Does Math Fit With Philosophy?

[hazelm]

Is it just me?  Or does anyone else get terribly frustrated when trying to read a philosophical article or a philosophical debate and have the ideas expressed as mathematical equations?  Especially untranslated math equations?

 

I have been wondering how much of this is necessary - using math equations to illustrate philosophy ideas.  Or even with science for that matter.  In physics, yes.  In biology? 

 

Opinions?

[hazelm]

I hope I am not just talking to myself but I did read something very interesting in relation to my OP.   Not intended; just happened.

 

First, though,  a friend e-mailed me that she also gets frustrated the same way - trying to read something and having math equations scattered throughout  and meaning nothing to her.

 

Anyway, I am reading Michael Gazzaniga's "The Consciousness Instinct".  Among many other ideas, he talks about how we get our particular talents - our skills that will lead us into our own particular interests and, perhaps, professions.  I do not know if this is already a scientific theory or only Michael Gazzaniga's hypothesis.  He says we come (are born) already equipped with a particular set of what he calls "bubbles" (and I call needed skills).  These bubbles are ready and waiting to be called upon when needed to solve problems, create new ideas, build a career.   The brain is full of these bubbles just waiting.  When one is needed the brain searches deeply for a "bubble" to help out.

 

And now, here is what soothed my tangled frustrations.  Apparently my friend and I are not the only ones who get frustrated when trying to read someone's very good article on a given topic and running into math equations.  Michael Gazzaniga says:

 

"To get a feel for this, consider what bubble you don't have.  For instance, I can tell you I feel frustrated when equations start popping up in lectures.  Though I wish I could, I cannot tell you what it is like to grasp highly abstract math, but I bet it would be cool."

 

Ah!  If someone of Michael Gazzaniga's caliber has a problem with Ph.D. math, why should I feel bad that it is far beyond me?  I do not feel badly at all in asking "how much of it is necessary;  how much of it could be expressed in words?"  If you don't know the definition of words, you have dictionaries.    How do we find translations of math equations?

 

End of talking to myself and no answers. 

[Vee]

Numbers are words. (duh)

[exchemist]

I hope I am not just talking to myself but I did read something very interesting in relation to my OP.   Not intended; just happened.

 

First, though,  a friend e-mailed me that she also gets frustrated the same way - trying to read something and having math equations scattered throughout  and meaning nothing to her.

 

Anyway, I am reading Michael Gazzaniga's "The Consciousness Instinct".  Among many other ideas, he talks about how we get our particular talents - our skills that will lead us into our own particular interests and, perhaps, professions.  I do not know if this is already a scientific theory or only Michael Gazzaniga's hypothesis.  He says we come (are born) already equipped with a particular set of what he calls "bubbles" (and I call needed skills).  These bubbles are ready and waiting to be called upon when needed to solve problems, create new ideas, build a career.   The brain is full of these bubbles just waiting.  When one is needed the brain searches deeply for a "bubble" to help out.

 

And now, here is what soothed my tangled frustrations.  Apparently my friend and I are not the only ones who get frustrated when trying to read someone's very good article on a given topic and running into math equations.  Michael Gazzaniga says:

 

"To get a feel for this, consider what bubble you don't have.  For instance, I can tell you I feel frustrated when equations start popping up in lectures.  Though I wish I could, I cannot tell you what it is like to grasp highly abstract math, but I bet it would be cool."

 

Ah!  If someone of Michael Gazzaniga's caliber has a problem with Ph.D. math, why should I feel bad that it is far beyond me?  I do not feel badly at all in asking "how much of it is necessary;  how much of it could be expressed in words?"  If you don't know the definition of words, you have dictionaries.    How do we find translations of math equations?

 

End of talking to myself and no answers. 

You can often write a simple algebraic equation in words. For example Newton's F=ma is "Force equals mass times acceleration. But is that really any clearer to you than F=ma?

