced of that? Each of us has a different vision capability with one eye or with both eyes, some diseases and even some drugs make dramatic alterations of the vision. A fly, with its prismatic eyes certainly has a different vision. How could be made a telescope or a microscope for that fly? How many axis are needed to that fly to define space? Simplicius: I am not quite interested to understand how a fly can see the world. For me is enough to
say that we can easily check it, for example, checking the people at the bottom of this courtyard is not so small as she looks like, by approaching her. Socrates: Right, it means that we need, for the space as for the time, a dynamic experience. In other words, the only experience of space we can have is our moving into the space. However, suppose that we need to go from one place to another, travelling without any visible spatial reference, in a total empty space. Simplicius: Stop stop, Master, our friend Saccens would not like estreme examples. Would not be sufficient to cite a travel on open sea or in a desert, or in the fog like Mercator was telling us before; or in the open air like a bird? Socrates: Because, my man, we would find on the road something—water, sand, air— which could act as a reference, an Arianna thread, or where I could leave some trace, like the snail trail. On the contrary, in a fully empty space one cannot cross anything.. Sapiens: Fine, in fact one could only rely on the elapsing time. However, if the arrival place is visible, I could see it in front of me, or on the right, or on the left, or even on the back. Socrates: Yes, but that does not allow you to estimate how much time you still need to arrive, if the place keeps the same dimension, i.e. remains identical to itself. In those conditions, one could not even estimate the amount of space he is covering toward it, since he cannot measure the
space ecept be his own steps. No speed can be defined if the space cannot be measured. Even keeping the arrival place in front of us, we cannot ensure to drive the shortest track. In the mountains, for example, it may be much shorter by following a ridge than crossing a valley. Not even can we be sure that is the correct track. When throwing a dart (on the Earth), one has to point it to a ploint different from the intended target … a hunter takes the aim in front of a moving animal … a sail boat proceeds by curved trails to reach the harbor. Simplicius: Hey, please to not walk faster when you discuss more heatedly ! Let us sit down for a bit. Socrates: Do yourself what you like, but let me continue to walk in front of you … I will have a lot of time later to stand in jail and my legs will be numbing … a bad sensation. Coming back to our subject, how do you understand that you are now standing ? Sapiens: Oh simple, because being sitted we rest in the same position with respect to the things around us in the space. Socrates: Not respect to me walking … Simplicius: Exactly! When I am standing the water well in the courtyard is always there, while you are moving from us and the well. Socrates: Correct, but … wihout well how to know who moves and who is standing, me or you? In the empty space we are talking about, how can one understand if he is moving or not ? Sapiens: Hit and … sunk!
Miles: How damn it is possible that you make such a lot of dust when walking ? No shuffling, dammit ! Fortunately it is almost time for you to come back to jail. Socrates: Here you came just in time. Can you loan me for a moment one of your darts? Miles: Hey, no kidding! Why damn you need it? Socrates: We are talking among friends of certain properties of space. You, as an expert archer, certainly know how to take the aim for hitting the target with the dart. Miles: Not for bragging, but I am the best in our team. With this two-feet dart, for example, should I have to hit that tile, I need to bend the arch of one palm and a quarter, and pull the string … I know how much … Socrates: So, let me take this dart … thank you, dont worry, I will use it carefully … It has three distict properties. If I head it toward … Miles: … hey, not to me, take in another direction … Socrates: … I would have bet that you were bolder! … you, it indicates a direction. Having a tip and a tail, we can distinguish between two ways of the direction, like the two ways of the traffic in a road. Third, the dart has a length. So, if I need to move in his direction, I can indicate it by pointing the tip in this way … Miles: … somewhere else, I already told you, dammit … Socrates: … and, if I move with a certain speed, I can represent that by the length of this dart. Did you understand what I am meaning ?
