25 May 2011

The norms of the scientific community

There are two answers to the question “Why is science so successful?” The most popular, and probably mistaken, answer is that science has a method for guiding the discovery process. The other answer, associated with Michael Polanyi and Paul Feyerabend, is that the success of science is due to the scientific community having a particular kind of social organization (works according to certain norms).

Willmoore Kendall describes these norms in the following way:

[T]he discussion  process  works  in  those  situations   in which  men  who  are  products  of  the  tradition organize themselves  for a serious  venture  in the pursuit  of  truth ... Such   men  demonstrably    proceed   on  some such  principles   as  these: 

(a)   The   pursuit   of truth  is  indeed  forwarded  by  the  exchange  of opinions  and  ideas  among  many;  helpful  suggestions    do   indeed   emerge   sometimes    from surprising  quarters;  but  one  does  not  leap  from these  facts  to  the  conclusion  that  helpful  suggestions  may  come  from just  anybody.  

(b)  The man  or woman  who  wishes  to  exercise  the  right to   be  heard  has   a  logically   and   temporally prior  obligation  to  prepare himself  for  participation  in  the  exchange,  and  to  prepare  himself in   the   manner   defined   by   the   community.

Moreover   (c),  from  the  moment   he  begins  to participate    in  the   exchange,   he   must   make manifest,  by  his behavior,  his sense  of the  duty to  act  as  if  the  other  participants   had  something  to  teach  him-the duty,   in  a  word,  to see  to  it  that  the  exchange  goes  forward  in  an atmosphere  of courtesy  and mutual  self-respect.

Next   (d),   the   entrant   must   so  behave   as  to show  that   he  understands   that   scholarly   investigation   did  not  begin  with  his  appearance on the  scene,  that  there  is a strong  presumption that   prior  investigators   have  not  labored  entirely  in  vain,  and  that  the  community   is  the custodian  of-let    us not  sidestep  the  mot juste - an  orthodoxy, no  part  of  which  it  is  going  to  set lightly   to  one  side. 

(e)  That  orthodoxy   must be  understood  as  concerning  first and  foremost the   frame  of  reference  within   which  the   exchange  of  ideas  and  opinions  is  to  go  forward. That  frame  of  reference  is,  to  be  sure,  subject to  change,  but  this  is  a  matter  of  meeting  the arguments   that  led  originally  to  its  adoption, and   meeting   them   in   recognition    that    the ultimate  decision, as to  whether  or not  to  change it,  lies  with  the  community.   

(f)  The  entrant, insofar  as he wishes  to  challenge  the  orthodoxy, must  expect  barriers  to  be  placed  in  his  way, and  must  not  be  astonished   if  he  is  punished, at  least  in the  short  term,  by  what  are fashionably   called   "deprivations";   he  must,   indeed, recognize   that   the   barriers  and  the   deprivations  are a necessary  part  of the  organized  procedure  by  which  truth  is  pursued.  

(g)  Access to  the  channels  of  communication   that  represent  the  community's  central  ritual  (the learned journals,  that  is  to  say)  is  something   that  the entrant   wins  by  performing  the  obligation   to produce  a craftsmanlike  piece  of work. 

(h)  The ultimate  fate  of the  entrant  who  disagrees  with the  orthodoxy   but  cannot   persuade  the  community   to  accept   his  point   of  view   is,  quite simply,  isolation  within  or banishment  from the community.

[The "Open Society" and Its Fallacies, The American Political Science Review, 54(4), 1960, pp. 972-979]

Lee Smolin describes the norms in the following way:

Science has succeeded because scientists comprise a community that is defined and maintained by adherence to a shared ethic. It is adherence to an ethic, not adherence to any particular fact or theory, that I believe serves as the fundamental corrective within the scientific community.

There are two tenets of this ethic:

1) If an issue can be decided by people of good faith, applying rational argument to publicly available evidence, then it must be regarded as so decided.

2) If, on the other hand, rational argument from the publicly available evidence does not succeed in bringing people of good faith to agreement on an issue, society must allow and even encourage people to draw diverse conclusions.

I believe that science succeeds because scientists adhere, if  mperfectly, to these two principles. To see whether this is true, let us look at some of the things these principles require us to do.

* We agree to argue rationally, and in good faith, from shared evidence, to whatever degree of shared conclusions are  warranted.

