World Science Scholars

1.5 The Continents of Mathematics Discussion

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    • Is mathematics something inherent to nature, or is it a purely human construct? Why do you think math is so effective in describing the physical world around us? Do you think math exists by itself without physics?

    • i) Maths is inherent to nature, so for example we can show retrospectively that maths applied before the human species evolved and before maths was discovered.
      ii) Physical problems that can be expressed as maths problems can be analysed and potentially solved as applied maths problems.
      iii) Some physics problems may not be expressible as defined or definable maths problems. This follows inter alia from completeness and computability theories.
      iii) Potential maths can exist without physics, but actual maths is constrained by the physics of information processing, so one might argues that in this respect maths and physics are mutually-supporting.

    • Intuitively, maths should exist without nature. The predictions it can conclude in the physics community are commendable but maybe, we are seeking artificial patterns. Anyways, it is always great to see the dots connect and redefine the reality in a completely new way.

    • The problem here seems related, as far as I can think or grasp, since I’m not a mathematician, to the question: what do we mean by the word ‘nature’? Is there something else? Above? Different? As a materialist, I’m inclined to say that nature is all there is…wether it be ‘things’, minds, and so of course ‘human constructs’, products of our brains or neuronal organization…of a very high complexity, I agree, but nonetheless a ‘material’ complexity…so maths, or whatever, cannot exist ‘without nature’ because I don’t see how anything could exist without nature…It’s obvious to me that the physics community can use maths discovered long before physics…but mathematical human constructs belong intrinsically to nature just as physics does, and also the physics community and also any ‘human’ construct…Spinoza: Deus sive Natura…if you endorse a flat ontology, it’s not surprising then that maths has such effectiveness when it comes to describing or explaining the world in terms of physical laws…

    • Is mathematics something inherent to nature, or is it a purely human construct?
      I prefer to frame this question as such: “Is mathematics something inherent to a universe void of beings that possess self-consciousness, or is it a purely an emergent behavior borne surreptitiously of a self-conscious beings language abilities?”. Either way, I tend towards the latter. I have the mindset that, although we have discovered/invented/evolved a certain flavor of math as humans (and other living species have likewise created (seemingly) less robust languages of math), there could be another universe with a similar paradigm as cause & effect in which a similar flavor of math could be invented/discovered/evolved. These disparate flavors of math I believe would be children of a higher mathematics. I wonder if this relates to Goedel’s proof that there are truths in math that are unprovable. If nothing exists as the vesicle by which mathematics emerges, is there mathematics? I don’t think so. I think at the core of math is observation. Would nature still exist? Sure, there just wouldn’t be a specific type of language to talk about it without the talkers.

      Why do you think math is so effective in describing the physical world around us?
      I believe that mathematics is very effective in describing the world around us for a few main reasons: its roots in the empirical, the rigor by which it is practiced, the proof building methodology that strengthens its incremental findings, and the continual abstractions that allow for more complex proof building on top of previous work. To me it seems to be the most extensive language we have developed to speak about the Physical world, so in that regard, it should be very effective at describing it certain aspects of it.

    • – Is mathematics something inherent to nature, or is it a purely human construct?
      It is irrelevant as we humans inhabit a period of time in a universe where mathematics exists.. It is what it is.

      – Why do you think math is so effective in describing the physical world around us?
      Because the physical world is so effective at describing the math around us.

      – Do you think math exists by itself without physics?
      Everything in the universe is codependent.

    • Mathematics is based on a set of elements and well-structured relationships (patterns), if for some reason these coincide with nature, the deductions also adjust that nature.
      This works because nature has been shown to follow patterns.

    • Rather, this question represents a dilemma, which I would not know how to answer with certainty because humans still do not know everything that mathematics is hiding from us for some reason; it’s just amazing. But if we realize it, the universe has somehow been there, and we humans have looked for ways to explain what we cannot explain, and I believe that the mathematics that we know today arose from there; but I am not saying that they did not exist from the beginning, perhaps we are giving a logical representation for us. The mathematics that we know today has a wide variety of tools and fields that help us every day to explain our actions, what we see, everything related to physics in some way, and these two are complementary.

