I’m curious will this new knowledge will lead to new discoveries which might not have been possible due to working with the incorrect lengths in calculations?
It is an example of a new technique being used on a common chemical with an eye towards using it on other chemicals once the technique is proven.
‘And as this technique can be applied to highly symmetric molecules, it opens the door to the characterisation of many chemically important species like polycyclic aromatic hydrocarbons.’ - a researcher quoted in the article
The idea that we can actually delete anything from a non physical system the hyper visor of which we do not control is absolute nonsense. Unless you have control over the physical system and the hypervisor all you can do is destroy your ability to access the information. We can never have confidence of how it truly works back end.
If pi is truly infinite wouldn’t it eventually express a sequence of information which would be self aware if expressed in binary in a programmatic system?
My understanding (which might be wrong) is that just because PI is infinite and non-repeating, doesn't necessarily mean that every conceivable pattern of digits is present.
As a contrived example, consider the pattern:
01 001 0001 00001 etc.
This pattern is infinite and never repeats but we will never see two consecutive "1"s next to each other.
Yes, it doesn't necessarily follow, but it is indeed conjectured that pi is a normal number, meaning all digits appear with the same frequency, but it is not known yet. https://en.wikipedia.org/wiki/Normal_number
The same frequency does not imply every subsequence appears. Consider the modification which rewrites every sequence of 123 to 132. All digits will have the same frequency but 123 will never appear.
You haven't read the link you posted though. Every digit appearing with the same frequency means a number is simply normal and it is not enough to get you what you want in this case (as pointed out by sibling comment). Normal number is a number where every possible string of length n has the same frequency of 10^(-n)
No, you haven't read the link he posted. https://en.wikipedia.org/wiki/Normal_number#Definitions: "A disjunctive sequence is a sequence in which every finite string appears. A normal sequence is disjunctive". If Pi is normal, then it is also disjunctive.
When I was at university, one of the senior number theory professors allegedly said during a tutorial that he accepts the normality of pi on the basis of "proof by why the hell wouldn't it be". With tongue in cheek, of course.
If your argument is "These algorithms have differing degrees of computational complexity" then that doesn't actually demonstrate that one can't be algorithmically determined
Describe the n-th digit of an irrational number without calculating all previous positions of the number.
If pi were a sequence of digits, there is no algorithm to calculate it other than by calculating pi but there is one for op's number. The very fact that he could show the algorithm for creating the sequence of numbers in his post is indicative of that.
For pi such an algorithm doesn't exist (other than calculating pi itself).
I wanted to emphasize this by talking about the "sequence of digits" in my original reply but apparently I failed at explaining this well.
I can't really tell to what extent you're not computing previous digits (or doing work that could quickly be used to come up with these previous digits) with this algorithm but O(n^2) seems quite heavy compared to
O(1) (I expect) to get the n'th digit of op's number.
Maybe I should rephrase it:
My assumption is: If there is an O(1) algorithm to determine the n-th digit of an irrational number x then the number is still "of a different class" than the likes of pi and there OP might not be able to induce things from this "lesser class of irrational numbers"
We know for a fact that pi is truly infinite, there's no "if" there. But we are not sure whether it contains every sequence of (e.g.) decimal digits.
Either way, your proposition works for "the list (or concatenation) of all positive integers in ascending order" as well. There is no deep insight in it, even if it were also true for pi.
if you accept the premise behind this question (which I wouldn't dispute) then theoretically any information at all would be self aware given the right computer
What you want is a disjunctive number, also called rich number or universe number.
It is an infinite number where every possible sequence of digits is present, and therefore, such a number contains the code of a self aware program, as well as the complete description of our own universe (hence the name "universe number") and even the simulation that runs it, if such things exist.
We don't know if pi is a disjunctive number, for what we know, though unlikely, the decimal representation of pi may only have a finite number of zeroes. It means we don't have the answer to your question.
The problem is text messages are being abused for purposes they were never intended. I don’t need people sending me links in text messages. If I wanted that I would use some internet messenger
So what you’re saying is that if you’re communicating with someone over txt because you have an iPhone and they have an android and you want to send them a link then you’d rather ask them whether or not they have the same OTT messenger as you, then tell them you will send a link to them using that, then send the link, rather than simply sending the link to them in the existing thread?
No what I’m saying has nothing to do with Android vs iPhone vs blackberry or any other phone. I can get a link on Skype or signal or anything. I don’t need clickable links in my SMS messages on any phone. Thanks
Whoever agrees with the philosophical idea of “Sin taxes” deserves whatever fascist world they end up creating. The idea that I owe someone because I decide to indulge in something unhealthy for me implies that other people own me.
In an unregulated system there are strong "sin incentives" created by (some) market forces. In a way people are manipulated to become passive couch potatoes craving trash food and sugary drinks, staying awake to binge watch some netflix series. It seems fair that governments take some corrective measures.
So it would seem you are suggesting we have no free will/agency? If so you cannot take credit for any achievement you accomplish or lay blame on anyone for anything no matter the deed because we would be nothing but products of our environments
so-called "sin taxes" are morally neutral but economically efficient. Explanation: one of the problems with taxation is that taxes distort the economy by changing prices which change consumption; "sin goods" have inelastic demand functions--smokers still want their cigarettes--so taxation doesn't change consumption, which lessens side effects of the taxation, for example not increasing unemployment of cigarette workers.
They can also be popular with the electorate ("first they came for the smokers, and I didn't complain because I was not a smoker..") because people make moral judgments which is what you are complaining about, but that's not the reason economists favor them when it comes to advising politicians on tax policy.
