Tag Archives: Relativity

Working Hard on Special Biological Relativity

I’ve been working hard on Special Biological Relativity and it is taking up most of my blogging energy.  However, I do have some fun results:

Define Biological Energy as the ability to do work, the ability to change the environment.  Then Fitness can be related to Energy because the higher the fitness the greater the ability to change the environment.

E ∝ f

If we consider an organism that lives in a place with infinite resources – a Garden of Eden – and also replicates at the speed of the chemical reaction of replication – there is no maturation process, it immediately starts to replicated as soon as it is created – then it’s life is identical to it’s replication process.  Define d to be the speed of the chemical process of replication.  Then the ability of this organism to change the environment is given by it’s fitness, the rate it replicates at and it’s life:

E = fd2

Or something.

Posted in biology, evolution, fitness, philosophy, science, Special Relativity. Tagged with , , , , , .

Special Relativistic Fitness, Preliminary Thought Experiment

Imagine two different tribes of biologists.  The first tribe is comprised of very fast people.  They survived for thousands of years by studying biology and being faster than their competitors.  The second tribe is comprised of very strong people.  They survived for thousands of years by studying biology and being stronger than their competitors.  After all this time, the first tribe is filled with very fast biologists and the second tribe is filled with very strong biologists.

Now imagine that two biologists, one from each tribe, are evaluating the fitness of two organisms.  One of the organisms is fast, the other is of average speed.  Other than the difference in speed, they are identical.  The strong biologist recognizes that one is faster than the other, but does not find this to be significant and assigns the two organisms equal fitness.  The fast biologist recognizes that one is faster and assigns it a slightly higher fitness because of its speed advantage.

Is the difference in fitness evaluations a matter of scientific opinion?  If it were an opinion that the fast organism was fitter, this would be a scientific opinion based upon environmental and competitive factors.  Given different competition and environment, the evaluation would have come out differently.  However, the fast biologist and her entire tribe have survived by being faster than their competition.  Her evaluation is not only scientifically based but also partly based upon her evolutionary heritage and Weltanschung that is finely attuned to how speed is beneficial.  It is these factors, unique to people of this tribe, that give more weight to speed as evolutionarily significant and makes it more than just a case of scientific disagreement.

Is the fast biologist unfairly biased? If we consider the perspective of the strong biologist, we can see that the strong biologist has no greater claim to her appraisal of an organism’s fitness: strength is just as arbitrary a trait as speed and this thought experiment could have equally been set up with two organisms that only differed in strength.  Hence the fast biologist could equally claim the strong biologist is unfairly biased toward strength and away from speed.  Generalizing, we can say that no one perspective, be it speed, strength, sight, etc., or any combination of traits, is privileged.  Hence their is no unfair bias because every scientific perspective based upon evolutionary heritage and an associated Weltanschung is as legitimate as any other.

Lastly, consider that every biologist will recognize the same amount of phenotypic difference between two organisms;  difference in phenotype does not permit variation in interpretation.  Therefore any difference in fitness evaluation is not due to a perceived physical difference by the biologists in the organisms studied.

Therefore this thought experiment implies that our determinations of fitness are not independent of the evolutionary history of the biologist(s) making those determinations.   Insofar as we cannot escape our own biology and how it shapes our views, it will determine the fitness value we assign to organisms, if only to a small extent.


In one sense everything on Earth has been evolving for the exact same amount of time, since the dawn of life, and hence no organism alive is any more evolved than any other.

However, from the perspective of the fast biologists, the fast organism is more evolved.  Insofar as the fast biologists believe that life is evolving towards moving faster, the organism that moves faster has adapted before the other organisms.  So, in the special circumstance of a population perceiving evolution to move regularly towards a trait, an organism with that trait can be considered more evolved.

