Math used to predict life events

[ki4jgt]

I'm looking for a mathmatical theory I read up on a while back. Which states that we basically can't predict everything in math.

Basically, me and some other guy got in an argument where he believes we can use math to predict everything which has happened, is happening and will ever happen. About a year ago, I remember reading about a mathmatical problem which disproved this altogether, but I can't remember what it's called.

The guy is trying to tell me that all my actions have been chosen before me and that I don't have a choice in my own actions. If I refuse to do bad things to people, I did not choose it, instead, all the variables in my life has chose it for me. Even though I believe they influence me, I believe you have to choose to let them. Anyway, does anyone know what my math problem is?

[dwhite]

chaos theory?

ps ab1mg here

[TeoBigusGeekus]

Quantum mechanics and the uncertainty principle prove that "God does play dice" (to paraphrase Einstein).

[krapp]

The guy is trying to tell me that all my actions have been chosen before me and that I don't have a choice in my own actions. If I refuse to do bad things to people, I did not choose it, instead, all the variables in my life has chose it for me. Even though I believe they influence me, I believe you have to choose to let them.

Where I'm from this is called the Unconscious.

[ki4jgt]

ps ab1mg here

What LOL?

[ki4jgt]

Where I'm from this is called the Unconscious.

Unconscious or subconscious b/c subconscious I get, but you can still retrain your subconscious.

After your change, I get it LOL

[dwhite]

sorry just assumed ki4jgt was an amateur radio call sign, and i was just saying my call is ab1mg

and chaos theory shows that even in simple systems that are completely defined mathematically (classical systems like the orbits of planets, etc) if the initial conditions are not known to absolute precision (not possible) there are conditions under which the future evolution of the system diverges, that is you can't predict its future state

[ki4jgt]

LOL it is. I don't get on the air much.

[Smilax]

this statement is false


think about this one





what your after is

Gödel's incompleteness theorems


which is all about,

it's about some problems are really hard, but we know they can be done,

some are impossible, but we know they are impossible,

but some are imposssible but we can't prove there impossible, so they might just be really really hard.

[gunfyter]

Quantum mechanics and the uncertainty principle prove that "God does play dice" (to paraphrase Einstein).

However, Dice or Chance does not mean you possess free will.

You don't "choose" the result of a roll of the dice.

"Any man who thinks he is free, is merely ignorant of the causes of his own behavior." BF Skinner Beyond Freedom and Dignity

Albert Einstein denied Freedom of the Will (See Einstein's Credo http://www.einstein-website.de/z_biography/credo.html) and Stephen Hawking denies Free Will ... in his most recent book, The Grand Design.


I do not believe in free will. Schopenhauer's words: 'Man can do what he wants, but he cannot will what he wills,' accompany me in all situations throughout my life and reconcile me with the actions of others, even if they are rather painful to me. This awareness of the lack of free will keeps me from taking myself and my fellow men too seriously as acting and deciding individuals, and from losing my temper.

--Albert Einstein--

In a Nutshell:
Essentially, all human behavior is governed by the chemical reactions of the Brain. All Chemistry, is governed by the Laws of Physics. All Physics is described by Mathematics.

All Matter is composed of quantum particles. None of the quantum particles are "Free" and neither are the sub-atomic particles, atoms, and molecules everything and everyone are made of. Since the components are not Free, neither are we.

But everything is NOT determined. Thats where the QED and Uncertainty principle come in. This uncertainty does not however grant us Freedom.

The name of the Theory you are looking for may be Reductionism www.reductionism.org

[TeoBigusGeekus]

However, Dice or Chance does not mean you possess free will.

You don't "choose" the result of a roll of the dice.

"Any man who thinks he is free, is merely ignorant of the causes of his own behavior." BF Skinner Beyond Freedom and Dignity

Albert Einstein denied Freedom of the Will (See Einstein's Credo http://www.einstein-website.de/z_biography/credo.html) and Stephen Hawking denies Free Will ... in his most recent book, The Grand Design.


In a Nutshell:
Essentially, all human behavior is governed by the chemical reactions of the Brain. All Chemistry, is governed by the Laws of Physics. All Physics is described by Mathematics.

All Matter is composed of quantum particles. None of the quantum particles are "Free" and neither are the sub-atomic particles, atoms, and molecules everything and everyone are made of. Since the components are not Free, neither are we.

