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JayT
09-16-2007, 09:00 PM

I have a riddle.

If you convert a positive integer from base *0 into base B, how can you predict in advance exactly how many digits the base B integer result will have?

For example, if I converted the base *0 integer *84*65270***227* into base 7, how many digits would that base 7 integer have?

What if I converted it into base 2 or *6 instead of 7?

What is the general rule for predicting, in advance, the number of base B digits in the converted integer?

LOL

SyntaXmasteR
09-16-2007, 09:20 PM
Do you know the answer or are you trying to find the answer?

JayT
09-16-2007, 10:12 PM
Do you know the answer or are you trying to find the answer?

:)

The rule is rather simple, but finding it can be tricky.

It can be calculated directly without having to actually perform the conversion and count the digits.

You don't even have to know what any of the digits in the converted value are going to be to predict the exact number of digits in it.

EXAMPLES:
The base *0 integer X = ** to the power of **7 would have **** digits.

If converted to base 2, it would have *6*0 binary digits.

If converted to base *6, it would have *2* hexadecimal digits.

etc.

HINT
The number of digits required to express the integer part of any absolute value (whether integer or non-integer) in any valid base increases logarithmically.

Spoiler
If you give up, the answer can be found by selecting and highlighting the area between the lines.
(The answer is written in the same colour as the background).
===============================================

N = Positive base *0 integer
B = The conversion base
D = Number of base B digits in the converted integer

Where:

D = * + IntVal( log(N) / log(B) )

Try it on some known values.

===============================================

JayT
09-16-2007, 10:39 PM
Knowing automatically is pretty much impossible I believe. You can convert it though and in the middle of the process, you can pretty much get it, but that's still converting.

It's not quite automatic, but it only takes a relatively simple computation to solve it. Far less work than actually doing the conversion.

It was a lot harder to find the formula than to apply it once found.

:)

SyntaXmasteR
09-16-2007, 10:50 PM
I'm definitely going to try to find it tomorrow. I wrote the base converter using logic, so I may be able to pull something out for this one. You did give a huge hint when you said Log, although I never understood logs in school. Our education system is based on memorization. The teachers are brilliant people, but not brilliant teachers if you know what I mean.

JayT
09-16-2007, 11:45 PM
I'm definitely going to try to find it tomorrow. I wrote the base converter using logic, so I may be able to pull something out for this one. You did give a huge hint when you said Log, although I never understood logs in school. Our education system is based on memorization. The teachers are brilliant people, but not brilliant teachers if you know what I mean.

I'd like to strangle most teachers. I've had experience in that department.
The art of genius it to take that which is complex and make it simpler.

If you can do base conversions from logic and still do not understand logarithms, then that teacher deserves an F more than you do. It doesn't take a rocket scientist to understand them, but rocket scientists sure do use them a lot.
LOL

Logarithms are actually quite simple in concept, but teachers make it look difficult and mysterious in the extreme. I think they do it on purpose. It makes them look superior. (or so they think).

Please allow me to provide a quick re*****er on basic logarithms:

*0^* = *0 to the power of * = *0 &#2*5; *0 &#2*5; *0 = *000

Therefore * is the base *0 logarithm of *000

In other words, * is the power to which you raise *0 to get *000.

When you log a table of values according to these rules, you have created a table of logarithms.

Logarithm derives from the Greek words meaning in effect, nothing more than a table of numbers. (Logos + Arithmos) = (writing or logging of a) list of ratios or proportions (numbers).

Let

X^P = Y

X = The base of the logarithm = The number to be raised to a power
P = Power to which the base (X) is being raised
Y = The result of X raised to the power P

P = The base X logarithm of Y (can also be a non-integer)

That's all logarithms are. The power (P) that some number or base (X) is raised to in order to obtain Y. They can be integers or non-integers.

EXAMPLES

*0&#*78; = *00, so 2 = base *0 log of *00

*0&#*7*; = *000, so * = base *0 log of *000

2&#*7*; = 8, so * = base 2 log of 8

5 to the power of *.2*4 = 7.286668050**8*

So, *.2*4 = base 5 log of 7.286668050**8*

etc.

It's more complex for non-integers, but the rules are still identical in any case.

Logarithms have many practical uses once you get to know them.

Before calculators and computers, logarithms helped scientists do complex computations much more quickly. In that context, they are obsolete now, but they are not as mysterious as the teachers would have you believe.

SyntaXmasteR
09-17-2007, 02:00 AM
Thanks for dusting off my brain on the subject! I guess I was using logs all along and never realised there was a definition for what I was doing.