Simplicius: … not so much … Socrates: Let me try again … to be clearer … now, I break … the dart in two parts … Miles: Wretch ! What you did ? It was the property of the Government ! That will cost you three days of special jail, damn to me ! Socrates: … then, if I walk at a certain speed, I might say that it is represented by half the dart. If I walk at double speed, I will double the length of the dart, joining the two halves together. Understood now? Sapiens: yes, it … Miles: Stop, PLEASE !! You run to jail instantly. Damn for letting me duped so easily. And all others get off. Socrates: My friends, I apologise … come back after the three days … and think about in the meantime. III Sapiens: Come on, let’s tap to the door, we are coming just to see the Master. Simplicius: … OK … I hope that the guy is now in good mood. Hey, open the door ! Miles: You again? Which is the purpose? Mercator: We have a flask of Samo wine for the master and … Miles: OK; come in … but I need to sequester the flask, it is the rule, … at the clause N° … ehm … Socrates: Dont care, gladily keep the flask.
My friends, please come in. I was not anymore hoping to see you today, so I was just planning to go to bed, if one can call this plank a bed. Mercator: Fortunately I had concealed this cheese. Simplicius: Let me see? What a good smell! It is a pity that there only water to chug it. Sapiens: Friends, please let us come to the reason of our visit. I am still curious to understand why the Master offered us the example of the dart. Socrates: I was in fact hoping to listen your request and present understanding. Sapiens: Clearly, Master, when talking of the properties of the space one can introduce the direction, and represent it by the dart, direction that can have two opposite ways, like the traffic on a road. This is a property that the mathematicians assign to a “vector”. Or, one instead can consider it in respect to another property, the distance, a totally different one, independent on the direction: in fact a single distance projected in all directions describes a sphere. Socrates: Bravo, but with the last statement you went too … far.. Sapiens: Why ? Socrates: The statement is correct only if the space around you in all directions is equally “dense”. Simplicius: What? … (cough) … Quick, please handle me some water … this cheese is so dry. Mercator can you tell me which herbs were used to cure this cheese ? Is very good.
Mercator: It is made by a friend. I think it contains fennel, rosemary and … I am not sure … a herb similar to parsley. But, Master, please serve yourself. Socrates: No, thanks. Like about mushrooms I am very suspicious about ingredients that I do not perfectly know: on this issue I do not like risking … so certainly I will not dye poisoned. Otherwise you risk not to know the end of this story! Dear friend, let me offer some examples. If I put a stick on water, the immersed portino of it looks shorter—also bended, but this is for another reason. Further, do you swim in water at the same speed you run in air on a road ? Sapiens: OK, but a feet length is a feet in air and in water. Socrates: Why you trivialise so the issue? Of course, but how useful is this fact if for covering that length I always need much more time in water than in air ? Here we are talking of “distance”, not of “length”. There are many other examples, some already made. The dart must follow a curved trajectory in the air because of its weight: the sail boat must proceed by jibes because of the wind; also a javelin must be hit upwind for the same reason. In all these cases, that is because in the space some “forces” act on the travelling object. Simplicius: … and if a bird needs to go from here to the bottom of the courtyard, it does not walk there, but takes the fly and then lands, needing less time than me. Sapiens: It looks like the distance between two places in the space, differently from length, is not a
property depending only on the initial and final positions, but also on the properties of the space and on the trajectory of the moving object. Socrates: In all instances, among the different distance values, there will always be one that is the shortest. Simplicius: Guys, this value is zero: if I move at infinite speed all distances will nullify! Sapiens: Not quite. Trusting on who tells us that speed cannot be indefinitely high, but has a maximum value, it comes that between any couple of places there exist a minimum distance different from zero. Actually this fact allows the concept of space to exist, I think! Simplicius: … Or the concept of time? Socrates: Yes and no. But I am now feeling tired. Do you agree to delay the rest of this discussion to tomorrow morning? Simplicius: … Speaking of the bold soldier, I am surprised that he did not show up so far, as usual … Mercator: … see why! He chugged our wine and felt sleeping … having even not finished it. Today youth has gone soft! Simplicius: Let me see ? Yes, there is still some wine. I will keep it with me to chug the rest of the cheese, very good but so dry. Let us meet tomorrow morning … not too early. IV Socrates: Come in, friends, but be careful since the my bold guard is still sleeping.
