"I believe in science..."
This statement reminds me of a similar line in the movie Nacho Libre (a movie I love). My question is...Is there a name for this? I have found that everybody, no matter their position on something (global warming, medicine, evolution...whatever) says and believes, "I believe in science". Of course, half or more are wrong. Is there a name for this bias? I find it fascinating.
I do not understand the scientific method but I have a position on this subject which I will defend by using jargon and convoluted syntax, and quoting organizations with sciencey sounding names.
A name for it- maybe- Scientism.
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...' "
Yes, I have noticed just how wrong Science, medicine etc has been. It's one thing to have a theory and even a theory that seems to work as far as you can prove but one should always continue the quest to get it right.
To do that, one should always be open to new ideas, new ways of testing, seeing, experimenting...but all the Sciences have been resistant to change, evolution of thought, constructive criticism and of course...history.
I suppose it's too much to ask these people, these pursuits, to be integrated while so much of what they study, are expected to know and remember, to be cognoscent of all the possible consequences, for they are so compartmentalized.
I don't think mankind is ready for "Wide Scope Accountability"...it really takes extraordinary dedication to work to get it right and to turn on a dime if need be because they didn't get it right.
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.
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."
https://www.scienceabc.com/eyeopeners...
Side note: We were witness to a pootaa plethora recently in the House impeachment proceedings.
1-(S(1)) = 1 - (1-1+1-1+1-1+....)
1-S(1) = 1-1+1-1+1-1+......
1-S(1))=S(1)
1=2S(1)
S(1)=1/2
Where is the pulled-out-of-the-ass assumption? I just see a logical derivation with no assumptions besides that you need S(1) gong infinitely for this to be true. I just say, this shows me that I don't understand infinity.
"From the axioms of addition, two other properties can be derived. One is the additive
identity property which says that for any real number a + 0 = a. The other is the additive
inverse property which suggests that for every number a, there is a number −a such that −a + a = 0."
It follows that any string S = -1+1-1+1... no matter how long must equal zero. There is
no stopping axiom. You are free to create one if you so inclined. But in no case can you derive a solution S(1) = 1/2 from the currently accepted axioms of addition.
https://science.jrank.org/pages/505/A...
The infinite sum -1+1-1+1... is not zero. The finite partial sums oscillate and the series does not converge to anything.
The limit S=1/2 cannot be obtained by arbitrary arithmetic, but can under a different meaning of the limit process that encapsulate an averaging process and is useful for some purposes, but that cannot be understood by someone who doesn't know the basic principle of limits and is still trying manipulate symbols without regard to the meaning of infinite sums as limits.
- .. Infinity, same.
- Calculations using an average as a representation of a numerical amount can be completely misleading. (eg- global average temperature).
Often the zero, the infinity and the averaging are implicit and will lead to conundrums or worse.
- The fallacy here is in the implicit assumption of when the series stops.
If on an odd number the answer is inadequate, if an even number likewise, so you take an average assuming it is one or the other. Wrong, an infinite series does not stop half way between an odd and an even number .. It keeps on going (like Ol' Man River) - until like the ooslum-bird going in ever decreasing circles it disappears up its own orifice, or the opposite, at the same time.
"The fallacy here is in the implicit assumption of when the series stops" - exactly, I agree. As long as it never stops, the mathematical demonstration is correct.
2. In the fallacious proof, the component series may, or do not, stop. But they do not combine into the series being studied, to define thus is an error.
Come back when you can demolish the rebuttal in-
https://skullsinthestars.com/2014/01/...
The limit for your "S(1)" does not exist because the sum is unbounded: lim n->inf of S_n = infinity. Infinity is not a number and cannot be treated arithmetically as a number. You cannot add and subtract infinities and numbers to manipulate infinity as if it were a number.
The false assumptions in the symbolic manipulations you quoted are that S(1) converges to a number, that infinity is a number, and that you can arbitrarily use the rules of arithmetic the way you did with infinities.
There is a whole theory of how to mathematically deal with limits, including infinite sums. If you want to "understand infinity" in that context that is what you must learn. You cannot just arbitrarily manipulate symbols and then ask what went wrong.
