Tag Archives: physics

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.

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* 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 , , , .

Positive and Negative Biological Time

In my biorelativity series I used mutations per generation as a measurement of distance. However, with my recent historical/generative musings, specifically the post on the logical foundations of biorelativity (the logic of which is at the foundation of how I arrived at biorelativity), I fear I may have ignored the distinction between a mutation and an adaptation.

Consider an organism with some feature. The feature can be considered both a mutation or an adaptation depending on what the organism is being compared to. If the organism is being compared to another organism, then the feature is likely to be called a mutation. If the organism is being discussed in reference to the ecosystem, then the feature will be referred to as an adaptation.

Now I am sure that there may be some technical properties/definitions having to do with genetics or whatnot that distinguish mutation and adaptation. This is not my concern, though, because in my arguments the two can be used interchangeably.

What does concern me is that there are different sets of related concepts associated with the two words. An adaptation is, to my ear, always a positive thing. A mutation can be good or bad, e.g. mutant freak. By this line of thought adaptations are useful mutations, a subset.

Since mutation is the measurement of time and adaptation is only those mutations which are useful, then we can use adaptation to signify the forward motion of biological time (and forward change of a species as adaptations per generation) which will almost always be what people are discussing (“as time marches on, as things adapt…”). Conversely, to describe biological time going backwards, we could say something like ‘unmutating’.

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On a slightly different note it is interesting that that there is no word for adapting in the opposite direction: it’s a significant gap. Unadapting? This could imply mere stagnation; the idea here is to think of what it would mean to be adapting in a way to specifically undo previous adaptations. I think a word like this does not nor cannot meaningfully exist: the logical/grammatical structure of adaptation presupposes forward progress.

Consider, “If there were a verb meaning ‘to believe falsely’, it would not have any significant first person present indicative.” (Philosophical Investigations Part II Section x)

“The species is currently *counteradapting*” — It just makes no sense.

Posted in biology, evolution, logic, measurement, philosophy, science, time, wittgenstein. Tagged with , , , , , , , , , .

The Logic of Biological Relativity [draft]

How can we represent biological relativity in logical notation?

Organism a is adapting relative to organism b

Aab

Organism b is adapting relative to a

Aba

Organisms a and b are adapting relative to each other

Aab & Aba

This schema is unsatisfactory because it describes the situation from an indeterminate outside perspective: a and b are said to be adapting relative to each other without regard to the observer describing the situation. Relativity applies to all the perspectives in question (with special focus on any observer perspective) and hence we need a way to include the observer perspective. This means we need to take into account how the observer is adapted such that the observer(s) can be compared to the organisms in question.

To remedy this problem let quantifiers range over organisms and include witnesses to identify the specific organisms in question:

For any organism x, for any organism y, there exists an organism z and there exists an organism u such that x is adapted relative to y according to organism z, and y is adapted relative to x according to organism u.

(∀x)(∀y)(∃z)(∃u)A[xyzu]

Unfortunately this formulation is insufficient because witness z is logically dependent upon both x and y (as is u as well) and we want z to only witness x and u to only witness y: as both z and u are dependent upon both x and y, both x and y must be chosen before selecting z and u. This means that organisms x and y are selected (logically) independent of the witness organisms defeating the purpose of having those witnesses.

Getting around this difficulty is not trivial in first order logic. There is no way in first order logic to linearly order the four quantifiers such that z only depends on x and u only depends on y (Kolak & Symons p.249 [p.40 of the pdf]). Independence Friendly logic suffices though :

(∀x)(∀y)(∃z/∀y)(∃u/∀x)A[xyzu]

This statement says that for any organism x, for any organism y, there exists an organism z that does not depend on y and an organism u that does not depend on x, such that organism x as witnessed by z, and organism y as witnessed by u, are adapted relative to each other.

However, though this statement gets very close to describing biological relativity, if we consider how the witnesses witness the organisms, i.e. how z witnesses the organism x, there is a problem. By stating that z witnesses x and that z is independent of y, the statement ‘x is adapted relative to y as witnessed by z’ is nonsense: since z is independent of y it could not be a witness to ‘x adapting relative to y.’ Likewise for u.

The solution is simple enough though:

(∀x)(∀y)(∃z/∀x)(∃u/∀y)((x=z) & (y=u) & A[x,y])

By letting x=z, making z independent of x and dependent on y, z witnesses y from the perspective of x without requiring x to be chosen before z. Likewise for u: if y=u, u is logically independent of y and u is dependent on x, then u may be chosen before y, u is dependent as a witness to the choice of x and witnesses x from the perspective of y. Perhaps more prosaically: x and y are adapting relative to each other, as witnessed by organisms z and u (who have the equivalent adaptations respectively to x and y), and it is not necessary to predetermine what those adaptations are.

Posted in biology, evolution, fitness, game theory, independence friendly logic, logic, measurement, Relativity, science. Tagged with , , , , , , .