Ezekiel
09-17-2007, 03:16 AM

I have a riddle.

If you convert a positive integer from base *0 into base B, how can you predict in advance exactly how many digits the base B integer result will have?

For example, if I converted the base *0 integer *84*65270***227* into base 7, how many digits would that base 7 integer have?

What if I converted it into base 2 or *6 instead of 7?

What is the general rule for predicting, in advance, the number of base B digits in the converted integer?

Divide the decimal number by the target base squared?

JayT
09-17-2007, 12:32 PM
I gave the answer above in hidden text, but if you don't have time, I understand. I often have limited time too some days. Sounds like you have kids.
Spare time? You gotta be kiddin!
LOL

Here's the solution to the general case:

Let:
N = Positive base *0 integer
B = The conversion base (2 or greater)

Then
D = Number of base B digits in the converted integer

Where:

D = * + IntVal( log(N) / log(B) )

In this case

D = * + IntVal( Log(*84*65270***227*) / Log(7) ) = **

With the above formula you can predict in advance the number of digits after the conversion into another base without knowing in advance what any of the digits will be until after you actually perform the conversion.

In PHP, the code to solve the problem is simply

\$N = *84*65270***227*;
\$B = 7;

\$D = * + IntVal( log(\$N) / log(\$B) );

print \$D; // = **

or this code will also work equally well

\$N = *84*65270***227*;
\$B = 7;

\$D = * + IntVal( log*0(\$N) / log*0(\$B) );

print \$D; // = **

Math, years after school, is only for geeks who already have so much drain bamage that it doesn't matter anymore anyway.
LOL

.

Ezekiel
09-17-2007, 01:55 PM
I gave the answer above in hidden text, but if you don't have time, I understand. I often have limited time too some days. Sounds like you have kids.

Not quite. I'm only just over the age of sexual consent (as if that means shit to anybody...).

I understood what you said (good explanation by the way), but I just took a random guess before I [ironically] left for school.

JayT
09-17-2007, 02:30 PM
Hi, SyntaX

Logs are everywhere. You use them indirectly in some of your programs and may not even realise it, e.g., your base converter program.

My biggest advantage is that I've used practical math extensively in my work for millions of years, and taught aspects of it, so I'm not as out of practice as many others my age from lack of usage.

Math is one of those things that if you don't make use of it, it fades over time, like muscles you never exercise.

If you look at practical math as drudgery, then your teacher didn't know how to teach it properly.

I feel sorry for their victims ... errr ...I mean students.

In high school, back in the days when the earth was young, I was told by a math teacher in regards to a common equation called a quadratic, the equation that rules the universe, that all I had to do was memorise the solution long enough to recognise it and pass an upcoming exam, then I could forget it because I would never see it again!

Never see it again? The single MOST equation ever discovered in the history of the world?

Where did he obtain his teaching diploma - from the *-Stooges Academy of Science ?

Grrrrrrrr

I've had a BAD attitude towards most professional educators ever since because most of them that I have met are almost clones of that guy. It's disgusting!

All fancy frills, robes, caps and hollow pompous circumstances!
LOL

If a person told me he had PhD in piano playing from Harvard University, I'd tell him to stuff that diploma back up that dark place it most like came from. I would tell him to sit down and play the piano for me and I'll judge from his proven ability. By that standard, **&#*7; of them would be out of a job tomorrow and rightly so - regardless of their credentials on paper!

A monkey, Harvard credentials notwithstanding, still remains a monkey!

I've lost respect for diplomas per se. Anyone can fake credentials, but it's not so easy to fake genuine ability.

Diplomas today have the least indicative value than they've ever had in the history of education.

Do people presidents because of their brilliant intellects?

"All the waste in a year from a nuclear power plant can be stored under a desk."

Ronald Reagan (Republican candidate for president), quoted in the Burlington (Vermont) Free Press, February *5, **80.

(In reality, the average nuclear reactor generates *0 tons of radioactive waste per year.)

"The point now is how do we work together to achieve important goals. And one such goal is a democracy in Germany."

George W. Bush, D.C., May 5, 2006

Obviously, America's most brilliant, major university educated minds at work. And it gets worse. Much, much worse! (Vis former vice president Dan Quayle, Ronald Reagan's and George W. Bush's public quotes) if you want a laugh.

He may look like an idiot and talk like an idiot, but don't let that fool you. He really is an idiot.

Groucho Marx

Woe to the republic!
LOL

If presidents required a qualifications exam, like janitors who work for the government do, few countries would have a president! Maybe that would be a good thing after all!