—– the analogs —–
evolutionary significant events are specific adaptations :: physically significant events are light flashes
regular evolutionary change is a population with trait selection :: regular motion is a non-accelerating inertial frame
difference in phenotype does not permit variation in interpretation, regardless of observer :: failure of addition of velocities of light, regardless of observer.
upper limit to adaptation- by definition, no jumps :: speed of light in vacuum defined as c

Posted in biology, evolution, fitness, philosophy, Special Relativity. Tagged with , , , , , .

Deriving Natural Selection = Fitness × Acceleration

As you can see from my previous post, I now have postulated a direct relation between Natural Selection and Fitness (N.S.=F.×A.).  This relation follows from the theory.

The short short short version of the theory is this general postulate: one organism’s traits are another’s environment and vice versa.  Hence all competition can be viewed as environmental phenomena.  This gives Natural Selection as a result of Fitness and an environmental factor, which I refer to as Acceleration.

If you want to see the paper as it stands now, you can access it here or below.[6in/120mm ebook formatted]

Posted in biology, evolution, fitness, General Relativity, philosophy, physics, Relativity, science. Tagged with , , , , , , .

Rewrite of Evolution

New theory of evolution!  Hooray!

Patched a bunch of things together to make a nice story.  Fixed the little issue about fitness being circular.  Expanded natural selection to apply more generally.  Causal structure.  Epistemological foundations.  ooOoOO0Ooooooo.

And it’s good fun.  I swear.  Epistemology, history of physics, evolution… makes me happy.  You should really read it.

Download here. [pdf, 304kb]

Posted in biology, epistemology, evolution, fitness, General Relativity, measurement, philosophy, physics, Relativity, science. Tagged with , , , , , , , .

Hypotheses Natura Non Fingo

Newton famously wrote [1] [2]:

I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses…  It is enough that gravity does really exist and acts according to the laws I have explained, and that it abundantly serves to account for all the motions of celestial bodies.

as a response to those who challenged him to provide causes of gravity.  He said, “Hypotheses non fingo,” or, “I feign no hypothesis,” or if you will, “I haven’t even a guess.”

Earlier in a letter he wrote:

That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.

These passages show that Newton recognized a fundamental causal problem within his theory: that although his mathematics described gravitational physics, it did not provide a causal explanation.  It was not until General Relativity 200 years later was this problem solved.

Recently another major fundamental theory of science has been accused of lacking the proper causal structure:  Fodor & Piatelli-Palmarini’s attack on evolution, What Darwin Got Wrong.  Consider what Fodor says in his recent reply to Block and Kitcher,

A mere chronicle of instances of adaptation would not therefore amount to a theory of adaptation. It would just be “natural history.” We haven’t the slightest doubt that Darwin thought that he had discovered a theory of adaptation. It was, to be sure, a pretty thin theory, as it would have to be in order to apply to evolving creatures as such, whatever their phenotypes and whatever their ecologies.

He is saying that evolution is a mere chronicle of natural history — not a cause of it — just as Newton’s gravitation described gravity without revealing its causal structure.  Later he says,

[Biologists should] give up on the project of finding a mechanism for evolution and study the fixation of adaptive traits case by case. Since all the evidence suggests that they are extremely heterogeneous, this should keep evolutionary biologists busy well into the indefinite future.

This means that biologists should give up on repairing evolution and just try to explain individual phenomena moving forward, just as physics moved forward even as Newton knew his theory was on metaphysical shaky ground.

Hence it is Fodor now saying, “Hypotheses non fingo,”  because he believes he can describe natural history accurately, but also has no guess as to what caused things to work out the way they did.

* * * * *

In light of this analysis, consider this statement from Block and Kitcher’s counter argument:

After our critique, Fodor and Piattelli-Palmarini have apparently decided that the crucial point is the lack of a “theory” of natural selection. But, as we have noted here, nobody needs a “theory” of the type they demand.