I suppose the logical question is what defines justification for any tax on anything; if this can be defined perhaps we can establish reasoning for what items should be taxed and not be taxed.
The idea that you "decide" to indulge in something unhealthy for you, and it was a free decision and companies had nothing to do with it, is a complete joke. We know humans are biased, we know we evolved to like fats more than salad and sugar more than water, we know advertisers influence us, we know companies spend tens of thousands of people's work and billions on advertising and that vastly outpowers a single person's ability to "choose freely", we know companies wilfully mislead and take advantage of our social nature (look at that respectable admirable sports star associated with our product! Look at the work of Edward Bernays and 'Torches for Freedom' getting women to start smoking cigarettes by associating them with the women's liberation movements) and take advantage of our judgement of colour and contrast and intensity (the same product in a cheap box looks less desirable than it in a bright stylish box - and both product, box and brands might be the same company behind the scenes), and our human decision fatigue and temptation for convenience by putting sweets near checkouts. We know companies specifically target children for their suggestibility with methods like adding toys to cereal boxes, advertising during Saturday morning cartoons or loot boxes in games. We know companies lobby for regulations which help them or hurt their competitors. We know society is organised so the big get bigger - McDonalds can outspend a startup Salad bar by millions to one. We know companies pay scientists to lie about the safety and efficacy of their products, and to hide results that say the opposite.
To then whine that fighting back is 'facist' or to suggest that you're so smart you are magically not influenced by any of this is an embarassment. Companies are permitted to operate in society by the collective will of the people, not by divine right. And the people collectively see that a company is taking the piss, they can change the arrangement to improve it. Saying "company, your behaviour is hurting people's collective health, you need to pay some more taxes to cover it" is one way of doing that. If the company then passes the tax increase to you in the form of higer prices, instead of lower profits, that's up to them.
The very framing of it as "sin tax" as if it's a personal failing and not a deliberate corporate abuse of our biological desires and limits, is a kind of victim blaming that anyone "immune to advertising" oughtn't be falling for.
Are you implying that we have no free will and that we lack the agency required for responsibility of our action? Dangerous doctrine there if so; it would imply that all criminals no matter how heinous the crime are victims of the system and thus cannot be punished without said punishment being just an emotional expression of vengeance. It would also mean that you could never take credit for anything you have done because it is just a reaction to your environment. These are only a few implications of a lack of free will/agency
I'm implying that people who dismiss the effects of the environment (advertising) on them by saying they Ayn Randian free-will themselves above it all, are either deluded or malicious. And that instead of systems which are openly hostile to humans which everyone must constantly burn free-will to defend against, we're a lot better acknowledging the predatory nature of advertising, and the limits and fallibility and weakpoints of free will, and en-masse building pro-people systems instead of pro-profit systems.
We are social animals. You derive a lot of benefits from living in society, it has a price.
Get over it and stop following libertarian religious sects, their teachings are only going to make you feel miserable and turn you into the annoying libertarian everybody dreads to meet in a party.
Isn't this a natural aspect of any system of government run "universal" healthcare?
If the state is paying for and controlling your access to healthcare, it seems obvious that restricting unhealthy food or behavior as preventative healthcare would go hand in hand.
No, because most states with a state-run healthcare system simply recognize that health is a basic human right. It's not about incentives, or efficiency, it is about basic human decency.
Even a drug addict who practices unsafe sex and riding motorcycles to do mountain climbing and ski down the slope deserves Healthcare when something bad happens to them, exactly as much as the fitness yoga guru.
As a counter example, look at how many countries have state funded healthcare with restricting unhealthy food or behaviour. By my count 66 countries have state funded health care and 0 have restrictions on unhealthy food or behaviour, (I admit my count was limited)
We do have those restrictions. Consider the UK's Bradford Sweet Poisoning of the 1858 when the standard of putting gypsum as cheap filler in sweets instead of more expensive sugar lead to an accident of using arsenic instead, and lead to regulations on danerous behaviour by chemists and on the adulterations of foodstuffs - https://en.wikipedia.org/wiki/1858_Bradford_sweets_poisoning
And of course there are regulations on insect contamination, mould and fungal contamination, on use by dates, on permitted/banned additives and preservatives, on quality of packaging material, on preparation and handling of eggs; the most egregious "unhealthy food" that causes serious sickness and death quickly has been restricted. What's left is a lot of "compounds over a lifetime of it" kinds of things.
And, of course, public smoking bans are an unhealthy behaviour restriction, so are drug bans.
So in the 66 countries you're referencing, none have restrictions on alcohol or tobacco? No warning labels, taxes or restrictions on sale?
None have different tax rates for staple foods than for packaged snacks or fast food? None have regulations about labeling of food for health claims or disclaimers?
Because all of those things are common throughout all the European countries I'm familiar with, but maybe your list didn't include any European countries
It can occur in free, capitalist societies too. And not in the sense that they "restrict" like an omnipotent government, instead they discourage what is bad and promote what is good. E.g. we have private medical health care here in SA and one of the biggest providers offers all sorts of free goodies and incentives and discounts. They literally partner with stores to get you discounts and points on healthy food choices. Now, I know they also use this data for other purposes but they also happen to help the health of the market. If we can keep it up without having the profit motive distort the benefits too much then its a win win.
Most non physical things you are capable of buying have absolutely no value except what gullible people in large numbers ascribe to them. What you really want to invest in are stars, planets and magical items.
Imagine what scientists would think if particle accelerators started receiving small but measurable patternistic statistical deviations in their data they get while the experiments are running only to discover they are evesdropping on some advanced form of interstellar or intergalactic instant quantum communications, only to realize it’s a bunch of alien gamers of different planets talking shit to eachother
