Yup. It began and ended with Adam Schiff's SNL skit with a made up phone conversation.

Now that's amusing, LOL! Of course, it falls apart right in the beginning at the S(1) "proof" where the result "1/2" is actually a pulled-out-of-the-ass assumption (pootaa), not an actual mathematical proof. The rest, of course, is amusing verbiage as a smoke screen to cover the original pootaa.

Side note: We were witness to a pootaa plethora recently in the House impeachment proceedings.

A straight forward explanation of the idiocy that the sum of the integers can equal -1/12 can be found here
https://www.scienceabc.com/eyeopeners...

Conceptually, cost accounting treats any element of a system independently. Operational research treats the system as a whole (with the W, as Dr. Ackoff used to say :-)). The latter is the systemic view, the former is not. As companies are systems, then systemic view must be the correct one.
One example can prove how cost accounting leads to costly mistakes. If you can understand some spanish, look at these videos. Try by yourself solving the problem first, and then watch the rest of the videos:
https://vimeo.com/203316528
https://vimeo.com/203317411
https://vimeo.com/203317968
https://vimeo.com/203318329
https://vimeo.com/203318674

This exercise was proposed by Dr. Goldratt in his book The Haystack Syndrome.

As for S discussion. Ramanujan had it in his notebooks. Gauss's formula is correct for the first n numbers as long as n is not infinite. And you're right, trust is the word, but quite frankly, there is no much difference. Remarkably, S = -1/12 is the result that string theory needs to validate some assumptions... I'm not advocating anything. I just say, I humbly accept how little I know.

Fish- you may care to post up here explaining how Horngren's Cost Accounting 16th ed. contradicts operational research.

Ramanujan as a person is fascinating even compared with other mathematicians of that caliber. The preposterous proposition that the sum S=-1/12, could not have been made by Ramanujan.

The formula for the sum of the first n numbers, Gauss' formula, was discovered by Gauss as a young schoolkid.

You may state with good argument that you believe some scientists sometimes, I think trust is the right word here, but this is not the same as a 'belief in science'.

You didn't show any fallacy in the proof leading to S = -1/12. You said it is flawed because the result is impossible (according to you). But the whole point here is that S is impossible to be calculated adding numbers because the moment you stop adding, you get a humongous number, nothing close to -1/12. Maybe the flawed assumption is that we understand infinity. That's why I don't jump so easily to conclude the contradiction. Therefore, if you can't say where the proof is flawed, but you discard it because you don't "believe" can be true puts you in the category you are accusing me of.
I can offer you another "absurdity" to have fun trying to understand. The so called Gabriel Trumpet. It is a volume defined by rotating 1/x, and you get a finite volume contained by an infinite surface. In practical terms, you can have the volume full with X liters of paint but you cannot paint the inner surface... absurdity!!!!!!!! Fine, but that is what integrals say, sorry.
Look, I deeply believe (no one can prove it, though) that knowledge is unlimited. Maybe you don't accept it... but if you do, consider another condition that I think it's true: human capacity is limited. These two lead to the following statement: no matter how much knowledge human kind has accumulated, it is nothing compared to the unknown. And this is true today, and it will always be true.
For the last. I want to refute one of your statements. You say that if you don't understand, you don't know. I'm afraid that almost all knowledge you and I have is under that umbrella: we don't understand it. One simple example: do you understand gravitational force? If you do, go for the Nobel. But we use the knowledge everyday. We know how it works, but we don't know why. So, undestanding happens at different levels.
There are more misteries than certainties. Perhaps it is worth reevaluating deep assumptions. Thanks for the exchange, it made me think, always a good thing.

Fish: " I will quote you: "This implies that you should be a lot more careful about what and whose work you accept as considered to be 'science', sticking to reputable published texts." You use the word 'accept' in a sense that I understand equivalent to 'believe'. And the problem could be exactly that many "reputable published texts" are wrong, partially or totally."

Your belief in an absurdity in the name of "great mathameticians" and science shows that you "should be a lot more careful about what and whose work you accept as considered to be 'science', sticking to reputable published texts."

You may or may not understand some scientific principle or how it was arrived at, but you can at least narrow your idea of what is purported to be science to serious works by credible authors. You haven't said what videos are promoting the mathematical absurdity.

