This is a good explanation of the explanatory scientific method and how it justifies the Austrian approach and invalidates many of the mainstays of mainstream economics and physics.
Why anarchy fails
Nice. I would have liked to have seen more fleshing out of the reasons for his particular assertions and categorizations... such as the necessity of positing causal agents, the grounding of cause-and-effect (why is cause-and-effect a necessary component of any explanation?) as well as how do we know that the method is complete, that there aren't things that we may have overlooked to include.
Prediction is raised in the comments section but there is an easy answer to this - his method actually already includes prediction, it's just not obvious. Prediction and explanation are both two sides of the same coin. If you can explain something, that means you can give a reason for it. What does it mean to "give a reason"? Well, it means that you can represent the phenomena under study with less information than would be required to give every particular. To put it into 21st century language, valid generalizations compress the data of particulars.
We can think of the hypothesis as a compression algorithm which allows us to represent the particulars in the much smaller form of generalities. Compression connects explanation and prediction. Explanation is a compression algorithm run forward, prediction is a compression algorithm run in reverse.
He is missing discussion of the feedback of the scientific method into itself. This feedback process is heavily distorted in mainstream science. Today, we treat the scientific method as a high-stakes game of monopoly tournament where the best scientific hypothesis completely wipes out all others and sucks up all the oxygen in the room and receives 99.999% of all available funding. Look at modern cosmology which is in a dramatically bad state of affairs. We have a pantheon of metaphysical absurdities parading around the cosmos in full naked glory while everyone who is wise enough to see them is supposed to pretend that The Cosmology is not, in fact, naked. Black holes with infinite density at a single geometric point? Elementary particles with infinite forces at their centers? Dark matter and dark energy that supposedly comprise 95% of all matter in the Universe??? Seriously?? 95% of all matter in the Universe is something which is non-observable except as it influences other matter through the force of gravity. This is religion, not science.
But there is a viable alternative which has been around for more than half a decade and sits neglected on the shelf of plausible scientific cosmological theories that didn't win the Grand Tournament of Peer Review and Government Grant Funding. It is called Plasma Cosmology, first put forward by physicist Hannes Alfven. Rather than investigating this and other alternatives, modern science plunges headlong into the abyss of metaphysical gibberish, throwing around infinities by saying "they're only in the limit and we choose to neglect the limit" and black holes supposedly popping into existence unobservably all around us like so many demons and goblins. This is religion, not science.
If you want to read an examplary of the scientific method, I recommend you take a look at Ernst Mach's The Science of Mechanics. He weaves together the process of hypothesization, theorization, observation and feedback into a seamless process that will make you cry when you compare it to the pathetic excuse for a science that is called "physics" today. Read the section where he carefully and perspicuously he goes through the reasons why the lever principle is true! Today, you are lucky if a single line of a physics textbook is given to explaining the equation: F*D = f*d. I guess they just assume you've read Mach even though they don't cite him. Read the section where he gives the limit argument for conservation of momentum... in physics class, I was taught that Newton just imagined something moving through empty Cartesian space and said "Aha! It would have no reason to come to rest so, therefore, it must continue on forever" and this is supposed to be the reason we today accept the conservation of momentum. Not so. Mach explains how the conservation of momentum is the inescapable conclusion of real experiment combined with thought-experimental continuation of the real experiment to its limit! It's truly mind-blowing!
Just from the Introduction... how often do you read something like this in a modern scientific textbook??:
An instinctive, irreflective knowledge of the processes instinctive knowledge of nature will doubtless always precede the scientific, conscious apprehension, or investigation, of phenomena. The former is the outcome of the relation in which the processes of nature stand to the satisfaction of our wants. The acquisition of the most elementary truth does not devolve upon the individual alone : it is pre-effected in the development of the race.
Clayton -
"why is cause-and-effect a necessary component of any explanation"
Are you posing this as something that he should've explained more, although it should be obvious, or are you really asking this?
Nice video and, Clayton, excellent post.
Clayton: What does it mean to "give a reason"? Well, it means that you can represent the phenomena under study with less information than would be required to give every particular. To put it into 21st century language, valid generalizations compress the data of particulars. We can think of the hypothesis as a compression algorithm which allows us to represent the particulars in the much smaller form of generalities. Compression connects explanation and prediction. Explanation is a compression algorithm run forward, prediction is a compression algorithm run in reverse.
What does it mean to "give a reason"? Well, it means that you can represent the phenomena under study with less information than would be required to give every particular. To put it into 21st century language, valid generalizations compress the data of particulars.
Exactly! What especially econometricians fail to understand is that the complexity of their models (explanations) is roughly of the same order of magnitude as the complexity of the events they are trying to explain. The robustness of both explanations and predictions is directly proportional to the amount of compression (sublimation) performed by the model that produces them. From this perspective, Austrian Economics wins hands down.
Clayton:Nice. I would have liked to have seen more fleshing out of the reasons for his particular assertions and categorizations... such as the necessity of positing causal agents, the grounding of cause-and-effect (why is cause-and-effect a necessary component of any explanation?) as well as how do we know that the method is complete, that there aren't things that we may have overlooked to include.
I think he's saying that after you specify what the objects in your theory are, you have to show how they interact. Like if you have particles, you'd have to specify whether they bounce off each other, go through each other, fuse together, etc.
Clayton:Prediction is raised in the comments section but there is an easy answer to this - his method actually already includes prediction, it's just not obvious. Prediction and explanation are both two sides of the same coin. If you can explain something, that means you can give a reason for it. What does it mean to "give a reason"? Well, it means that you can represent the phenomena under study with less information than would be required to give every particular. To put it into 21st century language, valid generalizations compress the data of particulars.
I agree. Only, I'd say explanation (in physics) is actually a movie of how something happens (mechanically). Prediction is basically trivial if you have a movie of the entire process. In economics you can only make a "movie" out of your own ability to model other human beings inside your head, based on yourself. Still has to be a sensory movie of some sort.
As to plasma cosmology, the thing I don't get about it is what "energy" and "plasma" are supposed to be. But I haven't looked deeply into it.
I completely agree that black holes are nonsense, even semantically the concept is incoherent on its face. There are a lot of religion-like aspects in modern physics, that I really wanted to believe for a long time because they seemed so magical and fascinating. More on the religion angle, curved space, black holes (infinity):
Porco: Yeah, I'm asking it - what is so important about cause and effect? Answering this question is doubly important because phenomenalism and empiricism either ignore or deny (respectively) causality.