* Each individual scientist is free to develop his or her own conclusions from the evidence. But each scientist is also required to put forward arguments for those conclusions for the consideration of the whole community. These arguments must be rational and based on evidence available to all members. The evidence, the means by which the evidence was obtained, and the logic of the arguments used to deduce conclusions from the evidence must be shared and open to examination by all members.

* The ability of scientists to deduce reliable conclusions from the shared evidence is based on the mastery of tools and  procedures developed over many years. They are taught because  experience has shown that they often lead to reliable results. Every scientist trained in such a craft is deeply aware of the  capacity for error and self-delusion.

* At the same time, each member of the scientific community recognizes that the eventual goal is to establish consensus. A consensus may emerge quickly, or it may take some time. The ultimate judges of scientific work are future members of the community, at a time sufficiently far in the future that they can better evaluate the evidence objectively. While a scientific program may temporarily succeed in gathering adherents, no program, claim, or point of view can succeed in the long run unless it produces sufficient evidence to persuade the skeptics.

* Membership in the community of science is open to any human being. Considerations of status, age, gender, or any other personal characteristic may not play a role in the consideration of a scientist's evidence and arguments, and may not limit a member's access to the means of dissemination of evidence,  argument, and information. Entry to the community is,  however, based on two criteria. The first is the mastery of at least one of the crafts of a scientific subfield to the point where you can independently produce work judged by other members to be of high quality. The second criterion is allegiance and  continued adherence to the shared ethic.

* While orthodoxies may become established temporarily in a given subfield, the community recognizes that contrary  opinions and research programs are necessary for the community's continued health.

...

I would call this kind of community, in which membership is  defined by adherence to a code of ethics and the practice of crafts developed to realize them, an ethical community. Science, I would propose, is the purest example we have of such a community.

But it is not sufficient to characterize science as an ethical  community, because some ethical communities exist to preserve old knowledge rather than to discover new truths. Religious  communities, in many cases, satisfy the criteria for being ethical  communities. Indeed, science in its modern form evolved from monasteries and theological schools — ethical communities whose aim was the preservation of religious dogma. So if our characterization of science is to have teeth, we must add some criteria that cleanly distinguish a physics department from a monastery.

To do this, I would like to introduce a second notion, which I call an imaginative community. This is a community whose ethic and organization incorporates a belief in the inevitability of progress and an openness to the future. The openness leaves room, imaginatively and institutionally, for novelty and surprise. Not only is there a belief that the future will be better, there is an understanding that we cannot forecast how that better future will be reached.

Neither a Marxist state nor a fundamentalist religious state is an imaginative community. They may look forward to a better future, but they believe they know exactly how that future will be reached. ... An imaginative community believes that the future will bring surprises, in the form of new discoveries and new crises to be  overcome. Rather than placing faith in their present knowledge, its members invest their hopes and expectations for the future in future generations, by passing along to them the ethical precepts and tools of thinking, individual and collective, that will enable them to  overcome and take advantage of circumstances that are beyond the  present powers of imagination. Good scientists expect that their students will exceed them. ...

The scientific community is thus both an ethical and an  imaginative community.

What should be abundantly clear from this description is that controversy is essential for the progress of science. My first  principle says that when we are forced to reach a consensus by the  evidence, we should do so. But my second principle says that until the evidence forces consensus, we should encourage a wide diversity of viewpoints. This is good for science — a point that Feyerabend made often, and I believe correctly. Science proceeds fastest when there are competing theories. The older, naive view is that theories are put forward one at a time and tested against the data. This fails to take into account the extent to which the theoretical ideas we have influence which experiments we do and how we interpret them. If only one theory is contemplated at a time, we are likely to get stuck in intellectual traps created by that theory. The only way out is if different theories compete to explain the same evidence.

Feyerabend argued that even in cases where there is a widely accepted theory that agrees with all the evidence, it is still necessary to invent competing theories in order for science to progress. This is because experiments that contradict the established view are most likely to be suggested by a competing theory and perhaps would not even have been conceived were there not a competing theory. So competing theories give rise to experimental anomalies as often as the reverse.

Therefore Feyerabend insisted that scientists should never agree, unless they are forced to. When scientists come to agreement too soon, before they are compelled to by the evidence, science is in danger. ...

