08.18.08
Posted in Idependence Friendly logic, Relativity, Special Relativity, biology, epistemology, evolution, fitness, fun, logic, measurement, mind, philosophy, physics, science, technology at 1:26 pm by nogre
I just returned from a cruise to Alaska. It is a wonderful, beautiful place. I zip-lined in a rain forest canopy, hiked above a glacier, kayaked coastal Canada and was pulled by sled-dogs. Anywho, as on many cruises, there was a casino, which is an excellent excuse for me to discuss probability.
What is probability and where does it come from? Definitions are easy enough to find. Google returns:
a measure of how likely it is that some event will occur; a number expressing the ratio of favorable cases to the whole number of cases possible …
So it’s a measure of likelihood. What’s likelihood? Google returns:
The probability of a specified outcome.
Awesome. So ‘probability as likelihood’ is non-explanatory. What about this ‘ratio of favorable cases to the whole number of cases possible’? I’m pretty wary about the word favorable. Let’s modify this definition to read:
a number expressing the ratio of certain cases to the whole number of cases possible.
Nor do I like ‘a number expressing…’ This refers to a particular probability, not probability at large, so let’s go back to using ‘measure’:
a measure of certain cases to the whole number of cases possible.
We need to be a bit more explicit about what we are measuring:
a measure of the frequency of certain cases to the whole number of cases possible.
OK. I think this isn’t that bad. When we flip a fair coin the probability is the frequency of landing on heads compared to the total cases possible, heads + tails, so 1 out of 2. Pretty good.
But notice the addition of the word fair. Where did it come from, what’s it doing there? Something is said to be fair if that thing shows no favoritism to any person or process. In terms of things that act randomly, this means that the thing acts in a consistently random way. Being consistently random means it is always random, not sometimes random and other times not random. This means that fairness has to do with the distribution of the instances of the cases we are studying. What governs this distribution?
In the case of of a coin, the shape of the coin and the conditions under which it is measured make all the difference in the distribution of heads and tails. The two sides, heads and tails, must be distinguishable, but the coin must be flipped in a way such that no one can know which side will land facing up. The shape of the coin, even with uniform mass distribution, cannot preclude this previous condition. Therefore the source of probability is the interdependence of physical conditions (shape and motion of the coin) and an epistemic notion (independence of knowledge of which side will land up). When the physical conditions and our knowledge of the conditions are dependent upon each other then the situation becomes probabilistic because the conditions preclude our knowing the exact outcome of the situation.
It is now time to recall that people cheat at gambling all the time. A trio of people in March 2004 used a computer and lasers to successfully predict the decaying orbit of a ball spinning on a roulette wheel (and walked out with £1.3 million). This indicates that after a certain point it is possible to predict the outcome of a coin flipping or a roulette ball spinning, so the dependence mentioned above is eventually broken. However this is only possible once the coin is flipping or the roulette ball is rolling, not before the person releases the roulette ball or flips the coin.
With the suggestion that it is the person that determines the outcome we can expand the physical-epistemic dependence to an physical-epistemic-performative one. If I know that I, nor anyone else, can predict the outcome until after I perform a task, then the knowledge of the outcome is dependent upon how I perform that task.
This makes sense because magicians and scam artists train themselves to be able to perform tasks like shuffling and dealing cards in ways that most of us think is random but are not. The rest of us believe that there is a dependence between the physical setup and the outcome that precludes knowing the results, but this is merely an illusion that is exploited.
What about instances in which special training or equipment is unavailable; can we guarantee everyone’s ability to measure the thing in question to be equal? We can: light. Anyone who can see at all sees light that is indistinguishable from the light everyone else sees: it has no haecceity.
This lack of distinguishability, lack of haecceity (thisness), is not merely a property of the photon but a physical characteristic of humans. We have no biology that can distinguish one photon from another of equivalent wavelength. To distinguish something we have to use a smaller feature of the thing to tell it apart from its compatriots. Since we cannot see anything smaller, this is impossible. Nor is there a technology that we could use to augment our abilities: for us to have a technology that would see something smaller than a photon would require us to know that the technology interacted at a deeper level with reality than photons do. But we cannot know that because we are physically limited to using the photon as our minimal measurement device. The act of sight is foundational: we cannot see anything smaller than a photon nor can anything smaller exist in our world.