Relativity in Biology notes from 2005

It’s always interesting to see the start of ideas. Although I don’t have anything from the Spring of ’04 when I recall realizing biorelativity for the first time, I have found a file with a ‘last modified’ date of June12, ’05, the contents of which are below:

Quantum Biology

biology: the study of the physical attributes of life.

the rate of mutation is constant, much as the speed of light

organisms mutate. light shines. hence organisms bend/curve life-time as objects bend/curve space-time. greater the mass, the more the curve… the greater the inertia (momentum), the greater the curve. so what is meant by inertia in biology (or in physics)? what does mutation light, as photons light objects? [mutation is the smallest unit of life. photons smallest things with momentum.] we use mutation to view changes of a species. so if a species remains the same, its genetic(?) inertia/ momentum is remaining constant. that with the greatest inertia/ momentum creates the most gravity. that with the greatest inertia/ momentum creates biological gravitation towards itself…

space as vacuum for objects, DNA as vacuum for mutations. objects bend space; mutations do what to DNA? organisms bend life. as objects move to the speed of light their mass (apparently) goes to infinity. as organisms move to the rate of mutation (sex), their DNA (apparently) goes to infinity. as objects slow to absolute 0, their mass (apparently) disappears; as organisms cease mutation (death) the DNA (apparently) disappears. [space is a non-material object, same as concepts, numbers, words etc]

so when there is some massive change to the organism.. say when bats developed sonar, every other mutation became pulled closer around that as to become a part of it. nose, ears, face… eyes are just satellites now

we can then use the fossil history to see what was a major mutative innovation of the day- when preexisting mutations became reoriented around a new mutation (as we can see objects by the change they cause in the motion of other objects, and know their relative size)

location * momentum </= const
species * mutation </= const

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Biological General, Special and plain Relativity in both physics and biology are all confused and mixed together and I was nowhere near my current understanding of biological mass (which didn’t happen till sometime in September of this year and perhaps I’ll go through how I came to that a bit later). It looks like I used DNA for biological mass.

Still, there is a lot of good stuff here.

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

The Logic of Relativity [draft]

How can we represent relativity in logical notation?

a is moving relative to b

Mab

b is moving relative to a

Mba

a and b are moving relative to each other

Mab & Mba

This schema is unsatisfactory because it describes the situation from an indeterminate outside perspective: a and b are moving relative to each other without regard to the observer describing the situation. Relativity applies to all the perspectives in question (with special focus on any observer perspective) and hence we need a way to include the observer.

To remedy this problem let quantifiers range over perspectives and include witness individuals to identify the specific perspectives in question:

For any perspective x, for any perspective y, there exists a perspective z and there exists a perspective u such that x is moving relative to y according to witness z, and y is moving relative to x according to witness u.

(∀x)(∀y)(∃z)(∃u)M[xyzu]

Unfortunately this formulation is insufficient because witness z is logically dependent upon both x and y (as is u as well) and we want z to only witness x and u to only witness y: as both z and u are dependent upon both x and y, both x and y must be chosen before selecting z and u. This means that perspectives x and y are selected independent of the witness perspectives defeating the purpose of having those witnesses.

Getting around this difficulty is not trivial in first order logic. There is no way in first order logic to linearly order the four quantifiers such that z only depends on x and u only depends on y (Kolak & Symons p.249 [p.40 of the pdf]). Independence Friendly logic suffices though :

(∀x)(∀y)(∃z/∀y)(∃u/∀x)M[xyzu]

This statement says that for any perspective x, for any perspective y, there exists a perspective z that does not depend on y and a perspective u that does not depend on x, such that perspective x as witnessed by z, and perspective y as witnessed by u, are moving relative to each other.

However, though this statement gets very close to describing relativity, if we consider how the witnesses witness the perspectives, how z witnesses the perspective x, there is a problem. By stating that z witnesses x and that z is independent of y, the statement ‘x is moving relative to y as witnessed by z’ is nonsense: since z is independent of y it could not be a witness to ‘x moving relative to y.’ Likewise for u.

The solution is simple enough though:

(∀x)(∀y)(∃z/∀x)(∃u/∀y)((x=z) & (y=u) & M[x,y])

By letting x=z, making z independent of x and dependent on y, z witnesses y from the perspective of x without requiring x to be chosen before z. Likewise for u: if y=u, u is logically independent of y and u is dependent on x, then u may be chosen before y, u is dependent as a witness to the choice of x and witnesses x from the perspective of y. Perhaps more prosaically: x and y move relatively to each other, as witnessed by z and u (who have the equivalent perspectives, respectively to x and y), and it is not necessary to predetermine what those perspectives were.

A time variable rounds everything out nicely:

(∀t)(∀x)(∀y)(∃z/∀x)(∃u/∀y)((x=z) & (y=u) & M[t,x,y])

So, at time t (say now) let’s let u be your (the reader’s) perspective and z be my (the author’s) perspective. Then this statement describes our current motions as relative to each other because my perspective depends upon y, which is your perspective and your perspective depends on x, which is my perspective. Success!

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

Evolutionary Drift, revisited yet again

With my recent paper on Measuring Fitness I realize that my previous responses to evolutionary drift, though not incorrect, may have not stated the solution particularly clearly. When fitness is defined and measured as described in the aforementioned article, evolutionary drift is irrelevant. The method of measuring the fitness of an organism or species makes no reference to any mutations whatsoever. Therefore evolutionary drift is no problem for the theory of fitness described here.

