Topic: Prime phreaking

[tarascon]

The following belongs under this topic due to its applications with contemporary encryption technology and data security.

I have a strange sort of head space. For example, I suck (I really, really suck) at arithmetic but am an avid reader of abstract mathematics; I seem to have a grasp for this stuff which I didn't discover until my 40's. My favorite topics are number theory, topology, set theory (particularly Cantor's Continuum Hypothesis and transfinite numbers), anything to do with Riemann's Non-Euclidean Geometry and the distribution of primes on the number line (aka The Zeta Function). On the last, I'd like to share this stuff with you. May it bring you perplexity and joy!

http://www.theguardian.com/science/blog/2010/nov/03/million-dollars-maths-riemann-hypothesis
The security encryptions which are used in today's world are derived from the above. It might be catastrophic if the Riemann Hypothesis actually gets proven. Some say yes, some say no.

And the image that the primes up to 10,000 project:


http://mathworld.wolfram.com/PrimeSpiral.html
Does it remind you of anything? (I realize the association is merely an artifact of the finite count--in reality the spiral should go on to infinity.)

[smokester]

Okay. If just reading your post gave me a headache, golly knows what the math would do.

[tarascon]

Okay. If just reading your post gave me a headache, golly knows what the math would do.

 
This thread isn't about maths--it's about curiosity, imagination, and the ideas which have led us to this point in history. We all post here via our computers and the zeta function, for instance, has helped keep us secure by making brute force cracking more difficult.
I have an intuitive grasp for some of this material and I'm not a logical thinker, per se. When I read the material, I avoid most of the equations and read the text as if it were science fiction... a science fiction based on real stuff. 

Spoiler (hover to show)

Arithmetic is about numbers. Mathematics is about relationships, patterns, and concepts.

Which reminds me... Euler's formula for Polyhedra (F - E + V = 2 *) states that all solid geometrical objects are not unique but are related to the number 2--a prime number. I find that fascinating. This equation is the root source of all modern topography which is not only about shapes and knots but is used in DNA research as well as astronomy.

* where:
F means "face"
E means "edge"
V means "vertices"
For example, a cube has 6 faces, 12 edges, and 8 vertices. 6 - 12 + 8 = 2. The exact count for these change dependent on the object (like a dodecahedron [12 - 30 + 20 = 2], etc) but the tally always comes to the number 2.
This fact is deeply weird.

And, speaking of computers, let me offer this:

Sorry for the book-length post. I'll knock it off now before I headache you folks to death.  Also, I'm not trying to show off... just wanted to share this with whomever might wonder at it the way I do.

[smokester]

I deal in faces, edges and vertices with the CGI I dabble with.  I am not sure what purpose that mathematical equation has.  It doesn't particularly help with anything - like poly count - it just seems quirky like the 9 times table.

Interesting nonetheless and I suppose it is an example of "seeing math" rather than being bogged down by its complexity.

[8ullfrog]

I can't math. Disability. I actually contacted and worked with the American Derpartment of Rehabilitation on this issue.

Mentally? I'm on the same level as someone who needs a wheelchair. Bleak level? They cut me loose. I did months on their crappy computers in various high schools, but they decided I can't math.

They actually said I should be a handyman's assistant. Like I'm that bless'ed devoid of meaning. Can't paint houses on my own, gotta be that guy's madam.

But Phreaking? Blows my mind. And I'm not alone. One of the reasons they locked mitnick in a hole is because a judge thought he could whistle into a phone and launch nukes.


Or at least, that's what the internet says.

I'd bless'ed kill if I could hack like in the movies. Twenty lines in a green and black interface and you're Billg.

[tarascon]

I'm actually reading Mitnick's memoir at the moment. Ghost in the Wires.
The book is very self-important and deservedly so. He's impressive. I did some phone phreaking back in the 70's. Minor stuff.
And, yeah, he was accused of that whistle into the phone and send the nukes flying thing... a Captain Crunch whistle, I suppose. LOL. But Mitnick claims that's a lie; he never could, nor tried, to do that. The Feds were desperate to convict and used whatever fallacious charge they could dream up. He was also accused of doing things which, in fact, were done by certain cronies of his. Still, he was awesome in what he did do.
I would say that if I were a hacker, I'd be a White Hat... or maybe gray. I differentiate between hackers and crackers. I totally approve of hackers.
Check out this film: http://www.imdb.com/title/tt3010462/

[goldshirt*9]

Have been listening to this Series
http://www.bbc.co.uk/programmes/b00srz5b
Very interesting even as a bystander.

