One plus One equals One

If I take one drop of water and add in another drop of water, I have one drop of water. 1 + 1 = 1. My point is, math is often presented as this fundamental, even beautiful endeavor, that “exists in the universe” and we’re lucky enough to tap into it. It’s the common universal language, etc. But it seems to me, at least at some level it’s just a human invention, as my little example shows. I’ve seen 1 + 1 = 2 presented as this marvelous equation showing the simplicity and elegance of math. 1+1=2 is just a human invention meant to be used in a particular context - counting of certain things. But 1+1=1 is valid in other contexts, like counting drops of water. (Not talking about volume of water, but counting again). So math may be beautiful in a sense, but not in any kind of grand “mind of god” way, but only in a limited human way. Doesn’t mean it isn’t useful, but let’s not go overboard in giving it some special meaning - it’s a manmade tool, nothing more. Go.

I think you are probably demonstrating the misapplication of Math with your example (You can’t, not talk about the volume of water). But I think I agree with your overall premise that Math is not something that comes from the Mind of God but rather it is a Manmade Tool.

Don’t remember where I got this from or who said it or exactly how they worded it but here goes: “The Planets are not calculating Integrals and solving Differential Equations as they orbit the Sun”. That Math is manmade. The Planets are doing something else.

I like that quote, thanks. I guess I just don’t like smug people, including physicists and mathematicians who ya, think what they’re doing is discovering god’s mind so to speak (though Einstein thought that too, so I’m torn). But when I found out that some of the same mathematics used in physics is used in economics of all things, it really made me wonder. Nothing wrong with using super advanced math in economics, but seems to take the wind out of all the “math is the mind of god” types. It’s just a tool.

Einstein did not believe in God. It’s a common argument I hear that he did (argument from authority fallacy), so I looked it up years ago. He apparently really didn’t like being labeled as an atheist, even outright denying that he was. But he refereed to both Jewish and Christian beliefs as “legends” and “superstitions” which were “childish”. I would suspect that a Jewish upbringing mixed with the time in which he lived gave him some trepidation about accepting the atheist label. He called himself an agnostic, apparently.

But in a 1945 letter as a reply to Guy Raner, when asked about a rumor that a Jesuit priest had converted him from atheism he gave this response:

I have never talked to a Jesuit priest in my life and I am astonished by the audacity to tell such lies about me. From the viewpoint of a Jesuit priest I am, of course, and have always been an atheist. ... It is always misleading to use anthropomorphical concepts in dealing with things outside the human sphere—childish analogies. We have to admire in humility the beautiful harmony of the structure of this world—as far as we can grasp it, and that is all.

Well no he didn’t. That’s why I said “so to speak”. He often used the word “god” but obviously meant something totally different by it. Anywho.

Mathematical symbols are man-made.

Mathematics is a universal algebraic relational “function”, i.e. it does not require symbolic representation in order to function mathematically.

In physics, spacetime is any mathematical model which fuses the three dimensions of space and the one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive where and when events occur differently.
https://en.wikipedia.org/wiki/Spacetime
steveklinko said; Don’t remember where I got this from or who said it or exactly how they worded it but here goes: “The Planets are not calculating Integrals and solving Differential Equations as they orbit the Sun”. That Math is manmade. The Planets are doing something else.
No you have that wrong. This is the fundamental concept of universal mathematics.
Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly enlarged the domains of application of the concept.

Functions are widely used in science, and in most fields of mathematics. It has been said that functions are “the central objects of investigation” in most fields of mathematics.[5]


https://en.wikipedia.org/wiki/Function_(mathematics)

 

@write4u - But see functions are just tools of approximation, and have nothing intrinsically to do with physics, or spacetime, etc. And that’s what I’m talking about.

And this: Mathematics is a universal algebraic relational “function”, i.e. it does not require symbolic representation in order to function mathematically.
What does it mean to "function mathematically"?
cuthbertj said ; @write4u – But see functions are just tools of approximation, and have nothing intrinsically to do with physics, or spacetime, etc. And that’s what I’m talking about.
No, that is not correct. All processes require a "function". This is basic physics. Here is another definition of "function" : https://mathinsight.org/definition/function
Function definition A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. This means that if the object xx is in the set of inputs (called the domain) then a function ff will map the object xx to exactly one object f(x)f(x) in the set of possible outputs (called the codomain).

The notion of a function is easily understood using the metaphor of a function machine that takes in an object for its input and, based on that input, spits out another object as its output.

A function is more formally defined given a set of inputs XX (domain) and a set of possible outputs YY (codomain) as a set of ordered pairs (x,y)(x,y) where x∈Xx∈X (confused?) and y∈Yy∈Y, subject to the restriction that there can be only one ordered pair with the same value of xx. We can write the statement that ff is a function from XX to YY using the function notation f:X→Yf:X→Y.


For more information about functions, check out the function machine or the function examples.

cuthbertj said: What does it mean to “function mathematically”?
What does that definition mean to you?

In short, Nature invented mathematics, along with the consistent regular processing of relational values, and humans have codified and symbolized these regular “relational values and algebraic processes” into a “language” which allows us to understand these “relational values and algebraic processes”.

