Thread is about data compression as clearly said in post 8. Your first reply is after post 8. Once again you proved yourself beyond stupid.
Reduce number to a formula?
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Thread is about data compression as clearly said in post 8. Your first reply is after post 8. Once again you proved yourself beyond stupid.
Post # 8, where you asked about expressing 15 bytes of meaninful data in 8 or fewer bytes? It can't be done. Data compression is about identifying unnecessary information. To get your equation, every bit is necessary.
As for Sloot, what he claimed and what has been replicated are two entirely different things. If you can replicate his algorithm, I shall cheerfuly concede that I was wrong about you.
As for Sloot, what he claimed and what has been replicated are two entirely different things. If you can replicate his algorithm, I shall cheerfuly concede that I was wrong about you.
''It can't be done.'' hehe, you know when Wright brothers flew, for a whole month many were still saying it can't be done.
If i told you others flew before Wright brothers not by aerodynamic means but control of gravity you would also say ''can't be done'' and would again be wrong.
If i told you lenz resistance in a generator can be canceled and free energy extracted from magnetic fields you would say ''can't be done'' and would again be wrong... list goes on.
The thing is it CAN be done, Sloot is just one example. When you start realizing this I shall cheerfuly concede that I was wrong about you. Sadly, it might take couple of lifetimes for you to outgrow the ''can't be done'' mindset.
pka
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Once again you proved yourself beyond stupid. That is exactly my response to this whole thread. Who in the mathematical world gives a damn about expression numbers as sums of powers of primes? My question is why or who cares?
Now, I do agree with you there are not infinite ways to express any mathematical sum.
What possible application justifies the question?
pka
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You do not want to get into a spitting contest with me.
Had you said something about linear representational theory for large integers, then maybe just maybe some of us with real mathematical qualifications might have found your post creditable. But no you assumed that you know more than any of the mathematical professionals here. Well lets see how really mathematically challenged you really are. Tell us about the history of your original post in the context of linear representational theory in number theory.
I just put actual number of possible functions in your calculation and what we get is (10+10+235)^7 = 70110209207109380 that is 16 digits.
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lev888
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From http://jansloot.telcomsoft.nl/Sources-1/More/CaptainCosmos/Not_Compression.htm#.Xdyn0PlKiCq
This is not compression, this is merely clever information
transmission economics. Or, if you still want to call it compression,
then call it compression with shared resources. An important trait
of regular compression is that it is self-contained; a blob of
information can be compressed by anyone and decompressed by anyone
else, without needing any external resource but the decompression
algorithm. If, however, the sender and the receiver share some
background resource, which in strict compression terms would be
considered cheating, it is possible to transmit very short coded
messages that merely point to the shared resource.
I know it's not about compression, i already said that so your meme makes no sense, as Roel Pieper said
"It is not about compression. Everyone is mistaken about that. The principle can be compared with a concept as Adobe-postscript, where sender and receiver know what kind of data recipes can be transferred, without the data itself actually being sent."
First comment under the article linked tho says exactly what i was thinking, that he used tiny keys to modulate analog signals and generate far more data than the keys themselvels contained. Sloot said ''digital is over'' or something like that.
lev888
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From Reddit:
A man goes to prison and the first night while he's laying in bed contemplating his situation, he hears someone yell out, "44!" Followed by laughter from the other prisoners.
He thought that was pretty odd, then he heard someone else yell out, "72!" Followed by even more laughter.
"What's going on?" he asked his cellmate.
"Well, we've all heard every joke so many times, we've given them each a number to make it easier."
"Oh," he says, "can I try?"
"Sure, go ahead."
So, he yells out "102!" and the place goes nuts. People are whooping and laughing in a hysteria. He looks at his cellmate rolling on the ground with tears in his eyes from laughing so hard.
"Wow, good joke huh?"
"Yeah! We ain't never heard that one before!"
---
Pretty good compression. Or maybe it's not compression? I'd say definitions are important so we are on the same page.
To quote the great comment from the linked page that reflects my thinking, both the analog part and the pi.