Why is it not possible to have a scientific theory of the natural world that is based entirely on correlation. "If you wiggle X, Y flashes... this correlation is observed 100% of the time and while we don't (or can't) know that X causes Y to flash, it doesn't matter since we know we can always make Y flash by wiggling X." What's wrong with this?
What's "wrong" with such a purely statistical correlation is that it is not an explanation, just a description. Descriptions are useful, but they are not science* -- more like cataloging relations.
Think of it in the case of gravity:
Any kid can tell you that if you let go of your pen it will fall to the ground under normal conditions. Anyone with the necessary measuring devices can track the speed, and with a little math they could come up with an equation that fits its rate of descent. Go further and you get Newton's equation. All that is very useful for certain things, but it will never bring you much closer to, say, building an anti-gravity device.
Assuming gravity manipulation is possible, there are basically three ways to figure out how to build an anti-gravity device:
1) Try a bunch of stuff haphazardly and get lucky ("tinkering")
2) Look around and find some situation where gravity is anomolous ("cataloging appearances") and try to reproduce it under controlled conditions
3) Figure out the underlying mechanism of gravity so that you can actually see how to manipulate it (what I would call "science"*)
What disturbs me most is that the mainstream has effectively given up on 3 in many areas, some even going so far as to say that 3 is irrelevant.
*I realize this is not how science is normally defined, but I hope to convince the reader that the term should be reserved for this use exclusively.
On the same subject, but from a different perspective: http://mises.org/Community/forums/t/23618.aspx?PageIndex=4 There I wrote:
I can predict that a female will come home with me with high accuracy if I hear certain noises from her. I need not - and don't - predict specific concrete visuals of her walking with me to a certain station and doing a certain thing, nor specific movements, other than the general change in location to my room. Yet I can predict this entirely through statistics: it has worked every time so far, so I am pretty confident it will work again. I don't need to know or ever consider the process teleologically. I can entirely comprehend the means without any teleological consideration at all. All I need is, "It worked before many times, so it will probably work this time."
Statistical methods are indeed useful, but without insight into the underlying mechanisms I cannot really hope to improve my success rate with the ladies other than by tinkering and cataloging. If, on the other hand, I have a theory of mind that suggests that a female's mind works in such and such a way (either like mine in some way (teleology), or through a mechanical metaphor), I can potentially boost my success rate to a whole new level.
Clayton:We can think of the hypothesis as a compression algorithm which allows us to represent the particulars in the much smaller form of generalities. Compression connects explanation and prediction. Explanation is a compression algorithm run forward, prediction is a compression algorithm run in reverse.
With respect to astrophysics/cosmology, are you familiar with the theories of paul laviolette? This isnt really my field, but I thought his explanation of redshift among observed bodies was interesting, as he postulated a "tired light" theory where gravity leeches energy from this radiation causing it to move towards the red end of the spectrum. If gravity is drawing energy in, it might explain the observation that generally speaking, the more massive a body is, the hotter it is.
I agree with everything you wrote, and I was wondering how you (and others) would distinguish between a sufficiently detailed description and an explanation. Does an explanation require reference to a theory?
I think we can tie anti-causality to absurdity. Here's how.
Imagine a box which cannot be opened. On the front is a Red light and a Green light. One or the other light is always lit (never both). On the front is a button. As we push the button, we notice different patterns in the alternation of the Red and Green light.
For example, let's say that every time we push the button the light switches from its current state to the opposite state (Red->Green or Green->Red).
Now, one possible explanation of the operation of the box is that, inside the box, there is a coin-flipping device attached to the button and that the Green light lights whenever the coin comes up heads and the Red light lights whenever the coin comes up tails.
After pushing the button twenty times and observing the light switching every time from Red->Green->Red->..., the probability that the coin came up heads, tails, heads, tails etc. is 2^-20 (which is approximately one in a million). As we continue pushing the button and observing the light switching from Red->Green, the probability of the heads-tail sequence goes to zero exponentially quickly.
On the other hand, another explanation of the operation of the box is that inside the box is a small computational device that alternates between two states every time the button is pushed and that each of these states is wired to the Red and Green lights respectively so that when the computational device is in State A the Red light is lit and when it is in State B the Green light is lit.
With some very technical (though rigorous) hand-waving, we can actually quantify the probability of such a device (so long as we take an abstract reference device called a Universal Turing Machine as a given for the purposes of the though-experiment). However improbable the posited device is, its probability is some fixed constant. The probability of the coin-flipping device, on the other hand, becomes vanishingly small by comparison.
Hence, we can say that it is exponentially more likely that the two-state computational device is alternating the lights on the panel of the box than that there is a fair coin-flipping device which keeps repeatedly flipping heads, tails, heads, tails, etc.
To assert that only correlation can be established (not causation) in scientific theory is equivalent to asserting that the mechanistic explanation is no better than the coin-flipping explanation of the Red-Green box. Such a view is only possible in an absurd universe where there are no explanations for anything, where all events without exception have happened by sheer, random chance. This is the definition of absurdity. Because I am rational and believe that the Universe admits to rational explanation, I reject the idea that every event in the Universe is just one, gigantic random outcome out of all possible outcomes and that the appearance of causal, mechanistic relations between events is sheer coincidence.
The less complex a posited mechanism is for a given pattern of Red-Green lights, the more likely it is compared to other, more complex mechanisms and the more likely it is versus a Red-Green box that is lit by a coin-tossing device.
This idea is not original to me though this particular way of arguing it is. See Solomonoff Induction.
Malachi:Does an explanation require reference to a theory?
In the explanatory scientific method as detailed in that guy's video in the OP, explanation = theory = movie of how you think something mechanistically happened.
Malachi:I agree with everything you wrote, and I was wondering how you (and others) would distinguish between a sufficiently detailed description and an explanation.
I had the same question initially, since usually description and explanation are pretty similar words. But I think I have it sorted out now.
In this context, "description" means describing the observed phenomenon (e.g., an apple falls to the ground; it accelerates at such-and-such rate). "Explanation" means making a movie, 3D model, or actual mock-up of the unobserved hypothetical phenomena that are proposed to mechanically produce the observed phenomenon (e.g., the earth is connected to the apple by an invisible lasso that pulls on it). Explanation could also be done with words if the words are clear enough that everyone ends up visualizing the same thing.
Some explanations (movies) are given in modern physics, like Einstein's gravity well:
However, here it is absolutely not clear how this warped grid, which is supposed to be space (=nothingness), mechanically pushes on the ball to explain how the ball is kept from flying away. If pressed on this point, I've found that physicists will back away from the movie (the explanation) and say it's just a visualization for laymen, and that the real deal is in the equations. All right, but the equations will just be a description of what happens, not an explanation of how it happens mechanistically.
