42, the meaning of life

dante

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Thousands of years ago children figured out how to troll adults. Whatever the adult says, the child just responds, "Why?" The child will always win.

I too assume that there is no end to such question. But sometimes and end (I'm not saying "an answer") comes in the most unexpected way. At one time people wondered, whether the earth is infinite, or there is an edge somewhere. No one could think of a third option. And you still can't be sure to have considered every possible option.

Likewise, it requires only finitely many elementary computations to verify that they have the property that we claim.

And what if you fail to find such numbers? Until you find a solution, Fermat's equation, in Turing's terms, is an undecidable problem, because you are not guaranteed to get an answer (assuming for a second that the answer can't be found analytically).

we should create a Chuck Norris of figure skating.

Speaking of figure skating (I know, it's a weird topic for a philosophical forum, but still). I see figure skating jumps as elementary particles. Toe loop, Salchow, loop, flip and Lutz are bosons, because they have an integer spin (±1, ±2, ±3, etc), while Axel and the waltz jump are fermions, because they have a half-integer spin (±½, ±1½, ±2½, etc).
 

Mathman

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That's what I am saying. For each subset A in 2[sup]c[/sup], we (or the gods) examine all functions f:A->C ...


But it is not clear to me that either we or the gods can do any such thing or that there is any meaning (external to our own whimsical thoughts) attached to such a request.

God knows every thing. But is a set a thing? Do sets exist, never mind the set of all functions from a postulated but ill-defined domain into some other space?

It seems possible to me that God knows that the questions we are asking are not well-formed and, indeed, are meaningless.

Suppose I say to God, I am very proud (forgive me) of my collection of vintage cars. Thank you for the blessing of giving me this collection. Come over to my house and see my collection!

So God drops by and I take him around to my garage. But the garage is empty! (God knew that, of course, knowing everything.) Still,

"It's not nice to fool God."

"Oh no," I say, "I did not promise that you would see any cars. I said I will show you my collection". And here it is, the empty collection."

Does the empty set exist, in the sense of, in the beginning God created the Heaven and the Earth? Or is it something that was invented out of pure smoke and mirrors by self-deluded humans?

I for one would not blame God if he said, this is an ignorant and ill-formulated question. It makes no sense to say that the empty set exists. It makes no sense to say that the empty set does not exist. You are simply playing a mind-game that you dreamed up, following the rules that you whimsically ad-libbed for playing. It serves you right that the game turned around and played a trick back on you.

(Or he might say, "Who is this that darkeneth council by words without knowledge? ... Where wast thou when I laid the foundations of the earth?") :)
 

Manitou

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But it is not clear to me that either we or the gods can do any such thing or that there is any meaning (external to our own whimsical thoughts) attached to such a request.

God will definitely do whatever he/she chooses to do. And if my request is not on his/her priority list there is no way he/she is going to bother. There are too many starving people around the world to care about, so my request to go over each of C[sup]C[/sup] functions is a lot to ask at this moment. I am not even sure how (s)he can count it anyway. If (s)he does those funtions one by one then, no matter how fast it is done, would prove C[sup]C[/sup] is countable, which is not really true. Maybe even God cannot verify each of C[sup]C[/sup]. Unless (s)he does it quantum way, which is by a continuous wave. Then I guess it can be done...
 

Mathman

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I too assume that there is no end to such question. But sometimes an end (I'm not saying "an answer") comes in the most unexpected way. At one time people wondered, whether the earth is infinite, or there is an edge somewhere. No one could think of a third option. And you still can't be sure to have considered every possible option.

It is also interesting to note that, after a million years or so the human race has become comfortable with the idea that the planet earth can be -- what a mind-blowing concept -- finite but unbounded.

Einstein invited us to imagine that the entire universe could conceivably have the same geometric property. A century later we still have trouble wrapping our minds around such models.

And what if you fail to find such numbers? Until you find a solution, Fermat's equation, in Turing's terms, is an undecidable problem, because you are not guaranteed to get an answer.

Hmm. I think I would rather say that in this case (we don't find an answer) then we don't know whether the problem is decidable or undecidable. If eventually we find the numbers, than at that point we know that the problem was decidable. Otherwise we don't know.