But everything is NOT determined. Thats where the QED and Uncertainty principle come in. This uncertainty does not however grant us Freedom.

Agreed; we're not free - but we're not predestined on the other side, as the op's friend suggests.

[Smilax]

here's a nice proof from

http://www.miskatonic.org/godel.html



The proof of Gödel's Incompleteness Theorem is so simple, and so sneaky, that it is almost embarassing to relate. His basic procedure is as follows:




Someone introduces Gödel to a UTM, a machine that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all.
Gödel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Call the program P(UTM) for Program of the Universal Truth Machine.
Smiling a little, Gödel writes out the following sentence: "The machine constructed on the basis of the program P(UTM) will never say that this sentence is true." Call this sentence G for Gödel. Note that G is equivalent to: "UTM will never say G is true."
Now Gödel laughs his high laugh and asks UTM whether G is true or not.
If UTM says G is true, then "UTM will never say G is true" is false. If "UTM will never say G is true" is false, then G is false (since G = "UTM will never say G is true"). So if UTM says G is true, then G is in fact false, and UTM has made a false statement. So UTM will never say that G is true, since UTM makes only true statements.
We have established that UTM will never say G is true. So "UTM will never say G is true" is in fact a true statement. So G is true (since G = "UTM will never say G is true").
"I know a truth that UTM can never utter," Gödel says. "I know that G is true. UTM is not truly universal."

[Thewhistlingwind]

An individual cannot be accounted for in the art of phychohistory. :popcorn:

[krapp]

What is the art of psychohistory (if that's why you're trying to say)?

[Thewhistlingwind]

What is the art of psychohistory (if that's why you're trying to say)?

It was a joke, friend.

(http://en.wikipedia.org/wiki/Foundation_series)

[wilee-nilee]

however, dice or chance does not mean you possess free will.

You don't "choose" the result of a roll of the dice.

"any man who thinks he is free, is merely ignorant of the causes of his own behavior." bf skinner beyond freedom and dignity

albert einstein denied freedom of the will (see einstein's credo http://www.einstein-website.de/z_biography/credo.html) and stephen hawking denies free will ... In his most recent book, the grand design.


In a nutshell:
Essentially, all human behavior is governed by the chemical reactions of the brain. All chemistry, is governed by the laws of physics. All physics is described by mathematics.

All matter is composed of quantum particles. None of the quantum particles are "free" and neither are the sub-atomic particles, atoms, and molecules everything and everyone are made of. Since the components are not free, neither are we.

But everything is not determined. Thats where the qed and uncertainty principle come in. This uncertainty does not however grant us freedom.

The name of the theory you are looking for may be reductionism www.reductionism.org

+1

I would paraphrase it a little differently from another field; Depth Psychology, but a good rhetoric none the less.;)

[krapp]

It was a joke, friend.

(http://en.wikipedia.org/wiki/Foundation_series)

Sorry, there are many holes in my SF reading, unfortunately!

[Thewhistlingwind]

A more concrete assertion would be that, as demonstrated by conway's game of life, the initial state of the game is potentially the most important (Or the only) defining factor. (Though it can't be the only one when you introduce randomness.)

EDIT: However, If I'm wrong please do correct me.

[krapp]

Isn't that game also known as Go?


Unconscious or subconscious b/c subconscious I get, but you can still retrain your subconscious.

I was referring to the Freudian Unconscious, which I'm not sure can be retrained, so much as patched over.

[ki4jgt]

Thanks guys. I have a lot of reading to do. I had started working it out in my head and knew it wasn't true, but had started seeing evidence of it.

[ki4jgt]

Isn't that game also known as Go?

I love that game. I actually was going to get some books on it a while back. and gain some levels (Forgot what they're called :-( been about three years)

[Thewhistlingwind]

Isn't that game also known as Go?

That's a different game entirely. However:

"Computers have been used to follow Life configurations from the earliest days. When John Conway was first investigating how various starting configurations developed, he tracked them by hand using a Go board with its black and white stones." - Wikipedia

[juancarlospaco]

Math is a human invention, ...an arbitrary one,
those imaginary numbers seems so fake, 2i, 3i, 4i

On Quantum Computers a bit can represent 1 and 0 at the same time,
so can be possible to divide by zero (?)
I hate math.