And this from Sober’s recent review [pdf]:

What is the net gravitational force now acting on the earth?  That depends on the mass of the sun, the moon, the stars, and of everything else.  It does not follow that there are no laws of gravity, only that the laws need to have numerous placeholders.  FP may object to my analogy because it is always the mass of these various objects and their distance from the earth that are relevant to the gravitational force that the earth experiences.  My reply is that this makes no difference…

Neither has understood the argument as presented above.  If Block and Kitcher had understood, then they would have recognized that yes, for the vast majority of people, the “‘theory’ of the type they demand” is unnecessary, but it is, nevertheless, of critical importance to the likes of Newton and Einstein.  If Sober had understood, then he wouldn’t have used the worst possible example to make his point:  by saying it is “always the mass of these various objects and their distance from the earth that are relevant,” and not mentioning motion, we know he was only thinking about Newtonian Mechanics.

* * * * *

Should we, with Fodor, believe that we are stuck in a philosophical absurdity?

No.  What I said in my original criticism of Fodor, found in What Fodor Got Wrong (18 March 09),  still applies.  Though the above description of the problem is likely clearer than my analysis based on his claims that Natural Selection is statistical and that the struggle for survival is only a metaphor, the problem of causal structure is the same.  My solution focuses on using individual struggles as local interactions of Natural Selection — like a gravitational field in General Relativity — and hence provides the causal structure that Fodor wanted.

[EDIT 6 April 2010:  I’m thinking I gave Fodor too much credit in this post.  I now think his arguments amount to saying that for each instance of evolution we have, we are merely relaying natural history, not a causal explanation.  The argument I attributed to Fodor above says that evolution by natural selection is natural history.  Fodor must be more agnostic about evolution’s ontology because of how he says it is possible to look for some alternative to natural selection in his reply to Block and Kitcher.  My solution is still viable though:  since I provide causal structure, this also provides how to describe evolution in a causal way.]

Posted in biology, evolution, General Relativity, philosophy, physics, Relativity, science. Tagged with , , , , , , , .

Aristotle’s Theory of TOPOS (Place)

[This is something I wrote before I had this blog, but I really like it and hope the readers here will find it interesting.]

The task of explaining Aristotle’s theory of place lies in the interpretation of this sentence: “Hence the place of a thing is the innermost motionless boundary of what contains it,” (Physics IV 212a20).  Now the idea of a motionless boundary for perceptible and obviously movable objects seems impossibly counterintuitive.  However, using Aristotle’s comments into the nature of place, we can understand how this theory extends beyond a simple boundary theory and into the modern era.

His discussion is started by making an observation:

The existence of place is held to be obvious from the fact of mutual replacement.  Where water now is, there in turn, when water has gone out as from a vessel, air is present; and at another time another body occupies this same place.  The place is thought to be different from all other bodies which come to be in it and replace one another.  What now contains air formerly contained water, so that clearly the place or space into which and out of which they passed was something different from both. (Physics IV 208b1-8)

Aristotle then makes some tentative moves into defining what could possibly fulfill the role of place.  First he discounts any idea that place could “be body; for if it were” he says, “there would be two bodies in the same place,” (209a6) and shows how this causes untold amounts of theoretical difficulty (ibid.).  Then he discusses how, as that which “primarily contains each body” (209b1), place could be viewed as the form or the matter.  Again he discounts either of these possibilities by noting that neither of them can be separated from a thing, whereas place may be.

The analysis turns at this point asking, “How many ways one thing is said to be in another,” (210a14) in the hopes of landing upon a useful interpretation of the notion of being-in.  Aristotle entertains the idea that a thing may be in itself, or more specifically, in itself “qua itself or qua something else” (210a27).  He gives the example of a jar of wine being in itself in virtue of the whole’s description in terms of its parts: the jar of wine is not reducible to a jar or some wine, but to their specific combination.  Hence that which is a subject may potentially be a container as well, as the jar is the container of the subject ‘jar of wine’.  However, he says this is impossible as no object is actually like this: the wine would have to be an equal part container, and the jar an equal part wine, else the whole of the ‘jar of wine’ will not be completely in itself.  It is in virtue of being different that the jar and the wine may come together, and hence he concludes that, “since the vessel is no part of what is in it (what contains something primarily is different from what is contained), place could not be either the matter or the form of the thing contained,” (210b27).