I think that the logic in these conundrums is somewhat obscured by the fact that we imagine these processes (searching for numbers) to be carried out in time. Today we search up to 100, tomorrow we search up tp two hundred. It seems impossible for us to step out of time while we contemplate these mysteries, but there is a difference between an actual nuts and bolts machine clanking along and the abstract logical considerations involved.

Maybe quantum computers taking advantage of entanglement will give new insight.

Speaking of figure skating (I know, it's a weird topic for a philosophical forum, but still). I see figure skating jumps as elementary particles. Toe loop, Salchow, loop, flip and Lutz are baryons, because they have an integer spin (±1, ±2, ±3, etc), while Axel and the waltz jump are fermions, because they have a half-integer spin (±½, ±1½, ±2½, etc).

! This puts new focus on under-rotations. What if your triple Axel (fermion) is pre-rotaed into a triple Salchow (boson), with an accompanying spray of ice chips as decay debris? :rock:
 

zounger

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It looks I missed the party here :biggrin:

I would say Mathman tends to be very Socratic. (ἕν οἶδα, ὅτι οὐδέν οἶδα) "One (thing) I know, that I don't know". And a reminder, when Pythia was asked who is the wisest man she replied: "Sophocles is wise, Euripides is wiser but Socratis is the wisest".

And I will agree with dante, seeing it a bit nationalistically, that there is a lot of Platonic, Aristotelic stuff that is still difficult to decide whether they been disproved or where wrong. Mainly of our lack to understand the ancient Greek language and secondly of the small amount of bibliography that was saved.
 

dante

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Hmm. I think I would rather say that in this case (we don't find a who were going to take part in the experimentsn answer) then we don't know whether the problem is decidable or undecidable. If eventually we find the numbers, than at that point we know that the problem was decidable. Otherwise we don't know.

If no solution of the equation is known a priori, and if we assume that a brute-force search is the only way to find it, then there is no guaranteed way to finish the search, which makes the problem undecidable by definition.

Maybe quantum computers taking advantage of entanglement will give new insight.

BQP has been a rather narrow class of problems so far, and I wouldn't hold much hope for that a certain problem will fall into it. I don't think quantum processors will be as revolutionary as tensor (neural) processors going to be soon.

! This puts new focus on under-rotations. What if your triple Axel (fermion) is pre-rotaed into a triple Salchow (boson), with an accompanying spray of ice chips as decay debris? :rock:

We had a chance to learn that, but the designers of the Large Skater Collider faced an uproar from figure skating fans, so thay had to stick to hadrons.

Another interesting possible effect is a falling leaf and a waltz jump forming a Cooper pair, making it a listed jump. Unlike chipping skaters' and ice debris, this can be done in a regular pair program.
 

Mathman

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God will definitely do whatever he/she chooses to do.

Theologians down through the ages have been fascinated by the question, "Is there anything God can't do."

Most religious people believe in miracles: God, the author of the Laws of Nature, can temporarily set aside those laws if he/she so wishes. God is above the Law.

But what about mathematics and logic? Can God create a triangle that doesn't have three sides? Would we be allowed to object that, by definition, the geometric object that God created is not a triangle?

Thomas Aquinas, the most influential Christian theologian in history, undertook this class of question in earnest. Plagued by conundrums like, "Can God create a stone that is so heavy that God himself cannot lift it," Thomas made a list of things that God can't do. God cannot lie. God cannot stop being God. Etc.

Also included on the list was, God cannot create a triangle whose angles do not add up to 180 degrees. Why not? Because Euclid said so. Euclid trumps God, in the view of Saint Thomas. I have often wondered what Thomas would have made of the non-Euclidean geometries that began to flourish in the nineteenth century.

(As a personal aside, I have to confess that this problem is near to my heart. In my youth the following question occurred to me. What if you have a triangle where two of the sides are lying right on top of each other, with the third side having length zero. Is that a triangle?

Euclid would had said no. And yet, if you think abut it, the three angles are 90 degrees, 90 degrees and 0 degrees, which does add up to 180.

This perplexing example morphed into a passion for investigating the mathematical structure of degenerate singularities, especially in the context of cosmological modeling, which I pursued professionally for 45 years. :) )
 
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Mathman

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If no solution of the equation is known a priori, and if we assume that a brute-force search is the only way to find it, then there is no guaranteed way to finish the search, which makes the problem undecidable by definition.

