Essay Abstract
In this short essay, I propose to explore the relationship between physics and mathematics using components of the information theory.
Author Bio
I am passionate about insights. In my professional life, I am designing supply chain solutions. I graduated in European Logistics Management.
The Kolmogorov complexity principle is what makes fractals so useful in transmitting information, describing nature. It also means the operation of nature in our scale applies at all scales - see my essay. I use trees use of energy.
You said fractal is useful transmitting information. I think it is close to the opposite, it is an open discussion ;-)
Fractals are one information duplicated in every dimension; it is poor in terms of information. That's why they can be reduced.
If you say: e = the generic information of the fractal. Then you decide to derivate the fractal on it (it is a little bit abstract because I take complex information (e) as referential).
You get: d(e) = 0
(sorry for my poor math formalism)
Similarly, a line in a one dimension environment is a fractal.
Dear Mr Fisher,
Thanks for commenting on my essay. I think your remark is interesting though I disagree with you on some points.
You raise the point that the world is real and should be easy to understand, not an abstraction.
I have a slightly different view of it. For example: if you look in a direction, you can see objects that are close to you (ex: a table) and you also see objects that are far from you (the countryside). You do not see them in the same way: the table is clear and obvious while the countryside details are fuzzy and more difficult to distinguish.
I might be wrong but I believe "understanding" can be compared to a sense. From an evolutionary perspective, we humans may have developed this ability to perceive nature/our environment through another way. At first, our understandings were weak, fuzzy, black or white, but as this sense developed, our ability to perceive our environment became richer, varied and even colorful though it is still a long way to the deepness of visual perception.
Looking through this angle, there is not one simple reality but an environment that we explore. Some objects are simple to understand, even chimpanzee can understand, while others are more difficult to distinguish. That is why I emphasized in my essay that objects are contextual and the smarter the perception, the more angles we can find to see the same object.
One can aim to enrich its perception, don't you think? Of course, one can perfectly have a happy and fulfilling life without going abstract.
Regards,
Christophe
Dear Christophe,
It is physically impossible to see a complete real object. One can only see a plethora of real surfaces no matter in which direction one looks. One does not see a complete nearby table. One sees the part of the real surface of the table top and part of the real surface of the objects on the table that are facing you, and part of the real surface of the walls and ceiling of the room that the table is in, and part of the real surface of the floor, and part of the real surface of a faraway vista if the room has a window.
Joe
Dear Sir,
Your statement that "mathematical models are applicable to physical objects when the information variance between the two is null" is important because validity of a physical statement is judged by its correspondence to reality and mathematics is a quantitative description of Nature. Further, measurement is a process of comparison between similars. This implies not "switching arbitrarily any variables in a model". Reducing to lower complexity is possible only where there is (part) similarity. When the similarities are non-linear, it can be long. The apparent randomness would depend on the pattern of non-linearity - the degree of complexity determines the length of chains.
Your second example is not related to complexity, but to interaction potential. The child is interested only on the objects trying to fit the triangle into the triangle slot, because, as you say, the bright colors have interaction potential for him.
Your statement that "objects that we perceive are contextual", brings in the concept of mind or its equivalent with memory playing an important role. We may look without seeing, because our mind is elsewhere. The equation is not valid to prove context because it does not have a physical resemblance, whereas all contextual perceptions/operations are related to memory of earlier perception or programming. Transitivity is the degree of interaction potential.
Subject to one exception explained above, we enjoyed your very well written essay. You are welcome to read our essay.
Regards,
basudeba
Dear Sir,
We clarify our statement: "all contextual perceptions/operations are related to memory of earlier perception" in the above post. Let us take the example of a dragon - a snake like creature that breathes fire. We know about snakes, fires, breathing and know the mechanism of breathing. But the special relation between them is non-existent, which makes the creature non-existent physically (at here-now). We see many such things in dream, where the constraints of the physical world are not present. But they are physically not possible. That relationship is zero, though the components are true and physical. The computers cannot dream. This is a difference that has to be kept in mind while designing memcomputers.
Regards,
basudeba
Dear Basudeba,
Thank you for your comment. By context, I mean that there is information defining the object outside the object itself.
In physical science, the standard process is to dissociate the object from its environment to analyze it. For example, we analyze the speed of a car by comparing the object "car" from the object "road" and we exclude everything that is around them. Science has clearly shown that this approach is highly efficient.
This dissociation can be difficult to make or impossible. For example, in social science, objects are interacting with their environments making the dissociation difficult to do. Additionally, dissociating an object from its environment is an arbitrary decision that we make. Clearly, it is efficient but that does not mean that we are not losing information in the process.