 

It seems to me that, as we are all taught nowadays in school enough maths to be able to understand F=ma, it is not unreasonable to expect that readers can deal with it. But more complicated things will lose readers, inevitably.  

Edited June 24, 2018 by exchemist

[hazelm]

You can often write a simple algebraic equation in words. For example Newton's F=ma is "Force equals mass times acceleration. But is that really any clearer to you than F=ma?

 

It seems to me that, as we are all taught nowadays in school enough maths to be able to understand F=ma, it is not unreasonable to expect that readers can deal with it. But more complicated things will lose readers, inevitably.  

No, I confess I did not know "a" meant acceleration.  A minor detail?  At any rate....

 

Thank you, exchemist.  Your point is well taken but  it (or more complicated ones) can be a foreign language to anyone who has never had occasion to learn all the math symbols.  Not everyone follows the same path through high school and/or university.  Not everyone is exposed to he same terms.  It depends on their intentions for the future.  Or, bless his heart - iike Gazziniga - was not born with a math bubble.

 

How would you react if a lecturer was going along fine with a lecture and you were really enjoying his ideas when he suddenly said to to the class "nos dawch" and walked out of the room? Unless you know Welsh, you might just think he got tired of all of you and left.  All he said was "good night".

 

I know.  It is a double-edged sword.  And a lot depends on the category.  Chemistry, physics - they are going, by necessity, to be loaded with equations and we who know nothing of the fields or the math that is attached to them keep a distance.   But if someone cannot describe the trajectory of a baseball or why oxygen contributes to rust without equations, I have questions for him and they aren't "please translate".

 

But that's the simple part.  Please rethink Gazzaniga's comment.  I'd love to know how much that is accepted by the scientific community but that's another topic.  The point he is making is that there are people who simply cannot grasp higher math.  And, forgive me  for reminding you (I know you know it), there is a whopper of difference between what is taught in high school and what is learned in high school.

 

So, all Gazzaniga and I are saying is "look, this is why I don't understand you.  Then, if you want the person to understand, you translate.  If not, you don't.    But if you can write a 1,000 word report and use plain English until the very end where you revert to putting it all in equations .....

 

I am leaving in just a minute ,  Just this which I may have posted before.  I have a book written by Albert Einstein.  It is called Relativity -  the Special and the General Theory.  This book has 178 pages and only in the last five or six pages do equations begin to appear.  Since he managed to write that much before he needed equations, could he not have translated those?

 

Oh, by they way, in case anyone does not know this book, it was written in 1915, specifically for those not versed in physics or higher math.  If Einstein could do it ..... 

 

Well, as I said, it's a two-edged sword.  I just had to vent my frustration after trying to read something that I really did want to read.  I finally gave up.  If you use words I do not understand, I have dictionaries.  Where do I go to translate a long equation?

 

Nos dawch.  :-)

Edited June 24, 2018 by hazelm

[Turtle]

When I run across unfamiliar elements in a text, whether mathematical or not, I stop reading and look up the element. Once confident that I have the element by the short-hairs, I return to the text, back up a paragraph from my stop point, and start reading again. Rinse & repeat as necessary until achieving a most happy conclusion. :read: :read:

 

On the topic of math as applies to philosophy, math underlies it whether or not explicitly invoked. If you doubt this, then reread paragraph 4 in that philosophical article you last math bashed with.   See, you can't go to paragraph 4 without knowing counting. There is no relief, and that is the first principle. :edizzy: The second principle is to always seek relief. 

Edited July 8, 2018 by Turtle

[hazelm]

When I run across unfamiliar elements in a text, whether mathematical or not, I stop reading and look up the element. Once confident that I have the element by the short-hairs, I return to the text, back up a paragraph from my stop point, and start reading again. Rinse & repeat as necessary until achieving a most happy conclusion. :read: :read:

 

On the topic of math as applies to philosophy, math underlies it whether or not explicitly invoked. If you doubt this, then reread paragraph 4 in that philosophical article you last math bashed with.   See, you can't go to paragraph 4 without knowing counting. There is no relief, and that is the first principle. :edizzy: The second principle is to always seek relief. 