The way we perceive photons will always be inherently distributed because of this too. We cannot uniquely identify a single photon, and hence we can’t come back and measure the properties of a photon we have previously studied. Therefore the best we will be able to accomplish when studying photons is to measure a group of photons and use a distribution of their properties, making photons inherently probabilistic. Since the act of seeing light is a biological feature of humans, we all have equal epistemological footing in this instance. This means that the epistemic dependence mentioned above can be ignored because it adds nothing to the current discussion. Therefore we can eliminate the epistemic notion from our above dependence, reducing it to a physical-performative interdependence.
Since it is a historical/ evolutionary accident that the photon is the smallest object we can perceive, the photon really is not fundamental to this discussion. Therefore, the interdependence of the physical properties of the smallest things we can perceive and our inherent inability to tell them apart is a source of probability in nature.
This is a source of natural randomness as well: once we know the probability of some property that we cannot measure directly, the lack of haecceity means that we will not be able to predict when we will measure an individual with said property. Therefore the order in which we measure the property will inherently be random. [Assume the contradiction: the order in which we measure the property is not random, but follows some pattern. Then there exists some underlying structure that governs the appearance of the property. However, since we are already at the limit of what can be measured, no such thing can exist. Hence the order in which we measure the property is random.]
————–
If I were Wittgenstein I might have said:
Consider a situation in which someone asks, “How much light could you see?” Perhaps a detective is asking a hostage about where he was held. But then the answer is, “I didn’t look.” —— And this would make no sense.
hmmmm…. I did really mean to get back to gambling.
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07.29.08
Posted in Idependence Friendly logic, Relativity, logic, measurement, philosophy, physics, science at 8:40 pm by nogre
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.
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04.26.08
Posted in Idependence Friendly logic, Relativity, fun, game theory, internet, logic, philosophy at 2:59 pm by nogre
I picked up Dependence Logic: A New Approach to Independence Friendly Logic by Jouko Väänänen. I figure I’ll write up a review when I am finished with the book, but there is one chief difference between Dependence Logic and Independence Friendly Logic that needs to be mentioned.
On pages 44-47 when describing the difference between Dependence Logic and Independence Friendly Logic Väänänen says,
The backslashed quantifier,
∃xn\{xi0,…,xim-1}φ,
introduced in ref. [20], with the intuitive meaning:
“there exists xn, depending only on xi0,…,xim-1, such that φ,”
…
The slashed quantifier,
∃xn/{xi0,…,xim-1}φ,
used in ref. [21] has the following intuitive meaning:
“there exists xn, independently of xi0,…,xim-1, such that φ,”
which we take to mean
“there exists xn, depending only on variables other than xi0,…,xim-1, such that φ,”
The backslashed quantifier notation is part of what Väänänen calls ‘Dependence Friendly Logic’, and is equivalent to the ‘Dependence Logic’ that the rest of the book expounds. This backslash notation makes the difference between Dependence (Friendly) Logic and Independence Friendly Logic clear by showing that the former logic takes the notion of dependence to be fundamental whereas the latter takes independence to be fundamental. Väänänen takes this to be an advantage because he says that Dependence Logic avoids making
one ha[ve] to decide whether “other variable” refers to other variables actually appearing in a formula ?, or to other variables in the domain…
However, this treatment misses an important philosophical difference between Independence Friendly Logic and Dependence Logic. Dependence Logic is fundamentally based upon Wilfrid Hodges work, ‘Compositional Semantics for a language of imperfect information’ in Logic Journal of the IGPL (5:4 1997) 539-563, in which Hodges lays out a compositional semantics for languages such as Independence Friendly Logic using sets of assignments instead of individual assignments to determine satisfaction (T or F). Väänänen infers that Independence Friendly logic is just a bit unruly when it comes to specifying variables because he is working within a system that assumes sets of assignments are a useful and unproblematic way to determine satisfaction.
However the unseen problem of using sets of assignments is that something is added by assuming the domain is a set. For example, let’s take try to define a location and take the set of all the points in the universe. However, we immediately run into relativity: All locations are defined relative to each other and the people trying to figure out where things are, i.e. There is no predetermined set of all the points in the universe. The issue is that the domain of potential assignments, the objects in the universe, may be dependent upon the person or people using them (the players of the semantic game in this case). If the domain is dependent upon the players, the set cannot be constructed until after the players have begun the game. Therefore, if we postulate that the domain is a set at the outset then the players know something about the game that they are playing, namely that it does not depend upon them because it was predetermined.