Fish: "So you define science as an accumulation of knowledge. From a dictionary: "Science is the intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment." Accumulation of knowledge could be a result of that. Or, unfortunately, as history shows, the result can be the accumulation of nonsense and sporadic advancements in knowledge from time to time."

When you open a science book or journal you find explanation of scientific knowledge, mostly that has been understood, validated and used for a long time, not endless "activity" that "could result" in knowledge.

A more legitimate word usage than your definition is "Study and knowledge of the natural world" or the "study and explanation of natural phenomena" (Webster). Science is systematic knowledge, which includes the means by which it is formulated and validated, not just "accumulation".

If you don't know why something is true you don't have knowledge. Science in particular requires systematic, objective means.

The attempt to switch the meaning of science to "activity" that may, "sporaticaly" or not, result in something that "works" for now is the result of bad philosophy, particularly Pragmatism.

When you trust a credible, accepted science text to be telling you what is known, the credibility comes from the nature of science as objective and the dominance of that attitude among those who publish it. If you have not done an experiment but understand it you presume the experimenter and those who checked it are telling the truth about what happened. You always know that the source of your understanding was indirect and do not equate that with having done all the experiments yourself.

If you don't understand something yourself, you still don't know it. A Big Name is not a substitute for understanding, let alone a reason to embrace contradictions in the name of "belief in science".

Fish: "The claim of S = -1/12 was made by Ramanujan among other great mathematicians, not a youtuber. I haven't found the fallacy of that demonstration yet. I assume you did... I'm all ears."

The closest you came to citing a source for that preposterous statement was "You can find the proof in many videos. Interesting challenge to 'common sense'".

Now citing an Indian mathematician and mystic who had unusual mathematical insights along with gibberish is an authoritarian appeal to take nonsense seriously in the name of science.

You wrote initially: "In many cases, we have to believe what some scientists say because of the impossibility of conducting the experiments ourselves" and "it is hard to believe that the sum of the infinite counting numbers is a negative and fractional number. So, saying 'I believe in science' is not that foolish after all."

No, you don't "have to believe" something you don't understand, and that kind of "belief in science" is foolish -- it is worse than foolish.

Can't you see for yourself why the claim that "the sum of the positive integers is -1/12" is necessarily false so that any purported "proof" must necessarily be fallacious?

Derivations of contradictions are themselves a form of proof that some premise is false (called "reductio at absurdum").

The sum of positive integers is positive, not negative anything, because all the positive integers are greater than zero. A sum of positive numbers gets bigger, not smaller than where it started.

The sum of all the positive integers is unbounded because the terms in the sum keep getting larger than any of the previous terms. For any number you pick, that number of terms in the sum leads to a sum that is larger than the number you picked. The sum is that number plus all the previous terms. For any N you pick, the sum of the first N positive integers is > N. That is the meaning of a sum being "unbounded", not -1/12..

The sum of the first n positive integers is n*(n+1)/2, as you can see from mathematical induction or by looking at the diagonal and numbers below it in a square array of unit cells (compute the area of the triangle). The sum of positive integers grows at the rate of n squared. It is unbounded, not -1/12.

There is no "proof", and there cannot be a "proof", that it is -1/12.

Sometimes you will find purported "proofs" of mathematical absurdities in which you don't immediately see the flaw, such as hidden divisions by zero. When that happens the proper approach is to acknowledge that you don't know where it is wrong but that it must be wrong -- or in cases where you don't understand at all simply say that -- not 'science tells us to abandon "common sense" by embracing contradictions'.

Your problem is more philosophical than mathematical. It appears to be an instance of "They use ["I believe in science"] as a way of declaring their belief in something they don't understand." https://www.galtsgulchonline.com/post...

Real science excludes belief in what one does not understand in the name of an authority called "science".

