>>>/lit/7409382
>The point is that science tends to ignore other forms of "knowing" like intuition or reflection, and base itself around complete adherence to empiricism, even though empiricism has plenty of arguments against itself.
How do I bring up the craziness of considering "intuition" to contribute to "knowledge"?
>Pic unrelated
It's not, really. All knowledge is intuition in a sense. when you get down to it, everything you learn comes from a long chain of sources that need to be trusted. A scientist does an experiment, writes a paper, the paper is published, your computer reproduces it for you and your eyes tell you what they see and your brain interprets the meaning. Every one of those links HAS been wrong before, so when you say you know something you're really just making a statement that you trust that the chain of sources was completely reliable for that specific piece of knowledge. You can make judgements about how likely a thing is to be true, based on the historical accuracy of each of those sources in reproducing information, but that's intuition; an assumption.
That's not to mention the fact that the scientific method is based on a few assumptions that can't really be proven, like that the laws of physics never change, and that they're the same everywhere in the universe. Those things have always been the case for you, so you can intuit that they will remain the case.
>>7694515
>How do I bring up the craziness of considering "intuition" to contribute to "knowledge"?
Intuition will completely fail in areas or situations which we are not used to, or which are new to us. Just take relativity. We are evolved animals, living at sub-relativistic velocities, so of course we couldn't have guessed relativistic effects from our intuition alone (at least, very unlikely). And the results being "unintuitive" certainly won't make them any less correct for the same reason.
But of course intuition CAN be used to formulate new laws which may turn out to be correct, and I wouldn't say intuition tends to be ignored. It's just that those laws would have to be tested, either way. Because, surprise, Newtonian physics simply isn't applicable in every situation, even though some would say it is the most intuitive.
As for reflection, you can of course reflect your own misconceptions and prejudices back and forth against each other, how do you know you're right? Can work or fail.
> even though empiricism has plenty of arguments against itself.
That is also true, like "only things that can be empirically proven are acceptable knowledge" can't be empirically proven.
Most sciences use math and that is not empirical (inb4 logical positivism).
Also, hypotheses are created using intuition and such. You don't just do random experiments. And either way, all results must be interpreted.
>>7694515
>How do I bring up the craziness of considering "intuition" to contribute to "knowledge"?
Quantum mechanics is very nonintuitive yet extremely accurate.
>base itself around complete adherence to empiricism
Theoretical physics doesn't really do this. ex. String Theory
>>7694515
>The point is that science tends to ignore other forms of "knowing" like intuition or reflection, and base itself around complete adherence to empiricism, even though empiricism has plenty of arguments against itself.
Physical intuition often motivates the development of theories that are later confirmed by experiment. See, for instance, the invetion of the Dirac equation and the ensuing discovery of the positron.
I'm not sure how you could come to know "know" something by reflection.
>>7694523
Yes yes, everyone has been familiar with all that jazz ever since the times of Hume and possibly even before that.
I'd recommend a good ol' American dose of John Dewey.
There is a difference between accepting the theoretical faults in the scientific method due to whatever problems of induction and what one actually pragmatically holds true.
Would you say that if someone dreamt he could fly and had an intuitive sense that he could that he "knows" he can fly?
The only way out of the grave you have dug yourself is to embrace some kind of skepticism or nihilism.
You seem like the typical undergrad impressed by himself for reflecting on how unconcrete scientific knowledge is.
>>7694533
>Quantum mechanics is very nonintuitive yet extremely accurate.
How does someone nonintuitive being true show that intuition doesn't reveal truth?
You've given an example that says nothing more than "intuitiveness is not a necessary condition for truth".
>>7694515
Source for the OP image?
>>7694609
nvm I found it
>>7694618
Care2share?
Quite tough problems btw
>>7694631
there was a thread here a while ago where they tried solving all of them. Unfortunately, the thread died before there was an solution for each question.
i really hate textbook authors
>problem is from 2005 olympiad and only 2 people solved it
>this problem is trivial and you should be able to solve it
why do they do this
>>7694691
Really? What?
>>7694699
I looked at the IMO results for 2005 and there were several people with perfect scores.
There were no perfect scorers on USAMO 2005.
1. All the a's are 3, except for the last one. This is because if you have a number greater than 4, say 5, it can be split into 2x3 > 2+3. At 4, you can split it into 2x2 = 2+2.
I'll do the rest in a bit. I'm eating.
>>7694787
And to round out the argument, 3*3=9>8=2*2*2, so any sums of six can be written best as {3,3}.
So, if n is a multiple of 3, write all 3s. If n is 1 plus a multiple of 3, then use {3,3,...,3,2,2}, and, if n is 2 plus a multiple of 3, use {3,3,...,3,2}
>>7694810
Exactly this.