Following this line of thought it seems possible to constructed a game in which the domain {Abelard, Eloise} is such that Abelard and Eloise are the actual people playing the game and the formula is ‘Someone x lost the game by instantiating this formula’ such that whoever instantiated that formula would win the game according to the rules. But then the formula would not be satisfied, so that player would have lost, but then it would be satisfied, a paradox. It is easy enough to declare that the domain must be independent of the players, but again this signals something about the game being played to the players before the formula to be is revealed.
Lastly there is something to be said about using logic to represent natural language here too: if you consider the set of all possible responses to some question, you are not ever considering all possible responses, but all the possible responses you can think of at that time. Therefore if we are using game semantics and imperfect information to represent natural language, then it is a mistake to predetermine the domain of all possible responses separate from the people involved. Again, the domain being linked to the people involved is at odds with the domain being a predetermined set.
Long story short, there is a very good reason for not always using sets of assignments to determine satisfaction. Depending on the situation, a set may offer non-trivial information about a game or misconstrue the game being played. Independence Friendly logic makes no assumptions about the type of game being played and is therefore of greater scope than logics that are based upon Hodges work. Of course one is free to use sets of assignments to determine satisfaction and derive set-theoretic results, but the compositionality gained comes at the price of limiting the types of games that can be played.
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02.06.08
Posted in Relativity, logic, philosophy at 7:49 pm by nogre
Apropos my earlier rant on people who think that paradoxes are meaningless, I figured I ought to take a stab at giving some meaning to paradox. To this end I reformulated a paradox in my terms. I suppose I should called it the Mirror Paradox, though ‘Looking-Glass Paradox’ seems more lyrical and has an historical nod. My apologies to whoever actually came up with this first, though I am sure I haven’t heard it before…
In my room I have a full length mirror. If I look at the man in the mirror and point to him saying, “There I am!” then where am I? If I am the man on the other side of the mirror, then I am not sitting on this side of the mirror. However, the man on the other side of the mirror has just pointed at me and said that he is not on his side of the mirror, but on mine. So I am not on my side, nor is he on his side. But then neither of us are on our side or on our mirror self side.
Now with semantic paradoxes and the like, we don’t have an agreed upon framework for analyzing what is going on in a paradox. Many times it is a paradox that signals that some such theory is unsatisfactory. However, this paradox deals with locations of people, namely me and mirror me, and we do have a general consensus on judging objects’ locations: in physics we determine some object’s location with reference to some previously agreed upon location.
Let us ignore for the moment that mirrors do not actually open up into other dimensions that you could enter if only your reflection didn’t get in the way. All that is important is that we have an exact double of yourself that at the instant you declare that you are where he or she is, that person does the exact same thing.
Declaring your location relative to your reflection is no different than declaring your location relative to anything else. Your reflection simultaneously declaring its location relative you is likewise unproblematic on its own. However, since the two non-identical perspectives are associated with only one person, we have a disconnect between perspectives and the person who holds the perspectives.
This problem of perspective is most telling. In Russell’s Paradox, there is no problem, no obvious contradiction that is, until the question “Is this set self-membered?” has been asked and answered twice. The first time through is arbitrary, let us assume no: Russell’s set is not part of itself. Now we ask, “If it is not self-membered, then is this set not self-membered?” Now we answer yes and have arrived at a contradiction. There is no problem yet, we merely have to revise our assumption: let us assume that Russell’s set is included in itself. Of course, then we ask, “If it is self-memberd, then is this set not self-membered?” and our answer is no: contradiction. At this point the paradox exists, but not before. It required us to look at the one set from two perspectives, one in which it is self-membered and one in which it is not.
The comparison of assumptions and perspectives that is drawn here is a good one. Our perspective, in a different sense, is our background assumptions. When we have contradictory perspectives on a subject we have incompatible background assumptions. The Mirror Paradox pulls our background assumption of location out of the background. We all assume that one perspective is associated with one location, but when you declare that you are someplace else and your reflection does the same, then you end up with two perspectives.
We can’t tell before hand whether we can have more than one perspective or a set that is defined by non-self-membership. Therefore, since the problem occurs with the selection of assumptions or perspective, the meaning of paradoxes, semantic or otherwise, is that your fundamental background assumptions are problematic. Sure, each paradox will only pertain to that particular system that it exists in, but for that system it will signal the most important and deep underlying problems.
