Does True Randomness Exist In Mathematics?

This is a bit of an overspill from the Religion post, but I'd be interested to find out if true randomness exists in maths? I've done a bit of a google, but cannot understand much of what I've read, though one site said that randomness cannot be achieved by any algorithm, and that implies it is absolutely impossible to describe randomness in any logical way.

Is this correct. I believe the slot machines in Vegas use a pseudo random number generator; and I'm guessing that a true random number generator would be better?

So, simple question, does true randomness exist in mathematics?
It exists in percievable reality. Whether it exists in reality just necessitates a larger equation, possibly larger than present computing power could resolve.

Maths cannot generate you a random number however, and for that matter no computer or computer programme can, because computers merely deliver an output based on the values you enter into it. consequently, if you taught one computer the programme that another computer was using in its random number generator, it would evedntually be able to predict the results.

In real life, things like leaves falling off trees have thousands more values going into them, weight, temperature, surrounding breezes, wind resistance, that mean it is much less predictable, though a large enough computer given all the variable parameters could still predict the point it would land at.

(all thta becomes irrelevant if your definition of "random" is equal to "that which cannot be predicted" in which case its a tautology)
Computers can't generate random numbers because they are finite state machines. Fundamentally, they're just a big box of transistors, each of which acts as a switch that can be either on or off. The computer moves between states in a predictable manner, governed by a program.

I don't think that a mathematical function can be developed to generate truly random numbers, although there are mathematical techniques like the Poisson distribution in statistics and the wave functions in quantum mechanics that try to predict the likelihood of a random event occurring. The duty physicist will know more about this than I do though.

True random number generators, such as those used in very secure cryptography, are based on natural phenomena like radioactive decay - you can never predict how long it will be before that Geiger counter goes click again. More practical devices are based on the 'shot noise' in electronic circuits. For example, current generally only flows one way through a diode but the odd electron will flow "backwards" through the diode if it's reverse biased.

You can buy true random number generators that fit into a slot in your PC or plug into a USB port. I think some Intel CPUs have a rng built in, as do the chips in smart cards like chip and pin credit cards.
Excellent question!

Off the top of my head all I can think of for the moment would be pi (π) but that's cheating a bit because it's an infinite number and therefore as it doesn't have an end you can't ascertain whether it's random.

You could try checking this out too:

BBC - BBC Radio 4 Programmes - In Our Time, Random and Pseudorandom

Melvyn Bragg and his guests discuss randomness and pseudorandomness.
Randomness is the mathematics of the unpredictable. Dice and roulette wheels produce random numbers: those which are unpredictable and display no pattern. But mathematicians also talk of 'pseudorandom' numbers - those which appear to be random but are not.
In the last century random numbers have become enormously useful to statisticians, computer scientists and cryptographers. But true randomness is difficult to find, and mathematicians have devised many ingenious solutions to harness or simulate it. These range from the Premium Bonds computer ERNIE (whose name stands for Electronic Random Number Indicator Equipment) to new methods involving quantum physics.
Digital computers are incapable of behaving in a truly random fashion - so instead mathematicians have taught them how to harness pseudorandomness. This technique is used daily by weather forecasters, statisticians, and computer chip designers - and it's thanks to pseudorandomness that secure credit card transactions are possible.
Marcus du Sautoy
Professor of Mathematics at the University of Oxford
Colva Roney-Dougal
Senior Lecturer in Pure Mathematics at the University of St Andrews
Timothy Gowers
Royal Society Research Professor in Mathematics at the University of Cambridge
Producer: Thomas Morris.
Yet another reference to IOT but as the archive is so extensive I may as well post the link, personally I find it easier to sit back and listen to a debate with experts than read pages worth of technical jargon.

Thanks for the tip Mr Smarty Pants but I was actually referring to the sequence of pi, not the number as a whole. 3.141346543436547346346 ad infinitum does not follow any particular pattern, unlike triangular numbers or square numbers. There's nothing to suggest there's more 4's than 3's or if it goes up in multiples of 8. It is as far as we can tell without a sequence and that's probably because it's infinite.

