Modern science should indeed arouse in all of us a humility before the immensity of the unexplored and a tolerance for crazy hypotheses.
Interpretation
Science teaches us to be humble about what we don't know and to accept unconventional ideas.
In this quote, Martin Gardner suggests that the vastness of scientific knowledge should inspire humility in us, recognizing how much remains unexplored. He also emphasizes the importance of remaining open-minded towards unconventional ideas or theories, encouraging curiosity and tolerance in our pursuit of understanding the universe.
In practice
This quote would be perfect for a presentation on the importance of scientific inquiry.
Politicians, real-estate agents, used-car salesmen, and advertising copy-writers are expected to stretch facts in self-serving directions, but scientists who falsify their results are regarded by their peers as committing an inexcusable crime. Yet the sad fact is that the history of science swarms with cases of outright fakery and instances of scientists who unconsciously distorted their work by seeing it through lenses of passionately held beliefs.
Debunking bad science should be constant obligation of the science community, even if it takes time away from serious research or seems to be a losing battle. One takes comfort from the fact there is no Gresham's laws in science. In the long run, good science drives out bad.
If all sentient beings in the universe disappeared, there would remain a sense in which mathematical objects and theorems would continue to exist even though there would be no one around to write or talk about them. Huge prime numbers would continue to be prime, even if no one had proved them prime.
In no other branch of mathematics is it so easy for experts to blunder as in probability theory.
There are, and always have been, destructive pseudo-scientific notions linked to race and religion; these are the most widespread and damaging. Hopefully, educated people can succeed in shedding light into these areas of prejudice and ignorance, for as Voltaire once said: "Men will commit atrocities as long as they believe absurdities."
A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?
A science is not mere knowledge, it is knowledge which has undergone a process of intellectual digestion. It is the grasp of many things brought together in one, and hence is its power; for, properly speaking, it is Science that is power, not Knowledge.
If you've read a lot of vintage science fiction, as I have at one time or another in my life, you can't help but realise how wrong we get it. I have gotten it wrong more times than I've gotten it right. But I knew that when I started; I knew that before I wrote a word of science fiction.
One can think of any given axiom system as being like a computer with a certain limited amount of memory or processing power. One could switch to a computer with even more storage, but no matter how large an amount of storage space the computer has, there will still exist some tasks that are beyond its ability.
In future, children won't perceive the stars as mere twinkling points of light: they'll learn that each is a 'Sun', orbited by planets fully as interesting as those in our Solar system.
I am mindful that scientific achievement is rooted in the past, is cultivated to full stature by many contemporaries and flourishes only in favorable environment. No individual is alone responsible for a single stepping stone along the path of progress, and where the path is smooth progress is most rapid. In my own work this has been particularly true.
Science, we are repeatedly told, is the most reliable form of knowledge about the world because it is based on testable hypotheses. Religion, by contrast, is based on faith. The term 'doubting Thomas' well illustrates the difference.
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