Simplicius: So why you do not think to get off from jail ? Socrates: Not at all ! Here I am protected from a lot of troubles … and from by wife. But for a short time anyway since now. Let us come back, if you agree, to our discussion and to the issue of upper limit for speed discussed yesterday evening. Sapiens: Mercator apologises for not coming today but he is on duty at the shop … Yes, please. I was saying that, should the speed able to reach infinity in value the concept of space could not exist, since we could find ourselves in any place of it at the same instant of time. Simplicius: What a plasure would be to be ubiquitous, and me, I could rest at the same time with my wife and with … I know who! And you Socrates could be at the same time here in jail and walkings in the Propileos. Actually, you would not mind the be in jail … as in any other place … mmm … it does not look so good as I was thinking before. Socrates: You see? You found yourself the reply. In all instances, I repeat, yes and no. In fact the speed is not a property of neither space and time. However, since the concept of speed places a relationship between the two it is certainly relevant to our inquiry, which basically is about whether the space IS simply time. Actually, should be determined that space is not definible since we are not able to measure it, also speed would become undefined and we could not discuss about its value, finite or infinite does not matter. However, I think that we did not advanced
enough in our discussion so far to resolve the issue, this also because we did not explore enough so far the concept of time. Simplicius: We have little to say about time, alas, except it is flowing without control, turning all instants of present into past. Sapiens: That is poetry! Instead I am asking myself if for a dog, or for a tree, or for a stone it has the same meaning. Socrates: ah, ah, my dear friend, it seems to me that you are considering for sure that time is subjective, i.e. a product of biological or natural rithms, while you denied that for space. Why? Sapiens: You are right, dear Master, I did so perhaps beacuse of the quite different way we can measure time and space. In fact, for space, when we need to measure the length of something … of this courtyard, for example, we always have the finish places available between which to place our length-measuring stick. Or, I put my foot here, close to the house wall and I can count … one, two, three, …, seven, eight steps until the fence, and I can do it any time I like … eigth, in fact, counting backward, from the time the courtyard has been built until the time it will exist, and getting the same result. With time is different. If I like to measure the time I take to drink this glass of water, I am obliged to reverse the clessidra exactly when I am starting to drink, and then I must wait until I end drinking to check it again. And that time interval could not occur before and cannot occur anymore, never.
Simplicius: I do not understand: you can refill the glass and repeat the measure again … Sapiens: Certainly, but not always there will be an ant to remove from the glass, and not necessarily I will have to loose some time for chasing the mosquito that was annoying me while drinking. The next time is another time, no repetition. More, for measuring time one must have memory of the time lapse. Some old people having lost memory, after some drinking and having lost thurst might even forget to empty the glass as initially planned … or the reverse, might refill the glass and drink again having lost memory of having already drinked. More, by looking at the clessidra in front of me, I might wonder whey it is there and think to have forgotten to store it in the closet to avoid the grandchildren to play with it. So, I actually asked if a animal, a plant or a stone can have memory, since a dog may be similar to us, but a warm, which seems going around in the grass with no apparent design, I do not think it may have. As to a tree, instead, uncapable to change place, it looks to me to have memory, by changing his ststus with time: it germinates, builds up leaves, is then loosing them. On the contrary, a stone cannot move by itself, unless it is transported by wind or rain, and only the memory of somebody else can discover in it the history of the world. Simplicius: What a beautiful description: I would not have been able to say better. However, I am afraid that I learned anything. Socrates: Actually, dear friend, pulled this morning by poetical inspiration, together with quite
interesting issues, you added several imprecise statements. Let me start from the former, in particular from memory as the wittness of time. Take the tree, that we consider a living being whose main feature is the impossibility to change location. Our natural philosophers studying them say that the trees have memory of the happenings and that they react to them. This reaction means that for them the happenings are an ordered series of events, being that, in my opinion, the meaning of memory, that is happenings subsequently in time. Many of these events come from what we are calling space. However, may a standing tree have of space the same sensation we can have of it? It seems to me that for a tree the space can only be pure elapsed time. Simplicius: How could be know, or even imagine, what a tree may think, assuming that this is possible? Socrates: You have some reasons, my dear friend, and to standing condition is not the only one inducing an alteration of the common experience of space. Take, for example a blind people, but not one like Tiresia, whose blindness came when he was already a boy and induced in him the capacity to see also future time, but a blind since birth people. He is like the tree for everything he cannot touch. On the contrary, but keeping his arms in front and proceeding by stumbling steps he can reach those objects whose existence he may only have suspected from other sensations, and touch them. Would that situation be sufficient to allow a blind people to represent in his mind a space