The claim of S = -1/12 was made by Ramanujan among other great mathematicians, not a youtuber. I haven't found the fallacy of that demonstration yet. I assume you did... I'm all ears.
However, the starting point here was the statement "I believe in science". I will quote you: "This implies that you should be a lot more careful about what and whose work you accept as considered to be 'science', sticking to reputable published texts." You use the word 'accept' in a sense that I understand equivalent to 'believe'. And the problem could be exactly that many "reputable published texts" are wrong, partially or totally. As an example, one of the most reputed, printed and used text in management is Horngren's Cost Accounting: A Managerial Emphasis (16th Edition). I can prove anytime that using the concepts of that book to make decisions is wrong. (It is not difficult, because that book contradicts operational research at many levels).
So you define science as an accumulation of knowledge. From a dictionary: "Science is the intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment." Accumulation of knowledge could be a result of that. Or, unfortunately, as history shows, the result can be the accumulation of nonsense and sporadic advancements in knowledge from time to time.
Summarizing, I do believe many things because I trust other people (apparently you also do). And there are some scientific theories that show me how ignorant I am, and yet I am pretty confident on the knowledge that I can use to create wealth.
So, yes, I believe that science is better than the alternative.

That was from his newsletter a year ago. But note that it recognizes that science is knowledge ("discoverable natural laws"), not just a process. Blarman is wrong in saying that science is not an outcome. An "outcome" consisting of knowledge includes understanding the means by which it is validated; and means have ends, not indefinite further process with nothing accomplished. The objectivity of scientific method results in scientific knowledge.

The sum of the integers is unbounded, not -1/12. There is no proof of such nonsense. There are many quacks out there, especially on the internet and they should not be gullibley echoed.

If you cannot follow a purported scientific "proof" and cannot detect and refute an obvious fallacy then you should not believe it and not spread it further yourself as 'science' gossip. The most you can say (to yourself or anyone else) is that someone claims something to be science but you do not understand it yourself.

This implies that you should be a lot more careful about what and whose work you accept as considered to be 'science', sticking to reputable published texts. Sensationalist youtube videos are not a good place to spend your time in search of knowledge you don't have.

The same goes for accepting Karl Popper's nihilistic skeptic philosophy. Science is an accumulation of knowledge, with occasional past mistakes detected and rejected, and some uncertain hypotheses explored on the frontiers, not a succession of exploded fallacies consisting of the already refuted versus that "in the queue" waiting to be refuted.

Thanks. Great quote. That nails it.

You are very correct. Mankind is certainly not ready. It's too easy, and at times profitable, to spout the accepted rhetoric without ever reading a scientific study.

Over a decade ago I turned off the tv and started reading. Now I can see that most people in America are living in a new dark age.

Thanks Lucky

In many cases, we have to believe what some scientists say because of the impossibility of conducting the experiments ourselves. That is one meaning for that statement (I believe in science).
The other meaning is I believe it is true what it is derved from a scientific process. In this sense, Karl Popper established a rule to call scientific a theory (I agree with this rule): Only a theory that can be disproved can be called scientific. So there are only two categories in scientific theories: those already proved wrong and those in queue. The latter are useful.
To think about this, consider the proof of S = 1+2+3+...(infinite) = -1/12 .... do you "believe" it? You can find the proof in many videos. Interesting challenge to "common sense". More interesting the fact that this result is a necessity in string theory... surprising. Anyway, it is hard to believe that the sum of the infinite counting numbers is a negative and fractional number. So, saying "I believe in science" is not that foolish after all. The courage required to act upon own beliefs is remarkable in some cases. (All that said, I am convinced that many "scientists" are not serious about science).

Which is why religion is irrelevant to knowledge.

Establishing and validating scientific knowledge takes a lot more than "questioning everything" and does not justify questioning literally everything for the sake of questioning with no basis -- which is philosophical skepticism. The freedom to question is a political and moral concept.

Science is the systematic body of knowledge that results from scientific methods of objective conceptualization and investigation (which does not consist of confirming or refuting arbitrary assertions). The results are inseparable from the method because knowledge includes how it was validated. Claims to knowledge without that are not knowledge.

Those who describe their position as "belief in science" are typically authoritarians with no clue as to how scientific theory is discovered and formulated. That outlook is increasingly used to promote "progressive" government control in the name of "science" and "data".