Science moves forward when we are forced to agree with something unexpected. If we think we know the answer, we will try to make every result fit that preconceived idea. It is controversy that keeps science alive, keeps it moving. In an atmosphere filled with controversy over rival views, sociological forces are not enough to bring people into agreement. So on those rare occasions when we do come to consensus on something, it is because we have no choice. The evidence forces us to do so, even if we don't like it. That is why progress in science is real. ...

While the progress of science relies on the possibility of achieving consensus in the long term, the decisions an individual scientist makes as to what to do, and how to evaluate the evidence, are always based on incomplete information. Science progresses because it is built on an ethic recognizing that in the face of incomplete information we are all equal. No one can predict with certainty whether an approach will lead to definite progress or years of wasted work. All we can do is train students in the crafts that experience has shown to lead most often to reliable conclusions. After that, we must leave them free to follow their own hunches and we must make time to listen to them when they report back. As long as the community continually opens up opportunities for new ideas and points of view and adheres to the ethic that in the end we require consensus based on rational argument from evidence available to all, science will eventually succeed.

The task of forming the community of science will never be  finished. It will always be necessary to fight off the dominance of  orthodoxy, fashion, age, and status. There will always be temptations to take the easy way, to sign up with the team that seems to be winning rather than try to understand a problem afresh. At its finest, the scientific community takes advantage of our best  impulses and desires while protecting us from our worst. The  community works in part by harnessing the arrogance and ambition we each in some degree bring to the search. Richard Feynman may have said it best: Science is the organized skepticism in the reliability of expert opinion.

[The Trouble with Physics, chapter 17, “What Is Science?”, pp. 301-307]

23 May 2011

Kirzner & Lachman on the “market process”

From The Foundations of Modern Austrian Economics edited by Edwin Dolan.

Kirzner, “Equilibrium Versus Market Process”:

In our classrooms we draw the Marshallian cross to depict competitive supply and demand, and then go on to explain how the market is cleared only at the price corresponding to the intersection of the curves. Often the explanation of market price determination proceeds no further—almost implying that the only possible price is the market-clearing price. Sometimes we address the question of how we can be confident that there is any tendency at all for the intersection price to be attained. The discussion is then usually carried on in terms of the Walrasian version of the equilibration process. Suppose, we say, the price happens to be above the intersection level. If so, the amount of the good people are prepared to supply is in the aggregate larger than the total amount people are prepared to buy. There will be unsold inventories, thereby depressing price. On the other hand, if price is below the intersection level, there will be excess demand, “forcing” price up. Thus, we explain, there will be a tendency for price to gravitate toward the equilibrium level at which quantity demanded equals quantity supplied.

Now this explanation has a certain rough-and-ready appeal. However, when price is described as being above or below equilibrium, it is understood that a single price prevails in the market. One uncomfortable question, then, is whether we may assume that a single price emerges before equilibrium is attained. Surely a single price can be postulated only as the result of the process of equilibration itself. At least to this extent, the Walrasian explanation of equilibrium price determination appears to beg the question.

Again, the Walrasian explanation usually assumes perfect competition, where all market participants are price takers. But with only price takers participating, it is not clear how unsold inventories or unmet demand effect price changes. If no one raises or lowers price bids, how do prices rise or fall? (p. 116)

The concept of “economizing” is insufficient for explaining the market process:

Robbins defined economics as dealing with the allocative aspect of human affairs, that is, with the consequences of the circumstance that men economize by engaging in the allocation of limited resources among multiple competing ends. ...

Robbinsian economizing consists in using known available resources in the most efficient manner to achieve given purposes. ... For Robbins, economizing simply means shuffling around available resources in order to secure the most efficient utilization of known inputs in terms of a given hierarchy of ends. It is the interaction in the market of the allocative efforts of numerous economizing individuals that generates all the phenomena that modern economics seeks to explain. ...