Wading ever deeper into the quicksand ... ;)

I am not a logician (much less a physicist or a computer guy). But I think this topic is more subtle than that. As I understand it, "undecidability" is a logical property that certain propositions in computational complexity theory possess because of their logical structure and content, and others don't. It is unrelated to what I know, or what some moss growing on the side of a hill on Mars, or an advanced civilization in another galaxy, knows or assumes. If we include "a priori knowledge," then we have changed the proposition that we are analyzing.

Proposition 1. Fermat's Last Theorem.

Proposition 2. If 123[sup]17[/sup] + 456[sup]17[/sup] = 789[sup]17[/sup], then Fermat's Theorem is false.

Proposition 2 is true. In fact, it is a tautology. If 123[sup]17[/sup] + 456[sup]17[/sup] does equal 789[sup]17[/sup], then Proposition 2 is true. And if 123[sup]17[/sup] + 456[sup]17[/sup] does not equal 789[sup]17[/sup], then Proposition 2 is true.

I am in doubt about what this says about Proposition 1. Have we (pre Wiles' result) "proved that no computational algorithm exists that will decide the issue?" I agree that is true that "If 123[sup]17[/sup] + 456[sup]17[/sup] = 789[sup]17[/sup]" then a systematic machine search will discover this fact after 2,634,554 steps, or whatever. But beyond that, I feel like I am in waters over my head. Is the answer to this decidability question different before and after 1996?

BQP has been a rather narrow class of problems so far, and I wouldn't hold much hope for that a certain problem will fall into it.

I have to confess that the whole P versus NP cycle of ideas is quite beyond my understanding (me and Socrates :) ). I just barely understand what the question is, and to me the conjecture P=NP seems obviously false. But many experts believe it to be true. And many doubt that this will ever be settled, or that it can be.
 
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Manitou

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"Can God create a stone that is so heavy that God himself cannot lift it,"

That’s the incompleteness theorem in the language of theology. :D

If we conclude God cannot alter mathematics, for example he cannot obtain truth from two falses, or cannot get a false from two trues, so if He has to obey the mathematical laws, then one can prove that, as a result, God cannot bend the laws of physics either, as they are straight results of the mathematical laws and formulas applied to some initial conditions.
So assuming God does exist, and I think the Universe has some realm we are not supposed to and will never be capable to understand, then God has to have some back door access to the reality. For example - the reality, including us, exist inside God’s mind. We are God’s game.
Still, it doesn’t answer my causality chain problem. Like: who and how caused God? Can God cause Himself?

Is the answer to this decidability question different before and after 1996?

Assuming we are talking before 1996, the answer to the Fermat theorem is decided. It's already objectively determined that the theorem stands or not.
Let F(a,b,c,n) = a[sup]n[/sup] + b[sup]n[/sup] - c[sup]n[/sup]
let X = { (a,b,c,n)∈N[sup]4[/sup]: F(a,b,c,n)=0 }
Fermat theorem is true <=> X = Ø
The set X objective. The same as set of diagonals NxN, that can be defined as {(a,b)∈N[sup]2[/sup] : a=b}.
There are no existential (qualitative?) or axiomatic differences between those two sets. They both have simple and very well defined arithmetic definitions. Their states are predetermined. We just don't know it, and if the axioms are too thin then we may never know it. But the answer is there and needs to be discovered. By computer or by God, but it's there.

Almost exactly equivalent statement is possible for the CH. The set between N and C is there or is not, and that is already determined. We will never be able to construct it, or be sure it doesn't exist, but the answer is there. If we have 2[sup]c[/sup] amount of time we can check it by brute force. The same as verifying the Fermat theorem, although is easier to try something N times than 2[sup]c[/sup] ... :)
 

Mathman

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If we have 2[sup]c[/sup] amount of time we can check it by brute force.

That is an interesting way of putting it. :cool: In fact, it seems that we have only "c" amount of time.

And that assumes that each individual computation can be done in 0 amount of time, all those 0s adding up to the continuum, like points on a line. So we will run out of time long before we complete our search, even though time is infinite. (In fact, Cantor's second diagonal argument seems to guarantee it.)
 