Your first expression "S(1) = 1-1+1-1+1-1+...." defines S(1) as an infinite expression. It's like asking "How high is up?". If S(1) were "up", then your second expression "1-(S(1)) = 1 - (1-1+1-1+1-1+....)" could be shown as 1-((up)) = 1-(up). Solve parenthesis first is a rule of math so you can clean up the left side of the expression by removing one set of parenthesis thus: 1-(up) = 1-(up), but your third expression "1-S(1) = 1-1+1-1+1-1+......" makes the false assumption that simply removing the parenthesis on the right side of the equation is valid to make the fourth expression 1-up = up. You can't do that because those parenthesis encapsulate an unsolved expression. The third expression is the pootaa and everything after it is as well.
S is defined as an infinite sum, which is exactly what happened there in all the steps.
You, on the other hand, did not use the original definition of S, so it is easy to demonstrate anything if you change the definition.
Yes, S(1) is an infinite sum without a finite solution, which is why it is written as it is in an equation. "(1-1+1-1+1-1+....)" is encapsulated in parenthesis because it is an unresolved expression and you can't remove the parenthesis until it is resolved as was falsely done to create the third expression above. The assumption that move could be made correctly is a false assumption.
The people using it tend to be left-leaning, indoctrinated in the pessimism of the fear-mongering Democrat Party whose end-game is the domination of every living soul (and income) on the planet.
After all, the people using this statement were "educated" in Democrat union-run schools and tend to also believe there are 57 genders, men can be women and vice versa. They don't believe a child in the womb is human and also haven't a clue what the term "photosynthesis" means.
They also have no idea that polar bears can swim. :-)
Basic science is NOT their forte and has nothing to do with this assertion.
When I see the phrase "I believe in science." I automatically assume that the speaker/writer is simply using a shorthand expression for 'the scientific method' in the true context of all that implies.
Unfortunately, my assumption is often an overestimation of the intelligence of the person making that statement. Unfortunately it takes additional conversation to ascertain that deficiency.
So, back to the OP's question; is there a name for the phenomenon? I think they used to call the person a 'blowhard' or a 'blatherer'.
But in today's society, using either term will have the so named person scurrying for a 'safe space' and get the person identifying said blatherer as such, labeled a bigot, racist, or just a plain old-fashioned bully.
-- In Liberty
S =-1+(1-1)+(1-1)+(1-1)... "=" 1
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.
More precisely, a theory that worked well under certain circumstances, can be proved wrong in other circumstances, and we have found the boundaries of application of that theory (example of Newton and Einstein). And then, knowledge was expanded. Of course you can destroy a full theory as well (I've seen a couple).
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.
“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
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).
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.
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.
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".
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.
There is no infinite knowledge. The infinite, as Aristotle identified, is a process not a thing (called "potential" versus "actual"). Knowledge is unlimited in that nothing limits us from learning more, and there is always more to learn, but it is always finite knowledge. Is that what you meant?
Unlimited knowledge and limited human capacity do not "lead to ... [N]o matter how much knowledge human kind has accumulated, it is nothing compared to the unknown". You don't know anything about the unknown. If you did it would not be unknown. We measure things by what we know, not by what is "unknown". Knowledge as "nothing compared to the unknown" is meaningless.
It is true that we expect to learn a lot more, possibly much more than is known now, as has happened in the exponential knowledge explosion of the last several centuries. That is not measurement with respect to "the unknown", which is impossible.
Fish: "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?"
We certainly do understand gravitational force. We do not know why masses attract or the full mechanism by which gravitational force is transmitted from one mass to another. We do understand the nature of the force and how it depends on mass and distance. We know in detail how to measure, use and predict it. Understanding of gravity has been fundamental in physics and engineering knowledge for centuries. That is understanding gravitation. It does not mean that there isn't more that could be discovered.
Understanding does not mean omniscience. That we don't know everything that does not mean we don't know anything. We know what we know based on sense perception of the world and our conceptual organization of it, not by mystically wrapping our consciousness around things with some kind of infinite insight. The standard of measurement of knowledge and its accumulation is what we do know.
If you don't understand what something means and why it is true then you do not know it. Knowledge is mental grasp of reality. If you don't understand how your knowledge is validated and what it means then you don't have that mental grasp of reality; you can't claim that the idea is true of reality -- you don't know. Someone else may understand and you may understand the meaning of the individual words he uses, but you don't know it yourself without adequate understanding. Floating abstractions are not knowledge.
Thank you for the discussion, anyway. I will leave it here.
On that basis you will never understand the mathematical infinity and infinite series, whose explanation has been well established since the 19th century in what was called the "arithmetization of analysis" that showed how to understand infinite limits in terms of finite numbers, which is all they can be.
Nor is it required when it results in a contradiction. Whatever details you have in mind don't matter because your assertion that the sum of positive integers is -1/12 is demonstrably false.