AT NO TIME DOES THE UNIVERSE HAVE ANY INTENT OR MOTIVE. THINGS JUST RELATE TO EACH OTHER IN A MATHEMATICAL WAY. THIS IS WY HUMAN MATHS ARE SO EFFECTIVE IN PREDICTING FUTURE EVENTS. NATURE HAS SHOWN US HOW IT “FUNCTIONS”, ALL BY ITSELF… :slight_smile:

I know exactly what functions are, but you’re putting the cart before the horse. The universe does what it does and humans try to get some idea about how it works using some generic tools, roughly summed up as mathematics. But there’s nothing intrinsic about the math that has to do with the universe. Similar functions can be used for both economics, a human subject, and stars, a non-human subject.

I think you’re where I used to be, thinking there’s some unique relationship between math and the universe but there isn’t. It’s just an invention. Other civilizations out there might have totally different ways to investigate the universe that would could be wholly different, in kind, from ours. Check this out to see what I mean.

We had a discussion similar to this a few months ago here and I believe were were at a consensus that there was a relationship between math and the universe, not because the universe is forced to follow math, but because math was designed to describe the universe. Take a painting of a person, for example. What you seem to think he’s saying is that the person looks like the painting because of some power the painting has. What he’s actually saying is that the painting looks like the person because it was painted to be a representation of that person. The same is true with math. The universe doesn’t follow mathematical rules, but rather mathematical rules were created to describe the universe.

Other civilizations out there might have totally different ways to investigate the universe that would could be wholly different, in kind, from ours.
You have me thinking about convergent evolution where two totally different animals from different backgrounds, evolve the same types of adaptations, because suddenly they find themselves in the same sort of niche (flying insects, birds, bats and such).

So okay you are a totally different kind of creature, with a different way of thinking - but if you live on this planet, in this solar system, and then develop the instruments to take a closer look at the solar system and thing it was nestled within. You’d wind up developing the same sort of math to describe what your instruments are telling you - wouldn’t you?

Heck even mastering the optics to start building those instruments, I mean can there really be radically different ways of describing Optics?

 

The universe doesn’t follow mathematical rules, but rather mathematical rules were created to describe the universe.
And the more accurate it becomes, the better the math must be.

Convergence ~ Consilience, with the reality we are perceiving.

 

@cuthbertj, Check this out to see what I mean.

… This is a typical linear algebra course that focuses on things like linear dependence, subspaces, eigenvalues, etc. and does not spend time on “practical applications”. As a result, a lot of the economics students have no idea why they should be taking the course. Since I don’t know the first thing about economics, I also have no idea why they should be taking the course. …


Hmmm, care to elaborate. :slight_smile:

Hmmm, care to elaborate.
If the same math can be used to explain human economics and non-human physical objects then the math isn't intrinsically linked to either. It's just a tool. I came across a quote from the Nobel Prize winning physicist Sheldon Glashow. Paraphrasing, he said "don't mistake the representations we use to describe the world as being the world itself." That's what I'm talking about. Nobel Prize please! :)
Cc: Hmmm, care to elaborate.

@cuthbertJ If the same math can be used to explain human economics and non-human physical objects then the math isn’t intrinsically linked to either. It’s just a tool. I came across a quote from the Nobel Prize winning physicist Sheldon Glashow. Paraphrasing, he said “don’t mistake the representations we use to describe the world as being the world itself.” That’s what I’m talking about. Nobel Prize please!


Okay, sounds like the Map v Territory thing.

 

Thanks.

 

I’ll be sure to send in my letter of nomination. :wink:

I was on the road when this thread came up so I missed it. Glad to see it found it’s way to the top again.

I’ve collected a few quotes from Einstein, trying to summarize his thoughts on this matter. I hope to find some more time to study his conversations with the mystic Tagore. Maria Popova helped focus my searching with this letter from Einstein to a 6th grade class. https://www.brainpickings.org/2013/07/11/do-scientists-pray-einstein-letter-science-religion/

He clearly states a non-belief in naive ideas of the supernatural, then also provides a more wonderous view of the mathematical nature of reality.

Unfortunately we are humans attempting to do math. We as humans are fully capable of practicing false belief systems.

As you ascribe a fundamental nature to addition it should be noted that the modern mathematician formalizes that operator from functional analysis and wind up with the binary operator as their tool all the way into abstract algebra. They have the cart ahead of the horse and there is no compiler level integrity other than one mathematician patting a friend on the back and saying 'Yes, I’ll publish." The academic pressure to publish new works guarantees that new works will be produced no matter how little value they may be of. Falsification need not ensue, for this is what departments are for. A divorce from physics and philosophy to boot ensures plenty of paper playground for all.

For the physicist there is the first cosmological principle: space is isotropic. Spacetime isotropic? Oh, careful renditions of this isotropic claim issue that ‘on average’ space is isotropic, and I must beg of you to tell me anything that is not isotropic after averaging. Black hole singularities matter not for all of the modern Astronomers; a class of men who bow to this first law.

Philosophers snatch words worse than mathematicians do. ‘Utilitarian’ takes on a hood under the modern philosophy paradigm. No doubt religion plays a part into all of these tendrils, but to get back to the root, yes, mathematics must be there in the roots. Axiomatic thinking does seem at least a valid start into some of it, but constructive freedom must not be denied. This is probably the biggest failing: Professors must at least once in the year declare their topics to be open to future superior expressions, translations, and interpretations.

 

Well I came across a very interesting paper on the topic. The author is very convincing in his argument that in fact the use of advanced math in economics, like I referenced, is definitely not the same as it’s used in physics.

The upshot is that in economics, even considering Nobel Prize winning economists, no one has used advanced math to make predictions. They’ve only ever used it for analysis. Since no one has ever made predictions (i.e. predictions that were proven correct, since anyone can MAKE a prediction) that means economists are not using it the way physicists do.