Great.  I'd argue with you but I withdrew from the numbers world when some (philosopher?  not sure.  maybe would-be cosmologist) tried to convince me that "the universe is math".  Trouble is that, when asked to explain, he could not.  Where is C E Moore when we need him?

 

Seriously, though - after my silliness - what you say is so true.  Google has a built-in system for just that.  Same with big words we don't understand.  Highlight the word, right-click the word, click "Search Google for system" and - voila - all the definitions one could ask for.   Sometimes I get to hung up in some article the definition refers me to that I never gt back to my original spot.

 

And now - as you suggest -  I should try that with math equations.  Why hadn't I thought of it?  Thanks.

Edited July 8, 2018 by hazelm

[Turtle]

Great.  I'd argue with you but I withdrew from the numbers world when some (philosopher?  not sure.  maybe would-be cosmologist) tried to convince me that "the universe is math".  Trouble is that, when asked to explain, he could not.  Where is C E Moore when we need him?

 

Seriously, though - after my silliness - what you say is so true.  Google has a built-in system for just that.  Same with big words we don't understand.  Highlight the word, right-click the word, click "Search Google for system" and - voila - all the definitions one could ask for.   Sometimes I get to hung up in some article the definition refers me to that I never gt back to my original spot.

 

And now - as you suggest -  I should try that with math equations.  Why hadn't I thought of it?  Thanks.

 

Argue all you want, but as soon as you make your first point, math has been invoked. Math doesn't give a whit whether you engage it or not because you can't escape its web. Cest la vis. :lol:

 

The ideas I suggested far predate the internet when we used papier things called books. Define a word; dictionary. Read up on a topic; encyclopedia. Need more, visit a library or heaven forbid, write a letter.

 

As we do have the web, I recommend you bookmark the WolframAlpha Computational Engine.

If you register for free you get some extra functionalities. :smart:

[hazelm]

 

Argue all you want, but as soon as you make your first point, math has been invoked. Math doesn't give a whit whether you engage it or not because you can't escape its web. Cest la vis. :lol:

 

The ideas I suggested far predate the internet when we used papier things called books. Define a word; dictionary. Read up on a topic; encyclopedia. Need more, visit a library or heaven forbid, write a letter.

 

As we do have the web, I recommend you bookmark the WolframAlpha Computational Engine.

If you register for free you get some extra functionalities. :smart:

 

Oh, heavens to Betsy, I know you are right.  I just don't want to know you are right.   And some of it - which really commits me to the ancient world, I do not even believe.  Math?  When I went to school  (shhhhh!!!!), math was arithmetic and was very simple.  But then, to paraphrase somebody we know,  what was was.

 

WolframAlpha Computational Engine?  What in the -------.   I am still trying to find out what space pixels are.  But  curiosity always gets me.  Will do Wolfram, hoping it will translate math equations for me.    I have two pages full of the symbols used with codes to typing them but nothing about translating them into English.  And therein is the stumbling block.   When did they teach this stuff?

 

Confession:  I still write letters (long ones as you can see) and spend hours reading books.  A smile for you before I go:  I recently went into Macy's and asked the man if he had a book case.  He said 'oh, yes", and pointed to a very flimsy piece of furniture.  The shelves were thin slabs of plywood with a vase here and there.  I said those  would never hold books.  He looked at me in absolute amazement and responded:  "You're going to put  books on them?  Oh, no, they won't hold books."    It's a book case!

 

WolframAlpha, here I come! 

[wiseshopper]

When I was still studying at the uni, I had a Philosophy class. One of the topics we discussed there is Logic. It's the most frustrating thing in the world for me because our prof literally used mathematical equations to explain the logic. I don't like math so I really struggled with understanding the concept behind those equations. But after I was able to practice and read more about the interconnection, it became easier for me. It's logical. It made sense.