If we are trying to identify whether a certain mutation makes an organism more fit, we can of course test it against an organism without that mutation. However if we are unable to test it (say we are studying a historical period or it is just unfeasible), then I believe my previous posts are accurate. I mainly argue that you can’t tell what exactly makes an organism more fit- it’s an underdetermination thesis of sorts – based upon our limited evolutionary perspective.

I think I just failed to say how irrelevant drift was to fitness before this.

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

Measuring Fitness

The basic premise is to measure fitness in a conceptually similar way to how we measure mass.  To measure mass we can use a scale to compare the effect of gravity on a test object to an object with an agreed upon mass, or we can compare the test object’s resistance to acceleration as compared to an object with an agreed upon mass.  These methods measure the ‘gravitational’ mass and ‘inertial mass’ respectively.

Gravitational Mass and Selection Fitness

Measuring an object’s gravitational mass requires a uniform gravitational field, e.g. the gravitational field at the surface of the earth.  The gravitational field accelerates things based upon how massive they are: the more massive an object is the greater the force that the gravitational field exerts.  To measure the mass of an object it is placed on one pan of a scale and pre-calibrated masses (objects of known mass) are placed on the other pan.  When the two pans are level the test object has an equivalent mass to the calibrated masses because they have equivalent forces being applied to them by the gravitational field.

To measure fitness we require a similar experimental setup.  First, a uniform gravitational field: according to the General Theory of Biological Relativity ecosystems create large natural selection fields.  A uniform natural selection field requires an ecosystem free from disturbances which could skew the reproductive rates of the organisms.  Secondly we would need organisms with a standard fitness.  A suitable organism would be easily clonable and of a fitness that we suspect our test organism to be near.  That organism’s fitness would be defined as one ‘biogram’ (or what you will).  Lastly we would need to see how the organisms fair in the ecosystem.  Their fitness will be proportional: if both proliferate (or die off) at the same rate, then their fitness will be equivalent, if one does much better than the other then it’s fitness will be proportionally higher.

Inertial Mass and Survival Fitness

Measuring an object’s inertial mass is measuring how resistant it is to acceleration as compared to how resistant to acceleration an object of known mass is.  To measure inertial mass the test mass is attached to a spring clamped horizontally to a stable structure.  The mass and spring are then pulled to one side and let oscillate back and forth: the more massive the object, the slower oscillations.  The number of oscillations per unit of time can be compared to the oscillations per time of a known mass and thence the inertial mass can be calculated.

As above a controlled environment and an organism whose fitness is known (even if by definition) is needed.  However the organisms need to be ‘accelerated’ for this measurement.  According to the General Theory of Biological Relativity environmental conditions will dictate how a species changes over time.  Therefore to ‘accelerate’ a species a changing environment is needed.  Simply put: measuring ‘survival fitness’ is measuring how well an organism or species fairs in a changing environment.  For example a plant that can survive in a wide range of temperatures will be fitter than one that requires a narrow temperature range.  If a test plant proliferates and the benchmark organism withers under a temperature swing, the test organism has a greater fitness.

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

NEWS: General Relativity in Evolutionary Biology Final Version and NYC Area Philosophy Mailing List started!!!!!

I’ve posted my final version of General Relativity in Evolutionary Biology to the articles section (and to GroundReport) and I’ve also started a mailing list/rss for philosophy events in NYC. So lots to check out.

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

General Relativity in Evolutionary Biology DRAFT

EDIT, July 2015:

See the full draft at the phil-sci archive: http://philsci-archive.pitt.edu/11557/

Also check out my other Research.

Below are old notes:

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I’ve discussed relativity in evolutionary biology with regards to uniform change but, as with the Special Theory of Relativity in physics, we want a theory that covers all change.

This means that insofar as relativity applies to biology under uniform motion, i.e. when a species is reproducing in a regular fashion, we want a theory of relativity that applies to biology even when a species is undergoing non-uniform motion, i.e. when the species reproductive cycle has undergone a serious change.

It is a fundamental equivalence of evolutionary biology that the struggle for survival and natural selection yield the exact same results.  This relationship has yet to be interpreted.  If we consider a person in love, financially secure and who wants nothing more than to raise children for foreseeable rest of his life.  That person may view this situation as the culmination of his struggle to survive and replicate.  That person may equally view the situation to be nature selecting him as suitable to continue life.

For what apparently are good reasons action at a distance is not allowed.  Struggle for survival does not occur at a distance; ‘struggle’ seems to inherently imply some local interaction.  Natural selection, however, is much more amorphous in nature: how exactly does nature select?  I suggest that we think of natural selection as a biofield that acts upon organisms.

Inertial ‘fitness’ and Gravitational ‘fitness’

The fitness of a thing creates a (teeny) natural selection field.  The fitness of a species creates a (small) natural selection field.  The fitness of an ecosystem creates a (large) natural selection field.

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

I just figured out general relativity for evolutionary biology

so stay posted, it’s coming soon…

Posted in biology, General Relativity, philosophy, physics, Relativity, Special Relativity. Tagged with , , , , .