A Thought Experiment with Spacetime and Simultaneity
Walter Dejonghe
Hogeschool West-Vlaanderen
Departement of Industrial Design
Most of the discussions on space and time, or spacetime, risk to remain very abstract. Space cannot be interpreted as the union of mutually excluding positions independent of what happens in it, and time cannot be interpreted as the union of mutually excluding moments independent of what happens in it. Spacetime cannot be interpreted as the union of mutually excluding events, independent of what happens in it. Space, time and spacetime however seem to be more than that what happens in it. Reality is different from “that” what we experience...
Give this hazy context, we however believe that the problematic is very close to all day reality, certainly in an industrial context of companies competing to be the best (or even to survive).
We have chosen to follow a very concrete road in this field: a thought experiment imbedded in the most common known personal pursuit of gain (or avoidance of loss). This will throw a new insight on spacetime. We will start to build the model with very well known concepts of activity distribution, planning etc... and we will end by relating this model to new concepts: the relation of simultaneity and the concept of mutually excluding states that are being developed in other papers.
The purpose of the model is to investigate what the possibilities are when people try to reduce the time it takes to carry an activity to a desired end. In the model we want to give a picture as realistic as possible. We achieve this because we give a well known ground for the reduction of the time: the personal pursuit of gain (or avoidance of loss) for an outcome that can be distributed among the agents (for example positive and negative values, yields and costs, profits and losses). In the model we will distribute the outcome inversely proportional to the time spent by the activity because we aim to investigate the possibilites of a reduction of the time spent.
To measure what happens in the model we will measure the following parameters, and these measurements are clearly defined and realistic:
· Who performs what (this easily can be measured by a local comparison of the transaction of activities: when someone has taken over, the previous agent has ended his activity).
· How much time is spent. Time is measured by any local circular process which activity runs simultaneously with the investigated activity. In this publication we sometimes will clearly state “local time”, but all uses of the word “time” is meant as “local time”. A circular process is anything with at least two mutually excluding reoccurring states. We count the amount of reoccurences of one of the states and use this number as time measurement. Local timespans are recorded at the moment of the transaction process. Transaction time is measured at the sender using the local time model. Local timespans are added up using conversions that are agreed upon (part of the model that all agents share). There is no need for a global time model. There is no need to accomodate for communication time (this is explained later).
To understand the model we have to make a distinction between activities with a goal and activities without a goal (activities with limits and without limits).
Although it is impossible to have a complete model for what we are doing, for some activities we have a model of what should be performed, or what should be the outcome or the goal of the activity. This model is available before we start the activity (and eventually (hopefully) agreed to by all collegues) and it is used during the process as measuring instrument: we compare what “should” and what “is”. Based on the difference the process is adapted (eventually held). The model of the outcome of the activity can be available during the whole process in several symbolic or conceptual forms. Their generic form is the following: with every action during the process we simultaneously experience the possibility of the outcome. Indeed, because we have that model available, we continue the process as long as the outcome is still possible, and we recognize the outcome when we do achieve it. More precisely: we recognise the outcome of an activity, when the real outcome simultaneously realises also the model of the outcome. And again: not only then; with every action in the process we simultaneously realise the model of the outcome. For example: with every action we realise the agreement we have with the others sharing the same model (for one goal there is one model recognised by all participants who execute possibly different activities with different goals to reach the common goal).
Based on a model, activities can be split up and organised between agents. This usually is done to have the activities performed by the agents with the best fit. It also could be done because it is impossible for one agent alone to perform the activity. Doing so a chain of actions is formed. An agent can start the next task in the chain only when the previous task has ended. This has to be understood as follows: it is only when an agent “takes over”, that the previous task ends. It is the responsability of both to handle and communicate the model such that this is possible.
Activities with a goal could be called economic activities.
We experience also activities not conforming to the picture already given. We experience that it is impossible to have a complete model of what we achieve when we want to achieve something. Simultaneously we always will achieve also something different, and this was not our goal. This outcome, not available during the activity, not manageable, can enhance or can destroy the outcome that was wanted. Anyhow, the activities without goal should not end (in contrast with the activities with a goal), they make that we can observe endurance, they create the context for the activities with a goal. Typical activities with an important share of this character are creations, language, communication, learning, ...
Activities without a goal could be called cultural activities.
We will show now the model at work, starting with the most simple assumptions.
We expect an activity to yield 1000.
“a” brings it to a favourable ending; “a” gains 1000.
Suppose that a needs a partner to arrive at a result: b
They agree on 2 tasks:
a spends 2 hours
b spends 3 hours
Hence: x/2 + x/3 = 1000
x = 1200
a gains 600
b gains 400
It has absolutely no sense to investigate where the yields are made. If a and b added value, but did not collaborate, there was no final yield at all, no final value to give a perspective to the local values, nothing to quantify and nothing to share. They would have performed an activity without a goal. The perspective that is provided by the final result frequently is more than the sum of locally added values (at least because always something different happens also).
