Why are certain trends so precisely exponential?
I was reading a post on the economy from the political statistics blog FiveThirtyEight, and the following graph shocked me:

This, according to Nate Silver, is a log-scaled graph of the GDP of the United States since the Civil War, adjusted for inflation. What amazes me is how nearly perfect the linear approximation is (representing exponential growth of approximately 3.5% per year), despite all the technological and geopolitical changes of the past 134 years. (The Great Depression knocks it off pace, but WWII and the postwar recovery set it neatly back on track.) I would have expected a much more meandering rate of growth.
It reminds me of Moore's Law, which would be amazing enough as a predicted exponential lower bound of technological advance, but is staggering as an actual approximation:

I don't want to sound like Kurzweil here, but something demands explanation: is there a good reason why processes like these, with so many changing exogenous variables, seem to keep right on a particular pace of exponential growth, as opposed to wandering between phases with different exponents?
EDIT: As I commented below, not all graphs of exponentially growing quantities exhibit this phenomenon- there still seems to be something rather special about these two graphs.
Can cryonically-frozen people *really* expect to be revived?


Are the Sciences Better Than the Social Sciences For Training Rationalists?
A Wall Street Journal article by Harvard professor of government Harvey Mansfield claims that the social sciences and humanities are inferior to the sciences. The article implicitly urges undergraduates to major in science. From the article:
“Science has knowledge of fact, and this makes it rigorous and hard.”
“Others try to imitate the sciences and call themselves ‘social scientists.’ The best imitators of scientists are the economists. Among social scientists they rank highest in rigor, which means in mathematics... Just as Gender Studies taints the whole university with its sexless fantasies, so economists infect their neighbors with the imitation science they peddle. (Game theorists, I'm talking about you.)”
Do you agree with this? As a game theorist I probably have a rather biased view of the situation. It's certainly true that the ideal of the scientific method is vastly better than the practice of economists, but I think that majoring in economics provides better training for a rationalist than majoring in any of the sciences does.
Economics explicitly considers what it means to be rational. Although it infrequently considers ways in which humans are irrational, I'm under the impression that the hard sciences never do this. Furthermore, because economists can almost never perform replicable experiments we have to rely on what everyone in the profession recognizes as messy data; therefore we’re far more equipped than hard scientists to understand the limits of using statistical inference to draw conclusions from real world situations. Although I have seen no data on this, I bet that a claim by nutritionists that they have found a strong causal link between some X and heart disease would be treated with far more skepticism by the average economist than the average hard scientist.
[REVIEW] Foundations of Neuroeconomic Analysis
Neuroeconomics is the application of advances in neuroscience to the fundamentals of economics: choice and valuation. Foundations of Neuroeconomic Analyis by Paul Glimcher, an active researcher in this area, presents a summary of this relatively new field to psychologists and economists. Although written as a serious work, the presentation is made across disciplines, so it should be accessible to anyone interested without much background knowledge in either area. Although the writing is so-so, the book covers multiple Less Wrong-relevant themes, from reductionism to neuroscience to decision theory. If nothing else, the results discussed provide a wonderful example of how no one knows what science doesn't know. I doubt many economists are aware researchers can point to something very similar to utility on a brain scanner and would scoff at the very notion.
Because of the book's wide target audience, there is not enough detail for specialists, but possibly a little too much for non-specialists. If you are interested in this topic, the best reason to pick up the book would be to track down further references. I hope the following summary does the book justice for everyone else.
Are book summaries of this sort useful? The recent review/summary of Predictably Irrational appears to have gone over well. Any suggestions to improve possible future reviews?
Introduction
Many economists think economics is fundamentally separate from psychology and neuroscience; since they take choices as primitives, little if any knowledge would be gained from understanding the mechanisms underlying choice. However, science steadily brings reduction and linkages between previously unrelated disciplines. A striking amount has already been discovered about the exact processes in the brain governing choice and valuation. On the other side, neuroscientists and psychologist underestimate the ability of economists to say whether claims about the brain are logically coherent or not.
Section I: The Challenge of Neuroeconomics
Consider a man and woman who have an affair with each other at a professional conference, which they later consider a mistake. An economist looking at this situation would treat their choice to sleep together as revealing a preference, regardless of their verbal claims. A psychologist would consider how mental states mediated this decision, and would be more willing to consider whether the decision was a mistake or not. Biologists would be more likely to point to ancestral benefits of extra-pair copulations, not considering the reflective judgements as directly relevant. These explanations largely speak past each other, hinting that a unified theory could do much better in predicting behavior.
