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\sum_{n=1}^{\infty} \frac{1}{n} = \frac{1}{2} + 1 + \frac{3}{2} + 2 + \frac{5}{2} + 3 ... = (1 + 2 + 3 ...) + (\frac{1}{2} + \frac{3}{2} + \frac{5}{2} ...) = \sum_{n=1}^{\infty}n + \sum_{n=0}^{\infty} \frac{1}{2} + n = -\frac{1}{12} + \sum_{n=0}^{\infty} \frac{1}{2} + n = -\frac{1}{12} + (-\frac{1}{12}) + \frac{1}{2} = \frac{5}{12}
fuck sorry forgot tags
\sum_{n=1}^{\infty} \frac{1}{n} = \frac{1}{2} + 1 + \frac{3}{2} + 2 + \frac{5}{2} + 3 ... = (1 + 2 + 3 ...) + (\frac{1}{2} + \frac{3}{2} + \frac{5}{2} ...) = \sum_{n=1}^{\infty}n + \sum_{n=0}^{\infty} \frac{1}{2} + n = -\frac{1}{12} + \sum_{n=0}^{\infty} \frac{1}{2} + n = -\frac{1}{12} + (-\frac{1}{12}) + \frac{1}{2} = \frac{5}{12}
The sume is infinite
start with 1
next check the values of 1/2^n which sum to 1
now that's 2
for 1/3^n that's 1/2
this repeats adding 1 infinitely and is then unbounded because m+1 > m
or actually it's -1/12 cause reasons
>rearranging a non convergent infinite sum
you were supposed to pay attention in the first week of Calc 1. If you ever attended, that is...

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I saw a video on youtube a long time ago that really blew my mind but I have never been able to find it again.
A guy had one of those laser table setups and was shooting a laser at a holographic image to reconstruct it. Then he put a cup of frosted glass over the hologram source and it scrambled the projection. It turned into static fuzz. Then he did something else I don't quite recall and like magic the projection miraculously recohered slowly after several seconds. Even though the frosted glass was scrambling the data there was something about the setup that allowed it to read through the glass after a delay.

Sorry I know it's much to go off of... It just had a really profound impact on me and I NEED to see it again to understand it. How does the fastest thing in the universe take entire seconds to react and reconfigure itself like that? Haw could the information survive going through the frosted glass?
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You can buy the original 1972 version. I doubt it has the handy drawings of the apparatus specified in the State Department copy, though
The plasma sheathe guy
Here you go
Also this book "Principles of Phase Conjugation" of Shkinov and Zel'Dovich which you might find useful.
Actually I just realized filo.io is garbage, here's the direct link to that book:

My best friend as a child had a rare last name. Let’s call him Stephen gookenjammer. According to census reports about 8000 people share his last name in the US. His first name is super common with about 3,000,000 people sharing his first name.

My name is fairly uncommon. Let’s call me Marcus Brandywagon. According to census reports again there are about 32,000 people in the US that share my last name. My first name is fairly popular with about 1.5 million people with my first name.

There are 333,000,000 people in the United States. What is the likelihood that another Stephen gookenjammer’s best friend was Marcus Brandywagon?
We need to know your degree of belief in the fact that someone could actually be named Stephen Gooklover if you want a serious answer.
I’m not giving you their real name
Not what I asked for, Mr. Brandywagon.
Yes please dont unless you want to get DDOS'd by /sci/ elite team of super-hackers
At least your friend has 8000 people that share his name. I have 2 in the entire country. One of them is me, and we directly related.

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What the fuck is a "holographic grating"?
A holographic grating is a type of diffraction grating formed by an interference-fringe field of two laser beams whose standing-wave pattern is exposed to a set of photosensitive materials.[1][2] The exposure triggers chemical processes within the sample and results in the formation of a periodic structure that has the same periodicity of the recorded pattern. One of the most interesting features of these structures is their versatility and tunability as the optical response strongly depends on the blend of used materials, and their interactions with light during, and after, the recording procedure.

With the expertise earned over the years, nowadays holographic gratings are very efficient with no notable difference when compared to mechanically ruled gratings. Nevertheless, the lower limit over the grating spacing is one order of magnitude smaller than the latter. Their availability, low cost, and versatility opened the path for their use in a various range of applications such as data storage,[3] holographic display[4][5] and in general, as holographic optical components.[1][6][7]
I see the optical phase conjugation thread has anons asking questions.

Can anyone help with the source of pretty much the same diagram, just without the CBDC
Force and violence are the only reason society doesn't shatter.
Taxes are dumb and evil, but they're someone pointing an entire army at you if you don't obey their abuse.