[gunfyter]

Agreed; we're not free - but we're not predestined on the other side, as the op's friend suggests.

Wow. I am going to have to spend more time here. In real life, I rarely bump into people who agree with me on this topic.:o
http://dl.dropbox.com/u/9633184/Photo%20Apr%2020%2C%2019%2044%2038.jpg

[ki4jgt]

Wow. I am going to have to spend more time here. In real life, I rarely bump into people who agree with me on this topic.:o
http://dl.dropbox.com/u/9633184/Photo%20Apr%2020%2C%2019%2044%2038.jpg

I also agree, we are not free, but do not believe we are destined to be anything in life, but what we choose.

[PC_load_letter]

this statement is false


think about this one





what your after is

Gödel's incompleteness theorems


which is all about,

it's about some problems are really hard, but we know they can be done,

some are impossible, but we know they are impossible,

but some are imposssible but we can't prove there impossible, so they might just be really really hard.

I'm no expert in Logic and what I recall from my undergrad courses is that Godel's incompleteness theorem (one of them at least) basically states that in a a 'theory' that has enough axioms (just enough to establish the existence of Natural numbers), then such theory will have statements that are 'true', but unprovable at the same time.

Math has been my profession for a while, and I haven't seen an application to this theorem in real life, don't get me wrong it's an awesome piece of intellectual work, but I don't think it applies in a useful way to say Physics. Maybe it will turn out that one of the long standing conjectures in Math. is such true but unprovable statement, but I haven't heard anything so far.

In my opinion, what the OP refers to is more akin to the decidability/undecidability of Mathematics and the laws of Physics. A mathematical model describing a Physical phenomenon is just a system of differential equations (ODEs or PDEs). In general, you want to prove the existence of a 'nice' solution that can help you understand the phenomenon, say by studying the geometric and topological properties of the solution as say people do in 'Dynamical systems'.
In most of the cases, getting an explicit formula for this solution is impossible, and what's even worse is that if the system has chaotic aspects, trying to squeeze a numerical approximation of the solution maybe futile.

Example: The three dimensional (and probably over simplified) Lorentz system that models the dynamics of fluid (air) between two hot plates, see for instance, here: http://en.wikipedia.org/wiki/Lorentz_system

This system is chaotic, albeit being only 3 dimensional, and the equations are not too complicated. By 'chaotic', as others have indicated, one means the sensitive dependence on the initial data. So, if you want to make correct, accurate, LONG time predictions of a chaotic system like the Lorentz system, you have to have your initial data accurate to an astronomical accuracy that makes it impossible.
That's why the best weather model can NOT be used to predict the weather for more than a 10 days ~ a couple of weeks, any longer and you will have to measure the system parameters to an impossible degree of accuracy.

All of this and we haven't mentioned Quantum uncertainty, so for people studying elementary particles there is a second layer of chaos and unpredictability due to QM.

[PC_load_letter]

Math is a human invention, ...an arbitrary one,
those imaginary numbers seems so fake, 2i, 3i, 4i

On Quantum Computers a bit can represent 1 and 0 at the same time,
so can be possible to divide by zero (?)
I hate math.

NO! I thought we were over this already (if you haven't seen it, there was a HUGE thread about division by zero a while back).

Division by zero is impossible because zero has no reciprocal. Bear with me, the reciprocal of 5, which is 1/5, is the one and only one solution to the equation:
5*x = 1
Division by 5, is just the multiplication by the reciprocal of 5
z / 5 = z* (1/5)

Now, the reciprocal of zero will have to be the solution to the equation:
0*x = 1 but there does not exist a real (or complex) number that satisfy this equation because
0*x = 0 Hence, we can't divide by 0. :guitar::guitar::guitar:

[dwhite]

all of this and we haven't mentioned quantum uncertainty, so for people studying elementary particles there is a second layer of chaos and unpredictability due to qm.


+1

[3Miro]

Math is a human invention, ...an arbitrary one,
those imaginary numbers seems so fake, 2i, 3i, 4i

On Quantum Computers a bit can represent 1 and 0 at the same time,
so can be possible to divide by zero (?)
I hate math.

Math is man-made, but it is not arbitrary. We start with basic definitions (which are somewhat arbitrary), but what builds on top is pure logic and it goes one way. In order to allow for division by zero, you need to change all the rules of algebra (which we have done and abstract algebras are used all the time in advanced math). There is nothing "magical" about division by zero and it certainly doesn't depend on any "hardware" that you may be using (silicon or quantum machine).