Aristotle then considers two sorts of boundary theories.  First, place is such that it is “some sort of extension between the extremities,” (211b7).  However, this sort of boundary exists independently of what is bounded and is permanent.  Insofar as anything moves, the place will change, and there will be two problems generated: 1. The boundary between, for example, the wine and air moving in a jar will be exactly coincident with the boundary between the air and wine, and each of these two boundary extensions will be partially coincident but must also be unique, and 2. There will be a place at the boundary of the displaced place, and so an infinite regress of places associated with previous places will be generated.

Finally Aristotle says, “place necessarily is… the boundary of the containing body at which it is in contact with the contained body,” (212a6).  Then, interestingly, he says, “Place… is rather what is motionless,” (212a17) and then, “Hence the place of a thing is the innermost motionless boundary of what contains it,” (212a20).  So how are we to make sense of containers that give us the boundaries but also do not move?

If we take our interpretation directly from the previous discussion of boundary, Aristotle seems to have made an awfully strange claim: place is a like a container that something perfectly fits in, and yet that container cannot itself move although what is contained therein necessarily can.  However, I would like to suggest taking him at his word in regards to place being necessarily a boundary.  It is necessarily a boundary of the containing body which is in contact with the contained body, but it is not sufficient that it be the boundary that most have in mind.  What has been missed by regarding the boundary as necessary and sufficient is the incorporation of Aristotle’s primary intuition into how we know place exists.

For us to notice any motion we need something stationary relative to the thing moving such that we may observe the motion as motion.  A stationary backdrop is necessary to view change.  Consider this example: it is a common experience to be sitting in traffic next to a bus.  When the bus starts to slowly pull forward sometimes it is possible to get the sensation that you have started to move backwards.  This sensation lasts until some other fact informs you that it was not you who were retreating, but the bus advancing.  In the first instance, the place that you inhabited was defined in terms of a stationary bus: any motion that occurred was relative to that fixed point.  When you realized it was the bus, and not you, that was moving, whatever it was that informed you that you were stationary became incorporated into the place.  Perhaps you saw a building and since it was not moving your senses of place and motion were reevaluated to accommodate this new information. Hence two different places were involved in this scenario: one corresponds to your (belief of) moving backwards and the other to the forward motion of the bus.  The first place has the innermost motionless boundary [illegitimately] defined in terms of the bus [since the bus was in motion], and the second has an expanded sense of place to include something motionless relative to both you and the bus. Place, therefore, not only encapsulates that which is moving, but also whatever is observing the motion and an independently stationary object.

When Aristotle says, “First then we must understand that place would not have been inquired into, if there had not been motion with respect to place,” (211a12) he was not making an idle comment on the ‘discovery’ of the phenomenon of place.  Instead, he was beginning his analysis with the most important feature to be explained.  Galilean relativity holds fundamentally that motion can only be defined relative to some “system of coordinates” (Einstein p. 14), i.e. something motionless with respect to the moving object.  Although Aristotle did not have the benefit of Descartes’ mathematical works he still recognized the need for a reference system unique to each motion.

Now that the meaning of the ‘motionless’ criterion has been explained, what does ‘innermost’ mean if the boundary may include objects at a significant distance from the one we are describing?  The Earth is, in some sense, the place of all sublunary objects, but it is surely not the innermost boundary.  Again appealing to the exact phenomenon that Aristotle was dealing with yields the correct explanation: the motion of an object with respect to its place cannot be described by saying that the place of the thing is Earth.  Instead the innermost boundary should be the first boundary for which the description of motion and place of the thing make sense.  In the example of swirling wine in a jar (with the jar held steady but the wine still moving), the place of the wine can be said to be the jar because it describes the closest motionless boundary.  One might say that the place of the wine is equally on the table, or in someone’s hand, but both of these descriptions are related to motion other than that of wine swirling in the jar, and are really just shorthand for ‘the jar of wine is on the table, or in hand’ (consider, “The wine is on the floor,”: no swirling to be had).  The correct place of the moving bus example was the street, which could reasonably include things such as houses and other stationary objects, the most important one being the road.  Aristotle gives the ancient version of this, just before his final definition of place, in terms of the motion of a boat, such that it must be defined in terms of the whole river, which is taken as stationary (212a19).

