We do know that over the last century the 'mathematization' of physics has taken on completely different proportions and has been accompanied by the loss of the 'physical' intelligibility. To some extent, a number of prominent physicists (including Einstein, Schrodinger, and Bell) have sounded an alarm, but of course to no avail: the price of the required change is too high for physicists.
Yet, I suggest that, paradoxically, the strength of modern physics has exposed its weakness: most of the 'physical' that is left has been reduced to the numeric. (We don't really know what mass, energy, charge, spin, etc. are, except for their numeric interrelationships.)
Thus, in my opinion, the most important scientific question becomes this: Since numbers, triangles, rectangles, etc. don't exist in nature, shouldn't we look for something else that might exist in nature and which might become the basis of our new understanding?
I propose that a good candidate for such entity is an appropriately introduced formal concept of "event", but not as it is presently (numerically) treated in physics. Do the structured events, in contrast to numbers, exist as "real" entities and should they replace the numbers as the *basis* of our new informational understanding of nature? Certainly, the particle physics does support this view.
http://www.cs.unb.ca/~goldfarb/FQXi_5.pdf
I do not believe, I'm dealing with science;)
You have yet to answer the question does your theory satisfy the Popper's falsifiability criterion or not (think about your "unobservable events").
"Physics really gone crazy with their inquiries to experiment!
Another thing, the mathematics that need only pencils and erasers.
And even better philosophers, and they do not need erasers." ;)
"Do the events, in contrast to numbers, exist as real entities ... ?"
What events? A wave is real? An electron is real?
I think that all branches of physics deal with models of the Nature that are checked by scientific method. Those models are mathematical models in most cases.
Once we accept that the Nature is out of our minds and we only are able to understand models (Plato's cave), then the question is (in my opinion) if some day would be new mathematical and/or physical models to explain new aspects of the Nature. I think the answer is yes: Neither Mathematics nor Physics will be ever concluded.
I support the view of Mr. Carriegos. Everything we talk about are models. So we may ask if a sort of "event" models may be created to understand the nature. My answer is "yes", there is a hope. I will invite a colleague who can discuss event-based models in detail, to join the discussion.
That is the main point: when we use numeric forms of data representation we must rely on models in this weak sense, but, I suggest, with the switch to events, we would be dealing with the models in a much stronger sense. It is expected that such events are, in a way, mirror copies of the "actual" events.
The main point of this discussion has to do with this.
In science, we have been spoiled into thinking that there is, basically, only one (numeric) way of recording scientifically useful information, and all other ways are reducible to it. There is some flirting with other forms of data representation in computer science (and AI)---e.g. strings and graphs---but those are not really taken seriously as rivals of the numeric representations.
However, I have been motivated for most of my working life (since the 1980s) by a different hypothesis that there is such a thing as a structural representation and it is fundamentally different than the numeric one, meaning that what it captures cannot be captured by the latter.
What are your thoughts on this?
First of all, it would be useful to provide some example.
On the other hand I'm a mathematician and your post suggest some kind of anti-cartesian point of view; that is to say, you are trying to find "something" out of Cartesian coordinates, "something" intrinsic to the problems. Am I right?
In Geometry you might be interested in Synthetic geometry as the branch of geometry using synthetic observations to draw conclusions, as opposed to analytic geometry based on algebra. This theory is of XIX century (I think) and one of main references is Jakob Steiner.
Finally, a (typical) joke: If you drop off coordinates and measures then geometry is transformed into topology where you cannot distinguish your cup of coffee from your donut. Perhaps this is fine for you, but you ought to be sure of what is your problem and your base assumptions (axioms) before performing Coordinate-free thinking.
Dear M.V.,
I'm not just "suggesting some kind of anti-Cartesian point of view". I'm suggesting that we might be at the threshold of a new scientific era---superseding the previous one that lasted several millennia---in which numbers will play not the dominant but an auxiliary role.
For a simple, *illustrative* example see pp. 61-67 of a popular exposition in http://www.cs.unb.ca/~goldfarb/BOOK.pdf
Hi Lev, to better understand your point of view: what do you think of Wolfram's "A new kind of science", and less dramatically of an explanatory attitude consisting in constructional asserts definable (only or mainly) in terms of algorithms or rules?
Your question provokes unorthodoxy, and I'd follow that suggesting that "theory" means ethimologically "sequence", "succession" (of facts, concepts, ideas), so in the name itself it is imbued with the concept of ordered appearance of events, thus ultimately with causality and time. If I had to start with a radical new view, I would question time and causality.
Hi Massimo,
Wolfram does not really deal with the issue of object representation. Also. by themselves, algorithms and rules should not be considered as adequate object/process representations.
The issues of causality and time are derivative ones wrt the issue of representation. I.e. their nature would be elucidated once the issue of representation is resolved. Indeed, in the case of proposed by us ETS representation, time and causality are embedded in it.