On the same note, imaginary numbers are not more or less "fake" than the rest of it. If you "hate" math, then you probably lack the background to understand Real Analysis, but in Real Analysis mathematicians start with just the natural numbers 1,2,3 and so on, define basic addition and more or less build the rest of algebra out of this (negative numbers, zero, multiplication, division, rational numbers, irrational numbers, complex numbers). Real Analysis is hard (it is called Real Anal for a reason), but there is no magic in it, just logic.

[gunfyter]

This is my Reductionist opinion:

"Real Magic" is Free Will.

It violates the laws and mathematics of Physics.

The "mind" is simply a phenomena of the brain. The brain a material thing is a Slave to the physical laws. No material thing is free. Every material thing is subject to the forces of Physics ONLY. As Aristotle put it...
"Every THING acts according to its own nature."

For a thing to act in any manner contrary to Physics (and Physics alone) would constitute -- a Miracle -- Magic.

"Mind over Matter"? NO. Reality is "Matter over Mind".

There is no free will, or any power whatsoever to make any "choices". Nothing happens except according to the physical laws. That includes our thoughts.

Mathematics, even if you believe an invention of man, simply would describe this reality.

I would say mathematics could be used to predict life events, but such predictions would be probabilistic... because the mathematics that describe Quantum Physics are probabilistic.

[krapp]

Using Aristotle to authorize your materialist conception of the mind--what an anachronism!

[tjwoosta]

"Mind over Matter"? NO. Reality is "Matter over Mind".

There is no free will, or any power whatsoever to make any "choices". Nothing happens except according to the physical laws. That includes our thoughts.




I wouldnt be so sure. We think we have a pretty strong grasp of the laws of physics and the nature of reality, but once we start to break things down to the quantum level some very strange things start to happen. Take for example the double slit experiment...

http://www.youtube.com/watch?v=DfPeprQ7oGc

[gunfyter]

I mean to use only his words, not the man himself ... yet identify the author of those words....

The point I think those words make is that the Nature of a thing determines how it acts....

[ki4jgt]

Math is a human invention, ...an arbitrary one,
those imaginary numbers seems so fake, 2i, 3i, 4i

On Quantum Computers a bit can represent 1 and 0 at the same time,
so can be possible to divide by zero (?)
I hate math.

Math isn't totally human. If we had aliens visit the Earth, the only language we would be able to communicate with them in is math, b/c it's universal. It's the same everywhere. 2 + 2 always equals 4 (Except in advanced math)

[gunfyter]

I wouldnt be so sure. We think we have a pretty strong grasp of the laws of physics and the nature of reality, but once we start to break things down to the quantum level some very strange things start to happen. Take for example the double slit experiment...

http://www.youtube.com/watch?v=DfPeprQ7oGc
Enjoyed the video. I received a BS in Optics at the UofR in 1981... and had the opportunity to work at the UR Laboratory for Laser Energetics www.lle.rochester.edu/ as a student . In the 70's the Lab was inducing fusion with a 24 beam laser on a Deuterium target. Same thing as in the Latest WALL STREET movie "Money never sleeps".


It may seem strange. It did to me when I first studied it 35 years ago... yet ... All occurs in compliance with the equations of Quantum Electrodynamics. Mathematically predictable. So would further argue in favor of predicting future events.

Hawking does a good job explaining the double slit in in The Grand Design and why it does not argue for free-agency.

[wolfen69]

I don't know about you, but I don't want to know what's going to happen. That's part of the mystery of life I can accept. It makes every moment fresh.

[gunfyter]

I don't know about you, but I don't want to know what's going to happen. That's part of the mystery of life I can accept. It makes every moment fresh.

I don't think we have to worry about it. Hawking also explains in The Grand Design why we couldn't practically do so. The amount of variables and data ... the uncertainty that exists because of the statistical and probabilistic nature of the calculations. The Multi-verse and M-theory. All possibilities exist but in multiple universes. We just can't crunch the numbers.

He says we don't really have free will but ... we because of all these factors, it is as though we have it -- Practically. A very good similation of free will.:D

I think what it means to address the OP question ... No your future is not set in stone. Its not because you actually have free will ... its because the "causes of your own behavior" (Skinner) are rooted in quantum effects and are therefore probabilistic like the video of the Double Slit experiment.

