42, the meaning of life

Manitou

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Finally a part of this conversation I can follow!

I mean, obviously, I exist because I'm here typing out this very sentence, now whether or not you exist as a different person or are just a figment of my imagination is a completely different story. And it's quite possible that I'm really just a brain in a vat and even this existence is simply some simulation.

I like a part in The Yellow Submarine where the Beatles are in an office building and if there is nobody in the office halls then all sorts of dinosaurs and creatures are running around. But as soon as any human comes out they are all hiding.
And the funny thing is that there is no possible proof that that scenario is not taking place. :)
 

elbkup

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Anyone here read Carlos Castenada... specifically A Separate Reality? I realize he has a reputation as a '70's counter culture guru but there is more to his philosophy .. my nephew, an Anthropology PhD
studied him as an undergraduate, early 2010's..
 

Orlov

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"There was a faith-healer of Deal
Who said, "Although pain isn't real,
If I sit on a pin
And it punctures my skin,
I dislike what I don't think I feel."


come on, solipsism, really? :laugh:
 

Mathman

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Finally a part of this conversation I can follow!

I mean, obviously, I exist because I'm here typing out this very sentence, now whether or not you exist as a different person or are just a figment of my imagination is a completely different story. And it's quite possible that I'm really just a brain in a vat and even this existence is simply some simulation.

Descartes would have been proud.:yes:

A half century ago I asked my philosophy professor, "Is the cogito ergo sum argument valid"? The proifessor (a disciple of Wittgenstein) replied, "What a delightful way of using words!"

By the way, as a mathematician Descartes is credited with inventing co-ordinate (analytic) geometry -- the idea that you can assign numerical co-ordinates to points in the plane or in three space and then describe various geometric shapes in terms of equations of these co-ordinates.

The circumstance of this discovery was this. Descartes as a young man lived in Paris at the height of the wars between the Catholics and the Protestants in the early 17th century. Scholars were accused by both sides of being spies and provocateurs for the other (and in fact later on Descartes did fight on the side of the Dutch against the forces centered at Paris).

Anyway, a group of philosophers and mathematicians regularly held secret meetings at the home of Marin Mersenne, a prominent academician of the time, to discuss scientific matters free from political and religious persecution. Descartes was the youngest of the group and was not much interested in the philosophizing of all the old codgers, so one time he found himself dozing off and staring at the ceiling. The ceiling was checkerboard tile and a fly was buzzing around up against the ceiling. It suddenly struck Descartes that he could describe the fly's location, as well as the trajectory of its path and something about its velocity, by simply counting how many squares from the east wall the fly was, and how many squares from the south wall, at various times.

(Or so the story goes. Maybe it was Orlov's snail. ;) )

Of relevance (sort of) to this topic, Mersenne is most famous for inventing a formula for finding very large primes. And indeed, the successive world records for the largestr known preime are Mersenne primes or related numbers. (The current record holder is the Mersenne prime 2[sup]82,589,933[/sup] − 1.
 
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Mathman

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What I'm saying the answer whether A=Ø or A≠Ø is independent of the axioms. It's just a state of some defined set. We can never know it, and that's what IT is saying.

Being "independent of the axioms" is a different question from considerations of what we know, what we don't know, what we will ever be able to know, etc.

The set A, the set Ø, the meaning of "=" -- these are meaningful concepts only within the artificial construct of formal axiomatic mathematics. It is not a legitimate question to ask if the set A is really, really, really and truly empty on not. The set A does not exist in the really, really, really and truly real, real world. It is something that we made up and then, having invented it in our imaginations, we impose rules about how we permit ourselves to use words representing thse concepts in sentences. (The rules are somewhat arbitrary, somewhat guided by analogies with things that do exist in the real world, somewhat guided by predice, by "beliefs," etc.).

At least this ius the point of view that is taken inthe discipline of mathematical logic.
 

Mathman

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I think you're confusing cause and effect.

I don't thinks so. In fact I don't think I have said anything about the "cause" or origin of mathematical models at all.

Well... it seems to be simple. Manitou started randomly shooting at the coconut, and I developed the science, made the necessary equations:

x(t) = x0 + V0_x*T
y(t) = y0 + V0_y*T - g*T^2/2

solved them, tilted the gun to the desired angle, fired and knocked the coconut down. Okay. But let's take a closer look at what exactly was going on in my head :)

Precisely. The equations that you invented (by observing snails, etc.) are models that can be used to predict the behavior of snails, bullets fired from a gun, the moon going around the earth, etc.