The notion of a Robbinsian plan assumes that information is both given and known to the acting individuals. Lacking this information market participants are blocked from Robbinsian activity altogether. ... We lack justification within this framework for stating, for example, that unsold inventories will depress price; we may only say that with excessive price expectations Robbinsian decision makers will generate unsold inventories. As decision makers they do not raise or lower price; they are strictly price takers, allocating against a background of given prices. If all participants are price takers, how then can the market price rise or fall? By what process does this happen, if it happens at all? (p. 118-9)

Entrepreneurship fills the gap:

Mises’s concept of human action embodies an insight about man that is entirely lacking in a world of Robbinsian economizers. This insight recognizes that men are not only calculating agents but are also alert to opportunities. Robbinsian theory only applies after a person is confronted with opportunities; for it does not explain how that person learns about opportunities in the first place. ... [W]hen the prevailing price does not clear the market, market participants realize they should revise their estimates of prices bid or asked in order to avoid repeated disappointment. This alertness is the entrepreneurial element in human action, a concept lacking in analysis carried out in exclusively Robbinsian terms. At the same time that it transforms allocative decision making into a realistic view of human action, entrepreneurship converts the theory of market equilibrium into a theory of market process. ... (p. 119-20)

The producer’s decisions about what product to produce and of what quality are invariably a reflection of what he believes he will be able to sell at a worthwhile price. It is invariably an entrepreneurial choice. The costs he incurs are those that in his estimation he must in order to sell what he produces at the anticipated price. Every improvement in the product is introduced to make it more attractive to consumers, and certainly the product itself is produced for precisely the same reasons. All costs are in the last analysis selling costs. (p. 123)

Robbinsian incentives can be offered in nonmarket contexts. The bureaucrat, employer, or official offers a bonus for greater effort. For entrepreneurial incentives to operate, on the other hand, it is necessary for those who perceive opportunities to gain from noticing them. An outstanding feature of the market system is that it provides these kinds of incentives. ... It would be good to know more about the institutional settings that are most conducive to opportunity discovery. It would be good to apply basic Austrian theory to the theory of speculation and of the formation of expectations with regard to future prices. All this would enrich our understanding of the economics of bureaucracy and of socialism. (p. 124)

Knowledge and expectations as the driving forces of the market process:

Ludwig M. Lachmann, “On the Central Concept of Austrian Economics: Market Process”:

The market process is the outward manifestation of an unending stream of knowledge. ... The pattern of knowledge is continuously changing in society, a process hard to describe.(p. 127)

The stream of knowledge produces ever new disequilibrium situations, and entrepreneurs continually manage to find new price-cost differences to exploit. When one is eliminated by strenuous competition, the stream of knowledge throws up another. Profit is a permanent income from ever-changing sources.

In the first place, how do we determine the true origin of any particular bit of knowledge? When and how do ill-founded surmises and half-baked ideas acquire the status of respectable knowledge? ... Two things we may assert with reasonable confidence. ... we cannot have future knowledge in the present. Also, men sometimes act on the basis of what cannot really be called knowledge. Here we encounter the problem of expectations.

Although old knowledge is continually being superseded by new knowledge, though nobody knows which piece will be obsolete tomorrow, men have to act with regard to the future and make plans based on expectations. Experience teaches us that in an uncertain world different men hold different expectations about the same future event. ... divergent expectations entail incoherent plans (p. 128)

Expectations must be regarded as autonomous, as autonomous as human preferences are. To be sure, they are modified by experience, but we are unable to postulate any particular mode of change. To say that the market gradually produces a consistency among plans is to say that the divergence of expectations, on which the initial incoherence of plans rests, will gradually be turned into convergence. But to reach this conclusion we must deny the autonomous character of expectations. ... If the stream of knowledge is not a function of anything, how can the degree of divergence of expectations, which are but rudimentary forms of incomplete knowledge, be made a function of time?

Unsuccessful plans have to be revised. No doubt planners learn from experience. But what they learn is not known; also different men learn different lessons. (p. 129)

All useful knowledge probably tends to be diffused, but in being applied for various purposes it also may change character, hence the difficulty of identifying it. (p. 127)

Two possible views of the market process:

For one view the market process is propelled by a mechanism of given and known forces of demand and supply. The outcome of the interaction of these forces, namely, equilibrium, is in principle predictable. But outside forces in the form of autonomous changes in demand and supply continually impinge on the system and prevent equilibrium from being reached. The system is ever moving in the direction of an equilibrium, but it never gets there. The competitive action of entrepreneurs tending to wipe out price-cost differences is regarded as “equilibrating”; for in equilibrium no such differences could exist.

