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oraphalous | 1 year ago
If everyone like you attempts to rail road the imaginative process at the beginning of hypothesis formation, then we'll never get to the point of being able to exhibit one, should one be possible.
The demand for rigour at this point in a discourse - which was pretty clearly signalled by the commenter to be offered at a stage prior to substantive hypotheis formation - just shuts down the imaginative process. It's not constructive.
rachofsunshine|1 year ago
I'm a mathematician by education, and I cannot tell you how many people insist on things like 0.999... < 1 without an understanding of (a) what the left side of that expression even means, (b) what a real number is, or (c) what basic properties the real numbers have. Going "no, you're wrong, and it would take me a couple of full lectures to explain why but trust me we're pretty sure about this" is a reasonable answer to that, provided that you have indeed established that to your own satisfaction, at least.
gryfft|1 year ago
From Wikipedia, an intuitive explanation of an elementary proof:
> If one places 0.9, 0.99, 0.999, etc. on the number line, one sees immediately that all these points are to the left of 1, and that they get closer and closer to 1. For any number that is less than 1, the sequence 0.9, 0.99, 0.999, and so on will eventually reach a number larger than . So, it does not make sense to identify 0.999... with any number smaller than 1. Meanwhile, every number larger than 1 will be larger than any decimal of the form 0.999...9 for any finite number of nines. Therefore, 0.999... cannot be identified with any number larger than 1, either. Because 0.999... cannot be bigger than 1 or smaller than 1, it must equal 1 if it is to be any real number at all.
And then:
> The elementary argument of multiplying 0.333... = 1/3 by 3 can convince reluctant students that 0.999... = 1.
bawolff|1 year ago
To put another way, there is a big difference between saying some specific alternative theory is wrong/unlikely/bad, and claiming there exists no alternative theories at all regardless of quality.
psychoslave|1 year ago
If we mean 9×10^-i for i from 1 to infinity, then let's just state so. Let's not blame people to interpret towards other direction when they are provided misguiding hints.
Regarding infinity, there is a constructive proof that it doesn't exists which work perfectly provided that there is an infinite amount of resources allocated to it's execution.
eszed|1 year ago
thrance|1 year ago
ants_everywhere|1 year ago
But the expansion of the universe has been thoroughly studied for over a century. We're past the brainstorming phase.
I generally think people should brainstorm to generate ideas and then filter them down. And it's true that filtering too early can significantly decrease the quality of ideas.
And it's also true that in a place like Hacker News there will be smart people from all sorts of backgrounds getting to experience the joy of exploring a new topic that they're not fully up to speed on yet.
The risk though is that somebody who thoroughly understands the field is reading your comment. So for that reason I think it's a good practice to always be aware that technical fields we're not expert in are usually more subtle than we initially think.
dtgriscom|1 year ago
alexey-salmin|1 year ago
Explaining is neither hard nor useful and it's not what science is normally concerned with. The goal is to predict new observations not to explain known ones.
JasonSage|1 year ago
I learn things all the time by wondering if somebody else is right. Much better than just thinking everything is simply the way I think it is now.
Even if you know somebody is wrong, talking about it is absolutely harmless.
tqi|1 year ago
On the other hand, who cares? This is a random internet forum, not the Proceedings of the National Academy of Sciences, so maybe there is no such thing as a proper response?
koolala|1 year ago
snowwrestler|1 year ago
xwolfi|1 year ago
For now, we dont know any other way to explain than to say it expands, except maybe imaginative fantasies from amateurs on Hackernews, but does it count ?
koolala|1 year ago
I looked it up on the Wikipedia page for Exotic Matter and there isn't much exploration or tested theories on it.