Quick Answers to small questions

[Quackers]

So what are "real" sciences?

I studied biology and chemistry. My chem teacher told me bio was a joke I slowly realised what he meant as i went though biology..

anybody got thoughts?

 

[Birdjaguar]

It's not senses that's the problem, it's our mental models. As moderate sized objects we evolved to model our world in ways that are useful to our daily lives. But the world isn't the same on the quantum scale.

We have math that predicts how it does behave, but it can be hard to map this math to physical interpretations.

I agree that our mental models have a basis in practicality, but those models are heavily dependent upon our particular senses that have evolved with us. Which came first, the senses or the models? If our senses were different, so would our models. Yes, mapping the quantum world to our senses would be quite difficult for the very reason that our minds are so adapted to the five senses we have. If we had different senses, how would what we perceive reality to be change? Which one would be true?

Hmm, it seem to me that the sense of smell is different to the other senses, in that it depicts what has happened, more than what is happening now (i know that there is a delay with light and sound,too, but it's not really on a human time scale). I was wondering if animals with a powerful sense of smell have different persective on their experiences compared to their surrounding, than we do, because of this?

Do the human reliance on the senses of sight,sound and touch makes us live more in the immediate moment and we use our minds to remember/work out what has happened, more than other animals who have a better sense of smell to rely on?

All good questions. BTW, the sense of smell is the only sense we have in which the brain has direct contact with the outside world. i would think that whatever senses a creature has has a huge effect on its perspective of its surroundings.

 

[nonconformist]

So what are "real" sciences?

I studied biology and chemistry. My chem teacher told me bio was a joke I slowly realised what he meant as i went though biology..

anybody got thoughts?

hope you got a nice set of colouring pencils

 

[GoodGame]

So what are "real" sciences?

I studied biology and chemistry. My chem teacher told me bio was a joke I slowly realised what he meant as i went though biology..

anybody got thoughts?

Biology is a real science. Your Chem teacher has a chip on his/her shoulder. Ultimately chemistry applies to all things macro-scale (cell biology/biochemistry and above) so it shouldn't be disposed of.

 

[peter grimes]

As long as an area of study is utilizing the principles of the scientific method - observation, falsifiability, experimentation, etc - I'd be comfortable calling it a science. After all, even in chemistry there is 'bad' science and 'good' science. The methods of the practitioner matter more than the object of inquiry.

 

[Ayatollah So]

Here's a small question for y'all: name some mathematical conjectures that looked good but were later disproven. There are prizes offered for proving or disproving certain conjectures - I'm curious about past conjectures that failed. Especially if, right up until the counterexample was produced, most people suspected the conjecture was true.

 

[ParadigmShifter]

Fermat numbers and Fermat primes were first studied by Pierre de Fermat, who conjectured (but admitted he could not prove) that all Fermat numbers are prime. Indeed, the first five Fermat numbers F0,...,F4 are easily shown to be prime. However, this conjecture was refuted by Leonhard Euler in 1732 when he showed that

F5 = 2^(2^5) + 1 = 2^32 + 1 = 4294967297 = 641 x 6700417.

There are no other known Fermat primes Fn with n > 4. However, little is known about Fermat numbers with large n. In fact, each of the following is an open problem:

* Is Fn composite for all n > 4?
* Are there infinitely many Fermat primes? (Eisenstein 1844)
* Are there infinitely many composite Fermat numbers?

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* Bernhard Riemann, at the end of his famous 1859 paper On the Number of Primes Less Than a Given Magnitude, stated (based on his results) that the logarithmic integral gives a somewhat too high estimate of the prime-counting function. The evidence also seemed to indicate this. However, in 1914 J. E. Littlewood proved that this was not always the case, and in fact it is now known that the first x for which pi(x) <li(x) occurs somewhere before 10^317. See Skewes' number for more detail.

 

[nonconformist]

Mathematic was postulateed being cool by Isaac Newton on February 6th 1606...Robert Hooke disproved this on February 7th 1606, in his famouse treatise "Gayeboyes who mathematics liketh and will as virgineths perish"

 

[Atrebates]

Bertrand Russell tried to compile a list of mathematical theorems to reduce number theory to a formal system with a few axioms (a la geometry).

But Godel f'ked him hard by showing that for any formal axiomatic system, there is always a statement about natural numbers which is true, but which cannot be proven in the system. Which is a real mindbender, but indisputably true.

 

[ParadigmShifter]

Not if you have an uncountably infinite number of axioms

 

[nc-1701]

Are there any good formulas or strategies that help me solve this summation?

Lim n->infinity of [The sum from i=0..n of (1+2i)/(1+i) +2*i*ln(i) - 2*i*ln(i+1)]
Which I can reduce to...
Lim n->infinity of [-2*n*ln(n) + The sum from i=0..n of (1+2i)/(1+i) + 2*ln(i)]

This comes from an integral I've been trying to calculate and should end up summing to approximately 0.26 (Trapezoid approximations ftw). So if anybody could point me to relevant theorems or strategies for this type of series I would really appreciate it

 

[Souron]

Don't know about formula's or strategies, but WolframAlpha is pretty good at answering these sorts of questions

For some reason, it seems to calculate the approximate sum some of the time, and the exact infinite sum at other times.

Anyway, it lists the infinite sum as -1-gamma+log(2)+log(pi), where gamma is the Euler-Mascheroni Constant.

 

[nc-1701]

Wow, thank you that really helps. Also bookmarking the site now that looks really helpful

 

[S.P.Q.R]

what does the k stand for in the Kimberling sequence?

http://mathworld.wolfram.com/KimberlingSequence.html

Given a sequence S_i as input to stage i, form sequence S_(i+1) as follows:

1. For k in [1,...,i], write term i+k and then term i-k.

2. Discard the ith term.

3. Write the remaining terms in order.

Starting with the positive integers, the first few iterations are therefore
[1] 2 3 4 5 6 7 8 9 10 11;
2 [3] 4 5 6 7 8 9 10 11 12;
4 2 [5] 6 7 8 9 10 11 12 13;
6 2 7[4] 8 9 10 11 12 13 14;
8 7 9 2 [10] 6 11 12 13 14 15.