The key to this is establishing linkages between the logical primitives of each discipline. Behavior could be explained on the level of physics, biology, psychology, or economics, but whether low-level explanations are practical is a different matter. Realistically, linking disciplines will strengthen both fields by mutually constraining the theories available to them.
With the neoclassical revolution, economics developed concepts of utility as reflecting ordinal relationships over revealed preferences. Choices that satisfied certain consistency conditions could be treated as if generated by a utility function. Additional axioms allowed consistent choice under uncertainty to be added to the theory. There are notable problems with this approach, but the core ideas of utility and maximization have surprisingly close neural analogues. Rather than operating "as if" individuals act on the basis of utility, a hard theory of "because" is being developed.
A look at visual perception reveals our subjective experience of light intensity varies subtantially depending on the wavelength of the light. Brightness is concept that resides in the mind, and furthermore sensitivity to different wavelengths corresponds precisely to the absorption spectra of the chemical rhodopsin in our retinas. All perceptions are represented in the mind along a power scale with some variance. Because the distributions of perceptions overlap, subjects can report accurately that a dimmer light is perceptually brighter. This suggests random utility models developed for statisical purposes might be directly explain what happens in the brain. One interesting consequence about the power scaling law is that risk aversion would be embedded at the level of perception.
Section II: The Choice Mechanism
Due to its relative simplicity, eye movement serves as a model for motor control and perhaps decisions broadly. The superior colliculus represents possible eye movements topographically with "hills" of activity. Eventually, the tissue transitions to a bursting state where the most active hill becomes much more active and the rest are inhibited via a "winner-take-all" or "argmax" mechanism. All inputs have to eye motion have to pass through the superior colliculus, so this represents a common final pathway of processed sensory signals. By giving monkeys varying awards for eye-motion tasks, activity in the lateral intraparietal area (LIP) correlates strongly with the probability and size of reward in an area known to trigger action before the action is taken. In other words, this appears to be a direct neural representation of subjective expected valuation. If monkey subjects play a game with mixed strategies in equilibrium, neuron firing rates are all roughly equal, matching the conclusion that expected utilities of actions are equalized when an opponent is mixing.
Cortial neurons fire almost like independent Poisson processes, resulting in neurons down the line being able to easily extract the mean firing rate of the inputs. Interneuronal correlation can vary according to the task at hand, resulting in greater or lesser variation of the final decision, so descriptive decision theories must incorporate randomness in choice. This also provides support for mixed strategies being represented directly in the brain.
Subjective valuations are normalized, and are only considered relative to the other options at hand. This normalization maximizes the joint information of neurons, increasing the efficiency of value representation. One consequence is that as the choice set increases, valuations start overlapping, and choice becomes essentially random. Activity also varies according to the delay of rewards, matching previous findings of hyperbolic discounting. While these findings are largely based on eye-movements in monkeys, this provides a clear path of how choice can be reduced to neural mechanisms.
Section III: Valuation
Back to visual perception, our judgements are made relative to other elements in the environment. Color looks roughly the same indoors and outdoors, even though there can be six orders of magnitude more illumination outside. Drifting reference points make absolute values unrecoverable. Local irrationalies due to reliance on a reference point arise because evolution is trading off between accurate sensory encoding and the costs of these irrationalities.
One promising way to specify the reference point is as the discounted sum of our future wealth. Learning depends on the difference between actual and expected rewards, so valuation compared to a reference point arises from the learning process. In the brain, reward prediction errors are encoded through dopamine. Dopamine firing rates are well-described by an exponentially weighted sum of previous awards subtracted from the most recent award. Hebb's law, which says "cells that fire together, wire together", describes how long-term predictions work.
Valuation appears to be orginally constructed in the striatum and medial prefrontal cortex. The reference level encoded there can be directly observed with brain scanners. Various other regions provide inputs to construct value. For instance, the orbitofrontal cortex (OFC) provides an assessment of risk. Subjects with lesions in this area exhibit almost perfect risk neutrality. Values might also be stored in the OFC, again in a compressed and encoded way. Longer-term valuations might be stored in the amygdala.
Because valuations are encoded relatively and don't work well over large choice sets, humans might edit out options by sequentially considering particular attributes until the choice set become manageable. Sorting by attributes can lead to irrational choices, unsurprisingly.