As I quoted Einstein earlier,
" You can do what you want, but you cannot Will what you want". Meaning, what you want, is caused by forces beyond your control... and we are ignorant of these causes (Skinner).

[tjwoosta]

Is it not possible that all possibilities exist at once, and the observer or collective of observers unwittingly determine the outcome by way of preconception based on past experiences?

[wolfen69]

I don't think we have to worry about it. Hawking also explains in The Grand Design why we couldn't practically do so. The amount of variables and data ... the uncertainty that exists because of the statistical and probabilistic nature of the calculations. The Multi-verse and M-theory. All possibilities exist but in multiple universes. We just can't crunch the numbers.

He says we don't really have free will but ... we because of all these factors, it is as though we have it -- Practically. A very good similation of free will.:D

I think what it means to address the OP question ... No your future is not set in stone. Its not because you actually have free will ... its because the "causes of your own behavior" (Skinner) are rooted in quantum effects and are therefore probabilistic like the video of the Double Slit experiment.

As I quoted Einstein earlier, Meaning, what you want, is caused by forces beyond your control... and we are ignorant of these causes (Skinner).

There's no need for that kind of talk. :confused: j/k

[ki4jgt]

Is it not possible that all possibilities exist at once, and the observer or collective of observers unwittingly determine the outcome by way of preconception based on past experiences?

This is what I like to believe. But it is up to the observer to make those decisions. I also agree with (Some) of Einstein's ideas including the one stated above you. I guess the reason this gets my goat so badly, is that, I've been through many hardships in life. Everyone one of them (The things I consider as a hardship is different than most people) inflicted on me by other people :-( Not once did I strike back (Until recently) yet they still continued to treat me like crap. So when someone says they don't have a choice in the matter of how they act, because it's their destiny to be a pain in the :-) I tend to be on the side that says, you're lying to yourself and just making an excuse so you can ignore how others feel. Yet when I was told numerous times to forget about it, I did not. Until recently, when a psychologist told me I was lying to myself and I had never felt anything. I began to forget, and because I forgot, I had a mental break down. When I got another psychologist, I was told that I was supposed to remember that stuff it's what was driving me in my life (Which I already knew but after being told you're wrong so long, you start to wonder, espescially when it's from a professional) I guess that's what ticks me off so much. The only people who can change the world, are the ones who believe they can and take other people into consideration along the way, and you can't do that, if you think your life is layed out for you before you're even born.

[wolfen69]

This is what I like to believe. But it is up to the observer to make those decisions. I also agree with (Some) of Einstein's ideas including the one stated above you. I guess the reason this gets my goat so badly, is that, I've been through many hardships in life. Everyone one of them (The things I consider as a hardship is different than most people) inflicted on me by other people :-( Not once did I strike back (Until recently) yet they still continued to treat me like crap. So when someone says they don't have a choice in the matter of how they act, because it's their destiny to be a pain in the :-) I tend to be on the side that says, you're lying to yourself and just making an excuse so you can ignore how others feel. Yet when I was told numerous times to forget about it, I did not. Until recently, when a psychologist told me I was lying to myself and I had never felt anything. I began to forget, and because I forgot, I had a mental break down. When I got another psychologist, I was told that I was supposed to remember that stuff it's what was driving me in my life (Which I already knew but after being told you're wrong so long, you start to wonder, espescially when it's from a professional) I guess that's what ticks me off so much. The only people who can change the world, are the ones who believe they can and take other people into consideration along the way, and you can't do that, if you think your life is layed out for you before you're even born.

But alas, some religious aspects and governmental biases can come into play. It's difficult to talk about some things without getting personal. But being how large ubuntuforums is, my acceptance of different (younger) members is going to be just fine.

[TeoBigusGeekus]

I don't know about you, but I don't want to know what's going to happen. That's part of the mystery of life I can accept. It makes every moment fresh.

I agree; but it would be nice to know some lottery numbers beforehand...

[ki4jgt]

But alas, some religious aspects and governmental biases can come into play. It's difficult to talk about some things without getting personal. But being how large ubuntuforums is, my acceptance of different (younger) members is going to be just fine.