Regards,
Christophe
My last sentence was badly written, please replace:
"Clearly, it is efficient but that does not mean that we are not losing information in the process."
by
"Clearly, it is efficient but we could be losing information in the process."
Dear Sir,
While essentially agreeing with your views, we would like to put the language differently, as your language can be misleading. In our essay this year, we have defined language as the transposition of information to another system's CPU or mind by signals or sounds using energy (self communication is perception). The transposition may relate to a fixed object/information. It can be used in different domains and different contexts or require modifications in prescribed manner depending upon the context. Since mathematics follows these rules, it is also a language, but it talks of only quantitative aspect of Nature. You are welcome to read it and comment.
In our essay: "INFORMATION HIDES IN THE GLARE OF REALITY http://fqxi.org/community/forum/topic/1776" published on May 31, 2013, we had discussed this subject elaborately. Perception is the processing of the result of measurements of different but related fields of something with some stored data to convey a combined form "it is like that", where "it" refers to an object (constituted of bits) and "that" refers to a concept signified by the object (self-contained representation). Measurement returns restricted information related to only one field at a time. To understand all aspects, we have to take multiple readings of all aspects. Hence in addition to encryption (language phrased in terms of algorithms executed on certain computing machines - sequence of symbols), compression (quantification and reduction of complexity - grammar) and data transmission (sound, signals), there is a necessity of mixing information (mass of text, volume of intermediate data, time over which such process will be executed) related to different aspects (readings generated from different fields), with a common code (data structure - strings) to bring it to a format "it is like that".
Obviously, as you have said, there is information defining the object outside the object itself. That is information, but it is related to the object through similarity. The description of your example is not appropriate. While analyzing the speed of a car, we do not compare the object 'car' with the object 'road' and exclude everything that is around them. We measure the interval between two events (position of car on different points on the road). This interval is compared with a standard interval (standard unit) and generalized over the total duration to get speed of the car. Everything is interdependent and interconnected with everything else in one way or the other. Thus, as you say, dissociating something from others "can be difficult to make or impossible". Whenever we do that, we must be "losing information in the process". But then information must be real, which corresponds to provable options that are knowable and describable using language. A computer can only compare, but cannot "know". If can obey commands to transmit information, but it cannot utilize language to transpose information to another system's CPU or mind.
Regards,
basudeba
Hello Christophe,
Thanks for sharing your perspective of things through your essay. You dwell on mathematical relationships in your essay so let me ask:
Does 1 2 = 3, have a very high probability of being correct or is it a certainty?
Since you like new insights to consider, I speculate that it is not a certainty that 1 2 = 3 but a very, very, very high probability, with the probability increasing with the size of the object being counted and reducing with the size of the object.
In other words, 1 house 2 houses = 3 houses is more likely to be correct than 1 electron = 2 electrons = 3 electrons.
As I discuss in my essay, it is more likely for an electron to perish than for a whole house during the process of counting to determine the sum total.
Regards,
Akinbo
I meant 1 electron 2 electrons = 3 electrons
Hello Akinbo,
Your question is interesting. In my view, if 1 and 2 are completely independent, it is a certainty that 1 2 = 3. The condition is independence.
Now, you highlight that the nano world do not follow the same rules as the macro world. Experiments seem to validate but why?
I do not know. We can easily see that the distance between 2 houses is longer than the distance between 2 electrons so the degree of independence is higher? The issue with this approach is that distance is not transcendental so there is something more to understand.
I will come back to you if ideas come up. It is not an easy subject!
Regards,
Christophe
Your experimental thoughts shows that its more conditional subjectively.
Best of luck!
Respectfully,
Miss. Sujatha Jagannathan
Dear Joe,
Agreed. You see the surface of a table, then you walk around the table and see the other side of the table, another surface. From there, you create a mental picture of a table. Do you agree with this statement?
I can continue but we first need to agree on this.
Regards,
Christophe
Dear Christophe,
Your ideas on contextually, transitivity and complexity are undoubtedly interesting, and as you say, should be developed further. After reading your essay we understand better your comments on our essay. We agree that decontextualisation is important and relevant for an experimental physicist too - it is something we have implicitly assumed in our essay, but yes a careful examination of this process is called for [from everyday life events to an actual experiment...deciding what experiment to perform]. For instance, if we make the observation "A beautiful bird is sitting on a tree" , a physicist would decontextualise/abstract to first drop the adjective beautiful, and reduce the observation to the prosaic "An object is resting on a surface". And ask as to what are the forces responsible for this equilibrium. A mathematician / biologist / poet would decontextualise differently from a physicist.
We tend to agree with "sufficiently decontextualised as to be transitive" as a good starting point to make the physics - maths connection.
Best regards,
Anshu, Tejinder
Dear Mr. Tournayre,
I thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.
I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.
All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.
Joe Fisher
