That’s if you add two of the same odd number. The more general proof is basically the same though: let n and m be integers, then 2n+1 and 2m+1 are odd. (2n+1) + (2m+1) = 2n + 2m + 2 = 2(n+m+1) which will be even.
Or you can just like, understand that an odd number is one more than an even number so if you add them together it’s two more than an even number, hence even.
Which is the layman’s terms of the proof… I don’t get what your goal is.
Is it a building block for learning to read mathematical works? Yes, of course it is. Is this a ridiculous formalized statement? Yes, of course it is. But that’s the point. We need to practice the trivial to build the scaffolding to tackle the exceptional.
I am not wont to draw conclusions with minimal evidence, but your post seems like you are a malicious reductionist that may be suffering from Dunning Kruger syndrome. I apologize in advance if I have miscategorized you based on this limited sample.
To confirm, you are asserting that the foundation for your answer (mathematical reasoning) does not require any mathematics to understand why it is true.
It’s very dangerous to take a reductionist approach and not be aware of the baked in assumptions you are using. For example, the terms even and odd (for this problem) are well defined as concepts for integers. Which means that your hand-wave statement is true as a result of definitions that were likely created to ensure this property held true.
The notion that “I don’t need math to understand why this is true” is like saying “I made an observation on a phenomenon and I don’t need science to know it’s true.” Which, as you are hopefully aware, is again reductionist and leads to a huge distrust of science from the science illiterate.
I don’t understand what you are trying to say. I just wanted to provide an easier way to reason why it is true, so that people who don’t do math as much as you do could also see the logic behind it. I don’t see how an easy to understand reasoning can be a bad thing?
Let me try: to narrow down a bit, we take a subset of uneven numbers. We know that almost all prime numbers are even so lets pick prime numbers at random and see what happens:
5+7=12 (even)
3+11=14 (even)
13+9=22 (even)
2+2=4 (even)
I’m out of ideas but maybe someone can take this approach and land somewhere.
Species 8472 has three legs. Three is an odd number. Four would be an odd number of legs for a member of Species 8472 to have. Three plus four is seven, which is odd (2x3+1). Two odd numbers can therefore add to an odd number.
I love how theyre so buoyant they kinda wobble around the oceans. So many way more effective and mobile species get unlucky while these little guys just putter around.
My bank started using Quickbooks file format if I want to download a transaction history in a specific date range, what a fucking nightmare. It’s not abandoned yet but nothing except the QuickBooks proprietary software seems to open them so far, only a matter of time. Honestly at this point I might prefer the nightmarish CSV filetype.
The problem is that it’s not really a standard. It’s reinvented ad-hoc by whomever programs it today.
Should there be any whitespace after the comma? Do you want to use pipes or some other character instead of commas (ASCII 0x1E is sitting over there for exactly this purpose, but it’s been ignored for decades)? How do you handle escaping your separator char inside the dataset? Are you [CR] or [LF} or [CR] [LF]? None of these questions have a set answer. Even JSON has more specification than this.
I'm pretty bullish on science investments, but I've heard multiple arguments that this thing is probably not worth the money. The most prevalent argument I've heard to the contrary is basically "we could discover something that might be interesting." But like very little in terms of concrete measurable returns on investment for it.
If they already knew the intended results it wouldn’t make sense to do it. Science of this kind is like “here’s something we haven’t tried yet”, which itself is pretty difficult to even come up with.
Also, money spend on something like this doesn’t just disappear. It goes around the suppliers doing it and returns to the state eventually. Of course someone will pocket some money but when talking billions it’s more of an investment in the area than a cost or even an investment in the actual collider. A used collider isn’t worth that amount of money , so where’d it go? It didn’t disappear. Money goes round.
It creates a lot of jobs and when looking at the entire supply chain, it feeds a hell of a lot of people, even if the scientific result is “oh well it didn’t do anything at all.” That way, it might be cheaper than supplying social security/basic income for that amount of people.
At the end of the day, in the grand economic scale, we’re all riding on the shoulders of whoever digs out the the resources from the Earth, so we need to make these kind of very important projects to make it appear as if everyone else is actually producing anything at all. The science is just a nice side effect.
Off the top of my head, I can’t think of any advance that didn’t at some point depend on people just dicking around to see what they could see.
“What happens if we spin this stick really really fast against this other stick?”
“Cool! What happens if we put some dried moss around it?”
“That’s nuts, man! Hey, I wonder what happens if we toss some of our leftovers in there?”
“C’mon over here, guys. You gotta taste this!”