Suppose that they have to make costs to arrive at a favourable ending. Suppose 1000.
It has absolutely no sense to investigate where the costs are made. If they make only costs and do not collaborate, there will be no yield at all, and costs cannot be put in perspective. The perspective that is provided by the final result frequently is more than the sum of locally made costs.
Hence:
x/2 + x/3 = -1000
x = -1200
a gains -600 (looses 600)
b gains -400 (looses 400)
In this example profits and losses are equilibrated. But in all cases: when profits and losses show a certain ratio globally, they show exactly the same ratio locally.
The model at work shows the major influence of time: the time someone is spending in the process has more direct impact for someone spending little time on the process than for someone spending more time. This means in general that when people expect a global profit that they will try to spend as less time as possible personally compared to the time others spend. They will try to achieve the personal goal of the local activity as soon as possible. When they expect a global loss, they will try to be associated with the process for a longer time. An activity without a goal does not fit yet in this image because we have something to share.
Suppose that b comes to the conclusion that he can perform very quickly some part of the task taken up (for example: he is skilled enough to make a certain choice without a lot of investigation) and that the other part could be done more quickly by c (this is known as “farming-out”). We suppose that c agrees with the expected profitable outcome, so he takes over from b and ends the undertaking.
There are 3 tasks now
a 2 hours
b 1 hour
c 3 hours
Hence: x/2 + x/1 + x/3 = 1000
x = 545.4
a gains 272.7
b gains 545.4
c gains 181.8
The same applies for costs that can be shared.
The profit/loss ration is higher for b now, with a higher ratio b has more profit, with a lower ratio b has more costs. This means: he only is incited to collaborate with others when he is convinced that this decision is one that reduces costs or increases yields.
Suppose that b realises that he can do very quickly some part of the task taken up, and that the other part could be done far more quickly by an other c. We suppose that this c agrees with the expected profitable outcome, so he takes over from b and ends the undertaking.
a 2 hours
b 1 hours
c 2 hours
The total time decreases now from 6 to 5 hours.
Hence: x/2 + x/1 + x/2 = 1000
x = 500
a gains 250
b gains 500
c gains 250
As expected, the share of b decreases, but the overall time, the time with which one enters in competition with other systems also decreases. This could mean: the group (a, b, c) has a profitable result to share, a competing group has no result, and nothing to share. As already mentioned: we want to stay as close as possible to reality: competition between groups and species is (and always has been) a major ground for trying to reduce the time that an activity takes.
In a competing environment, when actions are rewarded inversely proportional with the time spend, there is a tendency to teamwork. When actions are rewarded directly proportional with the time spend, there is a tendency to separate the agents, the fittest only counts, there is no stimulus to work on communication skills and a pressure only from outside can force agents to increase their (inter)action speed.
Let us investigate now how the (a, b, c) team could further reduce the globally spent time.
This could be done by carrefully selecting the best fit and changing the rules in the team or the team itself. Suppose that b knows that an other c is working more efficiently, but that b needs to spend more time in the communication to bring c to that point. The total time decreases further, the b time increases however.
In figures:
a 2 hours
b 1.5 hours
c 0.5 hours
Total time 4 hours only
Hence: x/2 + x/1.5 + x/0.5 = 1000
x = 315.7
a gains 157.85
b gains 210.47
c gains 631.4
Suppose that b did not care about the communication needs of that c, and decreased the time he spent on his task hoping that this would give him a higher profit. We suppose that this c agrees with the expected profitable outcome and what he gets from b, so he takes over from b.
a 2 hours
b 0.5 hours
c ... hours
This c however never comes to an end for the undertaking. Apparently the team spirit risks to get broken and the whole project is jeopardised. When there is no global result that can be shared, there is no local profit or loss and what the (a,b,c) group performed (an activity without a goal) is something completety different than the process they had in mind. The final outcome is in danger if nobody reacts. Because the three agents will share the same result (if any), they are motivated to see what happens and they could take the measures to come to an end. They do not act as individuals but as a team.
Suppose that b understands he is the agent who quickly can put more time in the process.
We distinguish now 4 tasks
a 2 hours
b 0.5 hours
b 1 hour
c 0.5 hours
A total time of 4 hours
Hence: x/2 + x/1.5 + x/0.5 = 1000
x = 315.7
a gains 157.85
b gains 210.47
c gains 631.4
Coming to a deadlock is not sanctioned automatically at the point where the process ends. Coming to a deadlock triggers the level of the internal communication.
In real life it is not always clear if the communication will succeed. A transparent structure of interaction therefore is more favourable. It is better that everybody in the team sees what happens, that there are no concrete walls making the structure less transparent. In real life we easily can observe that it is better that the agents in the group share a common culture. High performant systems will work in a very efficient communication culture and they will handle “farming-out” more effectively and efficiently. The time spent in the building up of a common culture will not end, it is not an activity with a goal, it is lasting and frequently more energy has to be put in. The result will be that the time spent for activities in the team with a goal drastically will be reduced. Teams are highly structured organisations, they are competing indirectly with each other in their use of activities without a goal for the benefit of the activities where they compete directly for a certain share. The benefits and costs of activities without a goal are not shared after the realisation of the model, but are shared in the activity itself.