In fact, the name of this particular model is "Newtonian (or classical) physics." It is the most successful mathematical model of the real world that the human race has ever come up with.

The marvel is that the real world is organized so coherently this model-building process is possible. As Einstein put it, "The most incomprehensible thing about the universe is that it is comprehensible." Why should all snails behave in the same way. Why should all bullets fired from all guns have any rhyme or reason to their trajectories? It is this question of why that is beyond the reach of the scientific method. (And this is where Manitou has us beat -- the reason that the universe is sufficiently orderly for the scientific method to work is because God made it that way.)

Anyway, now comes part II. We have our equations. Snails, check. Bullets, check, The moon, check. Game over -- we won.
But then one day we encounter something moving at a significant fraction of the speed of light. Another day we visit a very massive object like a black hole. Oh no! All of a sudden our equations don't work any more.

So we go back to the drawing board. We make refinements in our equations to accommodate the new data. We extend our reach to Special and General Relativity. As a last resort, if we are unable to refine our model in the light of the new information, then we must abandon our equations altogether and start afresh. This is the scientific method. It is the basis of all useful knowledge that we have obtained about the world.
 

Mathman

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PS. One more thing about mathematical models and the scientific method. Mathematicians and physicists are gluttons for punishment. They want their models to turn out to be wrong. (After all, if that never happened, then we would all be out of a job.)

A good model not only is willing to consider new data that happens to float by, but also it actively seeks for counter-examples, for something that doesn't seem to fit in. The model itself, if it is a superb model, gives suggestions as to where we ought to look to show that the model is wrong. In fact, the word "proof" actually means "test." A mathematical theorem is not considered"proved" until it has passed every possible test that anyone can throw at it.

And even then, we have our doubts -- as the example of Newtonian physics demonstrates.

This was the downfall of string theory, which seemed so promising in the 1980s. Nobody ever "disproved" string theory. It was just that the theory was so all-encompassing and amorphously defined that it could not be falsified even in principle. Every possible outcome of every possible experiment can be "explained" by string theory.

As they say nowadays, "String Theory is not even wrong." It is more like religion than science: I believe in strings.
 

Mathman

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Mathman said:
What mathematicians do is try to prove "conditional" statements of the form "If P, then Q."
No, no and again no.

My main idea was that "everything starts and ends in reality". Can you satisfy your hunger with "If P, then Q."?

We seem to be discussing different questions here. I know a lot of mathematicians. A I know a lot of mathematicians. I read the fruits of their labor. What they do is prove theorems of the form "P implies Q." That's what they do.

As for satisfying my hunger, IF I figure out that "IF I shoot my gun at certain angle angle THEN I will knock down a coconut," THEN I have made a contribution to the field of applied math. (And I will be paid more than if I make a contribution to pure mathematics, so I guess I have to concede the point. :) )
 
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Mathman

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4) That why I called math of "protocol for effective interaction of Homo Sapiens with reality".

I don't have any quarrel with this. I think that what I am calling a "model" is the same as what you describe as "protocol."

As for Homo sapiens, other animals like monkeys, some species of birds, etc., can count a little bit and measure a little bit, and as far as we can tell, their counting and measuring seems to be pretty much the same as ours. What we can do that other animals cannot (so we suppose) is to analyze our mathematical instincts and experiences. We can not only count, but (being Homo sapiens) we can observe ourselves in the process of counting. We can even (being of the subspecies Homo sappiens sapiens) think about the process of counting.

Anyway, this is a different topic -- the origins and genesis of mathematical thought.

The conundrums that plagued set theorists and people interested in the logical foundations of mathematics during the first half of the twentieth century arise for a different reason. All or our real world experience and intuition involving counting come from considerations of finite sets. We look up at the night sky. We see many stars. But we do not see infinitely many. When mathematicians attained a sufficient level of abstract mathematical thought (i.e., of separation from things in the real world) where infinite sets are introduced into our imaginings, then all of a sudden we have broken loose of our solid moorings and set adrift. All of our carefully won intuition about how numbers ought to behave -- well, suddenly they don't.

It seems obvious that there are more whole numbers altogether than there are even numbers alone, since, after all, some numbers are odd. But the most successful formulations of axiomatic set theory, starting with Cantor, say no, that's wrong. By some bizarre sort of mental gymnastics, not connected in any meaningful way to the real world, in fact I can prove that there are the same number of even numbers as there are numbers in total. This seems more like witchcraft than mathematics, and indeed Cantor was hounded by the German mathematical establishment of his time on exactly that point -- that he was practicing witchcraft rather than doing mathematics.