You're allmost there. Sloot just used an analog converter. The analog signal was created by a device that was parametrized by the data on the chipcard. The precise digital measuring of the output of the analog signal then generates the digital sequence. Digital compressors are extremely limited because computers use integer or real data to work with. Analog systems can contain millions (some unlimited) of times the quantity of information that digital systems contain.
Sloot was a tv-technician in the transition period from high-quality analog technology to the digitalisation. He made the link between the two. His technique would or will ruin a whole industry, making ''our'' hich-tech IT based on digital processing completely obsolete.
For the one who does not understand the upper part: Consider a circle. The relation between diameter and circumference is the nubmer PI. Thats, 3.1415... and an inifinite numer of digits never recurring. Thats quite an amount of information in a simple analog thing.
There are other simple analog things that contain lots of information, even if you stay in the ''rational number'' range. Every movie, ever made on DVD and goïng to be made on DVD or every file on a computer in the world can be drawn by a single line on one sheet of paper: the slope (Y/X) as a finite row of digits can be the result of a digital measurement. Replace the sheet with a (virtual) tv-screen, and you have the SLOOT-compression, or something like. It's a digital to analog- and reverse thing. No more no less.
Sloot himself spoke about the ''end of the digital era''.
You're allmost there. Sloot just used an analog converter. The analog signal was created by a device that was parametrized by the data on the chipcard. The precise digital measuring of the output of the analog signal then generates the digital sequence. Digital compressors are extremely limited because computers use integer or real data to work with. Analog systems can contain millions (some unlimited) of times the quantity of information that digital systems contain.
Sloot was a tv-technician in the transition period from high-quality analog technology to the digitalisation. He made the link between the two. His technique would or will ruin a whole industry, making ''our'' hich-tech IT based on digital processing completely obsolete.
For the one who does not understand the upper part: Consider a circle. The relation between diameter and circumference is the nubmer PI. Thats, 3.1415... and an inifinite numer of digits never recurring. Thats quite an amount of information in a simple analog thing.
There are other simple analog things that contain lots of information, even if you stay in the ''rational number'' range. Every movie, ever made on DVD and goïng to be made on DVD or every file on a computer in the world can be drawn by a single line on one sheet of paper: the slope (Y/X) as a finite row of digits can be the result of a digital measurement. Replace the sheet with a (virtual) tv-screen, and you have the SLOOT-compression, or something like. It's a digital to analog- and reverse thing. No more no less.
Sloot himself spoke about the ''end of the digital era''.
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Hehe, yea they are important, sometimes can mean difference of life and death, but in this example, it can be called compression despite the method, and an extreme one for that matter.
There is no such thing as digital, i thought about that long ago, all is analog in nature including the digital signals. Analog rules!
An interesting proposition, but demonstrably wrong.
A sum is a number. Let that number be n. Then the expression kn/k = n. But even if we restrict k to the positive integers, we get an infinite number of such equivalent expressions. And this does not exhaust the expressions that are equivalent to n.
lev888
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True, but OP wants to limit the space for storing the numbers.
What the OP wants to do has changed several times. He seems to believe that a bit string of length a can encode the same information as a bit string of length b, where a < b. I think he eventually wants us all to agree that Sloot had something. I am not going delve into that because I am utterly uninterested in unreplicated results (if, that is, there was even anything to replicate).
He started by asking for a formula for a number. Presumably he meant an expression. Pka says that there are only a finite number of expressions equivalent to a number. That is demonstrably false. He may have meant that there are only a finite number of expressions that are equivalent to a number and can be stored in fewer bits than the number itself, but he did not say that. I would be interested if it is true that any number can be expressed in fewer bits than its binary representation, and I'd not be surprised that only a finite number of ways exist to do that.
pka
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It is true. It is impossible to make an infinite list of any kind. Now of course we can make expressions that represent such lists but the expression itself is not infinite.
I said that you can put a subset of such expressions into one-to-one correspondence with the positive integers. I said nothing about an expression that is an infinite list. According to your argument, the number of positive integers is finite because it is physically impossible to list them.