Without such an explanation, there is no way to advance science more deeply. No hypothetical objects are proposed that mediate gravity, let alone a movie of how they would do so. We are still stuck at Newton's hypotheses non fingo ("I feign no hypothesis [for gravity]").
Clayton: To assert that only correlation can be established (not causation) in scientific theory is equivalent to asserting that the mechanistic explanation is no better than the coin-flipping explanation of the Red-Green box. Such a view is only possible in an absurd universe where there are no explanations for anything, where all events without exception have happened by sheer, random chance. This is the definition of absurdity. Because I am rational and believe that the Universe admits to rational explanation, I reject the idea that every event in the Universe is just one, gigantic random outcome out of all possible outcomes and that the appearance of causal, mechanistic relations between events is sheer coincidence.
Nice example. That's exactly it: when we move away from explanation and into pure cataloging of relations (equations), we are in effect claiming that "all beyond this point is fundamentally unknowable, inconceivable to the human mind even in principle, 100% absurd."
I suppose it could be possible for this to be the case, but it would be quite an amazing statement. After all, there is no way to know that a new explanation could never be proposed that would make it all conceivable again.
In other words, it is just a veiled way of giving up on science. Alternatively, viewed in terms of incentives, it could be a way of deliberately stalling when progress on the explanation front gets too difficult, so as to continue getting grant money in perpetuity.
I like this. It comes down to "what are we talking about and why" - we can never talk about "physics for the sake of physics", or physics as a "thing in itself" it becomes nonsensical. I think it may be our task to show that option 3 is unavoidable by the nature of our very being, it is what we are always doing anyway, and it can not be ignored. I think that Aristotle video that talked about perspectives kind of touches on that.
"As in a kaleidoscope, the constellation of forces operating in the system as a whole is ever changing." - Ludwig Lachmann
"When A Man Dies A World Goes Out of Existence" - GLS Shackle
I have to say, I came to this thread with a skeptical eye, but now feel I should withold judgment until I'm better acquainted with some of this fascinatiing material. I've always felt that the way in which the "scientific method" in a Popperian falsificationist form, actually betrays a lot fo the subtleties of reasoning, which is both deductive and inductive, underlying the formulation of scientific theories.
If you want to read an examplary of the scientific method, I recommend you take a look at Ernst Mach's The Science of Mechanics.
Thanks very much for the link Clayton. I must ask, have you read any of Landau's Course of Theoretical Physics, and if so, what do you make of it? I ask, as I recently perused one of the earlier editions of the volume on Statistical Mechanics and at the end of the 1st chapter, he contains one of the most thoughtful discussions concerning the problems with probabilistic rationales underlying the increasing entropy principle of the 2nd law of thermodnamics and how it must relate to time's progression. (Cf. Landau and Lifshitz, Statistical Physics: Volume 5, 3rd edition, pp. 29-34)
"When the King is far the people are happy." Chinese proverb
For Alexander Zinoviev and the free market there is a shared delight:
"Where there are problems there is life."
[My thoughts...]
I'll I'd add that, as a rule of thumb, a hypothesis means the WHAT (definitions, assumptions, invoked objects/exhibits); the theory hopes to answer WHY questions (filling in the movie blanks, possible causes, motivations); which also requires answering HOW (i.e. mechanisms) especially in fields like physics.
HOW would relate more to physics than, say, history. History might answer WHY questions in a theory about personal motivations. E.g. "Why did the British Government go to war?" / "Well, Churchill thought that ... The state conspired with ..." etc. This is mostly true of economics, too. But there is obviously overlap ("Napolean probably thought that ... which explains ..." [motivation/why] / "If the shooter's bullets ricocheted off the wall, then hit the soldier ... This suggests that ..." [exhibits/how]).
In physics we're dealing almost exclusively with existence (objects w/ location). So there are absolutely no motivations; only causes! Explanation/theory is ideally objective, yet ultimately an author's interpretation, which thus requires filling in blank movie frames with mechanical interactions and so on.
It's worth noting that there is a LOT of confusion (especially in positivist/empiricist schools) about the difference between subjective, objective, and rational/irrational. These three at least I think I've nailed and understand well. But there's more; trickier stuff.
An hypothesis is purely objective and geenrally descriptive. It paints the scene. There is no interpretation. All base assumptions, definitions, and facts are taken strictly on face value just as they are. We invoke a ball and a cube (exhibits), and an equation (fact). Maybe there was a ball, maybe there wasn't. But we have to proceed to use it in our theory, so we ASSUME (hypothesize) the ball/cube/equation/definition etc for the purpose of hearing the theory that follows (explanation).
A theory is filling in empty scenes from the past using bits and pieces from the hypothesis. Converting static images to dynamic movies. "Suppose that the ball fell on the cube, and bounced, this explains the equation because X represents ..." bla bla. This doesn't mean an interpretation of possible events is not rational. Two entirely different things as I understand it: one's ideas can be subjective but rational; or objective and rational. [Or plain irrational.]
Everything from a scientific hypothesis, to theory, to conclusion, MUST be rational (thought-through OR illustrated, step by step). Visualization through illustration is the most objective possible method of communication. This might not work for motivations (i.e. philosophy: history, economics, ethics) because these things cannot be well illustrated. However, this is where we need narrative (why) explanation, based on precise objective definitions. The way a scene is cut snd spliced, illustrated, and objects moved about, is entirely up to the theorist. Whether you agree or not about the likelihood of a movie having actually played out in the past, is post-scientific i.e. entirely up to you.
To summarize how I currently understand it:
Proofs and truth are subjective. Tautologies (A=A; 2+3=5) are just facts ('defined as such'; resolve to artificial base axioms) and may add weight to a conclusion (to sway the audience). Science is first and foremost RATIONAL and OBJECTIVE.
See some of BIll Gaede's ramblings, here... youstupidrelativist.com/02Sci/04Hypot/01WhatHypo.html / youstupidrelativist.com/02Sci/05Theory/01Theory.html / youstupidrelativist.com/02Sci/06Conclusion.html.
Curiously, Bill elucidates the following in his earlier work (possibly incomplete or edited since):
"A theory is believed or not, and in between there are gradients; degrees of belief. A hypothesis is accepted or not. It is a black or white issue. A conclusion includes a testable experiment or doesn’t. Another black or white issue."
SO what do you guys think?