[tarascon]

Nice.
If you get hooked and end up needing professional psychiatric help, you can always blame it on me. 


And don't get me started about transfinite numbers and the different orders of infinity. What's that, you say? Different orders of infinity!? Well, I'm really happy that you asked...

Real numbers are all numbers such as whole numbers, fractions, irrational numbers, etc. Natural numbers are the countable numbers such like the ones we all know on the number line, (1 2 3 4 5 6 7 8 9 10, 11, etc) which, we can all agree, continues into infinity. Now here's the thing... you can take any two numbers (say, 3 & 4) and try to count the fractions between them. 1/2, 1/4, 1/8, 1/16, etc... all the way down the rabbit hole. Now, between any two fractions smaller fractions exist and between them, smaller ones ad infinitum. The infinities of those fractions located between any two arbitrary numbers on the line (like 3 & 4, to repeat myself) constitute an infinity which is larger in numbers than exist on the infinite number line of countable or computational whole numbers. Multiple infinities exist. Using Georg Cantor's method of one-to-one correspondence between all of the whole numbers (1 to infinity) and the fractions between any two whole numbers are termed a correspondence or cardinality (i.e. members of a set) of the set of whole numbers and the set of fractions. Cantor called the set of all natural numbers aleph-null and the set of fractions aleph-null+1. Which is larger? If you're actually still with me, let's take a moment to introduce the continuum. This is the name given to the set of all real numbers and exactly how much more infinite is it than aleph-null? As Georg Cantor showed, there were no sets with a cardinality between that of the set of natural numbers and the set of real numbers. Put another way, the natural numbers were aleph-null, then all the real numbers could be was aleph-one. This became known as the continuum hypothesis and the fraction set (aleph-one) seems to be the larger set; one infinity is larger than another infinity. The "larger" infinity is nested with the "smaller" infinity. And the real kick in the ass is that there are other alephs besides the two I just mentioned.
But, mercifully, I will stop here.
By the way, Cantor ended up going through a series of nervous breakdowns which eventually had him permanently institutionalized in the Bonkers Bungalow where he spent the rest of his life writing essays about William Shakespeare.
O God, I could be bounded in a nutshell and count myself a king of infinite space, indeed.

Please don't hate me. 

[tarascon]

I guess I am hated.*



*

Spoiler (hover to show)

Shameless bump.

[goldshirt*9]

hated by whom ?

[smokester]

hated by whom ?

Some skirt that are fed up having to take flight in high heels.

[tarascon]

Women in heels don't appeal to me. I prefer women in boots or sneakers. 
I figure I'm hated for persisting in this hare-brained thread.

[brickbatz]

I'd have to understand it or give a poo to hate over it.

[goldshirt*9]

http://www.bbc.co.uk/news/uk-34444233

Edward Snowden interview: 'Smartphones can be taken over'
interesting but not surprised in the least.
runs off to get an old nokia out lol

[xtopave]

Edward Snowden interview: 'Smartphones can be taken over'

Poor people who might take over my phone. They'll end up like Percy Wetmore in The Green Mile. 

[dweez]

Blackphone 2
http://money.cnn.com/2015/09/29/technology/blackphone-2/index.html

[goldshirt*9]

a snip at the price

[smokester]

http://www.bbc.co.uk/news/uk-34444233

Edward Snowden interview: 'Smartphones can be taken over'....

I'd welcome the company.

[6pairsofshoes]

@t, I have a friend who is a professional mathematician.  He specializes in things like cohomologous and other imaginary spaces.  It seems like an extension of topology.  He works in a field known as mathematical physics.  I'm mostly unfamiliar with much of what you described above, although I did read some non-Euclidean geometry in a college history of mathematics course.

Math is interesting for its ability to describe space, movement, volume, and also to project conjectural spaces via those same methods of description.  It's a logical system that enables you to set up a series of definitions, terms and specific operations or functions that can be performed on those terms.  Rules.  Once those are established, you can play with the items set forth and see what results.  While mathematics may have evolved out of pragmatic real life applications, it eventually acquired increasingly abstract ideas, entities (like ZERO) and fields of description.

In short, it's not surprising that this would appeal to you.  I have good computational skills, but I struggled with Calculus.  I suspect it was due to the perfect storm of a bad textbook and a sucky lazy professor.  I was certainly eager to learn, but after spending hours on problem sets and getting no response to questions about them, and getting sick of observing the prof flirting with the other women in the class instead of teaching, I dropped the course.