One may think that I am being too charitable to Aristotle at this point because it may look that I have implied that the ‘innermost’ criterion of the theory will do all the work of translation between coordinate systems, which it does not seem to do.  However, Aristotle allows for the fact that we may treat a vessel such as a boat as a “transportable place” (212a14).  Hence we may allow for the things within a boat to have motion independent of a preferred fixed reference system.  This connection drawn between vessel and place gives the final aspect needed for a true relativity theory.  Historically the example of a boat on a river (212a19) is striking because Galileo uses the same example of a ship in his Dialogue Concerning the Two Chief World Systems (Salgado).


Historically Aristotle’s theory of place has been treated as a simple boundary theory coupled with a few very strange statements that were assumed to be preliminary investigations into different methods of solving blatant paradoxes (King 91).  My suspicion for why this happened is twofold.  First, philosophy of place sounds like the most dry and uninteresting subject possible and hence it was not given its due study time over the course of history (after Aristotle that is).  Secondly, the modern formulation of relativity is given according to Einstein’s theory of Special Relativity.  Insofar as this is a theory of relative motion, it is easy to overlook the fact that it applies to objects without motion, things in place.  Aristotle’s formulation is none the weaker because of the way he cast his theory, but it is much more obscure to the modern reader, as Aristotle’s relativity is developed in a somewhat inverse way with respect to modern relativity.


  • Barnes, J. ed. The Complete Works of Aristotle v.2, Princeton U. Press, Princeton 1995
  • Einstein, Albert Relativity: The Special and General Theory Lawson trans.  Pi press, NY, NY 2005
  • King, H. R., “Aristotle’s Theory of TOPOS,” Classical Quarterly #44 1950, pp. 76-96
  • Salgado, Rob “Galileo’s Parable of the Ship” http://physics.syr.edu/courses/modules/LIGHTCONE/galileo.html Accessed 2/24/06 (Link Dead) Archive.org backup, Accessed 16 December 2015.
Posted in philosophy, physics, Relativity, science. Tagged with , , , .

Time and the Limits of Science

Measurement takes time; measurement is a process.  So the measurement of time immediately yields this theoretical issue:

Since measurement takes time, our ability to break time into ever smaller pieces will always be proportional to the method of measurement used.  The faster our measurement device that measures time, the more divisible time will be.  Insofar as there are limits to how fast a measurement process can occur (relativistic or other), there will be limits on the lengths of time we can measure. From this perspective, time is discontinuous: there will be a point at which we can no longer split time into smaller pieces.

From a different perspective, time must be continuous: we can start our measurement of time whenever.  Since there are no restrictions on when our measurement may begin, each and every instant must be just as good as every other instant, hence time is continuous.

So which is it: Is time continuous or discontinuous?

Or is the question badly formed? The discontinuity argument is based upon the ideas of measurement and relativity.  The latter argument, for continuity, is based upon what might be considered a fact of modal reality.  Perhaps the two arguments are not talking about the same thing.

I can’t give an end-all be-all answer to the questions of time, but here is my opinion:   Time is continuous, but when we start to do scientific activities, time can and will only be able to be measured discretely.  Therefore the two arguments are not using one word to describe two different phenomena.

The question then becomes how doing science limits what we can observe.