These are just my initial thoughts and ramblings after reading this interesting thread, and others. I hope it's of some value. Any disagreements please let me know.
One thought I've had recently is this: is a HOW/WHAT problem just a subset of a WHY type question?
For instance:
"WHY is the sky blue?" [<< implies there are blank frames requiring general explanation?]
Could be rephrased as:
"HOW does the sky [object] create our experience [subjective] of colour [concept]?" [<< implies we need a movie of physical events?]
Or more generally:
"WHAT is (or do we mean by) sky/colour?" [<< implies we must hypothesize exhibits/definitions first!]
Is this even important? Am I just mixing words needlessly? Are WHAT/WHY/HOW terms slightly interchangeable or of themselves in need of better definition/association? Is it just more helpful to think primarily in terms of consistency and illustration?
I'd love to hear your thoughts.
vive la insurrection: 3) Figure out the underlying mechanism of gravity so that you can actually see how to manipulate it (what I would call "science"*) What disturbs me most is that the mainstream has effectively given up on 3 in many areas, some even going so far as to say that 3 is irrelevant. ... I think it may be our task to show that option 3 is unavoidable by the nature of our very being, it is what we are always doing anyway, and it can not be ignored.
... I think it may be our task to show that option 3 is unavoidable by the nature of our very being, it is what we are always doing anyway, and it can not be ignored.
I think that's key: navigating and manipulating the physical world is what we do from birth, and even what the animals we evolved from do.
gokuju:Is this even important? Am I just mixing words needlessly? Are WHAT/WHY/HOW terms slightly interchangeable or of themselves in need of better definition/association? Is it just more helpful to think primarily in terms of consistency and illustration?
What, how, and why can have a lot of different meanings, and then so can blue. So there's that.
But perhaps there is something that still needs to be clarified regarding description vs. explanation:
Description vs. Explanation in the Explanatory Scientific Method (click the arrow key to move forward in the presentation)
Hello everyone, I'm the creator of the video above.
Reading the comments I pretty much agree with the bulk of what AJ and gokuju are saying. Gokuju you mention Bill Gaede's writings, that is where a lot of the ideas came from.
There is a succinct version of Gaede's scientific method which can be found here.
For people interested in this stuff I'd suggest reading through Gaede's writings first. My goal was to more or less question whether or not Austrian economics could be formulated under a similar version of the scientific method. I'll try to answer some of your question the best I can tho.
"such as the necessity of positing causal agents"
"Causal agents" may not be the best way to put it. What I am trying to argue is that if an explanation is a version of how/why something happened, which we assume points to something whose existence is not contingent on our ideas (ie, can't be proven or disproven via observations), then the onus is on the theorist to communicate their assumptions with respect to this existence external to the mind. If their explanation involves supposing something like "X exists," then the theorist must be able to communicate the meaning of such a proposal. I can't begin to try to evaluate the truth or falsity of any such proposition like "X exists and does such and such" if I can't first understand the meaning of the proposition itself.
While I think it may be possible to formulate Austrian economics under an explanatory scientific method, I don't think the level of "objectivity" will ever compete with the set of definitions for physics. I cannot imagine any mode of communication more straightforward than using 3D shape as the inherent quality of an existing object. That being said, I still think Austrian economics can be communicated "objectively," ie, to the point where everyone perceives pretty much the same thing. I'm thinking that it is impossible to objectively communicate assumptions about the facts of someone else's experience, ie, like stepping into someone else's mind and experiencing something precisely as they experienced it. But I can at least suppose that there is an external mind, and that this mind is aware of certain things, like certain choices. Whether or not this will pan out I'm not sure, but I don't see why it shouldn't be possible.
"the grounding of cause-and-effect (why is cause-and-effect a necessary component of any explanation?"
I also wondered whether causality was necessary. I can show you a movie of my statement of the facts for how something happened, and I don't think you have to assume anything about cause/effect to watch and understand. For example, say I find that my TV remote has been chewed up. I suspect the dog and imagine him chewing the remote. If that qualifies as "explanation," then I'd argue that you'd have to break explanation down into two categories: how and why. A movie without causality is an explanation of how something happened, a movie presented with the cause/effect assumptions is an explanation of why something happened. I can communicate "the dog chewed the remote" all by itself, but if I want to go deeper I can try to answer why questions (why did the dog chew the remote? why do canine teeth cause remote plastic to deform?).
"Why is it not possible to have a scientific theory of the natural world that is based entirely on correlation. 'If you wiggle X, Y flashes... this correlation is observed 100% of the time and while we don't (or can't) know that X causes Y to flash, it doesn't matter since we know we can always make Y flash by wiggling X.' What's wrong with this?"
I think you've targeted the difference between prediction and explanation. This is an example of how the prevailing "scientific method" uses terms inconsistently. Sometimes "hypothesis" means "given X conditions, Y will result," sometimes it means, "X exists." I don't think there is anything necessarily wrong with prediction as long as it is separated from explanation. So as to the root of the difference between the two...In the physical sciences, it's almost taken for granted that we are talking about objects "out there," ie, outside of our minds. That is what makes them "real." We assume that the existence of these objects is not contingent upon our ideas of them. Likewise, our ideas of them are just mental constructions invented by the mind, ie, representations of the facts, not the facts themselves. So if the theorist plans to invoke "X exists" for the purpose of communicating an explanation, they need to decide upon a definition of "existence" prior to presenting us with the theory and remain consistent with it. The definition of "existence" must be taken at face value as it is a construction of the mind. So explanatory theories then can never be proven, they can only be judged based upon whether or not they are rational (ie, conceivable), consistent, and how well they explain the evidence. Prediction however is a convenient way of introducing terms like "prove" or "confirm." You can make predictions without having to define the term "existence" consistently. I predict that when I take my next step I won't perceive that I have fallen to the center of what I perceive to be the Earth. Done, verified. If I base everything on the facts of my sensory experience, I can use pattern recognition to make predictions without having to make any claims about what does or does not physically exist. This is fine, but it does not allow us to gain a deeper understanding of how or why things happen. It deals purely with predicting what will be observed given what was observed in the past.
"To assert that only correlation can be established (not causation) in scientific theory is equivalent to asserting that the mechanistic explanation is no better than the coin-flipping explanation of the Red-Green box. Such a view is only possible in an absurd universe where there are no explanations for anything, where all events without exception have happened by sheer, random chance. This is the definition of absurdity. Because I am rational and believe that the Universe admits to rational explanation, I reject the idea that every event in the Universe is just one, gigantic random outcome out of all possible outcomes and that the appearance of causal, mechanistic relations between events is sheer coincidence."