———————————-
A side note: I thought of this while in bed last night and didn’t look at a mirror until this afternoon, even though I do have that full length mirror. Then I actually did point and say “There I am!” It was a bit of a strange experience because for some fraction of time I felt like me and my mirror self were in some sort of vortex with the rest of the world frozen outside. Almost needless to say I was a bit surprised if not shocked- I wasn’t expecting a reaction. When philosophy grabs you, even for an instant, it is spooky. I suggest you try this and see if you have the same reaction if only because I don’t think there are other paradoxes to actually participate in, save becoming a very methodological barber. How often do you get to participate in an experiment that isn’t prefaced by ‘thought’? Between the small mirror in my bathroom and my full length mirror, the full length elicited a better reaction, so use a full length one if you can.
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01.29.08
Posted in Relativity, logic, metaphysics, mind, ontology, philosophy, religion, science, wittgenstein at 12:16 am by nogre
I didn’t think I’d be able to write this at all and I am still surprised now. It was only a few weeks ago that I had believed that it could be up to three years before anything would have been started. That said, I can’t speak much for the quality of the work. My own naiveté and lack of scholarship leads me to think that better people have long dismissed the few ideas that I have presented here. Still, in my defense, what I do present is what I sincerely believe and if there is nothing new here, then I at least have accomplished stating with whom I agree.
Writing this has made me feel more free than perhaps anything else in my life. All criticism is welcome.
Metaphysics 1
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Posted in Relativity, metaphysics, mind, philosophy, religion, science, wittgenstein at 12:07 am by nogre
1 Ontology
1.1 The Cogito
“… I must finally conclude that the proposition, I am, I exist, is necessarily true whenever it is put forward by me or conceived in my mind.” - R.D.
There are three things most should agree upon1
in light of this statement:
- When something is put forward or conceived, it is not possible to deny that something is doing the putting forward or conceiving.
- When something is put forward or conceived, it is not possible to deny that putting forward or conceiving exists.
- When something is put forward or conceived, it is not possible to deny that there is something put forward or conceived.
Simply put, there are things that conceive which I will refer to as consciousness, there is the subject of the consciousness which I will refer to as matter, and there is how consciousness describes the matter, which I will refer to as description. These are the three things that exist upon reflection, always.
1.2 Substance
“If the true is what is grounded, then the ground is not true, nor yet false.” - L.W.2
To analyze consciousness, matter and description, the analysis must be done in terms at least as fundamental as consciousness, matter or description. The only things as fundamental as consciousness, matter or description are consciousness, matter and description: these three are the only things that cannot be denied.
One option remaining is to analyze consciousness, matter and description in terms of each other. However, analysis of fundamental things in terms of each other leads to unexpected results. If matter and description are studied as functions of consciousness, then consciousness becomes neither describable nor indescribable and neither material nor immaterial. If matter and consciousness are regarded as descriptions, then description is neither alive nor dead and is neither material nor immaterial. If consciousness and description are functions of matter, then matter is neither alive nor dead and is neither describable nor indescribable. Therefore it is not possible to treat one of the three as more fundamental than the others without severe consequences.
In light of the results of the above discussion, all three are to be understood equally as substance. The three substances are consciousness, matter and description.
2 Explanation
With no one fundamental substance how is explanation possible?
2.1 Relativity
Relativity means there is no preferential perspective for the description of natural phenomena: each of us has a location as good as everyone else’s when it comes to describing the physical world. Relativity is applicable to substance as well: there is no preferential ontological perspective for substance and hence any understanding of substance is a legitimate place to begin analysis of substance. Anyone may consider the arguments from Section 1 regardless of prior ontological commitments.
Though I believe substance relativity to be self evident, a few words of support may be given. Consider the case if it were not true, i.e. there were preferential ontological situations, access to certain substances, that enabled those with access to have special insight to the mysteries of the world. People without this special access would have no way to gain it unless they were somehow given access by someone who had it; it would be undiscoverable. However, since we are investigating that which is common to everyone, as stated in Section 1.1, this is not the case and hence substance is relative.
2.2 Perspective
Relativity also means that the onlooker’s perspective has to be taken into account when describing natural phenomena: motion means motion relative to the agent describing the situation. When studying substance no one is free of ontological commitments and these need to be accounted for (just as any motion of the onlooker needs to be accounted for in physics). At any given point it is possible to be looking at a situation from the perspective of consciousness, matter or description.
