prime numbers

Prime Towers Problem

There are 1 billion towers in line on a plane. The distance between the n-th and the (n+1)-th tower is 1 kilometer. The first is 2 kilometers tall, the second is 3 kilometers tall, the next one is 5 … and the n-th is the n-th prime number kilometers high.

From which tower’s top, the maximal number of tower tops are visible? In both directions.

A discussion is anticipated there:

http://lesswrong.com/r/discussion/lw/pbe/open_thread_august_7_august_13_2017/dw37

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physics

Another Tactics

There are two kinds of people in this world. Those who find the humiliation of Paul Erdos by Marylin vos Savant as regrettable, and those who find it hilarious. I suppose I  would find it hilarious even if I was in his shoes.  Being in her shoes would be more than hilarious, of course.

Now, where can we strike again, to poke the pride of the “overwhelming majority of the scientific community” without letting them space to maneuver and weasel out? The previous post was a good example of such a strike, I guess, and this one shall be next.

As the general wisdom goes, the carbon dioxide in the atmosphere builds up for a century and more. When it’s in the air, it stays there for a very long time. The coal burnt decades ago, hasn’t been removed from the air, they say. Therefore we have more and more particles per million of carbon dioxide in the atmosphere. Hadn’t been so, we wouldn’t have a problem.

I am sorry, but this “persistence of CO2 in the atmosphere”, however probable and hard to dispute it may sims, is just another hogwash.

The rainwater has about 300 particles per million of CO2. In a year, about a meter of precipitations means 1/10 of the atmospheric CO2 washed down. The photosynthesis does a lot less.

So, we see this corner dogma quite weak.

And it doesn’t feel that good to strike at the already wounded bunch as well. Still, better than nothing.

 

 

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physics

A Tactics

You can’t attack complex scientific theories like Relativity, Quantum Mechanics, String Theory, Axiomatic Set Theory and alike. You just can’t do that. If you have some reservation against one of those, that’s your problem and most certainly not a problem of the scientific community behind any of the above big science chunks.

You see, almost nobody can argue with you, except some leading scientist from the field, who will most certainly won’t agree with you and your “reservation”  about let say Relativity. They will tell you, you don’t understand something, you would understand if you were one of his postdoctoral students, which you probably aren’t. And if you are, you will cease to be, if you don’t stop with this nonsense.

In the eyes of the second league, you are just a crackpot. Too bad that their professor isn’t here, he would refute you instantly. They do try to explain your mistake and they do have some limited fun mocking your stupidity. But nothing valuable comes out of that arguing.

And if that was not bad enough, I have a bad news for you as well. Yeah, most probably you really don’t understand something very fundamental and your knowledge isn’t sufficient here. Sorry, I can’t help you either, you probably are just a naive layman. Nothing to see here, move along! We all have just to wait for another Einstein to dent the General Relativity. And you aren’t one.

Well, there is a tactic however, you can openly ridicule the scientific community and get away with that. If you are Marilyn vos Savant, you can ridicule Paul Erdos probability proficiency and you win eventually. It requires an over 200 IQ score to have, which isn’t that easy condition to fulfill. If you don’t have it, you probably don’t notice the Monty Hall “anomaly”, either. Understand yes, but that is not the same as came up with it. But this trick has been used already and you have to come with another one.

As a matter of fact,  there is at least one more, you can use for an assault toward the scientific consensus. Every good math or physics student could understand, at least, how wrong and silly the scientific community was or still is.  How you were right against a so-called “scientific consensus”.

It’s of course about the so-called Faint Sun Paradox. I was writing about that before. The young Earth was warmer,  because of its faster rotation. The premise, that the Earth rotated faster is not disputed at all, but the causality: a faster rotation, a warmer temperature, everything else equal — is difficult to swallow. Even though it’s not that complicated. Even with the fainter Sun, much faster planet rotation yields to a higher temperature on the planet’s surface. Higher temperature despite lower energy flux.

This.

Or maybe this.

They are clueless and entirely confused about the relation between the planet rotational speed and its surface temperature. Something every physics student should understand. Yes, it’s a bit tricky, but not even as much as the Monty Hall is tricky. Yet, people like Carl Sagan and pretty much everybody else just doesn’t get it somehow.

When you’ll fully understand and internalize this conundrum, you will probably ask yourself – but do they really know everything about the Relativity or QM, when they collectively do such blunders in basics physics?

Hence, the title of this post.

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physics

A Physics Problem, Once Again

Those mating problems in 2D, 3D, 4D and so on, with standard chess pieces adjusted for dimensionality, are extremely difficult and I don’t find a lot about that Googling all around. Perhaps one day, we will have a well-founded theory about that.  Or maybe a solving algorithm for this kind of problems. “How many white kings can hunt down a black horse on a 3D chess board and how?” On the unbounded 3D chess board?

A generalized-chess-mating-SQL.

Perhaps we will have it one day.

Now something to relax. The sum of all gravity forces between each pair of atoms inside our planet Earth. Not as vectors, just the sum of all magnitudes. Approximately.

A discussion there:

http://lesswrong.com/r/discussion/lw/par/open_thread_july_31_august_6_2017/dvy0

 

 

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physics

Newtonism Question

A mass point of 1 unit is at 1 length unit.

A mass point of 1/2 unit is at 1/10 length unit.

A mass point of 1/4 unit is at 1/100 length unit.

….

Generally, it’s (1/2)^n mass at (1/10) ^n unit for every natural n, on the positive side of 0.

All gravitational net forces point to the left. Where is an opposite reaction force here?

 

 

 

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mathematics

Unexpected?

When you go up the natural numbers ladder, there are (on average) bigger and bigger gaps between consecutive prime numbers.

If you look at primes as islands, there are  lakes of composites between them.

The lake between 19 and 23 is 3 composite numbers long, for example. Or between 89 and 97 there are 7 composites.

Those lakes are greater and greater on average, as it is well known. Albeit there are always small ponds of just 5 composite numbers long, no matter how far you go. (There are likely infinity many lakes with just 1 composite, too. Which is another form of the so called Twin Primes Conjecture. A few years ago it has been proved that there are always less than 70000000 large lakes as you go up the naturals. Some time later, that 70 million has been improved to just 5, but not yet to 1.)

Say, that you have just sailed across some recordly wide composite lake and you are on a prime island again. What can you expect, how much wider will the next record lake be? Usually 2 more composites wider than the previous largest, right?

No. Every new record is usually quite greater from the previous one.

1,2,2,2,6,4,2,2,12,2,8,8,20,14,10,16,2,4,14,16,6,26,30,10,2,12,14,2,32 ...

These are the increments of every new record composite lake.

P.S. Haven’t been able to Google this story.

EDIT:

Then, have been able to Google some about this. The so called maximal prime gap goes like this, says Wikipedia:

Not as smoothly and gradually as those three coloured functions predict, but quite abruptly in reality.

 

 

 

 

 

 

 

 

 

 

 

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