No. 2 is also not bad.
x(x+1)(x+2)(x+3) + 1 = 379^2, so
x(x+1)(x+2)(x+3) = 379^2 - 1, and by difference of squares,
x(x+1)(x+2)(x+3) = (379 - 1)(379 + 1) = 378*380
but we can write the left side as a product of two numbers differing by 2 as well:
x(x+3) * (x+1)(x+2) = (x^2+3x) * (x^2+3x+2)
so that one solution is
x^2+3x = 378
which is a quadratic with positive root x=18.
>>7694595
>How does someone nonintuitive being true show that intuition doesn't reveal truth?
It shows intuition is irrelevant.
>>7694830
Yea, 2 is pretty pleb. Try #15 on for size.
>>7694830
your p good
>>7694853
Most of them look pretty rough, except for the first two, haha.
You could throw the cubic discriminant at it, although I wouldn't know it without looking it up, and it's pretty beastly, and so isn't in the spirit of the competition.
Also, the discriminant doesn't give us *exactly* the information we want, because it just tell us about the degeneracy of the roots; in particular, discriminant zero just tells us that at least two roots coincide, not whether exactly two or all three coincide.
Clearly there's some kind of symmetry we need to exploit.
>>7694875
Coming at it from another direction, the cubic has exactly one real solution if and only if it factors as
(x-b)((x+c)^2+d^2)
where b,c,d are real numbers, and d is not zero. Then, expanding, we have
x^3 + (-b+2c)x^2 + (-2bc+c^2+d)x + (-bc^2-bd)
and so we have the system of equations
-a = -b+2c
-2a = -2bc+c^2+d
a^2 = -bc^2-bd
which is still pretty shitty.
these threads could be so good but retards always ruin them
>>7694890
For consistency, replace every instance of the variable "d" with "d^2"; I made the assumption d>0 in my scratch work but not in my post.
With d^2>0 and a^2>=0, the last of the three equations forces b<0.
The first and second, after eliminating a, yield
4c = c^2+d^2 (**)
which we may substitute into the third equation to get
a^2 = -4bc
or
a^2/2 = -2bc
which we may substitute (along with (**)) into the first equation to get
-2a = a^2/2 + 4c
or
a^2+4a = -4c
>>7694907
Note: squaring both sides of the first equation yields
a^2 = b^2 - 4bc + 4c^2
but we also have that a^2 = -4bc, so that
b^2+4c^2 = 0
----
So I am pretty confident that I'm not too far from a solution, but I have actual coursework to do. Interpret this as cowardice if you'd like, but I will (maybe only temporarily) throw in the towel for now.
Feel free to pick up or drop my work, guys.
The optimal solution for the first problem consists of setting 2 of the variables equal to 2, and all the other equal to 3. It's pretty straightforward to see that in the optimal solution you won't have numbers greater than 3.
>>7694589
>Yes yes, everyone has been familiar with all that jazz ever since the times of Hume and possibly even before that.
Well, obviously not everyone, because OP is asking about it.
>You seem like the typical undergrad impressed by himself for reflecting on how unconcrete scientific knowledge is
I'd agree except that my post wasn't unwarranted. It was made directly in reply to someone that wanted to know that information. I think the OP post was more "typically undergrad" or at least reddit-tier for getting activated by someone on /lit/ suggesting that empiricism isn't infallible. And none of the other posts ITT are any deeper or more informed than mine.
I should have clarified that I do believe empiricism and the scientific method are probably the most groundbreaking developments in information collection and verification in recent human history. I'm not a philosophy memeboi but I do acknowledge that choosing which things to believe requires intuition even when some are confirmed by generally trustworthy institutions.
>check my own work after reading >>7695392
>oh, lemme just plug that in
>see that the constant term is a^2+1, not a^2
>realize that I wasted like 20 minutes after a copying error
Fuck.
>>7695392
I just evaluated the polynomial at a+1, and I got P(x) = 2, unfortunately.
>>7694515
>and base itself around complete adherence to empiricism, even though empiricism has plenty of arguments against itself.
what the scientist calls empiricism IS NOT empiricism.
the scientist calls himself an empiricist ONLY FOR THE CACHET of empiricism which avoids him to be called a speculative retard, this insult that he uses on anybody who does not accept HIS kind of empiricism.
The scientist allows only the empiricism which he likes, the empiricism which is bastardized by science.
the scientist denigrates any doctrine that is not the scientific rationalism:
-the total lack of empiricism is said by the scientist to be purely speculative because it does not connect to the empirical world. it is the religion, the metaphysics
-the empiricism which is the only true one destroys the scientific stance and therefore the scientist calls this ''radical empiricism'' since he has no means to refute this stance. the terrorism by the rationalist only shows his sterility in his attempt to connect back his speculations to the empirical world.
>>7696380
Get a load of how fucking insecure this guy is. Just because you haven't and never will contribute anything to human knowledge in your masturbatory philosopher armchair does not mean you should get angry at the people who do.