I'm sorry you can't have them back because I've eaten them.

You can still predict pi. if given enough digits. the fact it is possibly non repeating and non sequential makes it more likely you can predict the numbers.

If you got as far as 14159 then you could predict the next number in the series is 2, and the more digits you give the more reliably you could predict the next number, admittedly if you are only given the figure "1" it may be followed by either a 4 or a 5. but any investigation into a random pattern would require a reasonable starting point. Now if you wrote Pi in binary, youd have a random pattern of 1 and 0 that I think would be impossible to predict but then thats because my understanding of Pi lower than my understanding or red balloons.
Randomness is a perception and as such, can't be proven. If it could, it wouldn't be random - or, at least, it wouldn't be perceived as random.

For example, consider an atomic clock. You can predict that 24 hours after you record the time on it, it will show a time 24 hours ahead. You can record it for the rest of your life and produce the data to confirm your theory that it's not working to a random sequence. But as you lie on your death bed, you'll have a nagging suspicion that if you could have hung on for just five more minutes, you just might have seen an anomaly.

Random only needs to be random for the period that you need it to be random. Take a mechanical sequence of 1,000,000 actions that repeats every hour and you'll spot the repetition. Slow the mechanics down to one action per hour and you'll die before the sequence repeats. That's random enough for anyone (114 years).
Disagree. 1 Million per hour is not sufficient randomness for things like crypto. Child's play for a 1982 BBC B Computer.

However, the selection of the model of computer to resolve a random number problem is extremely random.
:? That's why I said to slow it down. By the time the sequence repeats, it will have served its purpose.
By way of analogy, let's say that I have a safe. I programme the electronic wizardry that allows the safe to be opened with a sequence that repeats every 1,000,000 actions and it operates at one action per hour. The lock requires me to enter the next 10 actions during the hour between one action and the next. It will then take another 10 hours to confirm that I'm right and allow its door to be opened.

You want to break into the safe. If you use mathematics, you can only predict the sequence after a full rotation and even then there's a degree of optimism. So for better confidence, you may be better to wait for, say, three full rotations. And you'll be waiting 342 years. By that time, the cream cake inside will no longer be edible.

So you don't use mathematics, you use guesswork and set a fast random number generator to enter millions of options into the safe. But that still doesn't work because the safe will only accept one set of 10 digits per hour and take 10 hours to process them. You may get lucky at some stage, but it's more likely that you'll be waiting millennia to get into the safe.

To all intents and purposes, to you, the sequence is random.
None of you have ever met my ex wife, obviously. Her brain is a totally random thought generator. Not all of her thoughts make it to the vocalisation stage, but those that do are stunning in their absolute irrelevance to whatever it is you / she is / are doing / saying at any given time.

But wait...... That means that her randomness is predictable .....

Ah there's hope then.
Is this one of those " if a tree falls in the wood with no one to hear it does it make a sound" type questions?

I would define mathematrics as reaching a defined answer via the use of pre determined formulae therefore it has structure and even the the most complex random number generator has some form of pre determined structure. The only randomness would be if the end result was different to what would be predicted by study of the formula.

Therefore is a wrong answer the only true randomness in mathematics.
Is this one of those " if a tree falls in the wood with no one to hear it does it make a sound" type questions?

I would define mathematrics as reaching a defined answer via the use of pre determined formulae therefore it has structure and even the the most complex random number generator has some form of pre determined structure. The only randomness would be if the end result was different to what would be predicted by study of the formula.

Therefore is a wrong answer the only true randomness in mathematics.
No, because even a wrong answer in maths has logic to it.
I can prove randomness exsists in maths. Ask me any mathamatical question twice and I will give you a different answer.

God I'm shit at maths
Does True Randomness Exist In Mathematics?
Interesting. Do truly random events occur anywhere? Evidence from eodmatt et al. gender watch would suggest so. Mathematics is a language apparently, but is it currently sophisticated enough to describe such an event? If it is then someone will probably have modeled it somewhere. Prepared to take that one on faith, like the computer waking up when I press the button with the hieroglyph on it.


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