I'm 22 so, I'm not that young. I agree. They can come into play, but when another person sees an idea that someone else is doing, they have the ability to copy and paste. That's why I love life (Used to love it even more) it's like one big book of Open Sourced knowledge. You have the ability to decide what you want to copy and paste.)

[HappinessNow]

I'm looking for a mathmatical theory I read up on a while back. Which states that we basically can't predict everything in math.

Basically, me and some other guy got in an argument where he believes we can use math to predict everything which has happened, is happening and will ever happen. About a year ago, I remember reading about a mathmatical problem which disproved this altogether, but I can't remember what it's called.

The guy is trying to tell me that all my actions have been chosen before me and that I don't have a choice in my own actions. If I refuse to do bad things to people, I did not choose it, instead, all the variables in my life has chose it for me. Even though I believe they influence me, I believe you have to choose to let them. Anyway, does anyone know what my math problem is?

I just watched this episode on The IT Crowd

[ki4jgt]

I just watched this episode on The IT Crowd

Can you give me a reference? Episode number?

[matthew.ball]

this statement is false


think about this one





what your after is

Gödel's incompleteness theorems


which is all about,

it's about some problems are really hard, but we know they can be done,

some are impossible, but we know they are impossible,

but some are imposssible but we can't prove there impossible, so they might just be really really hard.
Just be cautious, Godel's Incompleteness Theorem is a statement about any formal system which has the same expressive power as first-order arithmetic (actually, the system Godel used to show incompleteness is slightly weaker than arithmetic, but that's irrelevant). First-order logic for instance is complete and consistent. It's not until we start adding other axioms which break the system (in particular it's the axiom of induction).

Some Christian fundamentalists have attempted to use the incompleteness theorem to show that the world is inconsistent, but it doesn't work like that.

[HappinessNow]

Can you give me a reference? Episode number?

2007 Season 2, Episode 2 Return of the Golden Child

https://lh5.googleusercontent.com/_wj75JfyDVxs/Tczs1vdexWI/AAAAAAAAB5c/l8Fj8tPwqCE/screenshot-20110513-012940crop.png

[ki4jgt]

How's this (My reply):


The fact that you do not know the end variable in the equation of life, proves that you have a choice. Everyone knows, they don't have all the variables, and don't know the end variable. Thus, they know to get to the end variable, they must fill in the blanks. If they know, that they don't know, then they know that they should know. This is the one variable which is constant in humanity, thus, they don't want to know.

[wilee-nilee]

I'm 22 so, I'm not that young. I agree. They can come into play, but when another person sees an idea that someone else is doing, they have the ability to copy and paste. That's why I love life (Used to love it even more) it's like one big book of Open Sourced knowledge. You have the ability to decide what you want to copy and paste.)

Lol at 22 your brain is still developing, you have along ways to go, just saying.;)

[ki4jgt]

2007 Season 2, Episode 2 Return of the Golden Child

https://lh5.googleusercontent.com/_wj75JfyDVxs/Tczs1vdexWI/AAAAAAAAB5c/l8Fj8tPwqCE/screenshot-20110513-012940crop.png

Thank you very much, but I think I just got my answer. It somehow just came to me (I stopped trying to prove the guy wrong and started thinking. I think my response is good).

[lisati]

Lol at 22 your brain is still developing, you have along ways to go, just saying.;)

+1. I'm 50 and still have some way to go.

Having read through this thread, my head hurts.


What's mind? No matter. What's matter? Never Mind!

[Ichtyandr]

Maybe OP means the Libet experiment, with neuroscience and free will?

[ki4jgt]

Maybe OP means the Libet experiment, with neuroscience and free will?

I don't know what it is now, but I think I answered it quite well. What I was refering to stated pretty much what I just said to you guys. Since we don't know the end variable, we can't mold the problem's current variables accurately enough to meet what we don't know, so we have to choose what to place into the problem. It can be based on what we have already seen from the problem, but because we know the fact that we don't know the solution to the problem, we also have to know that we can study the solution and thus, we all have the choice on whether or not to try and find the solution. No one else but us, knows if we know the solution or not. So no other outside force can decide whether to pursue it or not. The atoms and proton which make us can be damaged thus making it harder for us to choose but they do not make it an impossibility since we do know that we don't know.

[juancarlospaco]

math is man-made,

but it is not arbitrary.

Which are somewhat arbitrary

:)