around him, independent on his temporal sensations and actions? Sapiens: Personally I am sure of that possibility. Who is able to move is also able to measure space. Simplicius: Also a fish in water? Socrates: Very nice case! In this case, I do not think that fishes can estimate anyting else than close or far distances. Sapiens: OK, but, Master, what can you … fish … from this example? Socrates: You made a method distinction between the measurement of time and space that I am not sure is justified. This is the reason why I asked you all to ponder those cases when time seems to determine—or replace—space. Starting from your viewpoint that time is memory, the similitude of time and space is even closer. In fact, it looks to me that also our experience of space basically depends on time. Actually it is almost a tautology, if experience means memory of past sensations or observations. I am saying ‘almost’ since, should connections between these sensations not be established—similar to what in language is called semantics— memory alone would not help in providing us what we call experience. Sapiens: If I understand correctly, you Master means that each of us builds a representation of space based on his everyday experience that accumulates tank to memory. Thus, our concept of space is founded on time. Socrates: Not only, but also the measure of space necessarily require laps of time, so involving memory of the sequence of operations.
Simplicius: Talking of memory, I only now remember, damn, that I promised my children to bring them to eat an hamburger for lunch. Socrates: Really we are so late ? Our bold guard is still sleeping! If you come back quickly we could go on before he gets awake and will bother us as usual. Simplicius: Master, do you like a hamburger too? Socrates: No, thanks. I will manage to have simply a bruschetta. Sapiens: OK, let see you soon … because, dear Master, I have several issues to argue about your arguments. V Simplicius: Voilà, back to you. But are you sure that there was not any sleeping substance in that wine? He is still sleeping! Socrates: You can reply to yourself, since you also have drunken that wine, and do not seem asleep more than usual. Sapiens: To come back to our discussion, please, while coming home I found on the way the usual things and my home too was in the usual place. And so was yesterday and will be tomorrow too, and the next days. That stability makes the concept of space independent on time. Socrates: Do you really think that it will be true in one thusand year time from now? Sapiens: By Zeus, certainly not. This would mean that the kind of space model that everybody of us can make is valid only for a speed of motion
sufficiently high, so that the stability in time can be preserved. Socrates: Furthemore, the expression "sufficiently high" can have various meanings, depending on the cases. I consider highly unlikely that it could be the same for an ant and for a bird, for an insect and for an elephant. Simplicius: … and, what happens if the world would change quicker than our expectation? It is not going to hold on only for us. How could we get a stable experience of space? Socrates: It seems to me that our friend is still thinking about his example of the fishes … Simplicius: … well, I am a staunch fisherman … Socrates: … for which all reference points around the other fishes are moving with a speed comparable with their own. I think to have noticed that they are generally unable to keep a direction for a long track, unless they make a compact swirling school of fish. In that case, the school seems to move around as a single entity, that is the space for those fishes seems to have become ordered—or have disappeared at all! The same happens in the air, for birds and their flocks, for insects and their smarms. I wonder if there is a specific fixed distance also in other cases that could cause the same effect for other objects, not only the animated ones. Sapiens: I am beginning to understand a bit your point. There is an even more extreme case, the one proposed by our atomist philosophers. If the atoms, as they say today, move parallel to each other, without never touching with each other, one
cannot say that there is any space in between them, because, never touching, they cannot have any experience of their reciprocal existence and distance. Socrates: Exactly, and I am pleased that you start appreciating my position. Anyway, should they collide, bumping in a perfectly elastic way, without being able to recognised any other single one, this fact would not generate any concept of space, being the collisions all equal and random. Simplicius: I wonder if there is a condition where also them would behave like the insects ... Socrates: There are also several other cases that do not allow for form ourselves a concept of space. We have already seen that without a change of position we cannot have experience of space, as it happens to the tree. Also a “too low” velocity of experience prevents to form the concept of space. But now I ask you: is there also an upper limit? Is it actually possible to reach infinite speed—remember it? Sapiens: Master, are you referring to which speed? The speed of the stimuli which I receive, or my own speed necessary to learn? Socrates: Why, do you see any difference? When we receive an external stimulus, can we locate it in our model of space before and independently from the fact that we are moving in order to build up our model? Sapiens: Damn, you got again me red-handed. Now I am finding again difficult to follow your reasoning.