Manitou

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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 }
In other words it's a set of all bijections between X and Y. It's empty if X and Y have different cardinals.
So if X and Y are given then B(X,Y) is equally given.
Let A = { a⊂C: B(a,N)⋃B(a,C) = Ø }
In other words A is a set of subsets of C that have neither bijections with N or C.
Because B(a,N)⋃B(a,C) is given for any given subset a then A is given as well.
So we have CH <=> A=Ø

So it basically shows CH is already determined. It's there for finding...
 

Mathman

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So we have CH <=> A=Ø

I accept that. But I do not see how we are any farther ahead.

Trying to decide whether the continuum hypothesis is true, false, or independent of the axioms of set theory is the same as trying to decide whether A=Ø, A≠Ø, or "the question of whether A is empty or not is independent of the axioms of set theory."
 

Manitou

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I accept that. But I do not see how we are any farther ahead.

Trying to decide whether the continuum hypothesis is true, false, or independent of the axioms of set theory is the same as trying to decide whether A=Ø, A≠Ø, or "the question of whether A is empty or not is independent of the axioms of set theory."

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.
That's what you once said: "the sought set might be right before our eyes". But our eyes are not good enough to see it... :)
 

Orlov

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To me, that is the huge question in all of science. How is it possible that this model building works at all? After all, a mathematical equation is just chalk marks on a blackboard. How is it possible that the mighty stars and planets in their courses care what we scribble on our blackboards?

I think you're confusing cause and effect. Although you don't do it as consistently idealistic as Manitou here. I believe that the root cause is physical reality, and "mathematics" arises as a protocol for effective interaction of Homo Sapiens with reality.

Let's simplify the situation and move from stellar processes to elementary problems of mechanics (in principle, nothing will change in the arguments). Let's say that Manitou and I have the same potato gun and we have to hit the coconut on the palm tree with them. (We will not ask where the gun and all the tools needed in the future came from, for example, we found them in the bunker, this is a gift from the previous civilization destroyed by nuclear war)

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 :)

First, in addition to the guns, I found a clock with a second hand in the bunker, and observing nature realized the concept of time, that time is linear - I have seen that when the second hand makes one turn, the snail crawls one centimeter (I also found a ruler). On the next turn - all the same. I measured 8 centimeters on the ground (I was bending my fingers, the squiggles drawn on the ruler were still incomprehensible to me), put the snail on the start, turned away and started "counting" the revolutions of the second hand by unbending fingers. When it was over, I turned around and the snail was right at the finish line. It was an incredible scientific victory! (Manitou looked at my joyful screams, shook his head - "stupid boy, messing around with snails" and continued to shoot :))

In the course of my experiments with the snail, when I didn't have enough fingers on both hands, I made special limestone marks on a flat stone, unbent all the fingers and started to bend them again. Quickly enough, I realized that it was easier not to bend my fingers at all, but to write on the stone all the time. And I also pretty quickly realized that the recording system I had invented was these incomprehensible marks on the ruler, and in the future I only used them.

There were two types of snails on our island - the second one crawled two centimeters in one minute. So I realized the concept of speed.

Studying the inverse problem - I wanted to understand how many seconds a fast snail will crawl 80 centimeters - I realized the concept of division. The concept of addition and multiplication arose before this naturally, but after the realization of the concept of division I realized them too. Looking at the pair multiplication/division, I realized the concept of subtraction as the antithesis of the concept of addition.

Up to this point, I had never for a moment forgotten that all my limestone records were just a convenient way to study behavior of snails. And that's all. It's just "snailology". But at some point I realized that snailology applies not only to snails, but also to the nuts that we collected with Manitou in between our activities to eat. And to the turtle eggs on the beach. Having seen in practice that the same results are obtained for snails, eggs, seconds, and limestone markers, I realized that in the future it will be more convenient to work only with records on stone. And then apply the result to whatever I want. So Mathematics was born (although I did not know this term and continued to use the term "snailology")

There was a high rock on our island. When I got bored and threw down the stones, I discovered that the stone, unlike the snail are moving at changing speed. The stone seems to fall faster and faster... At least when it falls to the bottom of the gorge, it crushes small stones, and when I just open my hand and stone falls at my feet, it doesn't crush anything. So the stone moves faster near the bottom, okey...