[JacquelineLamber]

Hard question! It is enough for me that philosophy is philosophy. I do not like to talk. Always I even order an essay to a university on an essay writing service. Probably, I chose the wrong specialty.  :zip:

[Moronium]

No, I confess I did not know "a" meant acceleration.  A minor detail?  At any rate....

 

 

Math is applied to "concepts."  If you don't understand the concepts, math formulas will be useless.

 

Let's look at f=ma.

 

What is the F?  What is force?  Well, let's say I swing a baseball bat as hard as I can.  That generates a force in the form of kinetic energy.  But how big of a force is it?  Well, big enough to bust your head wide open if the bat hits your head, I figure.  But that's not too precise.  How do we measure the magnitude of this "force?"

 

The m x a part is designed to measure that force.  Let's say that I take two identical swings, but the bat hits different objects.  Does that change the amount of force which impacts those two different objects?  No the force is the same, either way.  The amount force applied doesn't depend on the object(s) being affected by that force.

 

Now let's say one of the objects I hit is a golf ball and the other is a cannonball.   The golf ball might go hundreds of yards after being accelerated by this force.  The cannonball may go a few inches, or it may just go nowhere and break the bat.  That's a lesser amount of acceleration.  Which brings us to mass.

 

The more massive an object is, the less accelerated it will be by the same force.  OK, that sounds reasonable, doesn't it?

 

So now, what is mass?  Mathematically speaking, mass is f/a (force divided by acceleration).  But what does that mean?  Mass is not weight.  Mass is not a measure of "matter."  All you can really say about it, from a formal mathematical standpoint, is that it is "resistance to acceleration."

 

But, if you think about it, now you can see that the entire formula is merely circular.  It doesn't explain what "mass" is apart from a reference back to force and acceleration.

 

Math can never "tell" you anything about the world.  You have to tell it what you think you already know about the world first.  From there math just says:  "Well, OK, if that's true, then this would be true." It's the same with logic.  In fact, math is essentially just "applied logic."  Anything that be expressed in mathematical terms can also be expressed in words using the same concepts.  Math is basically just a shortcut.  We have shortcuts in language, too.  For example, abbreviating "The United States of America" to "the USA."

 

 

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality. (Albert Einstein)

 

 

Mathematicians, and many scientists, have a tendency to forget this. They start thinking that because there is only one correct answer to a math problem, then that proves that it provides an unassailable and absolutely correct answer to questions pertaining to things in the real world.

Edited February 24, 2019 by Moronium

[Moronium]

 

So now, what is mass?  Mathematically speaking, mass is f/a (force divided by acceleration).  But what does that mean?  Mass is not weight.  Mass is not a measure of "matter."  All you can really say about it is that it is "resistance to acceleration."

 

But, if you think about it, now you can see that the entire formula is merely circular.  It doesn't explain what "mass" is apart from a reference back to force and acceleration.

 

 

But you can also understand the CONCEPT of mass, without regard to the mathematical structure of F=MA (or the implication that M=F/A).  "Mass" is basically the same thing as "inertia."  Newton says that a body at rest will remain at rest and that a body in motion will remain in motion at the same speed and in the same direction UNLESS it is acted upon by a "force."  Anything that causes such a body to alter it's state of rest/motion/direction is called a "force."  The change itself is called "acceleration." 

 

The "law of inertia" says that it will take a force to slow down, change the direction of, or stop a moving object.  That too is "acceleration" (or, same thing, "deceleration" ).  Acceleration doesn't just mean making things "speed up."  You can see that the concept of "mass" can be stated in everyday words (of Newton), without resort to math.  And that provides a much better understanding of what mass is than merely putting an "M"  in the equation F=MA.

 

But why do objects have this tendency to resist acceleration?  What is the origin of, or "cause" of, inertia  (mass)?

 

Nobody knows.  And they won't find the answer by solving math equations, even if they solve a million of them.

Edited February 25, 2019 by Moronium

[fahrquad]

 

...But why do objects have this tendency to resist acceleration?  What is the origin of, or "cause" of, inertia  (mass)?