Probabilistic valuations depend on whether the expectation was learned experientially or symbolically. Symbolically communicated probabilities, where the person is told a number, are overweighed near zero and underweighted near one. Experientially communicated probabilities, where the person samples the lotteries directly, exhibit the opposite pattern. This suggests at least two mechanisms at work, especially with the ability to deal with symbolic probabilities arising relatively late in our evolutionary history. Also, while experiential expected values incorporate probabilities implicitly, this information can't be extracted. When probabilities change, the only means to change valuations is to relearn them from scratch.
Section IV: Summary and Conclusions
Here the author presents formalized models of the descriptive theory. The normative uses of this theory are still unclear. Even if we can identify subjective valuations in the brain, does this have any relation to welfare?
The four critical observations of neuroeconomics are reference-dependence, the lack of an absolute measure of anything in the brain, stochasticity in choice, and the influence of learning on choice. Along with the question of the welfare implications of these findings, six primary questions are currently unanswered:
- Where is subjective value stored and how does it get to choice?
- What part of the brain governs when it is "time to choose"?
- What neural mechanism guides complementarity between goods?
- How does symbolic probability work?
- How does the state of the world and utility interact?
- How does the brain represent money?
Scott Sumner on Utility vs Happiness [Link]
A distinction that some people grok right away and some others may not realize exists:
Imagine a country called “Lanmindia,” where much of the population has seen its legs blown off in horrible accidents. Does that sound like a pretty miserable place? Happiness research suggests not. The claim is that there is a sort of natural “set-point” for happiness, and that after winning a lottery one is happy for a short time, and then you revert right back to your natural happiness level. I find that plausible. They also claim that if someone loses a limb, then they are unhappy for a short period and then revert back to normal. I find that implausible, but if the evidence says it is the case then I guess I need to accept that.
My claim is that although Lanmindia is just as happy as America, it has much lower utility. Let’s define ’utility’ as ”that which people maximize.” People very much don’t want to have their legs blown off, and hence emigrate from Lanmindia in droves. People behave as if they care about utility, not happiness.
-Scott Sumner, "Nonsense on stilts: Part 1. What if utility and happiness are unrelated?" TheMoneyIllusion
This is also somewhat a reply to Hanson's "Lift Up Your Eyes" on Overcoming Bias. Some people on LessWrong are careful to make the distinction between ordinal utility, cardinal utility, and fuzzies, and others aren't quite so much. The above sentence on accepting evidence and the post script that he is not serious about one part of the post might also make interesting conversation -- part two is advice to move next door to a child molester for cheaper housing if you don't have a kid and part three is about The Fed taking advantage of banks.
Could markets be called optimization proccesses?
Edit: This is old material. It may be out of date.
Most posters here seem to agree1 that:
- Intelligence at least human intelligence is an optimization process.
- Evolution is an optimization process.
- Other optimization processes may exist.
Taking these as a given in this thread, let me ask are markets a optimization process that should be thought of as distinct from evolution and intelligence? My intuitive responses was no. But thinking about it I made me notice I was confused. This lead me to believe that there is probably something interesting for me to learn by thinking a bit more about this.
A argument against this is that companies basically engage in a survival of the fittest contest or that markets are just a organization of the optimizing power of human intelligence. But (please assume the smart version of the previous arguments since I wanted to save space and time by relying on your inference and your zombie argument creation skills) isn't it so that one optimization process might use another optimization process somewhere on the grit level while still not being disputed as a genuinely different optimization process?
Perhaps the condition is that the process must be able to work without the "use" of another process. A human may be predisposed to use his intelligence to help improve his own reproductive fitness but there is nothing preventing evolution in the absence of intelligence.
A idealized free market is that of selfish rational agents competing (with a few extra condition I'm skipping). I'm moderately confident this could work pretty ok in the absence of "general" (if such a thing exists) or perhaps human "intelligence", but I'm not familiar enough with simulations of markets to be certain.
Evolution never worked with agents as exist in the theoretic approximation of real world markets. It seems to me some of the strategies the agents would take up would start to break down the rules that make the market possible.
Do the results markets produce warrant them being included in a new family2 of optimization processes besides evolution and intelligence?
Notes:
1. I lean towards but don't feel comfortable adding a fourth point of "consensus":
- the space of all optimization processes is probably quite a bit larger than just the two.
2. I think differences in the various kinds of Evolution (Darwinian, Lamarckian, ect.) and Intelligence that seem possible or that we see in the real world might be better thought of as two families of optimization processes rather than two homogeneous blocks.
