When we are asked how we know something there are really two kinds of answer. We may explain how the truth in question was discovered, or we may explain how we learned (how we are taught) that it is true. Properly speaking, only the original discoverers know something for the first set of reasons. We might also add those close peers who either directly or indirectly replicate the original discoveries in subsequent work. But it is important to realize that you don't have to be Einstein to know that E=mc2. However Einstein may have come upon this knowledge, my knowledge is of a different kind. When Einstein had to explain how he knew it, he gave one sort of answer. When I explain how I know, I give a different sort of answer.
What happens if we ask how "we" know that E=mc2? How do we know it as a culture? Well, we have access to Einstein's original arguments, but also the experiments that demonstrated that he was right. And there are are scientists all over the world who are able to replicate those results to a high degree of accuracy. They are able to vouch for Einstein, and they largely keep each other honest. They also teach physics students how it is done, i.e., what mass-energy equivalence means.
But suppose, now, that physics went out of fashion. Suppose that for two or three generations no young people pursued physics degrees and careers. The scientists lost their funding; the teachers lost their jobs. Imagine a world where no one was qualified to test Einstein's formula. Historians could tell us that a man named Albert Einstein discovered mass-energy equivalence in the early part of the 20th Century. But it would be unclear that this is something we knew as a culture.
What I'm trying to say, somewhat fumblingly, is that our academic institutions are an important part of what it means for me to "know" that E=mc2. There's even a sense in which my children "know" it! They really do know that there is a lot of energy in the head of a pin; it's just that the knowledge is distributed through a network that reaches from Einstein's brain (back in 1905), through the history of science, through our academic institutions, and into their science classrooms, and then into their own brains. The knowledge is also contained in all the laboratory equipment that demonstrates the truth of Einstein's theories every day. But only in so far as there are people who know how to operate that equipment. That's the important thing!
We know things not just because they have been discovered by people at some point in the past and not just because children believe us when we tell them about it. Our knowledge is maintained by our institutions of higher learning. We can only know what a select portion of each generation is trained to be able to know, not just indoctrinated to believe. I sometimes worry that we are forgetting this. We are forgetting not just what we know, but how we know these things.
I'm not sure I know this any more, because its meaning is not longer available to me for retrieval. I couldn't explain it to someone else or teach it. When I took a physics course, I understood it and knew its meaning, but no longer. All I know is that it has something to do with expressing the relation between mass and energy.
ReplyDeleteI think I'm trying to say that you do know it because your culture knows it. You can assert it. You probably know that energy is mass times the speed of light squared, right? And you know that this means there's a lot of energy in even an ordinary object. You might even know that light has very little mass (zero at rest). Ultimately, though, very little of this knowledge is in your head. It's all "out there" in the culture, and I'm sure you know how to access it.
ReplyDeleteYes. I can get it when I want and could reteach it to myself.
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ReplyDeleteA few things that are not in disagreement but somewhat orthogonal to what you're saying: Like you, I recognize that is something like cultural knowledge or some sense in which I am aware that my culture knows something, but I disagree with way you phrase the matter.
ReplyDelete1. A lot of "-quotes in this post that you used to modify the meaning of "know" should be moved to E=mc2. It that not I "know" that E=mc2. Rather I know (in the ordinary sense, no scareqoutes needed) that "E=mc2" (that assertable sentence or strings of signs) is true. I don't myself quite grasp how that sentence is to be justifed nor even quite what it means. And if I don't even grasp what it means, then I cannot be said to know it. But I do know (no scare-quotes needed) that sentence could be justified and is held to be true by people more competent in physics than me. That I suppose could be called cultural knowledge.
2. At points, you seem to admit that I do not quite grasp what E=mc2 means, but that I somehow know that sentence to be true implicitly by accepting its dedcutive consequences. Your children, you say, "really do know that there is a lot of energy in the head of a pin." I am quite confident (and that is not irony) that your children are brilliant (after all, they are your children). But at least I am not sure that I know that "a lot energy" is stored (?) "in even an ordinary object" like a pin of a neeedle. I don't how to justify that proposition either and I have never (could never) assumed its truth as a premise for any practical inference. Most of my practical inferences, in fact, assume something like the opposite. I regard this sheet of paper at rest on my floor as possing no energy what so ever. (I don't have sheets of paper made of uranium lying around and even if I did the weightloss that they would suffer from spontanously releasing some of their energy would make no practical difference for the next 100,000 years.) What I do know, of course, is that some arcane branch of physics asserts some framework of description which implies that this ordinary sheet of paper can be regarded as possessing some immense amount of energy. This latter sort of knowledge, I suppose, could be called cultural knowledge. But I have no use for this framework of description and many of the frameworks of description that I do utilize contradict it.
3. Having surfed my cultures archive of knowledge (and yes, this proves your point), I've arrived that conclusion that not even Einstein knew that e=mc2, since he did not even believe that e=mc2. He took that expression to be an inaccurate metaphorical device. cf. http://www.stat.physik.uni-potsdam.de/~pikovsky/teaching/stud_seminar/einstein.pdf
Thanks, Presskorn. Maybe I set the bar a bit too high for myself by using (and, as you rightly point out, not merely mentioning) "E=mc22" in this post. I could have said that my children "know" that the Earth is round or that the sun is the center of the solar system. The scare-quotes around "know" are there to acknowledge the difference between a child's understanding of such truths and a scientist's. But I really do want to insist that they have a justified true belief about the relevant fact.
ReplyDeleteThe justification is not relative to the culture, i.e., it's not that the culture is a context that gives the expression "The earth is round" meaning, and only within this context, and given that meaning, is the sentence true. Rather, the justification for the true belief that the Earth is round is part of the content of our culture, as long as we maintain the disciplines (geography or astronomy as you choose) that allow some of us to justify the belief scientifically.
For a 12 year-old, knowing that E=mc2, doesn't mean much more than associating it with the name of Einstein, the theory of relativity, and, perhaps, something about the vast amount of energy in the head of a pin or an atomic bomb. That's good enough because it would let the interested child proceed towards the justification that our culture in fact contains, just as surely as Nature contains the fact that E=mc2.
The sun isn't at the exact center of the solar system, nor is the Earth perfectly round. And the energy of a thing is probably only approximately equal to its mass times the speed of light in a vacuum squared. All knowledge may be approximation in that sense.
I liked "E=mc2" because it seemed less trivial than "The Earth is round" but also because it's more obviously technical, although demonstrating Earth's roundness arguably requires almost as much technique and technology as demonstrating mass-energy equivalence. I also like the way its semantics are sort of halfway between "2+2=4" and "The Earth is round."
I'm not sure if this response is itself orthogonal to yours, but I'm trying to push back against the notion of something like "cultural knowledge" here. We (you, me, the culture, or the relevant scientist) either know or don't know. I'm trying to insist that you know that E=mc2 whether you like it or not. And I mean this in a nontrivial sense, by the way. I would not declare (nor even grant) that you know that that human CO2 emissions have been the main cause of a rise in global temperatures over the past 20 years. The justification for this (perhaps true) belief is (demonstrably) not culturally available to you in the relevant way. Importantly, however, it may well be available to a climate scientist. I (precisely) don't know. Michael Mann might know this. But you and I do not. We don't even "know" it.
Always great to have to have you stop by, Thomas! It forces me to think.