As Robert Tracinski put it last year:

"Some people may use 'I believe in science' as a vague shorthand for confidence in the ability of the scientific method to achieve valid results, or better yet, for the view that the universe is governed by natural laws that are discoverable by observation and reasoning. But the way most people use it, especially in a political context, is pretty much the opposite. They use it as a way of declaring their belief in something they don't understand."

I suspect that when one says he "believes in" science, he is about to tout "climate change", and use it as an excuse to destroy industry. But if someone think that science proves that industry (such as oil production) causes harmful pollution, let him go to court and prove it.

Some of the comments seem to ignore the paradigm effect. Paradigm being the set of "rules" that define the current theory. Individuals within a given paradigm can be blind to any data that conflicts with the existing paradigm! It is not ignored it is not seen! The classic example is a magician's deck of reversed color playing cards. Someone who "knows" what a deck of cards looks like can have all of the cards shown to them one at a time and will fail to see the reversed colors....yet they know which suits are red and which are black. My son and I played a game of cards for over two hours with others observing befor one of about 6 observers challanged us and ask to inspect the cards. He said that for about an hour that something was not right with the cards but could not figure out what it was. Theories which tested and fail the new test result in either a new theory (paradigm) or modification of existing theory to include the new data. That does not necessarily mean that the old paradigm is always discarded. We still use the physics of Newton for earth calculations since the answers it provides are accurate enough for earth based activities. But we know that Einstien rewrote the rules of physics.

People who say that have left one religion and joined another.

Rand suggested we think for ourselves, rather than parroting, "Ayn Rand says..."

Actual science is knowledge, and usually a specialized form of knowledge which is presented in a way that can be tested against physical reality by others. If it survives independent verification then it might be called "Science" with a capital S.

Even "established" science is open to inspection and revalidation. Sometimes surprises lurk in the most impossible places...

Isaac Asimov said, "The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' but 'That's funny...' "

Otherwise said: "I stay in my own lane!"

A more important statement would be:

I believe in the scientific process, where a theory can be destroyed by one counter example!

For the record, people were dying of AIDS without having HIV. This DISPROVES HIV as the ONLY Cause of AIDS.
So, in TRUE Government fashion, they changed the definition of AIDS to INCLUDE an HIV+ status. (Mind you, HIV+ means antibodies,
not infection). Which means, you could have died from AIDS, with an active HIV Infection, but since you had no anti-bodies, you were no longer counted. LMAO.
Or, you got "Cervical Cancer" and were HIV+ ... Now you have AIDS, even if you don't have an HIV Infection. And without ANY proof that HIV Causes Cervical Cancer,
but was declared an AIDS disease (to help increase the number of heterosexual women who were getting the disease IMO)...

Anyways, these are what has passed for science since the 1980s folks. I cringe to think how far back it really goes.

It's OK to say something like "I believe in evolution," because that's a particular theory with credible scientific process ongoing (although there real scientists who would dispute even that statement, as there are different schools of HOW evolution occurs). The statement "I believe in science" is illogical, of the order of saying "I believe in religion." Is it one particular religion, or the concept of multiple religions, or a religion you just made up?

I call it the ignorance between 'believing in' and 'believing that' meanings about objective reality. When those who say that they believe 'in' something, they are like all religious persons just believing by being too lazy to consider that their belief may not be questionable. Those who believe 'that' something is true have a better grasp of reality and know that there is a possibility that they might be wrong. When someone says that he believes that electrons exist, he is most likely referring to knowledge of evidence for that existence. When someone says that he believes in ghosts, he does not look for evidence that implies that ghosts exist.
As for believing 'in' science, one considers science to give correct knowledge regardless as to the experimental processes used. One can believe 'that' science can give knowledge of objective reality because of all the evidence about reality which one may infer that the evidence is correct. Science does not just pretend to be absolute about what it discovers. Reality has many surprises as better methods of measurement and means of analyzing data are discovered.

Here's a quote which I think summarizes this well:
“I feel that I do understand ‘science’, whatever that means exactly. Or at least I understand the scientific method. Which primarily consists of questioning everything – and feeling free do to so. One thing I do know is that anyone who states that the science is settled, and inarguable, and all the experts agree, and must therefore be right – clearly does not understand anything about science. At all.” Dr. Malcolm Kendrick