Axioms o Science principles that support it, Just as foundations do in a building, are ideas that, according to some scholars, are simply accepted, and believed.
To question these principles is equivalent to challenging them, simply because they are Believe it or not.
But doing so does not mean giving up knowledge or ceasing belief in it. Rather, it means opening up the possibility of building new knowledge.
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Are the parallels intersecting?
This is the case with mathematics. As a guiding principle Two parallel lines never touch They are also accepted.
This principle is the basis of the great “building” called classical architecture.
To doubt it would be to get out of this or another building, as it finally happened.
“There is a part in mathematics that must be accepted, in which principles are believed or not believed, and this has given rise to new fields of study. For example, when someone does not believe the intuition of parallels with classical geometry, they have created another geometry,” he says in meeting with Tec ReviewAnd the Camilo Camagi Garcia, Mathematician from the National Autonomous University of Mexico (UNAM).
Russian mathematician who challenged Euclid
Camhaji García refers to what was done in the twentieth century Nikolai Lobachevsky, A Russian mathematician, who denied the classical principle of parallels formulated by Euclid, a Greek mathematician from the fourth century B.C.
This led to another engineering in it It is mentioned that the parallels do not touch, Which is contrary to common sense.
Denying something that was believed more than 2,500 years ago is not easy. It was the idea that the parallels would never touch the foundations Egyptian cultures Or Mesopotamia from ancient times, “confirms this expert from the United Nations mission.
In fact, it sounds far-fetched I think two parallels touch. How is this possible?
The answer depends on changing the space, from flat to curved, according to Kamagi Garcia.
This is how the meridians of the Earth intersect, parallel to each other, at the poles.
This is impossible if you only think of flat space, as ancient mathematicians did.
There are always loose ends
He was one of the greatest geniuses of the twentieth century Kurt Gödel, The Austrian mathematician, who showed it The axioms of mathematics They will always generate an incomplete theory.
That is, Gödel considered that they would always be Loose ends As a result of those principles they were simply accepted as true.
“We must believe that the chosen axioms are not contradictory; that is to say, they will not maintain that the thing exists and does not exist at the same time. Once they are put in place, they will generate a theory, although incomplete, according to Gödel. At the end of the day, in She believes in the axioms of mathematical theoryKamagi Garcia confirms.
However, anyone can say that the axioms of parallels, be it the Classical version or the Lobachevski version, are not a matter of faith, because they are seen in the world but also serve Railroad construction Or calculate the time in any city on the planet. In light of this, the mathematician at UNAM answers:
“These are special cases, axioms should work with all states, but no matter how many specific states you see, they will never all be proven, because they are infinite. It’s also like an axiom of reciprocity.”Ranking of factors does not change the product), This can be verified for some numbers using a pencil and a notebook, but it will not be possible to prove this for all numbers.
Now, just as you can dig under the foundation of the building, you can also delve beyond the axioms of math and reach for logic, keep digging, and then get to the point. Padding, The indisputable basis of absolutely all human thought, according to Kamagi García.
The most famous filler flag in the world isTo be or not to be, that is the question“, I said from a party village, Character created by William Shakespeare, The greatest British playwright of all time.
There, the indisputable universal truth is clearly reflected on it Is it or not. There is nothing more. This is just so. It is a doctrine, a term of Greek origin synonymous with principle.
“The filler is always correct and not questionableBut it doesn’t say anything concrete about the world. For example, the padding “it rains or not raining” (equivalent to “to be or not to be”) does not say what conditions the world lives in, does not explain why it is raining nor does it say whether you have to carry an umbrella in case it rains or wear The shorts if it’s not raining, it simply says it’s raining or not raining. It is always true, if you believe in this, then it is true, and if you do not believe it, then it is also true, ”confirms Kamagi García.
Another popular filler is “to be” or “not to be.” Or how about this other one:All that is missing is missingAccording to linguistics, this final filler would be a pleonasm, although it is valid when one wants to give a certain (universally true) meaning to a discourse.
The Doctrines of Physics
Without having to go to these deep levels of knowledge, physics also has inherent beliefs that make it stand out.
An example of this is the principle of causation in the universe, which is simply accepted and if not accepted, it is outside of physics; “deprivation!” It will be said in religious terms.
In an interview with Tec ReviewAnd the Fernando Angelis UribeThe Coordinator of Control and Electronics Workshop at the UNAM College of Science explains this as follows:
“The principle that every effect comes from a cause (the principle of causation) is regarded as a belief. Here it comes Method of induction That what is observed so many times is always assumed to be true, throughout the universe; It is an assumption in physics that can be called an act of faith. “
Another claim of this scientific “belief”, according to Angelus Uribe, is that the universe arose at some point or that everything in the universe could finally be explained in a rational way.
They are useful and fruitful scientific axioms that motivate physicists to continue their research.
“If not, then why do we do science? So far they are the best principles that we have,” he concludes.
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