The other view, which I happen to hold, regards the distinction between external forces and the internal market mechanism as essentially misleading. Successive stages in the flow of knowledge must be manifest in both. Market action is not independent of expectations, and every expectation is an attempt “to catch a glimpse of future knowledge now.” (p. 129-30)

It might be held, however, that every process must have a direction, and unless we are able to show that every stage of the market process “points” in the direction of equilibrium, no satisfactory theory of the market process is possible. But this is not a convincing view. (p. 130)

The notion of general equilibrium is to be abandoned, but that of individual equilibrium is to be retained at all costs. It is simply tantamount to rational action. Without it we should lose our “sense of direction.” The market process consists of a sequence of individual interactions, each denoting the encounter (and sometimes collision) of a number of plans, which, while coherent individually and reflecting the individual equilibrium of the actor, are incoherent as a group. The process would not go on otherwise. (p. 131)

[T]he divergence of expectations, apart from being an obstacle to equilibrium, has an important positive function in a market economy. It is an anticipatory device. The more extended the range of expectations, the greater the likelihood that somebody will catch a glimpse of things to come and be “right.” Those who take their orientation from the future rather than the present, the “speculators,” permit the future to make its impact on the market process earlier than otherwise. They contrive to inject a glimpse of future knowledge into the emergent market pattern. Of course they may make mistakes for which they will pay. Without divergent expectations and incoherent plans, however, it could not happen at all. (131-2)

The consequences for capital theory:

Kirzner, “The Theory of Capital”:

A man’s future plans depend not only on the aggregate size of his capital stock but also very crucially upon the particular properties of the various goods making up the stock. Goods that can be used in a complementary relationship permit certain plans that a purely physical measure necessarily suppresses. ...

It is misleading to talk of a particular resource as being unambiguously associated with a definite stream of forthcoming output, in the sense that such an output stream flows automatically from the resource itself. Decisions must be made as to how a resource is to be deployed before one can talk of its future contribution to output. Because there are alternative uses for a resource and alternative clusters of complementary inputs with which a resource may be used, it is confusing to see a resource as representing a definite future output flow before the necessary decisions on its behalf have been made. (p. 139)

Lachmann, “On Austrian Capital Theory”:

The capital structure of society is never completely integrated. The competitive nature of the market process entails incoherence of plans and limits the coherence of the resulting order. A tendency toward the integration of the structure does exist. Capital goods that do not fit into any existing combination are useless to their owners, are “not really capital,” and will soon be scrapped. “Holes” in the existing complementarity pattern, on the other hand, must cause price-cost differences and thus call for their elimination. But expectations of early change in the present situation may impede the process of adjustment, and even when this does not happen, the forces of adjustment themselves may be overtaken by other forces. ...

As long as all capital is regarded as homogeneous, managers may respond to a marginal fall in the rate of interest by a marginal act of substitution of capital for labor. But heterogeneity of capital entails a regrouping of the existing capital combination; some capital goods may have to be discarded, others acquired. It is no longer a marginal adjustment that is called for but entrepreneurial choice and decision. ...

In a world of disequilibrium, entrepreneurs continually have to regroup their capital combinations in response to changes of all kinds, present and expected, on the cost side as well as on the market side. A change in the mode of income distribution is merely one special case of a very large class of cases to which the entrepreneur has to give constant attention. No matter whether switching or reswitching is to be undertaken, or any other response to market change, expectations play a part, and the individuality of each firm finds its expression in its own way. (149-50)

The subjectivity of capital value and the inevitability of fluctuations in the rate of overall economic growth:

Lachmann, “Toward a Critique of Macroeconomics”:

[E]very time [the interest rate] changes, so does capital value. True as this may be, the real reason for our inability to measure capital lies in the subjective nature of expectations concerning future income streams. (p. 153)

To opt for the market process against general equilibrium means to accept the implication that a fully coherent price system providing a basis for consistent aggregation can never exist.

We find here another reason why steady growth—uniform motion of that supermacroaggregate, the economic system—has to be regarded as absurd. Equilibrating forces in different markets, even if none is affected by unexpected change, require different time periods to do their work. This is obvious if we contrast agricultural produce markets with those for industrial goods. Steady growth, however, requires all equilibrating forces to operate within the same time period.