But how exactly does the speed of the stone change? I assumed that just as my snails increase their distance by a centimeter every minute, so every second the speed of the stone increases by 10 meters/second, for example. Since I did not know the exact value, I decided to writing the squiggle "g" instead of these hypothetical 10 meters/second, because I remembered the essence of my previous discovery - squiggles on a flat stone and meters in the real world add up the same way.

For the first second the stone will pass g meters of path, for the second second - 2*g meters, for the third second - 3*g meters... How far will the stone go in N seconds?

Never before have I encountered such a complex snailologycal problem...

Wait. If I add the last path N*g and the first path g, or add the penultimate (N-1)*g and the second 2*g, or (N-2)*g and 3*g, or (N-3)*g and 4*g - I will get (N+1)*g everytime. There are N/2 such pairs, so the total path of the stone is

H = g*N*(N+1)/2

Hmm... snails crawled smoothly - in half a minute they passed half a centimeter, and in 15 seconds a quarter of a centimeter, and so on.. Of course, that the speed of the stone also does not change sharply, per second...

And I will not consider per second! Let's assume that the speed changes every millisecond... No! A microsecond. No! A nanosecond! whatever... something small. Now I will mark that small time step "delta_t" and what exactly it is equal to I will figure out later... Okey, now the speed changes to g*delta_t, and steps of pass will be

g*delta_t*delta_t, 2*g*delta_t*delta_t, 3*g*delta_t*delta_t ...

Okey, I got it - in the previous formula of total pass I just need to replace g with g*delta_t^2

H = g*delta_t^2*N*(N+1)/2 = g*delta_t^2*N^2/2 + g*delta_t^2*N/2

wait-wait-wait... total time is T = N*delta_t, so

H = g*T^2/2 + g*T*delta_t/2

Eureka! I'll just take whatever small "delta_t" I want and the second term in the equation will become so small that there is no ruler anywhere that can measure it. I liked this snailologycal trick so much that I gave it special name - "a limit"

So I got the final formula

H = g*T^2/2

Further, since you probably already understand my main point :), I will tell you faster - I was convinced of the correctness of my hypothesis by dropping a stone from different heights and measuring the dependence of H on T - it turned out to be quadratic as predicted by the hypothesis. From these same measurements, I found that g = 9.79 m/s^2. Shooting the potato gun up and measuring the height of the potato take-off (by the marks on the rock), I found initial speed of potato. Than I found that the movement of bodies in the horizontal and vertical direction is independent. After discovering the basics of trigonometry I found a snailologycal connection between the projections of the initial speed of the potato and the tilt of the gun and eventually wrote down the equations given at the beginning.


After my hit with the first shot, a shocked Manitou asked me to explain how I did this miracle (he never managed to hit a coconut with a potato). I tried to tell him about snails, about turns of the second hand, about snailology. But it was too difficult to retell the six-month journey of my intellectual research in five minutes. All that Manitou could understand was that snails, nuts, stones, and everything else in the world are connected by a mysterious snailology. He declared me a powerful magician who could talk to great "Snailology". I didn't mind, because a week before that we had found women on a nearby island, founded a tribe, and started to regenerate humanity, so I needed to raise my social status. Three hundred years later, a new civilization build a 500-foot monument to me with a giant snail on my palm outstretched to all mankind. End of story :biggrin:

----------------------------------------------
Summarize.

1) Everything starts from reality and ends in it. (Anyone who disagrees with this basic thesis will be cured by a good punch in the face :biggrin:)

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

3) It is quite possible that "mathematics" is conditional and depends on our nature. We are "metrical beings" - we move in space to get food (and hide from predators), our existence is subject to cyclicality (sleep, a regular feeling of hunger, etc). The snail crawls every minute by an centimeter, the Manitou throws one nut in his mouth every fifteen minutes cuz he is hungry. And I can think about the concept of a "single nut", "two nuts", "a lot of nuts" and I can compare the sequence of nuts with the sequence of centimeters of the snail path, etc. We don't think about it, because this is the kind of life that originated on Earth. From the very beginning. But to say that life can only be like this, and only "our mathematics" could exist, would be rash, I think.