      • “But if we realize it, the universe has somehow been there, and we humans have looked for ways to explain what we cannot explain”

        Precisely.

    • I think that, at its most fundamental level, mathematics arises with the notion of

        difference

      . In a universe of total sameness, there would be nothing to count, no surfaces or discernable dimensionality, and no waves or motions. Everything that mathematicians study depend on differences of various kinds.

    • Is mathematics something inherent to nature, or is it a purely human construct?
      – My belief is that is inherent in nature, to the extent that one can discover the implicit order/rules underlying explicit order/behaviours. The key here is in the act of prediction ie. extrapolating a pattern to a data set not involved in the derivation of the rules. The best data sets are in the future. Take quantum mechanics for instance with it’s great predictive power of upon groups of like microscopic objects. The scale at which QM works is well out of our intuitive scale or range and the mathematical constructs serve to align our predictions with reality eg. Dirac’s prediction of anti-matter.

      Why do you think math is so effective in describing the physical world around us?
      – I reckon the effectiveness is due to the independence of mathematics from any one person, it’s trans-generational continuity, and much of it has arisen from careful curiosity applied to the physical world. That is our understanding, as a species, of the physical world has winnowed much grain from the chaff as it were, to produce logical constructs of high grade utility.

      Do you think math exists by itself without physics?
      – well some mathematics does and some doesn’t. My line of thought is that mathematicians tinker with concepts and possibilities, the physicists pick up the patterns by observation which is then better informed because of the applicable mathematics. It is a spectrum based on utility.

    • Maths, by my definition, is merely the relationships between sets and series. [For example, the number 3 in itself is a set of 3 1’s, and 3 + 3 is the addition of the sets.] While it is a construct that allows humans to process the elements around us, in this dimension at least, mathematics is an inherent language in all elements around us.

    • I would say that math simply exists, just like logic, in an abstract realm. By that token, it’s eternal and indestructible. It could be that it’s more than just abstract, maybe it has ontological powers, maybe math is “God” – something that is not bound by space and time and doesn’t need a creator. In a sense, it has no choice but to exist.

    • I tend to prescribe to the Platonic realm of mathematics; where it exists as a vast landscape in it’s own universe of logic. I believe it can discovered bit by bit by logical beings from all different perspectives. People are initially more prone to discovering some parts of it while logical beings of a different type are initially more prone to discovering other parts of this vast Platonic landscape. While nature changes and erodes, this vast universe of mathematics is eternal. Nature is built on this eternal framework.

    • Maths is inherent to nature. The whole Universe is exist under some fixed physical properties depend on different condition. We just discovered mathematics within this physical universe and use it as a special way to discover or properly describe those physical property of the universe. I don’t think so mathematics exists by itself without physics.

    • Mathematics is inherent to nature in how it processes and interpret nature’s information. Now, the way we as humans represent mathematics, with its symbols, is purely a human construct.

      Math is so effective in describing the world around us because it describes the fundamental roots of repetitive patterns present in nature. Thereby extrapolating its theories to different environments in nature.

      Mathematics couldn’t exist without physics because as I mentioned above, math is a universal language to interpret nature, and everything in nature is physics, even information.

    • Mathematics in itself is a great subject using which we can figure out a lot of stuff, but again without the laws of physics one cannot derive ‘useful’ information from mathematics i.e. information about physical reality….. Bernhard Riemann came up with the geometry of curved surfaces but without Albert Einstein’s General Relativity that theory would in itself be of no good. On the other side physical theories require Math to be comprehensive and useful in predicting certain things. So we arrive at the conclusion that Physics and Math are without a doubt pretty much dependent on each other. Physics is the part close to reality whereas Mathematics is the underlying mechanism that makes physics comprehensive and applicable to the real world. The theory of higher dimensions from math forms the basis of String theory while string theory is the one that describes physical reality.