But the main argument against steady growth is a necessary consequence of the divergence of expectations. Equilibrium in a production economy requires an equilibrium composition of the capital stock. ... A growing economy is a changing economy. It exists in an uncertain world in which men have to formulate expectations on which to base their plans. Different men will characteristically have different expectations about the same future event, and they cannot all be right. Some expectations will be disappointed, and the plans based upon them will have to be revised. The capital invested will turn out to have been malinvested. But the existence of malinvested capital is incompatible with the equilibrium composition of the capital stock. Hence steady growth is impossible. (p. 155-6)

The role of the stock market:

In a market economy, on the other hand, we have in the stock exchange a center for the consistent daily evaluation of all the more important capital combinations. This, to be sure, is not objective measurement. The measurement of capital is forever beyond our reach. But it is something more than mere subjective evaluation. Stock exchange prices of capital assets reflect a balance of expectations. ... Stock exchange equilibrium is market-day equilibrium. Tomorrow’s set of equilibrium prices will be different from today’s. (154-5)

[T]the stock exchange, a fundamental institution of the market economy, imparts an element of social objectivity to individual stock valuations. This is by no means its only, or even its only significant, function. It facilitates the take-over bid by means of which capital resources get into the hands of those who can promise their owners a higher return. (p. 156)

Perhaps the most important economic function of the stock exchange is the redistribution of wealth by means of the capital gains and losses it engenders in accordance with the market view about the probable success or failure of present multiperiod plans. (p. 157)

14 May 2011

The wishful thinking of the “serious Keynesian”

Paul Krugman (2011):
So if you’re a serious Keynesian, you’re for maintaining and even increasing spending when the economy is depressed, even though revenue has plunged; but you’re for fiscal restraint when the economy is booming, even though revenue has increased.

Milton Friedman (1962):

When private expenditures decline for any reason, it is said, governmental expenditures should rise to keep total expenditures stable; conversely, when private expenditures rise, governmental expenditures should decline. Unfortunately, the balance wheel is unbalanced. Each recession, however minor, sends a shudder through politically sensitive legislators and administrators with their ever present fear that perhaps it is the harbinger of another 1929-33. They hasten to enact federal spending programs of one kind or another. Many of the programs do not in fact come into effect until after the recession has passed. Hence, insofar as they do affect total expenditures ... they tend to exacerbate the succeeding expansion rather than to mitigate the recession. The haste with which spending programs are approved is not matched by an equal haste to repeal them or to eliminate others when the recession is passed and expansion is under way. On the contrary, it is then argued that a "healthy" expansion must not be "jeopardized" by cuts in governmental expenditures. The chief harm done by the balance-wheel theory is therefore not that it has failed to offset recessions, which it has, and not that it has introduced an inflationary bias into governmental policy, which it has done too, but that it has continuously fostered an expansion in the range of governmental activities at the federal level and prevented a reduction in the burden of federal taxes. (Capitalism and Freedom, p. 76)

13 May 2011

The Paradox of Chinese Censorship

1. Something happens.
2. => A newspaper writes about it.
3. Chinese censors want to stop the news from spreading.
4. => They add the story to a list of banned subjects for rest of the press.
5. The list of banned subjects periodically gets leaked.
6. => Chinese centors act as aggregators of all the bad stories + they bring more attention to them.

(via BHL)

Relative prices for energy sources


image
Electricity produced using natural gas in a combined cycle generating plant comes in at $66 per megawatt-hour. If one includes carbon capture and sequestration, basically burying carbon dioxide underground, the cost rises to $89 per megawatt-hour. In contrast conventional coal costs $95 per megawatt-hour rising to $136 using carbon capture and sequestration. 
How does natural gas compare with various carbon-free and renewable energy sources? Nuclear clocks in at $104 per Mwh, offshore wind at $243 per Mwh, photovoltaic at $211 per Mwh, solar thermal at $312 per Mwh, geothermal at $102 per Mwh, and biomass at $113 per Mwh. The only renewable sources that are close to competitive with natural gas are onshore wind at $97 per Mwh and hydroelectric at $86 per Mwh. With regard to transportation, the price of compressed natural gas currently hovers around the  equivalent of $2 per gallon of gasoline.
Keep in mind that the above is just a thought experiment. Junking coal-fired plants and dramatically expanding natural gas production as well as the infrastructure to burn it to generate electricity and dispense it as transport fuel would be costly. Increased demand for natural gas would also tend to boost its price.
More here, including a discussion of why environmentalists now oppose natural gas.