Simplicius: Sorry, Master, how could we go at infinite speed with our short legs? I think that even Zeus cannot. Socrates: Let stay aside who has no part in our reasoning. Instead, hear … are you going at the same speed riding a horse or walking? Simplicius: Me yes, since I am always scared by the horses, but I understand that my son runs much quickier on a horse. Socrates: So you can imagine that, one day, we could move much quickier than today, as much quick as we like. I add only that, talking of speed, I am meaning moving with respect to something else. Sapiens: That something can only be those stimuli reaching us and that form our representation of the world. Socrates: … and … I cannot preceed them in time. If I do not see yet the friend, I cannot go meeting her; if I do not yet listen the question I cannot reply to it. In all instances, we have esperience of speeds much higher than the one we can run. Sapiens: Certainly, for example that of sound. However, it is too limited. For example, if I am in front of a wall distant from me, like in some large gimnasia or in the mountain gorges, and I clap my hands, the clapping sound takes sometime to come back to me. That because the clapping sound takes that time to be reflected by the distant wall. Simplicius: I played a lot, when I was a boy, to the echo effect. Could you believe that I was thinking that there was a people there in front of me, repeating my words?!
Socrates: Why, nobody was there ? Simplicius: Obviously not!!! Socrates: But you learned that only “indirectly”, by experimenting, going there—that is, moving yourself—and verifying that nobody was there. … and, you repeated the trial, and you asked others for a similar experience, to be sure not to be tricked by your ears. In other instances, in fact, the experience has been found to be a simple so-called “illusion”, as in the case when the tone of the scream of a bird very quickly running toward you seems to change. Anyway, the experience needs stability of phenomena with time, or the possibility to reproduce it unchanged at any subsequent time. Simplicius: There is another issue that I was never able to understand. If a friend from a very far distance screams something to me, I see his lips moving and spelling words that I understand (I learned reading from the lips movements) before the sound reaches my ears. For a while it seems to me to be able to predict the future! Sapiens: Rather, his voice, when it reaches you seems to come from the past. The cause of the phenomenon is the same that is responsible of the delayed echo. Simplicius: But how? I cannot get the reason. Sapiens: Consider another case, certainly familiar to you. You see the lighting far away and only after a certain time you ear a frightening noise, the thunder. Simplicius: You say that the lightening talks with the voice of the thunder ?