This might sound like an extremely unlikely situation, but consider the case of organized sports.  When playing a sport or game you are bound, restricted, to following certain rules.  However, by following these rules, you and the other players can demonstrate skills and abilities that you otherwise would not have been able to observe:  Lots of people may be in shape, but only a small fraction of those people are professional athletes.  Those athlete demonstrate their superior physical and mental prowess by performing on the game field by being restricted by the official rules.

Getting back to science, does it now seem so unlikely that we restrict ourselves in certain ways in order to accomplish other tasks?  For time to be scientifically useful, we need to have some sort process that has a fixed point from which to start counting from, and a unit to count.  Then we can compare an unknown process to this known process, and we have done so with much success.

This comparison could not have occurred without the introduction of an arbitrary fixed point and unit of measurement: by restricting our concept of time to these particular processes we enable ourselves to perform scientific research.  Research is not possible if we use the unrestricted modal notion: no comparison can be made because there is no inter-modal process to compare a worldly (intra-modal) phenomenon to.  But with the use of fixed points, units and processes, we also become subject to relativistic limitations.  It seems like a very small price to pay considering the success of science.

To sum up: time is subject to modal considerations, which gives it special properties such as being continuous.  Once we start to do science, though, we restrict ourselves to the non-modal aspects of time, which allows us to use it as a tool in scientific research.  This also makes time appear to have different properties, but upon closer study, these properties are artifacts of the measurement process and not time itself.

Posted in measurement, ontology, philosophy, physics, Relativity, science, time. Tagged with , , , .


Readers of this blog may have noticed a lack of updates recently. I can’t apologize: I’ve been eating, breathing and drinking philosophy for so long, that now that I have written everything I wanted to write, I feel free.  I wish it on all of you. [Happy New Year Everyone!]

But this doesn’t stop me from thinking.  I was at a Christmas party  and got talking with an Indonesian economics grad student.  He was researching economic methods Indonesia could use to become treated as a major world power, such as investing in ports with international business significance.  Interesting stuff.

Unfortunately my knowledge of economics is woeful.  However, when I pressed him to explain exactly how his economics works, he used ethical terms.  This gave me the idea that economics is fundamentally based in ethics.  When economists speak of value, this use of value is not different than the value we use in ethics, only a bit more abstracted.

Money used to represent a commitment of the issuing institution to having a certain amount of a precious metal on hand.  The cash was a proxy for that metal.  Metal, of course, has no inherent value: it is just a lump of metal.  What gives a lump of metal value is its properties that people use for specific purposes, and these purposes are fulfilling the commitments we have in daily life.  Hence money is an eventual proxy for commitments.

Now, commitments are a relativistic metaphysical substance, something I have much more experience with (man that’s a funny thing to say).  Relativistic metaphysical substances can be analyzed along the general guidelines of physical relativity: there is a general theory, there is a special theory, and then there is quantum.

The forces of macroeconomics can be conceptually aligned with a general relativistic theory, and microeconomics with special relativity.  Unfortunately everyone already understands these things so there is little hope of finding some inefficiency to exploit.

What people don’t get is quantum mechanics: it is just accepted that things are weird in the quantum world.  My view is that quantum phenomena are a highly sophisticated relativistic measurement issue (yes, I have seen all the data against this view and I am still convinced).  This allows me to look in the world of economics for similar relations and, lo and behold, impulse buying fits the schema.

Impulse buying appears to unbelievably unstudied: it has 4 whole paragraphs dedicated to it in Wikipedia.  I know this isn’t the best judge of research, but other economic topics in Wikipedia seem to have textbooks written about them and impulse buying has 1 academic journal reference (about how distraction affects brand selection during an impulse buy, not exactly the underlying theory) and a reference to a ‘Natural Parenting’ magazine article.  I feel like I can declare myself an expert right now: I am the foremost leader in the economic theory of impulse buying.

I guess now that I am done with philosophy I can start a business to see if my theories are correct…. never thought I’d end up in experimental philosophy, but it just goes to show that you can never say never.

Posted in economics, philosophy, Relativity, science. Tagged with , , , .

something about time

There is something about time that I can’t seem to stop thinking about.