Here is a simple illustration of why the event-based explanation, even for a classical law, is both simpler and more meaningful than the conventional physical explanation.
Let's consider, for example, Kepler's second law. Its general version states that the regions swept out by the radius vector of a mass point moving in a central force field in equal time intervals have equal areas. Newton's proof of it can be found, for example in http://www.math.ku.edu/~lerner/m500f09/NewtonKepler.pdf .
Now, if we assume that the force is realized as a sequence of the corresponding events between the two mass points, where each event is associated with a unit of time, then the second law becomes self-evident, since the area is paved with the events, so that the units of the area correspond to the units of time..
Hi Lev,
Maybe I am wrong, but it seems to me that your event-based explanation is part of process philosophy:
http://plato.stanford.edu/entries/process-philosophy/
Dear Lev,
You are absolutly right, the best candidate for such entity is the "event", but this is the very-very-very old idea:
"An event is always a co∼being". Mikhail Bakhtin, 1920.
"Both mind and matter are merely convenient ways of organizing (grouping) events". Bertrand Russell, 1928.
"An event is a set of elementary outcomes". Andrew Kolmogorov, 1933.
"Matter waves are probability amplitudes associated with the occurrence of an event". Max Born, 1926.
"Mind arises there and then, where and when the ability to make a probabilistic choice of an event comes". Vladimir Lefebvre, 2001.
However, until very recently (including your book), this idea has existed only as a philosophical idea.
Only the discovery of a new mathematical event-language called eventology (the theory of events, O.Yu.Vorobyev, 2007) gives hope to give a new impetus to the development on its basis, both natural and human sciences.
Happy & healthy 2014!
Daniel, I have about a shelf of books on process philosophy: the idea is OK but some of it, like Whitehead's, is obscure. The important point is that the various forms of process philosophy do not lead at all to the productive scientific formalism.
Oleg, of course the idea of event, as the idea of information, are quite popular, but words do not make science. ;--) The point of the discussion is that we need the formalism in which the event is treated not as a numeric but "structural" entity.
Hi Lev, happy new year!
For me, this philosophy uses the formalism of logic, which is non numeric. Whether it is possible to use another type of formalism which would be helpful, I can't tell.
Lev,
Mathematics makes science and math is not only the numbers but also the sets. Without mathematics spells about structural entities are an empty phrase.
Eventology is a mathematical language of events. Without mathematical event-language to say something worthwhile about the events is unlikely to succeed.
Oleg,
Do you see the basic edifice of mathematics as based on sets to be unchallenged? I do not.
But in general, such discussions without focus on the formal nature of the new proposal are a waist of time.
Dear Lev,
You are absolutely right.
To make a meaningful discussion you need to start with a mathematical definition of what you want to discuss.
Since this was given as a beautiful philosophical formula, like every philosophical formula, is very far from reality.
Mathematics uses both numbers and sets.
If you want to offer something different, give a mathematical definition of the terms through the numbers and sets.
Other building mathematical blocks we do not have.
"Structural" entity? What is it mathematically?
Number? Not.
Set? Not.
At first give a mathematical definition of this.
Numerical representation in physics:
*Lev, I agree with your assertions concerning physics; theoretical physics is currently at level of mathematical complexity that it negates all physical intuition; why biology is better ;). However, sorry to say this, physics from the beginning has always been mathematical oriented, now math is just really complex.
*First Problem: Physics is equations; just ask any physicist, seriously. Any framework for physical analysis utilize in understanding motion, for example, without equation is useless for investigating physical phenomena in the lab or in industry; particular for any device or system that depends on these equations.
*The physicists you mentioned, Einstein ect, I highly doubt would be in favor of physical understanding apart from equations. Einstein-"politics are only a matter of present concern, an equation is forever."
For biological sciences, numerical data is almost a most:
(1)Numerical representation allows for accurate comparison of data between labs; reproducing experiments/verification of results.
(2) Many cases with laboratory data requires quantification, not comparison analysis.
(3) Numbers represents the easiest communication pathway for scientist to see results.
(4) Not sure how statistical tests would work for happiness.
Non numeric representation works well in non science disciplines.
*My biggest concern is that efforts to change numerical representation of data in science would be too much and would not provide that much more utility honestly.
Might it be possible that, rather than each of these areas (Wolfram, Lev G., Topology, Equations) competing to be the 'Next Science' - that all are needed?
We need a formal method of representing structural events, which change. These representations and the changes involved are based upon programs with (possibly simple) rules. These have geometric representations that also can have equations associated with them.
Feynman diagrams come to mind as a possible starting point (without enough event information). Also object-oriented programming comes to mind, where objects have structural 'interiors' and states leading to events.