Sapiens: Yes. Simplicius: Bah, possibly … but the example does not match. In the latter case, it is known that the ligh can travel instantaneously, while the thunder sound takes some time. On the contrari, the my talking friend is not a luminous ray: simple stands there. Sapiens: The situation is not that one, but I could not find a good way to explain to you. Socrates: Perhaps we can use the tale of the king betting that the milk was clearer than moonlight. Do you know it ? Simplicius: Certainly, and I always loved it a lot. Socrates: So ponder about its meaning. The milk is whiter than the face of your friend, but in the dark one could not see it. What does it mean? Simplicius: Means that without light we cannot see anything. Socrates: Right, and what else ? Simplicius: … which else …?. Socrates: For example, that the face is brighter at the sunlight than at thè moonlight, and less bright at the shadow of a tree. This means the image of the face reaches my eyes, like that of a tree or of anything else, only because it reflects part of the light it receives. It is an enlightened, not a luminous one—contrarily, for example to a candle, instea is instead the same for the blind. Sapiens: In fact, the only difference between us and a blind people, who we introduced a couple of days ago, is that we can see the enlightened and luminous objects. That is the meaning of vision,
and the only way for us to have an image of our world and a concept of what we call light. Socrates: It looks to me a good standing point for today. Let us go and awake our bold soldier, also because his snoring would cover mine tonight. Simplicius: I agree, but I propose that we have fun with him. Now is just the time of yesterday when he started sliping: let us move it under the tree in the courtyard while he is still sleeping. Socrates: Good idea, friends, we will make an interesting … experiment with him. Sapiens: … What about ? … Socrates: Let you see… Simplicius: … How he is heavy … with all that armour he is dressing … Done … Sapiens: Hey, wake up ! Miles: … Uh … but … where am I? … What happened? Socrates: Probably you feel tired, as you … travelled at infinite speed! Simplicius, Sapiens: … ? Miles: me? … what … ? What damn are you saying? Socrates: Simple. We were here talking among us, and you were sitted there in the room, busy in something, when you disappeared suddenly with a big bang and then we saw you where you are now lying. Would you please tell us what has happened? Miles: I have no memory since the moment when I let those guys to come in … and … oh, damn, I do not remember anything. I do not like this situation.
I go washing my face and, when I come back, you are to be in jail and the outhers out. Simplicius: … Excuse me, Master, but what about infinite speed? Socrates: Simple. Our soldier moved of several feet but, since he was sleeping, time for him did not flow effectively …s that happened for him in a null time.. Therefore … Sapiens: Ah, ah … that is really a good tale, I must immediately go to report it to Mercator! Socrates: To see you soon, friends. Miles: … Still here ? Simplicius: Don’t worry we go, but at … our speed! Miles: But you now explain me those facts of the infinite speed, since I have to report to the captain. VI Mercator: Dear Master, I was told the full story and I found it very, very amusing. Simplicius: Instead, my mother-in-law did not understand at all but scolted me because I was late for dinner. Sapiens: We came today because it is the day you should get out of jail, in order to escort you, but I hope that we will be able to find an end to our discussion too. Socrates: I hope so, but if not now, we will have time to continue later at the gymnasium. Not at my home, where the chaos if permanent because of all my children.
Sapiens: You reached the point where we agreed that all visual stimuli, which we are interpreting as images, at the end of the day are nothing else light. Socrates: True. Let us accomodate outside. Here is too much muggy, while outside there is fresh air and a beautiful sunset. To which speed do you think that are colours reaching our eyes? Simplicius: At none: the images are simply … there! Sapiens: Nope, at best things are there. If I am standing in a dark room, for example where there is the milk bucket that I cannot no see, and somebody opens the door, I can see it suddenly. Simplicius: Just right: suddenly … immediately … means at the instant. Socrates: But, the light hittng the surface of the milk how much time it takes to come to my eyes from the two feet the bucket is far from me? Simplicius: … None! Socrates: Zero time? … Then infinite speed! Just you who found ridiculous yesterday the surprise of the bold soldier! Simplicius: But that was a joke! Miles: Pardon … a joke? Simplicius: Don’t mind … nothing important. Sapiens: Actually, Master, your reasoning is perfect. So, since we excluded that an infinite speed is possible, because it would void the concept of space … Simplicius: … or of time? … Sapiens: … we need to admit that also light travels at finite speed.