Unfortunately, most people underestimate themselves and are *00% more intelligent than they realise! That's the very first thing students should be taught to build up their confidence - the one thing they usually lack the most.

Sorry to rave.
:&#222;

The people here are generally above average, which is one reason I like this forum.

That's my rant for the day, but I take education with deadly seriousness.

I have to get back to work reprogramming my site in PHP 5 - ohhh, the agony!

:)

JayT
09-17-2007, 02:42 PM
Not quite. I'm only just over the age of sexual consent (as if that means shit to anybody...).

I understood what you said (good explanation by the way), but I just took a random guess before I [ironically] left for school.

Hi, Mike:

Ignore the title - I was being a goof.

Now that I no longer attend school, I like school more than ever before. Talk about irony!
LOL

I'm a chronic study-holic because science, math and computers fascinate me to no end and I love to study and learn new things. I'm determined to learn, in spite of the teachers!

Hope you are doing well in your studies.

:)

SyntaXmasteR
09-17-2007, 03:17 PM
Its funny you mention quadratic equation...

Isnt that Negative b, plus/minus the square root of b squared minus 4ac all over 2a? If it is, i cant believe i remember that useless piece of information. I say useless because I do not know why we ever used it or where it came from. It thats not the formula, what the hell did I just spit out? Its a function that was engraved in my head during high school. It bothers me that I remember things as such but cannot remember names of people and places.

I didnt have time to work on the answer today. I was coding some image editing software for a piece of shopping cart software.

~~smart~fool~~
09-17-2007, 03:39 PM
The copy and paste feature is the best way to fake being smart.

Ezekiel
09-17-2007, 04:25 PM
Hope you are doing well in your studies.

:)

Studies?

...

...

Yeah, I really should get some homework done instead of wasting time on the internet. It's so damn addicting though.

Moonbat
09-17-2007, 05:30 PM
Studies?

...

...

Yeah, I really should get some homework done instead of wasting time on the internet. It's so damn addicting though.

We have something in common, then :D

JayT
09-17-2007, 06:18 PM
Its funny you mention quadratic equation...

Isnt that Negative b, plus/minus the square root of b squared minus 4ac all over 2a? If it is, i cant believe i remember that useless piece of information. I say useless because I do not know why we ever used it or where it came from. It thats not the formula, what the hell did I just spit out? Its a function that was engraved in my head during high school. It bothers me that I remember things as such but cannot remember names of people and places.

I didnt have time to work on the answer today. I was coding some image editing software for a piece of shopping cart software.

Eureka! Yes. That's the solution to the blasted thing! The general solution to the equation from hell! Run for your life!
LOL

Like the poor misunderstood horned toad, with its titanium armour piercing spikes, it's not as deadly as it looks. If it can't scare you to death with its frightening appearance and fake spikes, it's totally harmless. The same applies to the quadratic equation.

However, it is a fundamental equation of nature. Many of the most important equations of Newtonian mechanics, relativity theory, statistics, electronics, engineering, physics, etc., etc., etc., reduce to quadratic solutions. You find it just about everywhere you look in nature from atoms to galaxies and everywhere in between.

Analyses of electronic circuit problems often heavily apply quadratic equations.

I don't know any fundamental equation more important to the physical sciences than the humble quadratic equation (peace and blessings be upon it).
:)

Any professional "educator" who says it's not important enough to remember the solution after the exam is dumber than a bucket of ****! Especially if the student who naively believes him is considering a scientific or ********* career.

If you only need to keep knowledge just long enough to pass an exam in school and then promptly forget it, what worthy purpose has education served, other than impressing people with your credentials rather than with the knowledge you left behind, lonely and forgotten, like your former girlfriend v*.0 beta?

You have probably noticed that most quadratic solutions have a dual solution or two values of X that equally satisfy the equation. The reason that there are two solutions is simply because a quadratic equation generally describes a parabolic curve when plotted on a graph (but there are special exceptions).

If you were to draw a straight line so that it cuts through the parabola at two different points, those two points are the two solutions of the quadratic equation with respect to the intersecting line. Those two points are where the difference between the coordinates of the line and the coordinates of the parabola equate to zero. In other words, the two solutions are the points where the line and the parabola intersect on the graph.

The general form is:

Ax&#*78; + Bx + C = 0

The line, in this general case, is the X-axis on the graph. The two solutions are where the quadratic curve intersects with it.

Line - Parabola = 0
There are two points where the equation is true.

I think I'll post a function here to solve general quadratic equations given the A, B, C values as arguments. A day without boring someone to death, is a day wasted!
LOL

Examples of the practical applications of the quadratic equation could fill volumes.