That it is false isn't "according to me", it is false in fact as established by mathematics, which you were shown in three proofs showing what is already obvious but formulated in terms of the mathematical meaning of an infinite sum.
Of course whatever "proof" you have in mind is flawed. It is flawed because it results in a falsehood. Valid proofs don't result in proving the false to be true. It is a bald contradiction, with an appeal to a meaningless mysticism of infinity to try to save it.
Your assertion that "Maybe the flawed assumption is that we understand infinity" is true, but it applies only to you: The mathematical infinite is a process not a mystical place or thing or some undefinable incomprehensibly mystic realm, and that process is understood by those who learn the mathematics.
You cannot understand how to apply mathematical processes of infinite limits without understanding some basic concepts of mathematical analysis which are well established and understood. But you would have to learn them, not arbitrarily manipulate some symbols and then ask 'what went wrong', while grasping at a mystical notion of the infinite.
The principle of "reductio ad absurdum" rejecting a premise that leads to a false conclusion is also a matter of the logic of mathematics, not of I "don't believe". There are no logical exemptions form "jumping so easily to conclude the contradiction". The contradiction is staring you in the face. Abandoning the principle of non-contradiction in logic for the sake of a mystical infinite makes rational thought and discussion impossible.
Your own lack of understanding of the mathematical infinite does not justify the non-sequitur: "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." Mysticism is a rejection of logic, not an alternative form of knowledge relegating logic to no better than the "same category" of "belief".
This isn't a matter of competing authorities vying for your attention in the name of science. You either understand the science yourself or you don't.
If you don't want to learn it then you don't have to, but that doesn't justify infinity mysticism and denouncing those who understand as engaging in personal subjective "beliefs" for following logic claimed to be no better.
1. https://plus.maths.org/content/disapp...
I am a great fan of Ramanujan. From memory- he was a semi-literate clerk who came across a school book, a summary of geometry theorems. He read, memorized, and developed wide ranging views in mathematics. He sent his treatise to renowned mathematician GE Hardy in Cambridge UK. Hardy, who got much junk mail from cranks, accidentally read some of it and was 'knocked off his feet'.
.. for a good explanation of the s=-1/12 see-
2. https://skullsinthestars.com/2014/01/...
There is a nice example of the type of error in the s=1/12 'proof'.
y j_IR1776wg- thanks for the ref which I followed up on.
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'.
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.
Decisions are made on a set of data and objectives. Data sets are limited, but the universe, being unlimited, influences outcomes not contained in the data used. Proper decisions must take a wide view, a systems approach. But any system is part of a bigger system which is part of an unlimited universe. Decisions made on less than infinite data cannot therefore be correct.
Solution- Re-examine the premises.
Cost accounting as an evil, as an opponent of Operations Research (!) -
speaking from qualifications and experience in both-
Cost accounting, is now up-marketed to Management Accounting.
It makes use of data, arithmetic operations, and a host of assumptions, with the aim of guiding management decisions. This it does as limited by the sense and skills of the people involved. Operations Research, with less data and more mathematics, same same.
The view of cost accounting not having a sufficiently systems view should not be given to the public service, those guys already are expert at analyzing problems to death, they need no more excuses.
It does not mean that n can ever become infinite. Infinity refers to the open-ended process; it is not a numerical value for anything. n(n+1)/2 does not have a value "at" infinity and neither does the infinite sum have a value. It means that the farther out you go in the sum process the larger the result is without bound.
It does not permit a meaning that the n(n+1)/2 formula is somehow different in value from the sums or their limits, giving a different result for the two limits.
There are no loopholes to make 1+2+3+... = -1/12 and no reason to "trust" otherwise in the name of science. The assertion is flat out false.
That someone may think he "needs" "S=-1/12" as a mathematical rationalization for his physics speculations is not an argument that either must be true.
The value -1/12 "associated" with the series as used in string speculation has an entirely different meaning than an infinite sum = -1/12. It arises from the extension of something called the "zeta function" into the complex plane with the value -1/12 at x=-1. It does not mean that the infinite sum of positive integers is -1/12. It also still doesn't justify the string speculation.
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".
But what does it un-explain.
This an heuristic not a rule.
An example is how to view the global temperature Hockey Stick which contradicted a vast set of knowledge accumulated from many sources and different cultures over centuries. Thus it was viewed with caution, this caution no doubt led to the contrivances and biased statistical analysis becoming exposed with the whole edifice collapsing.
It should be applied to everything BUT religion.