Simplicius: That’s crazy ! Means that … until light comes is … dark ? Sapiens: Yes, basically yes. Simplicius: As it comes that way, why I never perceived this fact? Sapiens: Maybe light speed is extremely fast. Socrates: … and speedier than anything else? Sapiens: Golly, this evening my brain is starting smoking. How could we imagine that when the sound is certainly much slower and we are even slower? Socrates: Not a problem. Let us imagine a mechanical horse very, very speedy. Can you imagine what happens when approacing the speed of light stimuli? Simplicius: No. Socrates: Le me explore the issue … If I move in the same directions of a stimulus, … I will reach a speed such that the relative speed equals that of the light, so I could detect its slower speed in the same way I do for detecting the echo for the sound. … Should I run even faster, I would perceive the light stimuli coming to me slower and slower: … this means that the surrounding world would look slowing down more and more, until stopping at all when I would reach the speed of light! Should I be able to run speedier than light … I would run in full dark and I could not perceive anything anymore. Simplicius: Fully crazy. Sapiens: What happens if you would travel in the opposite direction of light?
Socrates: Let’s see … in this case I would anticipate the light stimuli. Reaching the same speed of light, … I would perceive the stimulus at the same instant it forms on the enlightened object. Should I even go faster … I would remain in the dark, in other words I would preceed the enlightening! I would preceed time flow, meaning that I would be back in time … Simplicius: Master, you are lucky that nobody else listened to you, otherwise you would risk to never come out from here, being considered a fool man. Sapiens: Thus, we can conclude that it is not possible to travel faster than light. Socrates: Not for all stimuli that we think to know. Neither to reach that speed, and neither to approach it, due to the slowdown of the past world that would result from it. As to the future world, we would be able to predict it more and more. At exactly the light speed, everything stops including time. Which is you comment, Mercator? Mercator: I say that these are things for philosophers. How could them be useful to us, normal people standing with the feet on solid soil? Socrates: You may use these concepts every time you contemplate a night sky, full of stars, like tonight.. Simplicius: I only become romantic. Mercator: I use it to travel during the night. Socrates: That happens because you probably never reflected on the fact that the light form the stars takes a loto f time to reach our eyes, and that the stars are so far that that time is extremely long.
Simplicius: … that at the beginning, now we have got it completely! Sapiens: That fully depends on the way you imagine our Universe. Simplicius: I already have more and more difficulties to imagine this world, with all the difficult concepts that you are bringing in. Mercator: I imagine that the stars are stuck in the sky like the seeds in a water mellon. Sapiens: In all instances, it is likely that they are there since a so long time that their light has fully arrived from all of them, irrespective to their distance, if the Universe is there since ever. Simplicius: Just as I have already said. Sapiens: However, we should not think that everything cannot change anymore, since, once we see them we can also follow their subsequent history, though with a long delay too, like in a movie. However, since the sky is not a tapestry, but is a deep space, each star can have a distance quite different from us, so, looking at the sky, I see a different instant of the past history of the Universe at each single point of it. For us, each star is located at a different place of the time ribbon registering the history of the Universe. Socrates: Thus, the sky is, for us, a map of time. What we call space is simply the footprint of past time. Simplicius: By the way, Master, it is time now that you come out of jail, to avoid anyone to have a double thinking about. Miles: … I did not receive any order yet …
Sapiens: Ask for, please, and get it … at a light speed! Miles: You see, it is not so simple … to save money they reduced the number of chars … there is less forage for the horses … Anyway, today the offices are already closed. What’s the big deal? If not today it may be tomorrow … Sapiens: … just now, a messenger comes, late as usual! Miles: Is there anybody able to read it? Looks written in Greek. Simplicius: … Ah, that is really unbelievable. They write that Mr. Socrates, born at … etc, cannot leave the jail today because the judge, on request of … (Name cancelled) …, has started a supplement of inquiry about the possibility that the named person has publicy used words that can istigate to the contempt of common feeling that avery good citizen should have. That until new order. Sapiens: This is outrageous and unheard! Socrates: No, unfortunately it has already been heard quite often.