2) The foundation of our mathematics arises from the metric of our universe - the linearity of time, the linearity of Euclidean space.

Is time linear? We thought so for the first million years or so of our existence. Given two events A and B, either A happens first and B afterward, or B happens first and A afterward, or else the two events happen at the same time, like points on a line.

But in 1905 Einstein advanced the idea that this belief in the linearity of time is not compatible with what we observe when we experiment with real objects and real events in the real world. In particular it is not compatible with the results of the Michelson-Morley experiment regarding the speed of light in 1887. (Einstein's genius lay in the fact that he stuck to his guns -- he had to go with what the real world data told him even if it meant tossing aside everything we ever thought we knew about time). The real world just does not have the property that of two events either A precedes B, or B precedes A. or A and B are simultaneous.

Is space Euclidean? The jury is still out. :)

Are space and time in fact fundamental properties of the universe at all?, Or are they merely "emergent" properties -- i.e., illusions caused by even more fundamental concepts that we have not discovered yet?
 
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Mathman

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"Laws of logic" is causality.

I think you would find a huge collection of scholarly discourse in journals of philosophy debating that assertion.

Again, I think the language of "model building" is appropriate. Historically, scholars came up with rules for logical inference in part by considering the (somewhat imprecise) relation of cause and effect that was observed in the real world (as they thought, perhaps being deceived). Abstracted from their natural environment and worked and re-worked over the centuries, eventually these rules became a recipe for stringing abstract symbols together that the great body of practitioners of the art agreed to accept.

Sort of like a virus. It is not exactly a living creature, but rather a chemical recipe for making more entities like itself. :)
 

Mathman

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Is it possible today?

That's what I like about mathematics. There is no such thing as "politically correct" or "politically incorrect" mathematics. Plus, as a group, mathematicians are not overly interested in partisan politics.

You never read about a mathematician who got fired from his job or run out of town on a rail for saying 2+2=4.

Fields like history and economics -- well, these disciplines do seem to attract practitioners who have strong political leanings one way or another; plus their writings are seized upon by politicians, the news media, and citizens in general as being either the gospel or else the lies of the devil, depending on what side the auditor is on.

The physical sciences are somewhere in between. It has, for instance, become impossible for climatologists to present the results of their research in a political vacuum. Even if you say something as politically neutral as, "I measured the amount of carbon dioxide in the atmosphere off the coast of Antartica, and it was 400 parts per million" -- someone will jump up and say, "What are you, some kind of Nazi? If you were a true patriot, you would have found only 200 parts per million."
 
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Manitou

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Fields like history and economics -- well, these disciplines do seem to attract practitioners who have strong political leanings one way or another; plus their writings are seized upon by politicians, the news media, and citizens in general as being either the gospel or else the lies of the devil, depending on what side the auditor is on.

How about gender research?
Isn't it like Soviet history test question from the 50s: who is the greatest man in the mankind history and why is it Stalin?
Isn't the entire science going in this exact direction? Where answers come first and then comes research? And if the research tells against the answer then too bad for the research and the researcher?
 

Mathman

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How about gender research?
Isn't it like Soviet history test question from the 50s: who is the greatest man in the mankind history and why is it Stalin?
Isn't the entire science going in this exact direction? Where answers come first and then comes research? And if the research tells against the answer then too bad for the research and the researcher?

I wouldn't pick on "gender research" especially. Is this really a science? However, it cuts both ways. A "scientist" might begin win the premiss, "women are inferior creatures fit only to be the servants of men," and go from there. Aristotle, for instance, loudly asserted that women (being inferior) have fewer teeth than men. All he would have had to do was count them. But he didn't, because he "already knew the answer" -- why bother to count?

But I think that you are right in general about "the answer coming first." In part I think this is because someone has to pay for the research. No one is going to fund a research project in the social sciences unless he has some stake in the outcome. If Bernie Sanders gives someone a million dollars to conduct a poll, that poll is pretty likely to prove that Bernie is winning. (That is why no one gives any credence to such "research," except the politicians themselves who put up the money and the news media pundits who get paid for commenting on it.
 
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Manitou

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I wouldn't pick on "gender research" especially.

