A (Long) Footnote about Science

Posted on November 7, 2017 by Loquitur Veritatem

In “Deduction, Induction, and Knowledge” I make a case that knowledge (as opposed to belief) can only be inductive, that is, limited to specific facts about particular phenomena. It’s true that a hypothesis or theory about a general pattern of relationships (e.g., the general theory of relativity) can be useful, and even necessary. As I say at the end of “Deduction…”, the fact that a general theory can’t be proven

doesn’t — and shouldn’t — stand in the way of acting as if we possess general knowledge. We must act as if we possess general knowledge. To do otherwise would result in stasis, or analysis-paralysis.

Which doesn’t mean that a general theory should be accepted just because it seems plausible. Some general theories — such as global climate models (or GCMs) are easily falsified. They persist only because pseudo-scientists and true believers refuse to abandon them. (There is no such thing as “settled science”.)

Neil Lock, writing at Watts Up With That?, offers this perspective on inductive vs. deductive thinking:

Bottom up thinking is like the way we build a house. Starting from the ground, we work upwards, using what we’ve done already as support for what we’re working on at the moment. Top down thinking, on the other hand, starts out from an idea that is a given. It then works downwards, seeking evidence for the idea, or to add detail to it, or to put it into practice….

The bottom up thinker seeks to build, using his senses and his mind, a picture of the reality of which he is a part. He examines, critically, the evidence of his senses. He assembles this evidence into percepts, things he perceives as true. Then he pulls them together and generalizes them into concepts. He uses logic and reason to seek understanding, and he often stops to check that he is still on the right lines. And if he finds he has made an error, he tries to correct it.

The top down thinker, on the other hand, has far less concern for logic or reason, or for correcting errors. He tends to accept new ideas only if they fit his pre-existing beliefs. And so, he finds it hard to go beyond the limitations of what he already knows or believes. [“‘Bottom Up’ versus ‘Top Down’ Thinking — On Just about Everything“, October 22, 2017]

(I urge you to read the whole thing, in which Lock applies the top down-bottom up dichotomy to a broad range of issues.)

Lock overstates the distinction between the two modes of thought. A lot of “bottom up” thinkers derive general hypotheses from their observations about particular events. But — and this is a big “but” — they are also amenable to revising their hypotheses when they encounter facts that contradict them. The best scientists are bottom-up and top-down thinkers whose beliefs are based on bottom-up thinking.

General hypotheses are indispensable guides to “everyday” living. Some of them (e.g., fire burns, gravity causes objects to fall) are such reliable guides that it’s foolish to assume their falsity. Nor does it take much research to learn, for example, that there are areas within a big city where violent crime is rampant. A prudent person — even a “liberal” one — will therefore avoid those areas.

There are also general patterns — now politically incorrect to mention — with respect to differences in physical, psychological, and intellectual traits and abilities between men and women and among races. (See this, this, and this, for example.) These patterns explain disparities in achievement, but they are ignored by true believers who would wish away the underlying causes and penalize those who are more able (in a relevant dimension) for the sake of ersatz equality. The point is that a good many people — perhaps most people — studiously ignore facts of some kind in order to preserve their cherished beliefs about themselves and the world around them.

Which brings me back to science and scientists. Scientists, for the most part, are human beings with a particular aptitude for pattern-seeking and the manipulation of abstract ideas. They can easily get lost in such pursuits and fail to notice that their abstractions have taken them a long way from reality (e.g., Einstein’s special theory of relativity).

This is certainly the case in physics, where scientists admit that the standard model of sub-atomic physics “proves” that the universe shouldn’t exist. (See Andrew Griffin, “The Universe Shouldn’t Exist, Scientists Say after Finding Bizarre Behaviour of Anti-Matter“, The Independent, October 23, 2017.) It is most certainly the case in climatology, where many pseudo-scientists have deployed hopelessly flawed models in the service of policies that would unnecessarily cripple the economy of the United States.

As I say here,

scientists are human and fallible. It is in the best tradition of science to distrust their claims and to dismiss their non-scientific utterances.

Non-scientific utterances are not only those which have nothing to do with a scientist’s field of specialization, but also include those that are based on theories which derive from preconceptions more than facts. It is scientific to admit lack of certainty. It is unscientific — anti-scientific, really — to proclaim certainty about something that is so little understood the origin of the universe or Earth’s climate.

Probability, Existence, and Creation: A Footnote

Posted on August 29, 2011 by Loquitur Veritatem

Mario Livio writes:

[H]umans invent mathematical concepts by way of abstracting elements from the world around them—shapes, lines, sets, groups, and so forth—either for some specific purpose or simply for fun. They then go on to discover the connections among those concepts. Because this process of inventing and discovering is man-made—unlike the kind of discovery to which the Platonists subscribe—our mathematics is ultimately based on our perceptions and the mental pictures we can conjure….

[W]e adopt mathematical tools that apply to our world—a fact that has undoubtedly contributed to the perceived effectiveness of mathematics. Scientists do not choose analytical methods arbitrarily but rather on the basis of how well they predict the results of their experiments….

Not only do scientists cherry-pick solutions, they also tend to select problems that are amenable to mathematical treatment. There exists, however, a whole host of phenomena for which no accurate mathematical predictions are possible, sometimes not even in principle. In economics, for example, many variables—the detailed psychology of the masses, to name one—do not easily lend themselves to quantitative analysis. The predictive value of any theory relies on the constancy of the underlying relations among variables. Our analyses also fail to fully capture systems that develop chaos, in which the tiniest change in the initial conditions may produce entirely different end results, prohibiting any long-term predictions. Mathematicians have developed statistics and probability to deal with such shortcomings, but mathematics itself is limited, as Austrian logician Gödel famously proved….

This careful selection of problems and solutions only partially accounts for mathematics’s success in describing the laws of nature. Such laws must exist in the first place! Luckily for mathematicians and physicists alike, universal laws appear to govern our cosmos: an atom 12 billion light-years away behaves just like an atom on Earth; light in the distant past and light today share the same traits; and the same gravitational forces that shaped the universe’s initial structures hold sway over present-day galaxies. Mathematicians and physicists have invented the concept of symmetry to describe this kind of immunity to change….

I started with two basic, interrelated questions: Is mathematics invented or discovered? And what gives mathematics its explanatory and predictive powers? I believe that we know the answer to the first question. Mathematics is an intricate fusion of inventions and discoveries. Concepts are generally invented, and even though all the correct relations among them existed before their discovery, humans still chose which ones to study. The second question turns out to be even more complex. There is no doubt that the selection of topics we address mathematically has played an important role in math’s perceived effectiveness. But mathematics would not work at all were there no universal features to be discovered. You may now ask: Why are there universal laws of nature at all? Or equivalently: Why is our universe governed by certain symmetries and by locality? I truly do not know the answers, except to note that perhaps in a universe without these properties, complexity and life would have never emerged, and we would not be here to ask the question. (“Why Math Works,” Scientific American, August 2, 2011)

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Tag Archives: physics

A (Long) Footnote about Science

Probability, Existence, and Creation: A Footnote

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