 

 

Rather than ask the origin of mass, perhaps we should ask what is mass?

[Moronium]

Rather than ask the origin of mass, perhaps we should ask what is mass?

 

 

We already know that, from a mathematical standpoint, anyway.  As I said, it is "resistance to acceleration" (F/A).  If you want to understand it from a conceptual, rather than merely mathematical, standpoint, then read Newton's "law of inertia."

 

Once again, it is important to note that the math was derived from the concepts, not vice versa.  The concepts were not derived from, or dictated by, the math.  For thousands of years, the concept of inertia played no part in physics, because no one had yet conceived it.  It took geniuses like Galileo and Newton to develop the concept.

 

Guys like Exchem, Oceanbreeze, and GAHD (among many others here) may never grasp that simple fact, though.

 

As I said before:

 

Mathematicians, and many scientists, have a tendency to forget this [i.e., the wise observation of Einstein which I quoted].  They start thinking that because there is only one correct answer to a math problem, then that proves that it provides an unassailable and absolutely correct answer to questions pertaining to things in the real world.

 

 

Those types seem to quickly lose sight of, or just ignore, the concepts underlying the logical (mathematical) consequences which the concepts generate. At that point, they never question the concepts again. They don't even think of things in terms of concepts. Instead they want to rely on mechanical mathematical exercises to provide the correct answer. They think the math IS the concepts.  They think math IS physics.  If you raise a question pertaining to the underlying fundamental concepts, they think that "doing the math" gives the answer.  It doesn't.  The concepts precede the math, not vice versa.  

Edited February 24, 2019 by Moronium

[Moronium]

Guys like Exchem, Oceanbreeze, and GAHD (among many others here) may never grasp that simple fact, though.

 

Despite their lack of a coherent understanding of the relationship between math and physics, they feel quite smug and are self-assured that they have a superior understanding of the physical concepts involved.

 

"Education, n.: That which discloses to the wise and disguises from the foolish their lack of understanding." (Ambrose Bierce)

 

 

Hazel, I hope you don't think I'm trying to unfairly attack your friend and mentor, Exchem.  I'm just giving my honest assessment  here--nothing personal about it.  If you're interested in the issue you raised, I'm hoping that you will read my comments.  You don't have to accept my conclusions, but you should at least understand them before you reject them.  I'm trying to help, that's all.

Edited February 25, 2019 by Moronium

[Moronium]

 I have a book written by Albert Einstein.  It is called Relativity -  the Special and the General Theory.  This book has 178 pages and only in the last five or six pages do equations begin to appear.  Since he managed to write that much before he needed equations, could he not have translated those?

 

Oh, by they way, in case anyone does not know this book, it was written in 1915, specifically for those not versed in physics or higher math.  If Einstein could do it ..... 

 

Hazel, one point I have been trying to make, in a roundabout way, is that understanding the concepts is sufficient.  As you note, Einstein could put it all into words, because he had a brilliant, methodical mind AND because he thoroughly understood what he was talking about--trying to convey.  He knew, in advance, all of the questions that might occur to readers because he had pondered them himself, often at great length.  He therefore knew how to answer those questions in the very process of explaining.

 

Many, probably most, mathematicians and run-of-the-mill working scientists, don't really have those skills to any extensive degree.  The math equations are generally not required at all to understand the concepts.  They are often included just for the formality of it.  The give a mathematical "proof" (not to be confused with an empirical proof) of the points being made, just to show that they are mathematically consistent.  They are quantitative, not qualitative.  Assuming that you're reading a competent author, you can skip right over them and take his word for the mathematical correctness--it's not essential to understand the concepts under consideration.  You're not missing out on anything nearly as much as you may think.

 

If you're dealing with an author who can't clearly communicate with words, find another one.  Guys like Feynman for example.  He said something like: "If you can't explain it to a 12 year old, then you don't understand it yourself."

Edited February 25, 2019 by Moronium