Here is a proposed event to simulate:
A billiard ball hitting another ball on a table. This event is on the earth revolving around the sun, which moves in the Milky Way galaxy. Also part of this event are all the 'interior' structural parts, such as wood and plastic particles, molecules, atoms, & quarks.
We need tools that can handle this entire range of scale as an event. Somehow, current numeric measurements at any one level of scale seem woefully inadequate to this task.
Oleg:
" "Structural" entity? What is it mathematically?
Number? Not.
Set? Not.
At first give a mathematical definition of this."
Sure, see sections 3 & 4 of this (main) paper
http://www.cs.unb.ca/~goldfarb/ETSbook/ETS6.pdf .
=================================================
Michael,
Some of your concerns are dealt with in the first chapter of
http://www.cs.unb.ca/~goldfarb/BOOK.pdf
You are still missing the point that I'm proposing to switch from the motion/force/field oriented view of reality to the new informational one. Of course, eventually they have to merge but this point is still quite away.
By the way, biology, as is the formalism we are proposing, are class-based. And it is this class-based view of reality that is being proposed (informational version of the Plato's and Aristotle's views). So as in biological perception, classes of objects/processes take precedence over equations.
==================================================
Donald,
The various levels and stages in the representation of reality are very naturally dealt with in parts III & IV of the main paper http://www.cs.unb.ca/~goldfarb/ETSbook/ETS6.pdf .
To pick up the notion of "event" in Heidegger it appears as "Ereignis" and means something that is arising and appearing (as in organic development). Given the biologization of physics here proposed, there is plenty of philosophical justification.
Nelson,
I am quite aware of the rising role of "events" in philosophy: http://www.pdcnet.org/pages/Products/electronic/eventsbib.htm
But I do believe that we have proposed a simple and at the same time more general *formal* concept of an event as a transformation, which transforms several input (informational) "processes" into several output "processes". See for example Fig. 1.6 on p. 17 in http://www.cs.unb.ca/~goldfarb/BOOK.pdf .
Lev,
This is not only revolutionary, but it is clear. I congratulate you.
Lev,
Until I see only 13 pages of complex text
("Sure, see sections 3 & 4 of this (main) paper
http://www.cs.unb.ca/~goldfarb/ETSbook/ETS6.pdf ."),
but I do not see the mathematical definition of the event.
Could you explain this with a simple example.
Take a coin toss (this is an event without a doubt)
and describe it in terms of your 13-page definition.
Oleg,, I want to suggest that you will not get the proposed concept of event relying on the familiar to you examples.
A non-formal intro is in section 4 of http://www.cs.unb.ca/~goldfarb/BOOK.pdf
and a simple illustrative example is in section 2.9. of the same (starts on p. 62)
Lev,
Unfortunately, I could not find in your book this classic example.
Hmmm... It is very strange.
In other words, toss the dice is not an event in your understanding?
Did I understand correctly?
Oleg,
Tossing a die is a "struct" (in the ETS terminology).
Certainly, it is a complex stream of events.
Lev:
I agree with the direction and need for structural formalisms - especially for a unification of structural and measured methods.
The difficulty I see, which Oleg seems to also be getting at, is with identifying a single event. I believe you will need to define your classes from a particular perspective and within a limited scope of application - in particular limiting 'global' (or 'universal') aspects of that event. This makes the classes relative to the perspective of the person identifying them (and questions being asked) and not inherent in the natural world.
Take the coin toss event. Not only is there a coin in motion relative to, say, a football field, but there are metal structures (and flaws) in the coin. The coin is made up of metal (possibly alloy) molecules and atoms. All these internal objects have a generative 'history' to them (consider the metal flaws) and most are also in motion relative to the coin. So too is the football field spinning on the surface of the earth moving around the sun, moving through the Milky Way and with the local super cluster. What about possible neutrinos or comic rays passing through the coin (as part of its generative past)?
There is another aspect of reality that current science implicitly avoids due to limitations of number-based methods - that of scale. Concerning an 'event' - how can this be limited to one scale (eg. ours and that of a coin tossed on a football field), unless the limitation is due to our own limitations and perspective? The characteristics and interactions across scale (and generative structural aspects across scale) make up another huge area where current mathematics is at a loss to measure and provide models for. And it is something the concept of 'event, which is not inherently limited to one scale like measurable quantities are, is likely to also need to address.
I think you have picked a very important direction of study - which also opens up other cans of worms.
Lev,
Event in your understanding is not an event in the classical sense.
You do not talk about events. You talk about microstates of the World. It's a different concept. Unfortunately until in your theory there is no mathematics. Now, your theory is just philosophy. It's not so interesting for me. Thank you. I wish you success in your endeavors.
Thanks, Oleg.