Moreover, there is an other possibility to reduce the time it takes to bring the process to a favourable end.
Suppose that more tasks are performed, take 6.
a 2 hours
b 0.5 hours
c 0.25 hours
d 0.5 hours
e 0.25 hours
f 0.25 hours
The total time is 3 hours 45 minutes
Hence:
x/2 + x/0.5 + x/0.25 + x/0.5 + x/0.25 + x/0.25 = 1000
x = 60.6
a gains 30.3
b gains 121.2
c gains 242.4
d gains 121.2
e gains 242.4
f gains 242.4
When some tasks can be executed in parallel, only the tasks situated on the longest path (the critical path) will determine the time of the whole process. Hence, as long as a task is not on the critical path there is a slack related to it. We can imagine that such a task is ended only when the following task on the critical path is started, although the task could have ended earlier in reality (recall our definition of an ending task).
Suppose that three tasks (b; c + d; e) run in parallel as one block between a and f.
The longest path is a + c + d + f and takes 3 hours.
Because b and e work in parallel with c + d, the time spent can only be the sum of times by c and d: 0,75 hours
Hence:
x/2 + x/0.75 + x/0.25 + x/0.5 + x/0.75 + x/0.25 = 1000
x = 75,9
a gains 37,9
b gains 101,2
c gains 303,6
d gains 151,8
e gains 101,2
f gains 303,6
A consequence is that the tasks on the critical path will attract all attention, conformable to their influence on the total process time. People also only will try to perform tasks in parallel when possible, if it is needed to decrease the whole time the process takes. They will have to balance the global results with their own profits. They will have to understand the global context (the competition), so they will have to spend time on this.
When we envisage parallel systems within a global project, we also can envisage that with an internal competition between teams (all trying to realise simultaneously the model of the outcome) the whole system tries to find the quickest way. In a competing environment with identical models of the outcome of activities, the quickest road is the road with the highest organisation. Teams with the highest organisation are best fit.
We can easily understand that the time related to the slack (0,25 hours for b, 0,5 hours for e) is better spent in enhancing the communication in the group (cultural activity) or it can be used as free time. These activities are activities deliberated from any direct goal, they can be spent to enhance the global communication culture and are not rewarded with any outcome distributed inversely proportional to the time spent by its activity, because there is no common model. These activities will structure the group and probably make it more successfull compared to other groups.
The time spend during the slack of the process clearly shows the influence that the reduction of spent time has on activities: one has to introduce a more complex structure in the process elements. Structure is space-like as we will show in the next paragraph.
Still the time spent can be reduced further. When performing a task it is possible to perform an other task simultaneously. This is something different than “running in parallel”. When I perform two tasks simultaneously, than, with an action on the first task, I also perform an action on the second task, there is no need to take a second separate decision.
Because this can sound too abstract, we give first some physical “space-like” examples: when I move a bottle, I move simultaneously the liquid in it (what I wanted). I not only move simultaneously the liquid however, but also the air in and around it (what does not bother me, neither the movements of the liquid inside the bottle).
When I drill a hole in a plate for a shaft, I simultaneously change the free surface of the plate and I increase its temperature (what could give me problems). These ‘side-effects’ do not ‘consume’ more time. Matter seems to be organised in space. With every change (ordering in time) simultaneously a lot of other events happens. We can understand that, with an other level of organisation, other events happen.
Thus we define: two points are experienced simultaneously when, with my choice for one of them, also the other is chosen. One decision introduces other points. This means that I do not have a freedom of choice between the points any more.
If we agree that I always have a certain freedom of choice, than it follows that two points are experienced simultaneously when I have (experience) the freedom of choice between one of the points and something different from the other point. It is exactly because I have not a specific freedom of choice that there is no time spent. This limitation on a certain freedom of choices is the structure that we carry with us. It is exactly because a certain structure is available that there is no time spent.
Most of the time simultaneities are self evident and are lived unconsciously (and this is what we call “unconscious”). This is typical for winning teams: with every action the “team-spirit” is lived simultaneously, a whole context is taken into account unconsciously by every member.
We believe that we can make these simultaneities more conscious, and that we can design these simultaneities with the purpose to achieve something (for example to reduce the time it takes to carry an activity to a desired end).
To investigate this further we have introduced in other papers this definition of simultaneity in a very formal way. We argue that there is no need to make a difference between the simultaneity of intrinsically correlated points (when one point is a subcategory of another point) and the situation where one point causes another point. If “cause” implies “time”, we believe that time can be designed indeed. In this field my interest as designer is situated.