Who predicts the future successfully for a living?
I assert that we have a great deal of study of 3 distinct groups, each of whom depends for their livelihood on the ability to predict the future.
- Scientists (also, applied scientists like Engineers, Doctors, Programmers)
- Gamblers (also, otherly named gamblers like Investors, Actuaries, VC's, etc.)
- Children (Kids spend their first 10 years in an almost constant state of trying to make sense of their world...well, and get what they want)
- Everyone sucks at predicting new and complex stuff, all the time.
- Specifically, untested theory is almost always wrong. It isn't quite right to suggest that anyone pushing a theory without it having been tested should automatically be assumed to be wrong...but it's not that wrong either.
- Successful predictors talk in terms of probabilities, or probability spaces. Sane prediction methods never say, outside of very odd cases, "X will happen." Rather...with innumerable forces in play, the only sane claims are: there is roughly a P% chance that a result within range ε (epsilon) of X will happen. Predictive intelligence happens when we get serious about the P and the ε. The X is mostly bloviation.
- Induction appears to be the primary/only path. Gather large amounts of data...look for patterns. Occasionally, if you've gathered enough data, you can see patterns that are there, rather than fictional. If extra-lucky, your pattern may extend beyond the narrow space you're looking in.
- Aside...can one model mathematics (esp. advanced maths) as being an exploration of the space of all possible patterns? So as to be more able to recognize the patterns when they appear elsewhere? This would solve Einstein's question about why math describes the world.
- There's very little substitute for the Gembutsu approach. If you want to understand a topic, Get Your Boots On, and go DO it for a while. Thinking about a topic abstractly ain't good for much.
- People build models of the world...they do not discover them. Learning is the process of people building their own models of the world which correspond better to some external standard.
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You wrote "can one model mathematics (esp. advanced maths) as being an exploration of the space of all possible patterns?"
Solomonoff induction is close to this, but it's highly impractical. More practical less ideal approaches in the same spirit can be defined using the MDL (Minimum Description Length) principle. Or if you don't want to start by forcing all questions into a digitally coded form, there are methods in statistical learning theory that arrive at a similar results while letting a lot of the analysis be done using more physically appealing concepts like real numbers.
"This would solve Einstein's question about why math describes the world."
How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? --- Albert Einstein
As far as I can see, to "model mathematics as being an exploration of the space of all possible patterns" doesn't "solve[s] Einstein's question". After "modelling mathematics as being an exploration..." Einstein's question seems to become roughly "how come our exploration arrives at so many useful precise results so astonishingly fast?" We know no particular reason that so much of what happens in the universe must be accurately described by a few equations which have a nice concise mathematical form. E.g., why Newton's law of gravitation instead of a 14,000-volume set of mathematical tables characterizing the idiosyncrasies of the interaction in various cases? Or a set of tables so vast and strange that human minds wouldn't be able to start noticing the regularities unless a human civilization continued for trillions of trillions of years?
Eric S. Raymond on the Utility of Mathematics.
William,
1. Welcome to the blog.
2. I think there's at least 2 sides to the Einsteinian question. I read it as primarily a response to the idealist notion of mathematics as created from thin air. IF humans create math from nothingness...why does it work in the real world? AFAICT, you are reading a different aspect of the question: why is the simple part of the world so simple?
To whatever extent that Einstein should be read how I've been reading him the last dozen years or so...I think my statement largely does dispose of the question.
If there are additional resources that suggest which way he ought to be read, or (more likely) proportions of his question to take in different ways?
3. I'm moderately familiar with Kolomogorov complexity, but I was looking at something more vague. For instance...Abstract/Modern Algebra is an analysis of number systems in general. For any possible arithmetic, Abstract Algebra analyzes which rules still apply. Algebra is looking at one corner of the space of all possible patterns (ways in which bits relate to one another). I haven't looked at the ways to translate from a discipline like abstract algebra into computational/algorithmic approaches.
Math is good at physics because it was originally derived from physics.
It may, in addition, have the properties you speculate.
It should not be at all surprising to the logician that the properties of physics we call 'math' are consistent with other properties of physics.
Aside from the mammal equivalent of birds counting eggs, the first use of math that I know of was to count cows and wheat. If it didn't reflect the physical behaviour, it would be useless. Thus, physics. Mathematics as a whole is simply the generalization of the behaviour of cow stock.
Alrenous, yes, and in a sense I would even go further than that. Even if we hadn't optimized math to cope with early physical examples, we made it with brains that were optimized to deal with physical problems.
However.
The kinds of physical problems that physics has learned to deal with since Maxwell or so --- notably EM, thermo, relativity, and QM --- are pretty different from the physics problems that our brains, or our earlier math, was optimized to deal with. Almost everyone finds them confusing and nonintuitive when they first learn them. So how come mathematically they're only a little bit different? and sometimes in ways that let us start using old underused pure abstractions (like imaginary numbers) directly for physics (like time evolution of wavefunctions)? It is peculiar that the mathematics of cows turns out also to be concisely and exactly the mathematics of radio, spectral lines, antimatter, and black holes.
2 + 2 = 4 is quantum physics. The cows are all made of protons, neutrons, and electrons.
This section of physics we've cordoned off as 'classical' in fact implies and requires quantum physics to exist. Verification: try to find an area of quantum physics one could change without changing classical physics.
The earlier math appeared optimized for classical, but that's an illusion. Rather, it's a precise description of some particulars of a physical system.