I'm not looking for what you call "mathematics": I'm after the general model of events not microstates. A state is typically associated with a spatial representation, while I'm after the 'informational', or structural, representations, which have not been considered so far in science. (By the way, I do believe that, as a result, we should see a complete restructuring of what we call "mathematics".)
I do not believe, I'm dealing with science;)
You have yet to answer the question does your theory satisfy the Popper's falsifiability criterion or not (think about your "unobservable events").
"Physics really gone crazy with their inquiries to experiment!
Another thing, the mathematics that need only pencils and erasers.
And even better philosophers, and they do not need erasers." ;)
Oleg: "You have yet to answer the question does your theory satisfy the Popper's falsifiability criterion or not"
Of course it does.
The first applied tests are happening in such informational fields, for example, as pattern recognition and data mining. You represent objects, (including web pages and images) as structs, build the corresponding class representations, and then test how good these class representations are (test them on new objects from those classes).
I think you still didn't understand what this new representation is all about, that is why you treat it as "philosophy".
Lev,
Before creating a new theory, it is necessary to examine all the existing ones.
I think you absolutely have no idea what modern eventology is. If you would know, then you would be quite obvious that in your theory there is no mathematical apparatus. Just so it is a philosophy now. You must prove that your theory is not philosophy. Others instead you will not do it. In the form in which it is presented, it is not interesting to me. Sorry;)
Oleg: "In the form in which it is presented, it is not interesting to me."
I'm also sorry, but I'm not interested in making presentation "interesting to you".
My best wishes to you with the eventology
We live in an interesting time when there can be:
1) Many people working on similar problems with new ideas (historically there might have only been a couple people working on new ideas)
2) Technology has provided the means of each person producing lots of output - papers, articles, experimental data, reports on data
3) The Internet providing a means for those many people to connect up with others - to bounce ideas off of, present ideas to others, and find others working on similar problems.
One thing has been lost in all this - which is the time for any individual to read through all that material produced by so many people.
As individuals we must make decisions on priorities of what to look into and what not, especially based upon limited time.
I think this is, in part, Oleg's dilemma and is also likely the reason for Lev's aside "without first, at least superficially, acquainting themselves with the relevant material".
I think science's reliance on strict numeric measurements needs to be expanded into other methods of inquiry. The structure of events (especially with a 'generative' approach) looks quite promising. The need to expand our models beyond single levels of scale is also needed, as are new numeric tools for accomplishing this.
There are a number of important new ideas occurring, which can no longer be encompassed by a single individual - or even a small group of similarly educated individuals. There are questions on Researchgate about how to address different methods of article and peer review. There are questions about submitting to major or lesser known journals.
So one of the tasks in front of all of us looking to bring new ideas into the main stream is how to get through to all those 'other' people - individuals - with time and priority limitations. Websites like researchgate attempt to address this by connecting people together, however the situation of too much to read through remains. The tools allowed on Researchgate for presenting ideas (written papers, articles) are still the same old tools (ever tried out Prezi.com - or tried to link from Researchgate?)
The importance of (and money in) 'Science Writers' today - people who 'translate' the details of science for a broader audience - cannot be overstated in this situation.
If we have new ideas, there is a certain amount of time needed to 'educate' others on these ideas - and not simply refer them to written articles.
Donald: "So one of the tasks in front of all of us looking to bring new ideas into the main stream is how to get through to all those 'other' people - individuals - with time and priority limitations."
As I mentioned several times here at RG, we live in historically very 'tragic' times, when there is an enormous gap between the unprecedented but urgent scientific tasks at hand on the one side, and the extremely meager intellectual efforts each of us from an extraordinary large crowd of "scientific workers" is able to offer for those tasks, on the other side. There is also the gap between the education needed for those tasks and the actual education of "scientific workers".
I'm writing the above book to clarify my views for the proverbial "reasonably well educated" (including philosophy and mathematics) person. Do you know how much efforts I'm putting in this book? This is probably the best I can do, short of various substantial applications which will require collective efforts. I believe the exposition in the developing book is quite readable and am always prepared to discuss any 'dark' places in it at any length.
Donald: "If we have new ideas, there is a certain amount of time needed to 'educate' others on these ideas - and not simply refer them to written articles."
Donald, I'm prepared to put any additional efforts into "educating others" but only those that can contribute to the development (including falsification) of the proposal, but my experience tells me that there are very few such people. Besides, look at the questions I initiated and the discussions I have participated just here at RG to get an idea about my efforts. But there is a limit to how much efforts I'm willing to 'waste'. ;--)
Again, as to the experimental verification of the above proposal, one should keep in mind that such verification will probably come first in such central information processing fields as pattern recognition, data mining, search engines, etc. This is because the conventional idea of "experiment" will need to be reconsidered, and only then one can.gradually move to natural sciences, though the applications to developmental biology might come earlier.
Of course, this does not mean that we shouldn't be thinking about the implications to physics and chemistry.
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