I am. Because it's the biggest ridicule of science (or whatever it is) I have witnessed in my life. And it's extremely dangerous. Forget this Corona-nonsense. Focus on what is really dangerous.
Can you imagine? San Francisco raised emergency level in the city despite the fact they have ZERO Corona cases, while the whole city is infested by feces from the homeless. That's the thinking that is taking place today.
 

Mathman

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I see by this morning's news that California's first corona virus case (not the result of travel abroad) was diagnosed yesterday. Better safe than sorry. The threat may blow over -- or it may leave us wishing that we had acted more vigorously sooner.

As for the homeless, I am all for programs that lend a helping hand to people in need, and for supporting the efforts of cities to deal with the problems caused by chronic indigence and mental illness. There but for the grace of God go I.
 

Mathman

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I am (against gender research).

I take a different view of research in general. I would never tell a scientist or scholar, no, don't study that. I like mathematics; but I would not ridicule someone else for having different interests.

For one thing, you never know when you begin what you might learn. I had a colleague who wrote his PhD dissertation on the Ninth Eye of the Horseshoe Crab. The circumstance was, this guy was a medical doctor and a psychiatrist. After he was in practice for a few years he made the observation that none of his patients ever got any better as a result of being in his care. He decided that the reason is because not very much is known about the human brain and nervous system, so he went back to school and studied how the nervous systems of primitive animals worked.

Did anything come of it? I don't know, but the work was utterly fascinating on its own.

Let people study, let them gather information, let them form hypotheses, let them publish. If their argumentation is unconvincing or their conclusions badly supported, OK, dive in and shoot off your own paper to the appropriate journal.
 
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Manitou

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As for the homeless, I am all for programs that lend a helping hand to people in need, and for supporting the efforts of cities to deal with the problems caused by chronic indigence and mental illness. There but for the grace of God go I.

So let me ask you this question: how do you specifically support helping those people? Or you are just talking about it on Internet for PR, as it costs literally nothing. Or do you invite them to sleep and poop at your neighbours' front doors, as, obviously, you would not let them do it at your own door...? And do you think it really helps them?
 

Manitou

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You see, you don't seem to understand some basics. I am paying taxes for specific reasons. One of them is taking care of my own city. And I expect the city to use my taxes for this purpose. My life is not devoted to helping the world. My life is devoted to help myself and to the people I care about. This is why I want my street and my city to look safe and clean. I am taking care of myself and others also take care of themselves. If somebody is NOT taking care of himself then it should be entirely up to me how far I am going to reach to them. And in 95% the reason those people have mental issues are because of their own decisions they made in the past.

I don't want the city to make a decision on my behalf to allow people with mental issues to live on my property. It's my property. I have been working very hard for this property.
And I am treating the city I am giving my taxes to my property also. I feel responsible for it. For all the people who work as hard as I am to keep it nice, clean and safe.

And if you want me to take care of people who need help then please ask me first. I don't mind helping to some extent, but it's should be up to me. And I am already helping. One person, not the entire world. Sometimes helping one person is helping more the entire world than helping the entire world.
 

Mathman

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You see, you don't seem to understand some basics. I am paying taxes for specific reasons. One of them is taking care of my own city. And I expect the city to use my taxes for this purpose. My life is not devoted to helping the world....

I do inderstand that you feel this way. Others take a more expansive view and do not consider themselves to be naive fools for doing so.

As for me, if I knew how to solve all the problems of the world, I would jump right in. But since I don't, I would rather retreat to a subject that is more within my compass of competence. I think I have figured out what it is that I have been struggling to say about the mathematics of infinite sets and it's relation to the logical foundations of mathematics. Let's go back to this:

OK, let's do this:
Let F(X,Y) = {f:X->Y} - all transformations X to Y, where X and Y are sets. It's equal to Y[sup]X[/sup]
Let B(X,Y) = { f∈F(X,Y): f is a bijection }...

Let A = { a⊂C: B(a,N)⋃B(a,C) = Ø }....

I think that what twentieth century mathematics teaches us -- indeed, rubs our faces in -- is that none of these mathematical entities, such as the set A, has any existence except in our own fertile imaginations. We are not going to stumble upon the set A while strolling about in God's creation. Just as God, being God, can create a universe having any properties he wishes, so can we, the creators of the universe of infinite sets, endow our creation with those features that best please us.

We can declare by fiat: "our set A is empty." Or we can declare "Let there be an element in the set A." Just as God can declare (if he wants to) "Let there be light!"

The content of the theorems of Goedel and Cohen on the independence of the continuum hypothesis say that whichever choice we make, that choice will do no harm to the rest of the mathematics.
 
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