Exactly. If the universe is so bizarre and outside of our ability to understand rationally, then we just have to give up and admit that we can't understand it. It is beyond our ability to comprehend and we are relegated to just making predictions about what we will observe. No amount of irrational physical interpretations can save us fom our ignorance of the how and the why. But given the amount of regularity that we are surrounded with, there is good reason to believe that there are rational, mechanistic possible explanations for what we observe.
malachie -
"I was wondering how you (and others) would distinguish between a sufficiently detailed description and an explanation. Does an explanation require reference to a theory?"
I'm with AJ on this one. I think a description is a narration of sensory experience ("an apple falls to the Earth," "this is what an apple looks like," "i made such and such measurement") whereas an explanation actually deals with attempting to represent facts which are not contingent upon sesnory experience ("this is how the fusion of helium occurs," "this is why gravity holds us to the Earth").
As to the precise difference between theory and explanation, I pretty much use them interchangeably, but I suppose you could say a theory is the stage of the method where explanation is presented, whereas an explanation is an account of how/why something happened. What is really required for a specific explanation is a series of assumptions in the hypothesis that set the stage for the theorist's account of events.
gokuju -
"One thought I've had recently is this: is a HOW/WHAT problem just a subset of a WHY type question? For instance: "WHY is the sky blue?" [<< implies there are blank frames requiring general explanation?] Could be rephrased as: "HOW does the sky [object] create our experience [subjective] of colour [concept]?" [<< implies we need a movie of physical events?] Or more generally: "WHAT is (or do we mean by) sky/colour?" [<< implies we must hypothesize exhibits/definitions first!] Is this even important? Am I just mixing words needlessly? Are WHAT/WHY/HOW terms slightly interchangeable or of themselves in need of better definition/association? Is it just more helpful to think primarily in terms of consistency and illustration? I'd love to hear your thoughts."
"One thought I've had recently is this: is a HOW/WHAT problem just a subset of a WHY type question?
I'd love to hear your thoughts."
Color is a tricky one. Is the question about the mechanism behind how a sensation is produced in the mind, or about the mechanism behind a certain wavelength of light being produced? If the why question is about the wavelength, then the objects of the theory, ie, the WHAT, would be the atoms in the atmosphere, etc. Otherwise, color seems to be a qualitative experience which is not reducible to physical phenomena. It seems by asking, "why is something a particular color" you are attempting to bridge the explanatory gap, ie, to explain why certain qualitites of our experience are the way they are. Why does poking a tac into my thumb produce the uncomfortable sensation that it does? How do you go from neuron activity to actual sensation? I'm not sure the mind is capable or reconciling these apparently different realms of existence. As such, I think color is something taken for granted, it's something you point to. There is no way to explain its specific qualitites. But I am not sure that is exactly what you are inquiring about.
As for what/why/how, I am somewhat confused on the distinctions. Here is what I am thinking:
what: the objects
how: the statement of the facts of an event absent causality, a movie of just the relative motion of the objects
why: a statement about the causes of the events shown in the how statement, justification of the how with causal reasoning
So if the sky question was about the mechanism behind wavelength, the what would be the objects, like atoms in the atmosphere. The how would be the statement of the facts of what the objects actually did, like the atoms pumped like this and signals went down the ropes like this. The why would be the statement of the causes of the events shown in the how, like why atoms pumping causes signals to be sent down EM ropes. Perhaps because the threads push on one another in a certain way, the cause being collision, and the effect being repulsion, etc. I think those distinctions can be used consistently.
Nice prezi AJ. I see what you are talking about now with the potential of these prezis.
Imagine if the statistical method of science was in vogue in Copernicus' day. Poor Copernicus is laboring away day and night searching for the equations to "fit" his data using regression analysis. In fact, this is precisely what all of Copernicus's predecessors had done, they had developed amazingly compact and elegant equations by which to predict and "explain" the motion of the Sun, Moon, the stars and each of the known planets. But Copernicus hit on the idea of thinking about the whole thing in a completely different manner. "What if it is the planets that go round the Sun?"
In the process, he "unknotted" the conceptual problem of the motion of the heavenly bodies. Suddenly, not only did we have elegant mathematical equations (which remained formally equivalent to the older equations, obviously) but we had a clear and easy-to-conceive picture of why those equations describe the motion of the heavens.
The process of thinking about the world in completely new ways and exploring the consequences of the new ways of thinking (through deduction and experiment) is the real source of scientific progress. Most new ways of thinking are dead-ends... either they are eventually discovered to be inconsistent or to add nothing new to our existing understanding.
I believe that there is a social component at work here - the sciences imitate, to a degree, the political structure. The political structure of society is monopoly tournament. Like an Olympic race, there is only one First Place and everyone is competing to be King of the Hill and topple whoever is the current King of the Hill in order to get there. There is One Right Theory of Physics and so all research must go in this direction.
Science has lost sight of the fact that we don't know what the next breakthrough is going to be. String theory is a great example. Everyone understands that String Theory adds nothing to our understanding of the world, it's just a particular way of systematizing the existing Standard Model equations according to the metaphor of a "vibrating string." But all the PhDs and the dispensers of research grants have decided that if there can be a breakthrough in basic physics, it will be in the direction of String Theory.
But all the PhDs and the dispensers of research grants have decided that if there can be a breakthrough in basic physics, it will be in the direction of String Theory.
With all due respect, I think this is a bit of an over-generalisation. I know it is dangerous to abstract too much from personal experience, but I think this is not necessarily in the case in Theoretical Physics. Where I received my masters degree a few years ago for instance, nobody in the Theoretical Physics department was engaged in quantum gravity research, let alone string theory, but in far more grounded problems in condensed matter, solid state, cold atom and quantum statistical physics, as well as superconductivity (I don't suspect they were unique). I do agree however, as far as fundamental research goes, there does seem to be an overinvestment in string theory, within the quantum gravity line of research, which is perhaps too bloated a field itself for the funding it deserves.
Also, please could you answer my above question? I'd love to get your take on Landau's work.
@abs: Oh, sorry, meant to respond to that but forgot. No, I've not read any of Landau. I looked online and didn't see his stuff available for free.
I'm not disparaging all of physics - clearly, a lot of the work that is being done is as you say grounded. But this isn't the kind of work that makes the headline news. The trouble lies with the Establishment mindset that creeps back in after suffering a blow from each new advance. The mindset is that "we basically know how the Universe operates, sure, there are a few missing details but we're just millimeters from a Grand Unified Theory of Absolutely Everything".
