Philadelphia, PA

Dear Matos,

I would say that the question of the limitations of scientific knowledge is itself an empirical question --in a wider sense. New discoveries are always being made, and new lines of research are opened up by them. With new discoveries we get new questions, and whether we will find adequate answers to questions, old or new, is something settled only by further expansion of scientific knowledge --though some questions are also simply given up as mistaken in one fashion or another. There is no predicting the outcomes of scientific research, instead we have to wait and see how it turns out. This also suggests that there is no predicting the limitations which scientific research may encounter.

Though we have heard much of late about prospective "theories of everything." These proposals are actually extremely abstract; and one may suspect that even if they were successful, in physics, we would still have many unanswered questions in the various sciences--and maybe in physics, too.

The fact that measurement is never exactly precise, but only exact within some particular limits, may suggest limits to scientific knowledge. But on the other hand, the ultimate uncertainty of measurements may also suggest that there is nothing beyond to be measure.

H.G. Callaway

Dear Yuri,

The limits of Science are mainly in our minds that cannot put clever enough questions to be measured or calculated. Thus the problem is not the accuracy of a measurement or the exactness of a calculation, but our intelligence in discovering or explaining what the scientific facts can teach us. For instance, the results that Maxwell electrodynamics didn't fit well in Galilean transformations or to understand that Lorentz transformations were more than a mathematical trick, needed Einstein's thoughts to understand them and to make Science knowledge.

Philadelphia, PA

Dear Matos,

I would say that the question of the limitations of scientific knowledge is itself an empirical question --in a wider sense. New discoveries are always being made, and new lines of research are opened up by them. With new discoveries we get new questions, and whether we will find adequate answers to questions, old or new, is something settled only by further expansion of scientific knowledge --though some questions are also simply given up as mistaken in one fashion or another. There is no predicting the outcomes of scientific research, instead we have to wait and see how it turns out. This also suggests that there is no predicting the limitations which scientific research may encounter.

Though we have heard much of late about prospective "theories of everything." These proposals are actually extremely abstract; and one may suspect that even if they were successful, in physics, we would still have many unanswered questions in the various sciences--and maybe in physics, too.

The fact that measurement is never exactly precise, but only exact within some particular limits, may suggest limits to scientific knowledge. But on the other hand, the ultimate uncertainty of measurements may also suggest that there is nothing beyond to be measure.

H.G. Callaway

Science fails to answer questions on beliefs in cosmology

I'm with sir H.G. Callaway

Hello Yuri,

I like your question, but I have a problem with your use of the word 'precise', and by extension with the word 'precision'. In classical measurement theory, the accuracy of a measurement was made up of two parts: precision (an indication of random error) and bias (an indication of systematic error). While precision is a measurable, bias is not - it is estimated by calculation. In other words, if you make the same measurement N times and calculate the sample standard deviation and from that estimate the population standard deviation, you may find the resulting number is quite small (good precision), but if the bias is very large, then you are precisely wrong and so is your inference. On the other hand, if the scatter of N measurements is quite large, but the bias is very small, then you are inexactly right, and, perhaps, so is your inference.

The same thing can be said of inductive reasoning. N people can look at M particular cases and come to the same generalization (high precision): the motion of the planets is best described by epicycles around the Earth. But suppose their bias is very large, then they might be exactly wrong. But the N+1'th person might look at the same M particular cases and decide that conic sections situated around the Sun is more salubrious. Low precision, because it is only a single person, but very small bias - at least by contemporary standards.

Since bias can never be truly known, we are forever revisiting old ideas (entropy, arrow of time, origin of the universe, epigenics, consciousness) in the sure and certain hope that, like Captain Ahab, we will finally harpoon the Great White Whale of Truth. Captain, I think we need a bigger boat!

Of course, my use of an analogy with classical measurement theory might be specious. But is it anymore specious than the predilection of scientists of each epoch to describe the solar system, and by extension the universe, in terms of the dominant human mechanical/electrical/etc. artifact of the day? Classical physicists and astronomers compared the solar system to a celestial clock, and today we compare the universe to a computer. What next, will future generations compare the universe to the financial markets: a non-stationary veiled temptress: an engine, not a camera as Donald MacKenzie titled his book on the same subject. In other words, will we be like Dr. Ian Malcolm (Jeff Goldblum) in the movie "Jurassic Park" who tells Dr. Ellie Sattler (Laura Dern) that he is always looking for the next ex-Mrs. Malcolm?

Regards,

Tom Cuff

I think it depends on the identifiability of natural phenomena (themselves), this is the theoretical limit of science, the accuracy of a measurement is the technological limit.