Why Technical Drawing is important? Because anything we envision in our mind is in essence a 3-D model. If we can draw it on paper it helps to clarify our thoughts. We can not envision anything 4-D, can we? Being able to draw 3-D objects on paper(or computer) with correct perspective is invaluable I now think.
> We can not envision anything 4-D, can we? We definitely can draw 4-D in paper. It just needs much more work.
I find it impossible to visualize 4-D objects in my head. On paper the best you can do I think is show the projection of a 4-D object onto 3-D space which is then projected onto the flat 2-D surface. But I still can't visualize how a 4-D object would "look" because it seems our brains are hardwired to comprehend "objects" as 3-dimensional beings.
Having just finished the epic Making of the Atomic Bomb by Richard Rhodes, my mind goes to a different place —- Heisenberg was at the core of the German bomb project. Speculatively, I wonder how things might have gone a different way had he been required to be a brilliant experimentalist too. Success versus failure hinged on nitty-gritty experimental details, not on sweeping theoretical insight. Probably not, but the…
You might also like Now it Can Be Told: the Story of the Manhattan Project by Leslie R. Groves I thought it did a good job at talking about how the Army made everything happen.
Thanks for this suggestion. I couldn’t believe the quality of the Rhodes book.
It's sort of a yes and no. The belief that Einstein was bad at math in school is a myth. He did just fine in mathematics at school. But relative to other theoretical physicists he was not the strongest mathematician.
Which other theoretical physicists were amazingly great at mathematics? I am genuinly curious. I am certainly not alluding that Einstein was great at maths. But I do think he was good enough. von Neuman is someone I think was a beast but he was more of a mathrmatician than a physicist (at least I think so).
I'm not an expert by any means, but my understanding is that Dirac was a highly accomplished mathematician, and of course Hilbert made his name in mathematics before moving to study physics.
Which other theoretical physicists were amazingly great at mathematics? I am genuinly curious. I am certainly not alluding that Einstein was great at maths. But I do think he was good enough. von Neuman is someone I think was a beast but he was more of a mathrmatician than a physicist (at least I think so).
I'm not an expert by any means, but my understanding is that Dirac was a highly accomplished mathematician, and of course Hilbert made his name in mathematics before moving to study physics.
Dirac came from a later generation than Einstein. For example during Einstein's annus mirabilis (1905) I doubt very many physicists knew of tensor calculus considering it was only developed a decade beforehand. During that time the mathematics physicists learnt was very much the traditional topics of analysis: series expansions, special functions, integral equations, calculus of variations, quadratic forms and of course partial differential equations. Hilbert himself actually wrote a textbook with Richard Courant covering these topics: Methods of Mathematical Physics. As such I don't really think many physicists of Einstein's generation knew lots of mathematics simply because it wasn't taught at the time. In the decades since physicists gradually has generally become more "mathematised" so to speak. In Dirac's generation tensor calculus and group representation theory became important, than in general abstract algebra and functional analysis, then as differential geometry became more well developed that gets taught and closer to the modern day you can find top theoretical physics students learning all sorts of abstract mathematics like algebraic topology.
Yes, first and effectively only. First definition at MW: > of, relating to, or consisting of words https://www.merriam-webster.com/dictionary/verbal
https://www.lawdepot.com/blog/are-verbal-agreements-legally-... > When two or more parties come to an agreement without any written documentation, they create a verbal agreement (known formally as an oral contract). I think that alone demonstrates that verbal contrasts with written.
The fact that many people use it in opposition to written is insufficient proof that all dictionaries are wrong. Eventually it may only mean oral, but today it doesn’t.
That isn’t at all clear to me as a physicist Are you a physicist?
So you think your being a physicist gives you special insight into whether Sommerfeld, Born and Heisenberg understood the significance of what they were working on? Explain.
Yes, of course. I am an expert in physics, you are not...
I question if today’s hyper-agressive attitudes are any useful in Science, and, if they just don’t contribute to the toxicity that plagues Academia.
There are other ways to express disagreement, no?
It seems it’s just people discharging and inflicting their sadistic & abusive pus on - many times livelihood-insecure - others because the System enables them to.
So you think your being a physicist gives you special insight into whether Sommerfeld, Born and Heisenberg understood the significance of what they were working on? Explain.
Yes, of course. I am an expert in physics, you are not...
That's not an explanation, that's a rather trite attempt at an ad-hominem evasion. What (and how) does your exhaustive knowledge of physics allow you to conclude about how Sommerfeld, Born and Heisenberg viewed the significance of what they were working on, that you assume is not available to me? Use whatever physics is necessary to explain how you came to your position - I might know more than you assume.
There is an even scarier story about Heisenberg, from late in WW2. From https://journals.sagepub.com/doi/full/10.1177/00963402114330... : > In November 1944, the OSS learned that Heisenberg planned to visit Switzerland the next month. Former major league baseball catcher and then OSS officer Moe Berg was dispatched to Zurich with orders that “Heisenberg must be rendered hors de combat” (out of action) if Heisenberg g…
Zes, I recall the movie titled "The Catcher Was A Spy" which has this series of events captured in satisfactory detail.