It mitigates against progress by punishing "oddball" and "crank" physics with ridicule and removal of funding, while showering resources on those who keep blindly pushing the envelope of the status quo. The "if we could just build a bigger particle accelerator" mindset is part of what I'm talking about. Particle accelerators are great and everything but just building bigger and bigger particle accelerators will not yield the answers to our questions. Someone's going to have to come up with a fundamental insight that clarifies and unifies the mountain of data we already have.
Blockbuster research budgets are no substitute of brilliant insights. We may just have to wait for the next genius to come along and get his flash of insight that moves us to the next level of understanding of the physical world and this is a question of how resources should be allocated (an economical question). Perhaps our money would be better spent cultivating geniuses rather than indoctrinating people into the status quo of physics and then blowing hundreds of billions of dollars on mega-particle accelerators which at best can hope to give us a yay-or-nay on a few abstruse questions in physics, such as the existence or non-existence of the Higgs boson.
In my view, this is all symptomatic of the increase in public subsidy of science research. A tiny number of bureaucratic decision-makers are determining how mountains of research money are being dispensed. If those monies came from private individuals - as used to be the case - the spending would represent the much more dispersed interests and knowledge of many decision-makers. Fundamental scientific research is perhaps the limiting case of human uncertainty - we can't be more uncertain about anything than we are about the next scientific breakthrough or the next brilliant scientific insight precisely because so many of the smartest humans are thinking about these problems all the time and they don't know what's next. Where uncertainty is the greatest, variation is the most important.
Let me give an example of the kind of crank science I have in mind (I've been thinking about this quite a bit lately). Consider relativity theory which is largely taken for granted these days. First of all, the foundation of relativity theory has both theoretical and empirical problems that are not widely recognized.
The theoretical problem I see with relativity theory is that it rejects the ether which is actually not the "no big deal" that modern physics makes it out to be. In every other instance where we observe a wave (including EM waves of which visible light is merely a frequency band) other than small particles, there is some medium the disturbance of which constitutes the wave. We have thrown out the ether but have not explained how it is that the wavelike properties of photons or electrons arise absent a medium. What is it that is waving, or to be less ontological, why do we observe a wave if there is not a medium which is being perturbed? I have not read a satisfactory response to this (doesn't mean one doesn't exist, just that I haven't read it).
The empirical problem I see with relativity theory is that the failure to detect the ether wind by the experimental means which have been tried so far is not as decisive as it is generally taken to be. I recently read about the physicist Dayton Miller who spent a good portion of his life attempting to detect the influence of the ether. He believed he was detecting some amount of ether wind though his contemporaries argued that his readings were far too low and his readings have since been explained away as down to error margins.
However, it seems to me that neither the original Michelson-Morley experiment nor the later experiments by Morley and Miller were decisive of the matter because we do not know the extent to which the Earth is, in fact, dragging around the ether with itself. Imagine if space was filled with air instead of being empty and imagine that the Earth was revolving about the Sun through this air medium. Now, the Earth's gravity would still create a troposphere around us. Imagine that winds on Earth were always very light and imagine that we wanted to detect the medium through which sounds arrive to Earth from space. It could be argued that there is no air medium through which these sounds are arriving from space because the Earth is racing around the Sun at thousands of miles per hour but we feel no wind or the readings are so small as to be discounted as anomolous.
Because we do not know the velocity of the medium relative to the Earth in the vicinity of Earth, what would really need to be done is to launch an experimental apparatus at speed to detect whether it experiences effects from motion through the medium. I think this is true today. Has anyone tried launching a rocket with a Michelson-Morley apparatus in it? Also, Miller was highly concerned about the effects of shielding. Given that the ether, if it exists, mediates the propagation of electromagnetic waves and given that we know that a Faraday cage, for example, completely shields its contents from external EM disturbances, I would like to see an experiment with a rocket-mounted M-M apparatus in an unshielded (say plastic or glass) configuration. The configuration would have to be highly sensitive as the rocket's maximum velocity would have only a tiny effect on the propagation of light in the hypothesized ether. Has anyone tried an experiment of this sort?
The earth rotates at about 1,000 mph. The earth also revolves around the sun at about 67,000 mph. The sun revolves around the galactic center at about 500,000 mph. Given this, the "ether" could not have a stationary reference frame with respect to the earth.
Recent M-M experiments [Phys. Rev. D 80, 105011 (2009)] show no detecable ether shift to 1 part in 10-17. Conclusion: no ether.
Clayton, excellent point about waves. Waves without something waving is pure reification. There is one other possibility for the ether: it is not that matter floats in the ether, but rather that matter consists of wave patterns of the ether. And so do all the phenomena we already consider wave phenomena. It would just be that the former are standing waves and the latter are traveling waves. Such an ether would presumably not be detectable by such types of experiments.
@Josh: We know the Earth and the Sun have powerful (in aggregate) magnetic fields that extend far out into space. Given that the ether would be responsible for propagation of EM waves, it seems to me that perhaps the ether is influenced by magnetism. If so, it could be being "dragged along" with the Earth's and the Sun's magnetic fields so the relative motion of the ether to the Earth may actually be quite modest.
The ether, if it exists, could even be playing a role in gravitation itself. It's not like modern physics has just almost got everything all wrapped up into a complete theory. We can actually estimate how wrong modern physics is... it's about 95% wrong. How do I know this? Because modern physics says that about 95% of matter in the Universe is non-observable except as it influences gravity. Dark Matter. At least there were some good a priori reasons to believe in the ether. There are no good reasons to believe in Dark Matter.
Clayton, I think physicists have (correctly) rejected the kind of static ether theory originally believed in the late 19th century and disconfirmed by the Michelson Morley experiments. I do think however, the matter is not wholly settled with regard to the fact that as I recall one of my old lecturers in fact pointed out to us, one of the things we know from quantum field theory and its confirmed results is the existence of vacuum field groundstates of nonzero energy, so clearly the notion of "empty space" has some problems (especially given the number of creation and annihilations that simultaneously take place in it). Hence this might be somewhat a sign of "tension" in effect between Quantum Mechanics and Relativity in one sense here (Wikipedia claims, Dirac's attemped to reinterpret the quantum vacuum as an aether with a state of motion in 1951 but failed)
Also, the Michelson Morley experiment failed to indirectly detect a velocity w.r.t the hypothesized medium, given no difference in the time displacements between orthogonal slits. But this is supposed to simply be a manifestation of relativity, the fact that these observations will be invariant to reference(and in fact symmetric in each in SR, until acceleration breaks symmetry). I was under the impression the latter was a well established fact, and pertains to most practical applications of relativity theory (which again accords with experimental confirmation to the type of degree the economists we regularly criticise on this forum could only dream of getting). How would a modified ether theory cope with this fact?