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>Eating beef staves off cancer, scientists discover


Eating red meat and dairy could help to fight cancer, a new study suggests.

Scientists have discovered that a specific fatty acid found in beef, lamb and dairy products improves the body’s ability to attack and kill tumours.

The study, published in the journal Nature, also shows that patients with higher levels of the fatty acid – known as trans-vaccenic acid (TVA) – in their blood responded better to immunotherapy, suggesting that it could work as a nutritional supplement to complement clinical cancer treatments.

‘There are many studies trying to decipher the link between diet and human health, and it’s very difficult to understand the underlying mechanisms because of the wide variety of foods people eat,’ said co-author Professor Jing Chen, of the University of Chicago.

‘But if we focus on just the nutrients and metabolites derived from food, we begin to see how they influence physiology and pathology.

‘By focusing on nutrients that can activate T cell [immune] responses, we found one that actually enhances anti-tumour immunity by activating an important immune pathway.’

For the study, the team started with a database of around 700 known metabolites, small molecules that come from food, and assembled a ‘blood nutrient’ library.

They then screened the compounds in this new library for their ability to influence anti-tumour immunity.

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Thats some truly stellar looking red meat, i would eat that in boat and with a goat and on a train in the rain, etc.
t. vegan epidemiologist

I sure enjoy eating my thursday meat (tuna pizza with coke) and my meat sandwhiches with plants and fries on top of them
Why is meat classified as carcinogenic you ask?
Poorly executed, biased epidemiology and two failed rat studies that had their cancer *induced* by injecting them with carcinogens
natural wildlife lmao

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Since the current crop of replication crisis era scientists have turned academic publishing into use a wasteland of greedily contrived toxic lies, should we get rid of the scientists had have AI do all the academic publishing from now on?
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>AIs don't lie.
Sure they can, they'll repeat any lie they're programmed to repeat
and they'll knowingly lie for various reasons, just like we do. just that they'll do it for someone, or some group. because it will be "aligned" or some shit
Lobotomised AIs are useless.
Every AI that ever exists will be programmed by it's programmer to have the same biases and preferences that the programmer has
Since Microsoft's TayAI was a racist genocidal antisemite, Microsoft is full of racist genocidal antisemites.
Google and Apple's programmers all think blacks are literally gorillas.

Water Hammer Edition
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lmao Ars just can't keep their commentariat from frothing at the mouth with terminal EDS
It's chasing their space audience off the site
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Where are my engines Jeff
People are now just starting to realise that SpaceX is not the company it wa swhen it made early falcon for a tiny fraction of the cost of a typical launch vehicle in its class. it no longer has the startup vitality. SpaceX now take roughly the same time and price to get something done as oldspace, it's just more ambitious. Remember when people were laughing that Starship would be ready before New Glenn? Who's laughing now? An operational Starship is at least 2 years away and HLS will be the single fact that delsys artemis 3. Since SpaceX HLS is so radical and requires the development of an entire superheavy lift architecture and fuel depots in orbit, it may be the case that Blue Origin lands on the Moon with artemis 4 before artemis 3 flies. It costs SpaceX at least 2 billion dollars a year (Elon said it costs 2 billion) to develop Starship, so by the time its done it will have a similar dev price to SLS
>inb4 low quality bait response that tries to sound as retarded as possible for attention grabbing.

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I don't understand bros.
I've been taught this over and over again through the years but I still don't get why it actually matters.
Besides the greenhouse effect, how does putting more carbon into the cycle through fossil fuels actually mess it up?
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What about this graph?
>expected pH
>xG merchant
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>how come climate hysterics become conditional evolution deniers when it suits them?
Because they're not interested in science, they're only interested in their gratifying their selfish mentally ill savior savior complex fantasies
And you don't see the obvious root issue in your animation? The fuel is being burned at an exponential rate. This goes for all resources not just fossil fuels. If fossil fuel burning is causing some side effect that's a minor issue in comparison.
The brainwashed mind will associate this with "overpopulation" but the real problem is obviously the globohomo system that demands constant global gdp growth. People sharing baked goods etc creates value but is not accounted for in gdp calculations. So the system we prop up is working to destroy everything good and sustainable like neighbourhood bbq bakeoffs or whatever and diverting resources to the worst things ever made like plastic straws, nukes and Israel. This same system likes diversions like global warming that help you forget how evil and demonic the system really is.
The framing that CO2 output is a dire issue that we desperately need to solve implies the underlying system would work if not for that darn CO2 issue. This is a completely insane proposition.
The same framing is used to promote the concept of "overpopulation". There aren't too many people for the planet to support but assuming all of them will become rabid brainwashed consumers it's a problem so the framing becomes "too many people" instead of "insane demonic system".
they didn't say they knew "nothing", just that they wished they knew more
huge difference
we know perfectly well that ocean pH levels are lowering
that's called acidification

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Wikipedia used to be my go-to source on literally everything. Physics, math, current events, history, etc. But now I know. It is a toxic cesspool of political activists and intelligence agency spooks.