    • Math is both inherent in nature and a human construct. In it’s simplest form it is born out of a desire of the human mind to quantify elements of the physical world we live in. One sheep, two shoes, three blind mice etc. It is a tool with which humans can quantify and measure the world and this, in turn allows us to find useful relationships between these quantities. From these basics we can derive further relationships by applying the rules of logic to ensure that from these basic truths (relationships) any newly derived relationships would also be true. And so we build a system of demonstrative mathematics – a deductive system where truth is demonstrated by proof. Euclid’s “Elements” is the template (or more accurately the Bible) of such mathematical systems.

      From this we can see why math is so effective in describing the world around us. It builds rigorous systems of truth through proof (via logic). Whether or not these systems ever find expression in the real world, they none the less generate systems which are internally consistent. If the basic axioms are true then the rest of the system that follows from these is also true.

      Does math exist by itself apart from physics. Yes. It is grounded in the real world but it has matured to the point where we can generate systems which may or may not exist in the real world. Some may turn out to exist in the real world, as with the Riemann-Einstein example that we have been given, but others may not. But that does not mean that we will not find or invent a way to make use of such abstract knowledge in the future. Part of the excitement is that we can not predict what will suddenly become useful.

    • Is mathematics something inherent to nature, or is it a purely human construct?
      I believe that mathematics is not a human construct. Humans just mimic the world around them. And in our attempt to understand the mimicry we applied symbols to objects. Math is a language, just as brail is a one or sign language, it is just another way for us to transfer our understanding to one another, to transfer data.

      Why do you think math is so effective in describing the physical world around us?
      Because it mimics the world around us. It is copy and pasting what see, or believe to real into a language structure that allows for complex communication.

      Do you think math exists by itself without physics?
      Neither could exist without one another, physics is the philosophization of math, and math is the language used to transfer the philosophy of physics to one another.
      If a tree falls in the woods and no one is around to hear it, does it still make a sound? If math didn’t exist, would physics still exist? Let us say that if we used another form of language another form of symbol to understand the concepts around us, the symbol doesn’t matter if it is a 1 or a 0 or a dictionary of different shaped rocks. The same principles would still arise, one rock would mean one rock and a differently shaped rock would mean two rocks. We would just ascribe it to something else. The concept was hidden within, and it was in our perception of the world that we unlocked the answers that lay before us. If math didn’t exist, then neither would physics, nothing would exist, because then there would be nothing to mimic.

    • 1. Mathematics is inherent to nature
      Mathematics is the natural language of science. The structures of mathematics are intrinsic to nature. Simple abstract equations define complex physical things beautifully, elegantly. There is no question that the logic and order that underpins mathematics, has served us in describing the patterns and structure we find in nature. It is up to us to discover mathematics and its workings–this will then assist us in building models that will give us predictive power and understanding of the physical phenomena we seek to control. Math is fundamental to existence!
      2. Math is so effective in describing the physical world around us by revealing hidden patterns that help us understand the world around us. Mathematics closely describes reality; deals with data, measurements, and observations from science; with inference, deduction, and proof; and with mathematical models of natural phenomena, of human behavior, and of social systems.
      3. Math and physics exists together. Math is intrinsic to nature and Physics is based on observation of the world around us. The result of mathematics is facts, theories & theorems that describes the world around us.
      NB: After reading on some articles & watching youtube lectures on this topic, I am in favor of Derek Abbott (Physicist and electronic engineer) thoughts. Here attached some Articles on the topic!

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    • Math is found by humans, but aliens would find the same thing. 📝📏📐🔨

      Math effectively describes the world around us. There are repeating and predictable patterns and concepts to repeat the patterns. Symetries of topics can exist. ➕➖✖➗

      There was a statement earlier in the course that math can be independant of physics.

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