How would a modified ether theory cope with this fact?
I think I'm out of my depth here... All I can say is that from an a priori point-of-view there is a good argument that if we see a wave, there's "something" that's waving because in every other case where we observe a wave, there is a medium. When you combine this with the growing cracks in the edifice of modern physics - Dark Matter/Energy, Pioneer anomaly, anomalous energy discharge during the Deep Impact mission, etc. - you begin to sense that there's something maybe wrong in the foundations.
the notion of "empty space" has some problems (especially given the number of creation and annihilations that simultaneously take place in it)
This is interesting.
Feynman said: "It always bothers me that according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space and no matter how tiny a region of time ... I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed and the laws will turn out to be simple. ... But this speculation is of the same nature as those other people make - 'I like it','I don't like it' - and it is not good to be too prejudiced about these things."
I think there is something wrong with so much going on at every unit of space... at some point (in the small), space must become "simple" or at least "statistically uniform" or there must be some law that describes the nature of space as you go down smaller and smaller (even if that law itself yields really bizarre things like fractals or something).
gokuju:An hypothesis is purely objective and geenrally descriptive. It paints the scene. There is no interpretation. All base assumptions, definitions, and facts are taken strictly on face value just as they are. We invoke a ball and a cube (exhibits), and an equation (fact). Maybe there was a ball, maybe there wasn't. But we have to proceed to use it in our theory, so we ASSUME (hypothesize) the ball/cube/equation/definition etc for the purpose of hearing the theory that follows (explanation).
This is crucial setup for the theory, because if the "actors" (physical objects) in your mechanistic movie are themselves inconceivable, there is of course no way that the movie as a whole can be conceivable.
So this explanatory scientific method (ESM) is pretty simple if we leave out the words and just do it visually:
1 - Hypothesis: Show a picture of the objects hypothesized to exist.
2 - Theory: Show a movie of how these objects are hypothesized to mechanically interact in order to produce the observed phenomenon.
Observations and measurements, etc. happen before and after, as motivation for coming up with the theory or as motivation for looking for a new one.
unlapped_dog:While I think it may be possible to formulate Austrian economics under an explanatory scientific method, I don't think the level of "objectivity" will ever compete with the set of definitions for physics. I cannot imagine any mode of communication more straightforward than using 3D shape as the inherent quality of an existing object. That being said, I still think Austrian economics can be communicated "objectively," ie, to the point where everyone perceives pretty much the same thing. I'm thinking that it is impossible to objectively communicate assumptions about the facts of someone else's experience, ie, like stepping into someone else's mind and experiencing something precisely as they experienced it. But I can at least suppose that there is an external mind, and that this mind is aware of certain things, like certain choices. Whether or not this will pan out I'm not sure, but I don't see why it shouldn't be possible.
On this topic, I made a different version of the above prezi, geared toward praxeology / a priori economics. Watch it here: http://prezi.com/m0wdftavsag5/austrian-economics-description-vs-explanation-in-the-explanatory-scientific-method/ (use arrow button to advance)
unlapped_dog:I can show you a movie of my statement of the facts for how something happened, and I don't think you have to assume anything about cause/effect to watch and understand. For example, say I find that my TV remote has been chewed up. I suspect the dog and imagine him chewing the remote. If that qualifies as "explanation," then I'd argue that you'd have to break explanation down into two categories: how and why. A movie without causality is an explanation of how something happened, a movie presented with the cause/effect assumptions is an explanation of why something happened. I can communicate "the dog chewed the remote" all by itself, but if I want to go deeper I can try to answer why questions (why did the dog chew the remote? why do canine teeth cause remote plastic to deform?).
I'd say those are just deeper questions to be answered by a later theory at a deeper level of analysis. If we merely want to know how the remote got chewed up, which is after all a practical question, we don't necessarily care about those other questions. Or if we do, it'd only make sense to resolve the initial question first - the question of whether it was the dog or not.
When you break down causality to its core components, it really is just "seeing movies." Experientially, all we know is that Sensation A follows Sensation B in a significant number of cases. But that's usually a little too deep to be useful for physics. For the purposes of physics, causality means how something mechanically happened - that is, seeing movies.
Any mechanical oddities that we might one day encounter, such as portals like in the game Portal, would require us to fall back on the deeper "Sensation A follows Sensation B" notion of causality, because we can no longer use the familiar mechanical machinery we were evolved and raised to understand. I have never yet seen any need for this, however. No "portals" have ever been found.
unlapped_dog:Exactly. If the universe is so bizarre and outside of our ability to understand rationally, then we just have to give up and admit that we can't understand it. It is beyond our ability to comprehend and we are relegated to just making predictions about what we will observe. No amount of irrational physical interpretations can save us fom our ignorance of the how and the why. But given the amount of regularity that we are surrounded with, there is good reason to believe that there are rational, mechanistic possible explanations for what we observe.
+1
unlapped_dog:As to the precise difference between theory and explanation, I pretty much use them interchangeably, but I suppose you could say a theory is the stage of the method where explanation is presented, whereas an explanation is an account of how/why something happened. What is really required for a specific explanation is a series of assumptions in the hypothesis that set the stage for the theorist's account of events.
I might lean toward dropping all the baggage of "science," "scientific method," "theory," etc. and just state what we are doing directly: observing, positing objects and possible mechanical interactions of those objects that would produce the observations, and then deciding which such objects and mechanical interactions seem most plausible. We could define "science" or "physics" as just the bold, or as all the underlined. Or we could call it something else if people object to the terminology.
I think I'm out of my depth here... All I can say is that from an a priori point-of-view there is a good argument that if we see a wave, there's "something" that's waving because in every other case where we observe a wave, there is a medium.
That is a common objection of Quantum Mechanics that probably dates as at least as far as Schrodinger developed his wavefunction formulation of quantum mechanics, the nonrelativstic version of which makes up the staple of undergraduate teaching in the subject today. I think there is something to be said about relying too much on our intuition based on our experiences of the molar world to guide us here. What Quantum Mechanics teaches, under the Bohr interpretation (which I began to sympathise with more, the further I studied the subject), is that really the terms "particle" and "wave" do not necessarily describe reality, but depending on the conditions which we have constrained, what we mean by these 2 terms suffices to describe reality approximately so well, that we may drop our caveats against their unambiguous use. One good, pretty simple illustration of how the convergence occurs can be seen by showing the correspondence principle with regard to a quantum harmonic oscillator.