For example take the question, “Does the sun shine?” From the perspective of consciousness, the answer is no: the sun is not conscious and hence it doesn’t do anything. From the perspective of matter the answer is yes: the ball of matter called the sun radiates photons, and radiating photons is shining. From the perspective of description the answer is possibly sometimes: when the sun is conceived of as shining, then it is shines.3
Whichever of the three ontological commitments is being appealed to will dictate the answer or explanation received. No one is beholden to any particular substance and can change ontological commitments in an instant, as long as the requirements of Section 1.2 are met, which does mean that there may be more than one `correct’ answer for a given question. This does not mean that all the answers are equal: saying `If you say it does,’ may be technically correct from the descriptive perspective, but many times only an answer from the other perspectives is accepted (or advised).
3 Instances
In physics, motions and locations are determined by perspective; what is determined by perspective in substance?
3.1 Commitment
As mentioned in the previous section ontological commitment determines what the explanation or answer that is given to a question. Making a commitment is an activity that only a conscious thing can do. Moreover:
- If something is put forward or conceived, then something committed to putting that thing forward or conceiving it.
If this is false, then something was put forward and nothing committed to putting that thing forward; it was put forward or conceived without some conscious thing committing to having done so. If this was done without the commitment of the conscious thing, then it was not put forward: only conscious things can put things forward or conceive of things. Therefore all conscious things that put forward or conceive of things make commitments.
Commitments and perspective are relative to each other: perspective depends upon what commitments are held, and perspective determines what those commitments are. For example if I am committed to one person then my perspective on other people will no longer include those people for a variety of activities. If my perspective is that monogamy is unrealistic, then a commitment to one person is likewise unrealistic.
3.2 Things
The things that exist are determined by perspective too. Depending upon available information and theory, different perspectives on what sort of things make up this world can be presented. Life, death, dogs, personality, atoms, words, food, pain, etc. Whatever can be put forth as a subject of the consciousness is a thing. No thing is `wrong’ in the sense that it is the subject of a consciousness.
Things and perspective are relative to each other: perspective determines what sort of things populate the world, and the things that populate the world determine perspective. Until the discovery of the subatomic particle, many people believed that the atom was the smallest building block of the universe. The discovery of a new kind of thing forced people to change their perspective on what the universe was made of. Conversely, if I have had a few too many unexplainable experiences then my perspective might allow for things like ghosts without me ever having witnessed one.
3.3 Meaning
The meanings of our descriptions are determined by perspective. You can pick your own examples of the meaning of a sentence meaning something different depending on perspective, but Rodney Dangerfield provides classics:
A girl phoned me the other day and said… Come on over, there’s nobody home. I went over. Nobody was home.
Rodney’s perspective caused him to believe the sentence to mean something other than the literal meaning, which was exactly what the girl intended. Conversely, if a rosy picture is painted, then this description is meant to determine the perspective taken on the situation.
Meaning and perspective are relative to each other: perspective determines what descriptions mean and what our descriptions mean determine our perspectives.
Footnotes:
1The statement, “Something happened or something did not happen,” is also always true. If people object to the use of the Cogito, perhaps this sentence will provide a sufficient alternative. Other tautologies (It’s raining or it is not raining) introduce something new (rain) and hence are not as fundamental.
2Wittgenstein, L. On Certainty #205
3“Will the Giants win the Superbowl?” Consciousness and matter are silent. This question asks what you can conceive and hence is purely descriptive. Unfortunately it is looking like this is as likely as conceiving a round square. Go Eli!
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12.24.07
Posted in Relativity, metaphysics, ontology, philosophy at 1:58 pm by nogre
There is no preferential ontological perspective. I hope your new year is awesome.
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12.05.07
Posted in Idependence Friendly logic, Relativity, biology, evolution, fitness, game theory, logic, measurement, science at 7:57 pm by nogre
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.
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12.04.07
Posted in General Relativity, Relativity, Special Relativity, biology, evolution, fitness, measurement, philosophy, physics, science at 8:22 pm by nogre
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
——————-
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.
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11.26.07
Posted in Idependence Friendly logic, Relativity, game theory, logic, measurement, physics, science at 2:22 pm by nogre
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!
——————————
- Daniel Kolak and John Symons, “The Results are In: The Scope and Import of Hintikka’s Philosophy[PDF],” Quantifiers, Questions and Quantum Physics, in Daniel Kolak and John Symons, eds., Quantifiers, Questions, and Quantum Physics, Dordrecht, The Netherlands: Springer 2004 pp. 205-268 ISBN 1-4020-3210-2
- To see a (distant) predecessor to this paper, see my “Discourse, Perspectival and Public Identifications, and Tautology“
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