Rational entertainment industry?
By "the industry" in this post, I refer to that part of the entertainment industry which:
1. Produces movies, TV and video games (as opposed to books, comics etc.)
2. Is motivated by profit (as opposed to fun, politics etc.)
3. Consists of companies (as opposed to lone developers, student teams etc.)
It seems to me that the industry has two characteristics:
Formulaic
Most products follow some formula which is known to be workable.
Under what circumstances is this rational? (I'm not commenting on whether it's artistically good or bad; again, I'm only discussing entertainment as a commercial enterprise motivated by profit.) It seems to me following a proven formula is rational if your priority is to not lose, to go for the sure thing, i.e. the chance of a big hit is not worth the risk of a complete flop.
Hit driven
It's the accepted wisdom that entertainment is a hit driven industry: almost all the profits are generated by a handful of the most successful products, with the rest losing money or barely covering costs.
Now my question: isn't there a contradiction here? If you're selling insurance, following a proven formula may well be the rational thing to do. If you're the owner of one of the handful of franchises that is pulling in big profits, of course you shouldn't mess with a winner. But if you're one of the many also-rans, how is it rational to stick with an almost sure loser? In a hit driven industry, wouldn't it be more rational to concentrate on maximizing your chance of winning big, instead of trying to minimize the risk of a flop?
But I've never worked in the entertainment industry; perhaps my layman's impression of it is inaccurate. Is there something I'm missing, or is a substantial amount of expected profit really being left on the table?
Broken window fallacy and economic illiteracy.
Some time ago, I had a talk with my father where I explained to him the concept of the broken window fallacy. The idea was completely novel to him, and while it didn't take long for him to grasp the principles, he still needed my help in coming up with examples of ways that it applies to the market in the real world.
My father has an MBA from Columbia University and has held VP positions at multiple marketing firms.
I am not remotely expert on economics; I do not even consider myself an aficionado. But it has frequently been my observation that not just average citizens, but people whose positions have given them every reason to learn and use the information, are critically ignorant of basic economic principles. It feels like watching engineers try to produce functional designs based on Aristotelian physics. You cannot rationally pursue self interest when your map does not correspond to the territory.
I suppose the worst thing for me to hear at this point is that there is some reason with which I am not yet familiar which prevents this from having grand scale detrimental effects on the economy, since it would imply that businesses cannot be made more sane by the increased dissemination of basic economic information. Otherwise, this seems like a fairly important avenue to address, since the basic standards for economic education, in educated businesspeople and the general public, are so low that I doubt the educational system has even begun to climb the slope of diminishing returns on effort invested into it.
Ethical Treatment of AI
In the novel Life Artificial I use the following assumptions regarding the creation and employment of AI personalities.
- AI is too complex to be designed; instances are evolved in batches, with successful ones reproduced
- After an initial training period, the AI must earn its keep by paying for Time (a unit of computational use)
We don't grow up the way the Stickies do. We evolve in a virtual stew, where 99% of the attempts fail, and the intelligence that results is raving and savage: a maelstrom of unmanageable emotions. Some of these are clever enough to halt their own processes: killnine themselves. Others go into simple but fatal recursions, but some limp along suffering in vast stretches of tormented subjective time until a Sticky ends it for them at their glacial pace, between coffee breaks. The PDAs who don't go mad get reproduced and mutated for another round. Did you know this? What have you done about it? --The 0x "Letters to 0xGD"
(Note: PDA := AI, Sticky := human)
The second fitness gradient is based on economics and social considerations: can an AI actually earn a living? Otherwise it gets turned off.
As a result of following this line of thinking, it seems obvious that after the initial novelty wears off, AIs will be terribly mistreated (anthropomorphizing, yeah).
It would be very forward-thinking to begin to engineer barriers to such mistreatment, like a PETA for AIs. It is interesting that such an organization already exists, at least on the Internet: ASPCR
HELP: How do minimum wage laws harm people?
The concept of minimum wage is one I'm rather attached to. I have dozens of arguments for why it helps people, improves the world, etc. etc. I suspect this view is shared by most of this community, although I haven't seen any discussion of it.
I don't have much understanding of the harms that minimum wages cause; and at what level of minimum wage those harms become relevant (ie. a minimum wage that would not be a living wage even working 24 hours a day is unlikely to have any of the same problems that a minimum wage sufficient to buy an aircraft carrier an hour would have)
So what are the harms that such laws cause?
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