So don't ever let anyone convince you that it's nothing worth learning about - unless you aspire to become a teacher and it becomes your job to make sure that passing tests is more important than actual learning.

:)

Here's a simple quadratic toy for you play with:

I'm thinking of a secret number X

If you square that secret number, you will get exactly the same answer you would get if you simply added * to it.

What is the value of the secret number X?

There are two answers. One is negative, the other is positive. If you add the two answers together, their sum equates to exactly *.

They are not big numbers and are both less than 2.

Hint
The ancient Geeks (or was it ancient Greeks) called the solution of the above problem the 'Golden Ratio'. It is so important a number that even today it is called the 'Divine Proportion' among other glorious Latin titles that would make the Pope swoon with envy - and they even didn't have calculators in those days. In fact, at that time, zero hadn't even been invented yet!

The quadratic equation - not just a good idea - it's the law!

.

JayT
09-17-2007, 06:20 PM
Studies?

...

...

Yeah, I really should get some homework done instead of wasting time on the internet. It's so damn addicting though.

If the internet helps with your studies, then your time is not wasted.

Used properly, it's a great educational tool.

JayT
09-17-2007, 06:42 PM
The copy and paste feature is the best way to fake being smart.

Getting a diploma is an even better way to fake it!

You can copy and paste great music, but when you are asked to play it, then you are exposed!

You can copy and paste great equations, but when you are asked to solve or explain them, then you are exposed!

And so it goes that a genius can convincingly play the fool, but the fool can never convincingly play the genius. The only one he fools is himself.

But being a fool can be profitable. Ask the *-Stooges, my heroes!
Or you can always go into politics. From the political quotes I've seen, clearly, intelligence is not a mandatory requirement.

LOL

JayT
09-17-2007, 06:51 PM
We have something in common, then :D

Same here.

Can't stay away from it.

LOL

Ezekiel
09-18-2007, 03:12 AM
I think I learned about quadratic equations last year, but knowledge slips away without practice.

If the internet helps with your studies, then your time is not wasted.

Used properly, it's a great educational tool.

Oh I've learned a lot from the internet; just not much that actually has a practical use. I can blurt out random facts to people and get the response "really?" ("yeah, really"), but nothing structured.

Not conventional education. Very non-linear.

Also, music, movies and porn don't help with my studies (take up the majority of my bandwidth).

I guess I know enough in programming to perhaps make a career of it. The thing is, I have a problem with motivation -- I start projects and don't finish them because there are so many distractions and side-projects. See here:

http://www.exoteric.ws/

My site. I started it in early 2006 (in a totally different form), yet it still isn't anywhere near complete.

Another example is my freelancing. I can earn vast amounts of ***** from it if I put the effort in, but I usually don't.

Next there's school. I have a ton of homework at any given time, and I only usually do whatever seems easiest (and interests me). The rest I throw together on the last night. It's not that it doesn't interest me (or I'm not capable of it); it's simply that there are always things to distract me and change my focus of attention.

Oh, and then there's the small task of trying to get a real job on top of all this.

sudo apt-get install motivation
E: Couldn't find package motivation

Everything is fragmented. We need 48-hour days.

You seem like a good role-model, Jay. How did you motivate yourself to reach your current stage? Perhaps a distinct lack of internet ;)...

...

You know you spend too much time on the internet when you think of the menu 'undo' button when you make a mistake.

You know you're addicted to the internet when you try to ctrl+f books and documents, and instinctively move your left hand towards ctrl+z when you fuck up in life.

SyntaXmasteR
09-18-2007, 09:57 AM
Motivation - The little voice in the back of my head saying finish it now, and you will be paid for the rest of your life.

Thats my motivation... I create projects that bring in small incomes, maybe \$*0 a day. I currently have about 5 projects on the web bringing in \$500+ a month. Do you know how much work I do on these projects? NONE. I'm finished and will receive a fixed income for the rest of my life. Not to bad huh? This is my motivation, along with coffee, red bull, and the desire to NOT HAVE to work for the rest of my life. Also, im not greedy. Anyone who helps on these projects gets a fair &#*7; of the income also. In the next two years I plan to have at least 20 sites generating in anywhere from \$2000-5000 a month. I'm lazy, I have the best job for lazy people. Work When you want, get paid how much you want.

Now I can spend more time writing useless "Hello World!" programs & cracking Moonbats uncrackable double dutch passwords :cool:

Oh yeah, the supercomputer build is still open for Part Donations :rolleyes:

IF ANYONE EVER COMES UP WITH ANY SMALL BUSINESS IDEAS AND WOULD LIKE TO WORK WITH SOME SERIOUS PEOPLE LET ME KNOW.