4) That why I called math of "protocol for effective interaction of Homo Sapiens with reality". We are "metrical" and therefore it was effective for us to focus on metrics when interacting with reality. But to declare (as Manitou does) that the basic principle of building the universe is based on a convenient to us protocol would be unjustified anthropocentrism.
 

Orlov

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I would say this:. The sense in which mathematics is "conditional" is that mathematical theorems generally do not make any definite claims of fact. Rather, what mathematicians do is try to prove "conditional" statements of the form "If P, then Q." Mathematicians rarely if ever try to prove P (or even to speculate about whether P is true of false).

The topic of the referenced thread was that the cherished traditional hope of mathematics, that everything can be reduced to logical analysis (P implies Q) was dashed by mathematical logicians themselves int he late nineteenth and early to middle twentieth centuries. So ... (?)

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."? No, you can't. You will be fed only if you get a coconut. To do this, you need numerous intermediate "tools". Including "If P, then Q", starting with the simplest - "if the potato hits a coconut, it will fall". Logic is just a tool.

Again. I am a metrical being. My existence depends on my movements and my position in space. To succeed, I have to solve metric problems, in this simplified case, to knock coconut. I study the basic properties of space - linearity, causality. I find an effective way to quickly solve my metric problems - work with dashes of chalk on the stone. Me, who consistently makes dashes on the stone, no different from a snail, consistently crawling centimeters of its path. But I make my dashes faster. And in fact, this is the main meaning and purpose of mathematics.

But a creature that does not live in the world of "monotonously crawling snails and Manitou monotonously throwing nuts into his mouth" сan learn to effectively solve their problems in a different way. How exactly? I do not know, because I live in the world of "snails and Manitou" :)

This is exactly what I meant when I said that "mathematics is conditional".
 

Manitou

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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."? No, you can't. You will be fed only if you get a coconut. To do this, you need numerous intermediate "tools". Including "If P, then Q", starting with the simplest - "if the potato hits a coconut, it will fall". Logic is just a tool.

Again. I am a metrical being. My existence depends on my movements and my position in space. To succeed, I have to solve metric problems, in this simplified case, to knock coconut. I study the basic properties of space - linearity, causality. I find an effective way to quickly solve my metric problems - work with dashes of chalk on the stone. Me, who consistently makes dashes on the stone, no different from a snail, consistently crawling centimeters of its path. But I make my dashes faster. And in fact, this is the main meaning and purpose of mathematics.

But a creature that does not live in the world of "monotonously crawling snails and Manitou monotonously throwing nuts into his mouth" сan learn to effectively solve their problems in a different way. How exactly? I do not know, because I live in the world of "snails and Manitou" :)

This is exactly what I meant when I said that "mathematics is conditional".

How do you prove you even exist? That you are not a result of a mathematical formula. Yes, I know you believe in "reality", but what is reality? You have a definition?
I would even say the laws of logic are more real than your coconuts.
I tell you this - you see only what you can see. What you are designed to see. Chicken sees only grubs in the dirt and there is no argument to convince it there is more. The only reality for the chicken are the grubs.
 

Orlov

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How do you prove you even exist? That you are not a result of a mathematical formula. Yes, I know you believe in "reality", but what is reality? You have a definition?
I would even say the laws of logic are more real than your coconuts.
I tell you this - you see only what you can see. What you are designed to see. Chicken sees only grubs in the dirt and there is no argument to convince it there is more. The only reality for the chicken are the grubs.

These are just words :) Reality is the feeling of hunger in your stomach and the need to knock coconut. I tell you, the best way to understand "what reality is" is a good punch in the face :laugh:

"laws of logic" is causality. "If the snail crawled a centimeter, then its initial position is free." "If the spatiotemporal coordinates of the potato and the coconut match, the coconut falls.". "Logic" is the same "chalk marks on stone" about causality.

I don't need to prove that "I even exist". There is only a struggle for survival. And only this. Which I do effectively - "making marks on the stone"
 

Ducky

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How do you prove you even exist? That you are not a result of a mathematical formula. Yes, I know you believe in "reality", but what is reality? You have a definition?
I would even say the laws of logic are more real than your coconuts.
I tell you this - you see only what you can see. What you are designed to see. Chicken sees only grubs in the dirt and there is no argument to convince it there is more. The only reality for the chicken are the grubs.

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.
 
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