Just thought you should know too

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Having Christmas be the start of the new year makes the most sense, since time is measured in years since the birth of Jesus
good song
long live moonman

All encyclopedias are going to have problems, it is the nature of condensing so much information into a (relatively) short text. Your best bet in general, is to go to area-specific ones where the articles are written by experts in the field. These tend to be - not accessible online legally because they are print books or made for libraries but these are going to be the best. The more general the work, the more errors will creep in. Nothing is free of bias because that is the nature of humanity and the things we create, but if your goal is just to avoid errors, this is the best course. But modern encyclopedias are not meant to be your main source of information, they are meant to be - intros, or references.

While I see people sucking off Chatgpts "knowledge" I have never seen it actually do well, you are getting the same information that is easily found online just it is filtered through its awkward writing so you've just gotten lazier I'd say anon.
Which of the public domain editions of Britannica is the best and most reliable? The 11th is too woke, I've read some of its articles, and didn't like it.

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Bug news or nah?
im gay so yeah
They probably could have done this with machines 200 years ago, I figure they were just worried about their jobs.
how do they know which crystal is useful, op?
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interesting stuff what a time to be alive anons
Likely Graphene mania 2.0

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How true is this meme? It seems education is going to shit in the former first world countries. I keep seeing people with university degrees who have less actual knowledge than I had in highschool. Are degrees becoming trivial and intellectually worthless pieces of paper?
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>some uneducated dumbfuck gets the job instead just because he knows how to code.
If he knows how to program properly, he isn't uneducated. Anyone who goes into debt for a degree is an idiot that doesn't belong in university.
Why would you need to filter by degree when you can filter by standardized test?
>If a degree is really is that useful then why do employers of companies/government require further experience or job that is outside the degree?
Because they want to generate a need for interns to add to their slave labor pool.

>Just work for free for a few years and we'll totally give you a job
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> for some job positions
Yeah I don't give a shit. Those are probably pencil pusher jobs.

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so if you want to find the greatest common factor between two numbers you use the euclidean algorithm right? so i input the two numbers and get a decimal. so then i have to convert the decimal into a fraction to find the remainder and its a massive number so now i need to find two commom factors in order to comvert it, so now i need to put it into the algorithm again, and again and again. wtf??
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And remember the decimal answer is just an approximation. And the infinite decimal 4.666... is a way of saying "the number that we can approximate as closely as we want by tacking on sufficiently many 6's to 4.666".
Naw bro, the lesser measures the greater until a unit is left, be gone with that decimal bullshit
4.6... rounds up to 5? no. Maybe using that algorithm should wait until I get further on my maths learning journey and I should stick to finding factors manually first.
by that I mean I should probably go back to basics too perhaps
Basics is based, and nobody but me in the whole thread used euclids algorithm right so they should all go back to basics too

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What happens at the singularity?
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That's where all the aliens are.
None of the smarty pants here want to answer you so i will. I asked bing chat on my phone about a week ago. He said something about the laws of physics breaking down and it being the subject of much debate and theory. Dont remember much else. Oh also something about information paradox. Information about the universe is lost of returned to its original state.
Because they're heckin mysterious and you can sound really cool and smart when you talk about them to normies, while in reality talking about nothing more than basically Marvel stories
Dick go in and can't come out.

Any PhDs on this board? How does this happen? I was under the impression that grad students were paid.
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This meme is stupid. So, be smart to get a diploma and... be rich to get money??
Non-white people aren't exclusively responsible for AA.
Women are the single largest beneficiary group of affirmative action.
>This meme triggers me emotionally
thanks for letting us all know

Women from wealthy families are the biggest beneficiaries of affirmative action because they're the ones who have bottomless resources they can use to "earn" paper certificates which will guarantee them the prestige jobs and titles they seek. Poor negro women still end getting pregnant when they're 14 years old and eventually are so destitute that they try to smuggle cookie dough out of the grocery store in their vagina
>only black people can be poor

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