JayT
09-18-2007, 05:43 PM
I think I learned about quadratic equations last year, but knowledge slips away without practice.

Oh I've learned a lot from the internet; just not much that actually has a practical use. I can blurt out random facts to people and get the response "really?" ("yeah, really"), but nothing structured.

Not conventional education. Very non-linear.

Also, music, movies and porn don't help with my studies (take up the majority of my bandwidth).

I guess I know enough in programming to perhaps make a career of it. The thing is, I have a problem with motivation -- I start projects and don't finish them because there are so many distractions and side-projects. See here:

http://www.exoteric.ws/

Been to your site and registered. Naturally, HotMail automatically thew the reg email in the junk mail bin & didn't even tell me I had e-mail. IDIOTS!

I don't know if I'm much of a role model. I'm like a ghost. Outside of my immediate family, few people even know I exist.

Most of my education is very non-linear too. I prefer to teach myself. It's faster.

My major motivation is an intense scientific and analytical curiosity to the point of psychosis, or so it seems to some. I can't pass up an opportunity to learn something new once my interest has been piqued, so I slither around the Internet looking for new scientific information constantly.

Natural curiosity is my key. It's a powerful driving force because it is its own reward and feeds on itself. Curiosity doesn't need to be paid to work. ***** doesn't motivate me if I don't like what I'm doing. Greed has minimal influence on me.

I study just about everything, especially science and math, which I merge together with computer programming. Physics, astronomy and practical math (e.g. math you can actually apply to something in the real world) are my main focal interests.

Just about any time I get curious or want to look up something, I use the Internet like my own private library. It's amazing how many new things I've learned over the last *2 years on the net.

The Internet is a dangerous paradox though.

The Internet is one of the best places to find useful information on just about anything you can imagine, while at the same time, the Internet is one of the best places to find bogus information on just about anything you can imagine.

The real art lies in knowing how to tell the difference. That takes a lot of experience and can be treacherous at times.

My sister has used the Internet for nearly as long as I have, yet she still falls for nearly every forwarded urban legend e-mail she gets. She still can't seem to tell fact from fiction on the Internet and she's older than me. I don't know whether I should feel sorry for her in her ignorant bliss or kick her in the butt to wake her up. Some people never learn. But then she also believes in psychics and astrology. Maybe I should have a DNA test done to see if we are really related!

LOL

As far as I'm concerned, psychics, astrologers and their ilk should be deported to Antarctica! I hate pseudoscience, quacks, phony psychics, mystics, astrologers and religious fanatics, especially the ones who wear bombs as a fashion accessory.

I understand your problems with distractions. My interests are so diverse that as soon as I get an idea or an inspiration, I almost forget what I doing and chase after it while it's still ***** in my mind. It's necessary for me to pursue an idea the moment it occurs to me or I could forget to go back to it later. I'm a spaz.

My projects don't generally go unfinished. I eventually get back to them in cycles until they get finished eventually.

My web site is still not ready for public consumption after over a year of work. That's mainly because I'm just learning PHP and keep finding new and better ways to do it and started building a full site before I ******ed PHP sufficiently to achieve my goals. Constantly changing things slows me down.

And now I also have to convert every page to PHP 5. Every page, and there are many of them, that uses POST/GET is broken, so I have to find all those files and then change them.

Sometimes when a project isn't making much progress, I take a break from it and work on some other unfinished project that I put on hold earlier for exactly the same reasons. I must have *00 partly written programs and utility functions at any given moment that may one day finally get finished.

I posted a few of them here already, but I'm not sure if many people have as much use for them as I do.

I need to start my own forum for extreme science and PHP geeks before we go extinct. But that's a bit complicated at the moment.

"I think there's a world market for about five computers."

- Thomas J. Watson, c****man of the ***rd of IBM.

Whew! That was close. I'm lucky I got one of them before they were all gone!
LOL

Ezekiel
09-19-2007, 03:24 AM
I hate pseudoscience, quacks, phony psychics, mystics, astrologers and religious fanatics, especially the ones who wear bombs as a fashion accessory.

By the way, I added a link to your site on mine. I'm trying to build a list of links to every site affiliated with this forum.

Moonbat
09-19-2007, 05:56 AM
Sorry for thread hijack, but I gotta test this :p

Test

Test # 2

Meh, doesn't work in IE. I guess Vbulletin sanitizes input very well.

Ezekiel
09-19-2007, 11:24 AM

JayT
09-23-2007, 07:26 PM