The other danger w.r.t emphasis of intuition, is to be clear, that the type of "waves" implied by state vectors (by taking the modulus of them) of quantum phenomena are not waves in the classical sense, describing the actual latitudinal/longitudinal movement, and whose only interpretation arises from taking the modulus square over certain regions with varying degrees of freedom to interpret a probabillity distribution for the phenomena described taking certain parmeter values upon measurement. The simples example of this could be seen with distribution produced from an identically repeated experiment using a particle with a known and derived state vector or its modulus (wavefunction) passing through a single slit before "striking" a screen.
As I think it relates somewhat to the theme of this thread, I think it might be important to note that Menger too did not see such a fractious divide in the methods of the sciences, hence why he considered himself to simply be applying what he referred to as the "empirical method" (given the book is a translation, I understand I should be a little weary of the risks of reading too much into certain connotations). He also notes the dangers of carrying naturalistic analogies from other branches of knowledge in an automative fashion to where they do not belong, and interestingly cites Francis Bacon in his support (otherwise panned by many, including Rothbard as a naive empiricist).
All this he stated quite clearly in the preface to his Principles.
I think it might be important to note that Menger too did not see such a fractious divide in the methods of the sciences
I haven't really got very far into this, but it is something that I have been paying more and more attention to with regards to the social sciences. I haven't read much of Mengers articles on method, but they may be key. It seems like focusing on the similarites and differences of Menger and Mises and what is meant by "empiricism" (I think Barry Smith and Peter Boetteke/ Leeson get a bit into this). Either way, it seems to be a crucial question that I do not think can be stressed enough.
The social sciences as we know it really know little of what Menger and Max Weber were trying to say - the Anglo American tradition just simply doesn't know about it, it was never really that hot of an issue over here.
What seems to be mostly being discussed in this thread is well know to physicists. No-one actually imagine space is a thing independent of other things.
Idea that space does not exist and philosophy of general relativity (all motion and time are just coordinate invented by us and relative and there are no preferred coordinates) were stated by Leibniz and then Boskovich, and very well re-stated by Julius Mayer and then by Ernst Mach.
Physicists such as Einstein and Robert Dicke called it simply Mach's Principle whenever they made use of it.
Actually, because of Mach's Principle, we may talk entirely of curvature of empty space-time without contradiction.
It just formulism to talk about non-local relations more easily: space is merely set of all relations of things between themselves, therefore when we talk about nothing except empty space-time, or deform it, we are using a continuous formalism to discuss in fact changes in relations of things, since space is just another way of talking about relations.
Hence things like spinors or 2-spinor formulisms (e.g., Roger Penrose & Wolfgang Rindler) using abstract tensor notation such as twistors: by talking exclusively about space, we actually discover relations between things once we decode our formalism back into discussing things.
We can talk about particles interacting with particles without any coordinates at all, or what is same thing, about empty space-time, since that is merely defined in terms of overall configuration of particles.
This further illustrates the main point: descriptions are not explanations. This space-time formalism has the appearance of an explanation, but it is merely a fancy way of summarizing a bunch of observations. What happened to the question of what underlies those observations?
@AJ: I agree. Now, I acknowledge that there is a bit of arbitrariness here... when we say that the laws of electromagnetism "explain" it, what we really mean is that if we invoke these concepts of "electric current" "mangetic field" "capacitive reactance" "inductive reactance" and so on, we can explain the phenomena in terms of these conceptually "more basic" entities.
Newton's and Einstein's theories of gravity do not involve conceptually more basic entities that serve as the "causal agents" of gravitation and that is what we mean when we say that they do not "explain" gravity. Rather, they organize the phenomena of gravity into mathematically elegant form. We have not advanced as far as we might like from the Ptolemaic view of the planets: they are at this and this and then this position at this and this and then this time and here is the very mathematically elegant equation which computes the relationship between them.
I think there is something to be said about relying too much on our intuition based on our experiences of the molar world to guide us here.
I agree, intuition is a feeble guide, at best. But my objection is based more on the idea of a "balance of evidence in similar cases" not intuition. Sound waves are not "intuitive", but they are real and they propagate over the medium, air. And so on for any other kind of wave besides the waves of elementary particles.
I agree with Bohr's allowed uses of "particle" and "wave" because that is what any elementary concept in physics really is, just a label for a concept that is accessible to my brain that is, overall, a "good fit" to the physical phenomena.
And note that I do not mean that it is not possible that the universe is, at root, some gigantic wave equation, such as Schodinger's.
In my spare time, I'm working on a widly speculative theory based on digital physics. The idea of digital physics is this. A computer can compute any function. So, the problem of "modeling" the universe can be thought of as searching for the right computer with the right program on it that, when executed, causes all the state information of this actual Universe to be computed. OK, fair enough.
However, most DP theories strike me as horribly obtuse. For example, the Cellular Automata model is very popular and people think maybe they can construct a 3-dimensional or even 2-dimensional (?) lattice of cellular-automata and then think of the universe as being "made out of" a gigantic cellular automata lattice and all macroscopic phenomena as "arising" from this lattice. It's not completely far-fetched when you realize that physics still has a lot of "room at the bottom" since our ability to resolve the physical world is about 20 or so orders of magnitude from the Planck length. In any case, I still don't like the idea of assuming this a priori spatial structure from the outset. Yes, my brain perceives the Universe in three dimensions but why should space necessarily originate as a fundamentally 3-dimensional phenomenon? Why is the number three so special??
So, I asked myself how would you build a continuous computer, a wave computer? Quantum computation is a field that exists and is real and comes very close to answering this question. In fact, Seth Lloyd wrote a book called "Programming the Universe" about QC and he asserts that "the Universe is indistinguishable from a Quantum Computer."
I don't understand the mathematics of quantum computation and I suspect, in any case, that the mathematics of quantum systems are unintentionally obfuscatory. So, I'm working on my own purely mathematical approach and my current idea is to use the complex exponential function as the basis for a new numbering system (like the decimal numbering system) that treats complex values as properly basic entities which can be computed and operated on like any other. In other words, rather than a+bi, I would like to just have z, where z is encoded in such a way that both the a and the b can be recovered from it in the same way that the 3 and 0.14159... can be separately recovered from the decimal encoding of the real number pi.
If I ever succeed (not a high probability of this... :P), it will be possible to construct a "wave computer" from the complex numbers though I haven't worked out how.