@8ully, there are so many different ways to be intelligent.  You may have difficulties in some areas, but you are a genuinely bright guy.  Never let anyone tell you otherwise.

[tarascon]

@8ully, there are so many different ways to be intelligent.  You may have difficulties in some areas, but you are a genuinely bright guy.  Never let anyone tell you otherwise.

I absolutely agree with that post, 6.

@t,...
In short, it's not surprising that this would appeal to you. 

Lest anyone give me credit where none is due I have to repeat what I'm sure I've posted before (Having just returned from a two day train trip and very much sleep deprived, I am very tired and don't feel like hunting up and quoting that post)... Edit. Duh, the OP.

I absolutely suck at doing arithmetic but found out rather late in life that I am able to read material on mathematical concepts--am quite good at that, in fact--and comprehend a lot of it. Where that ability comes from is an utter mystery to me! My passions are Number Theory (Primes and sets, for example) and the Transfinite numbers (and multiple infinities of the number line) which Cantor "discovered." For me, the trick is to read this stuff as if it were imaginative science fiction. I also very much enjoy mathematical physics and tackle that the same way.
As a youth, the systematic destruction of any sense of wonder when it comes to things like math & science--as "taught" in school--pretty much ensured that boredom and a general bewilderment would quash the desire to try and understand wtf they were getting at.

[smokester]

To be fair there is a massive distinction between mathematics and arithmetic, and they are barely related to one another. Mathematics is beautiful, elegant, abstract, theoretical and philosophical, but completely unnecessary and desperately unsuited to schoolchildren: arithmetic is absolutely necessary, and essentially simple, therefore it must be taught to all at school, but because it is so simple it is boring.

Someone misguidedly decided that the beauty and elegance of mathematics may attract the young and so they mix it in to the arithmetic - this causes nothing but problems.

Adding is easy. Anyone can learn to do it, and everyone should. Once you have the hang of adding, taking away, repeatedly adding (multiplying) and its inverse (dividing) are easy too. And that is where school can justifiably finish. If all schoolchildren came out of school with a perfect grasp of these four things, then their time at school was not wasted. We need to dedicate our not inconsiderable resources into making this education effective, even though the subject matter is desperately unattractive to children.

But there is no excuse for subjecting generation after generation to calculus, algebra, matrices, logarithms, geometry, statistics or any of the other stuff. That is wonderful, mind-expanding stuff, but completely chuffing useless to 99.99 % of the population.

We mathematicians love the beauty of our art, but it is totally unfair to subject each generation of schoolchildren to it.

In my son's case: he likes "calculus, algebra, matrices, logarithms, geometry, statistics" because understanding gives him a thrill - whether he ever uses it on the real world or not.  A bit like the off-side rule to millions of pub goers.

[smokester]

Yup. Some people like (and are good at) ballet, opera, painting, acting, dancing and a bunch of other things: they should be free to follow their hearts, and we should spend taxpayer money to support such learning, but it shouldn't be compulsory for everyone to do it.

We have developed a core curriculum in which there are a set of prescribed subjects that everyone must learn - in itself a good idea - everyone should have a grasp of English and Science (and there may even be a case for some grounding in a few apparently useless humanities and/ or languages), but my point is that the compulsory element should include arithmetic but not mathematics.

I am of the opinion that most lawmakers and educationalists are blind to the difference - possibly because of the asinine insistence of calling the sums that we do in kindergarten "mathematics" "maths" or even "math" in the apparent misguided belief that there is no difference between arithmetic and mathematics.

Forcing all children to do something useless and unnecessary is, in the modern idiom, abuse.

Kids aren't kids for that long, even less when they were the ones to judge when they are old enough to stop doing what they are told. You are left with a brief opportunity to cram what you can into one of their ears, knowing full well that most of it will fall out the other. If you're lucky, they may well learn enough in that period to allow them to further themselves under their own steam.

Never happened for me. I gave up lurnin' at around the age of eleven and it shows every day in some way or another.

The 3 Rs for me consist mainly of rum.

[tarascon]

The 3 Rs for me consist mainly of rum.

Riemann https://en.wikipedia.org/wiki/Bernhard_Riemann
Ramanujan https://en.wikipedia.org/wiki/Srinivasa_Ramanujan
Robson https://en.wikipedia.org/wiki/Eleanor_Robson