We measure time by agreeing upon an event and then counting from that point onward.  Today is October 17, 2008 AD.  It is this AD that keeps my attention.  It has been 2008 years, ten months and seventeen days since the birth of Jesus of Nazareth: AD stands for Anno Domini, or year of our lord.  Those not wanting to be explicitly Christian use CE, which stands for Common Era, which is just a nice way of saying the same thing without recognizing Jesus as the lord.  Wikipedia dates the use of this term to 525 AD, though this is how everyone has been measuring time forever. AD began to be used in 525, but before that people just used other events (like natural disasters, battles worn or lost, etc.) as starting points to count the date from.

The only result is that time is not universal but relative to whenever people agree to start counting from.  This is nothing new, but maybe like The Ring, if I pass it along, then it won’t bother me any more.  If you become similarly afflicted, I apologize, but you know what to do.

Posted in measurement, Relativity, science, time. Tagged with , , , .

Relativity as Informational Interdependence

Ever have the experience of sitting in traffic and believe that you are moving in reverse, only to realize a second later that you were fooled by the vehicle next to you moving forward? You were sitting still, but because you saw something moving away, you mistakenly thought you started to move in the opposite direction.

Two different senses may be at work here: your sight and your balance. Lets assume that your balance did not play any role in this little experiment (you would have been moving too slowly to feel a jolt). Your sight told you that you were moving in a certain direction (backwards) because of something you saw, say a bus pulling forward. Then you saw something other than the bus, say the ground, and you realized that your initial appraisal of the situation was incorrect.

At the point when you look away from the bus, you believe that you are moving backwards. Then when you see the ground, you believe that you are not moving backwards. You reconcile these two contradictory beliefs by deciding that it was not you who were moving backwards but the bus that was moving forwards.

What this illustrates is that objects require something other than themselves to be considered in motion. Without the ability to reference a ‘stationary’ system (the ground), it is impossible to make a determination who is moving and who is staying still.

Now imagine this situation was taking place in a very gray place. The only things visible are yourself and the bus on a gray background. Then you notice that the bus is getting smaller. There is nothing for you to use as a reference (no stars, no ground, no nothing) to decide if it is you who is moving away from the bus or if it is the bus moving away from you, or both*. The only thing you have is the information that you and the bus are moving away from each other.

I refer to the statement that you and the bus are moving away from each other as information and not a belief because it is much more certain than what I called beliefs above, namely that you were in a certain kind of motion, which quickly turned out to be questionable.

The information that you and the bus are moving away from each other is not your everyday sort of information. It would be inaccurate to reduce this statement to a conjunction (you and the bus are moving), which is incorrect, or a disjunction (you or the bus is moving) because you are only moving with regard to the bus. By claiming that either you or the bus is moving, it makes it seem that the motion of one has nothing to do with the other. The motion of you and the bus need to be mutually dependent upon each other, and a mutual interdependence is not reducible.

If we return to the everyday, we can say that you have the information that you and the bus are moving away from each other and you and the bit of ground you are on are not moving away from each other. Since the bit of ground we initially selected was arbitrary (we could have chosen anything, like another bus) it is subject to the same issues as the bus; we merely take the ground to be stationary for most purposes, but this is a pragmatic concern. Hence all determinations of motion (or non-motion) are instances of informational interdependence.

The result that relativity is part of a larger class of mutually interdependent structures is non-trivial. Minimally this formalism will allow us to specify exactly when the use of relativity is warranted, but more importantly it will allow us to identify and provide insight into other situations of informational interdependence. Cases of mutual interdependence are relatively rare as far instances of logic go (they can’t even be described in first order logic) and having such a well studied example gives us a head start on this phenomenon.

* or if the bus is shrinking, or you are growing, or all of the above, but lets assume no Alice in Wonderland scenarios.

Posted in independence friendly logic, logic, measurement, philosophy, physics, Relativity, science. Tagged with , , , .