At worst, a project like this keeps a lot of curious people in one place where we can make sure they don’t cause harm with their explorations. At best, whole new industries are founded. Never forget that modern electronics would never have existed without Einstein and Bohr arguing over the behaviour of subatomic particles.
Say the actual construction cost is $100 billion over 10 years and operational costs are $1 billion a year. Compared to all the stupid and useless stuff we already spend money on, that’s little more than pocket lint. We could extract that much from the spending of one military alliance and it would look like a rounding error. Hell, we could add one cent to the price of each litre of soft drinks, alcoholic beverages, and bottled water and have money left over.
Has the LHC resulted in any kind of tangible returns on investment so far? I know they proved the existence of the Higgs Boson, but all that did as I understand it was verify what we were already pretty sure of.
I'm just having a hard time understanding why we can't blow 30 or 100 billion or whatever on something else like fusion research. Or just something with a more concrete "if we pull this off it solves <gigantic international problem>" kinda prospect.
I understand science can walk and chew gum at the same time, but this in particular seems like a shitload to spend and a lot of land to disturb so that particle physicists can nerd out in an underground torus proving theories but maybe not moving the needle much for mankind.
The thing is, that you can’t predict, what fundamental science will lead to. In the case of the LHC the tangible returns are technologies, that can be adapted to other fields, like detectors. There are enough other arguments, why a bigger accelerator is a bad idea, where you do not need to trash fundamental research as a whole.
You have any links to info on these technologies? I've done some googling today and in the past and come up with little specifics on the LHC gave us X or helped lead to the development of X that is now being used for Y.
And I'm not saying we need to trash research. Just that research could be done on things that more directly answer some of the very real problems we have right now before this planet goes up in flames. Building another even bigger more expensive collider seems really indulgent from where I'm sitting.
And we can agree to disagree. I'm not big mad they're proposing this. I just don't think it makes a lot of sense based on the information I have available.
These things are really special interest. They developed small scale particle detectors, that are nowadays used in medical physics for example (PET scanners and so on). Then their electronics need to be very insensitive to radiation damage, that is also important for everything space related. There is probably some R&D on superconducting magnets as well, that can be adapted to other purposes, but I am not too up to date in this field and I am not sure, if Cern is a major player there.
I also think there are better places to put this kind of money, including on projects that we are certain have obvious potential to change the world for the better.
What I was getting at was the very idea that we absolutely have to know what the return is before we start. Just because we know the potential return doesn’t mean that it’s not research (as in your fusion example), but just because we can’t identify a return ahead of time doesn’t mean there won’t be one.
Also, I don’t know if there have been any tangible benefits from the LHC. Precision manufacturing? Improvements in large-scale, multi-jurisdiction project management? Data analytics techniques? More efficient superconducting magnets? I don’t know if those are actual side effects of the project and, if they are, I don’t know that the LHC was the only way to get them.
Edit: or, like the quantum physics underlying our electronics, maybe we won’t know for 50-100 years just how important that proof was.
Yeah, but you could also fund a lot of other research with this budget. The point is, physicists just don’t know, if there are more particles existing. There is no theoretical theory there predicting particles at a certain mass with certain decay channels. They won’t know what to look for. That’s actually already a problem for the LHC. They have this huge amount of data, but when you don’t know, what kind of exotic particles you are looking for and how they behave, you can’t post-process the data accordingly. They are hidden under a massive amounts of particles, that are known already.
Yes, with finite resources, we have to make choices. As long as there are some resources for people to just poke around, I’m good with whatever. If we’re actually looking for some place to drop a few billion, I actually don’t think another collider should be on the list, let alone at the top.
The problem as I see it is that “but what good is it” is used to limit pretty much all fundamental research.
So why don’t they just use post processing to remove all the known particles and start looking at the particles that remain, discover a new one, remove it, continue until there’s none left?
There are multiple reasons for that. We don’t know the decay channels of already discovered particles precisely. So there might be very rare processes, that contribute to already known particles. It is all a statistical process. While you can give statements on a large number of events, it is nearly impossible to do it for one event. Most of the particles are very short-lived and won’t be visible themselves in a detector (especially neutral particles). Some will not interact with anything at all (neutrinos). Then your detectors are not 100% efficient, so you can’t detect all the energy, that was released in the interaction or the decay of a particle. The calorimeters, that are designed to completely stop any hadrons (particles consisting of quarks) have a layer of a very dense material, to force interactions, followed by a detector material. All the energy lost in the dense material is lost for the analysis. In the end you still know, how much energy was not detected, because you know the initial energy, but everything else gets calculated by models, that are based on known physics. A neutral weakly interacting particle would just be attributed as a neutrino.
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