Simply by deriving all the conclusions that are consistent with the first one, starting with multiplication, you end up with descriptions of all systems that are logically consistent with 2 + 2 = 4. Why does it surprise you that all these logically consistent things are physically permissable?
From the comments section of Ed's latest blog post:
"The more I think about it, the more I fail to see how the modern, "loose and separate" so-called "mechanical philosophy" is even a coherent view. It seems to me that if you attempt to state it in any sort of detail, you end up with just an unnecessarily complicated variant of the A-T metaphysic.
Whenever I put ice under hot water, the ice is melted. The A-Tist would say that being in a melted state is a potentiality of the ice, and that it "points to" or has an inherent tendency toward being melted when exposed to heat. The ateleologist would say that cause and effect are "loose and separate", that there is nothing intrinsic to ice or to heat that points to the ice being melted, and that it's simply a regularity we observe that the event of ice being exposed to heat happens to be followed by the event of the ice melting in our experience.
But presumably the ateleologist isn't claiming that it's just pure chance that the ice always happens melt under hot water when I'm looking, right?! There must be *something* accounting for why it always happens, and if it's not the nature of the ice and the heat themselves, then what? Here I guess the ateleologist might say that it's physical laws which the ice and heat "obey," thereby basically conceiving of natural laws as actual active agents that direct events rather than as mere abstractions of the predictable ways in which physical things behave by virtue of their intrinsic natures.
Well, okay, but I still don't see how this escapes the A-T view. Rather it's just an unnecessarily complicated version of it. Even if we postulate that the Laws Of Thermodynamics (or whatever other law you wish to postulate for any given phenomena) are actual active entities, it remains a fact that the laws consistently cause the ice to *melt* specifically and not turn to into a puppy dog or dance the Macarena. So all you've really done is attribute teleology to the reified laws themselves. Additionally, it remains a fact that the laws consistently cause *ice* (as opposed to, say, stainless steel) to melt under *heat* (as opposed to, say, while in the freezer), so the intrinsic nature of the objects following the laws is still part of what determines how the laws act on them under this view.
In other words, if you try to state this "extrinsic", "mechanical", "ateleological" view in a way that makes sense at all, you end up attributing intrinsic teleology to material things *as well as* hypothetical, reified "natural laws." It's basically just the A-T view with a bunch of unnecessary kruft tacked on. Applying "Ockam's" Razor (which thanks to TLS I know wasn't Ockam's creation), we can then eliminate the superfluously multiplied entities (the reified natural laws) because the natures of the material things themselves are explanatorily sufficient to understand why we see regularities."
herz,
The angle of the comment is completely wrong.
The chemical compound known as H2O has known behaviors under various temperature/pressure combinations. H2O + 1 atmosphere of pressure + 25 degrees celcius results in a liquid.
H2O + 1 atmosphere of pressure + -25 degrees celcius results in a solid.
Is water a potentiality of ice? WTF? water is a particular chemical/pressure/temperature combo. There's no potentiality involved...unless you want to map the combinations for all temperatures and pressures of water like this: http://www.lsbu.ac.uk/water/phase.html
The potentiality discussion is incoherent, and based of the crazy idea that our experiences are somehow important to the water.
Someone needs to talk to some physicists/chemists.
I'm a mereological nihilist.
There's not really any such thing as 'water,' 'ice,' 'hot,' or 'melting.'
You can define them but they cannot be made arbitrarily precise; they are inherently ambiguous.* If your error threshold is high, it's fine, but physics cannot have an error threshold relative to itself.
There are, however, quarks and electrons.
The problem here is attempting to describe the interaction of ice and hot water as some fundamental thing, rather than as shorthands for arrangements of quarks and electrons spewing virtual photons at each other.
*For example the surface of ice is actually a haze of middle states, as is the surface of water. At the triple point this haze becomes macro-sized.
On the plus side, the author is inches from realizing a fundamental problem.
"There must be *something* accounting for why it always happens, and if it's not the nature of the ice and the heat themselves, then what?"
But what accounts for the properties of the ice? What accounts for the laws? Or: what accounts for accounting itself?
I have realized I have no idea how supercooling works.
Alrenous,
You've gone all intrinsicist on me again. Quarks and electrons are MODELS that explain our experiments. They are not "out there".
Something has to be intrinsically out there. Physics can't be a model of itself.
More precisely: right now, I'd bet on those things being quarks and leptons. One hundred years ago I'd have bet on atoms. Also, if I'd been alive then and lived to be 100, I would have changed my mind.
Show me the evidence that quarks aren't really out there. If they're not, such evidence will exist. If it exist, it will eventually be found.
This recent Feser post deals with your "scientism" quite nicely:
http://edwardfeser.blogspot.com/2011/11/reading-rosenberg-part-ii.html#more
Herz,
I read that...I've read his whole rosenberg series...and even sent you to look at it. I'm pretty unimpressed. AFAICT, he's operating in a "teleology is reasonable" position, while I haven't gotten there yet. I suppose I owe you part III.
Alrenous,
1. I agree that there is something out there. However, I am awful close to Parmenides (Zeno's teacher) in saying: It Is is all we can say. Everything after that is models. I don't mind if you like your quark/lepton model...so long as you keep track of the fact that quark/lepton is a model we use to predict...just like atom is a model we used to use to predict. Atom works pretty damn well, though.
2. I continue to insist that the best thing Quantum Mechanics did was to remove us from the question of what "is there", and instead in a question of what can we predict.
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