Totally disagree. Mathematics is not a science at all because there is no any possible experiments in the Math fields.
And remember what David Hilbert has told about one of his students who decided to go into arts instead of keep learning Math with him. He told "he did not have enough imagination to become a mathematician".
Experimental mathematics is not a field of mathematics, but an approach. In the link you have given I found two approaches called experimental mathematics: proofing theorems by computer contrary to proofing with a pensil, and searching new problems contrary to solving some existing ones.
I was responding to your apparent claim that experimentation is not possible in mathematics. Maybe I misunderstood what you meant.
From Halmos' quote from the wiki page:
"Mathematics is not a deductive science—that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork. You want to find out what the facts are, and what you do is in that respect similar to what a laboratory technician does"
- it sure sounds like he thinks experiment/experimentation a key part of maths.
What evidence would convince you that mathematics is empirical?
If your argument was a tautology then what’s the point?
Would you consider interactive theorem proving to be empirical or not? The sort of experiment you perform is you try to see if the computer accepts your proof or not.
It sure seems like the goal posts are being moved.
Every experiment is an experiment of nature.
Humans are part of nature.
Human constructs are part of nature.
Every interaction that results in the testing or falsification of some hypothesis is a valid experiment. Irrespective of the object being experimented/interacted with.
I am experimenting with (testing/falsifying hypotheses against) your linguistic constructs right now.
I think you're missing the point. Mathematics isn't a natural science, and that's what I was trying to point out. There is a term for doing science on human constructs - it's called social science. Is your thesis that mathematics is a social science?
> Humans are part of nature. Human constructs are part of nature.
Humans physically are part of nature, sure. Human constructs are not considered to be as far as classification in the social and natural sciences.
I am not sure why you are using the phrase "natural science", is there any other kind? Lets revisit with the wikipedia definition:
Science (from Latin scientia 'knowledge') is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
That seems pretty general and all-inclusive to me. Any knowledge about humans; or societies; or the stuff human societies invent is knowledge about the universe. Because we are part of the universe.
Now, you seem to be trying to differentiate the different sciences from one another - tell us why. What's the purpose of drawing a distinction between science and (what you call) "natural science"?
I am not doing so. I am saying that if you want to classify mathematics as a science on the basis of the existence of theorem validation software on which someone may experiment, then it is a science on human constructs, ie, a social science, and not a natural science.
The argument here for math to be a science is very tortured and contrived, but if it has any even technical validity then it makes the argument for math as a social science.
>if you want to classify mathematics as a science on the basis of ... The argument here for math to be a science is very tortured and contrived,
I am not classifying Mathematics as a science on the basis that you claim. I am not even making an argument! All I am doing is empiricism!
I am observing a fact about the universe: What humans call science is any enterprise which builds and systematically organizes knowledge about the universe. I am also observing that Mathematics is one such enterprise. So it's a science.
If you think society's definition of "science" is too broad - that's fine.
If you want to use a narrower definition which renders Mathematics a non-science - that's also fine.
But I am still asking why?
Why does it matter whether Mathematics is classified as a science; or a non-science; or a social science; or a natural science?
I disagree. People haven't had a Mathematics before Pythagoras. All Mathematics people had at that moment was that 1 golden coin + 1 golden coin = 2 golden coins or one copper knife. But trading is not mathematics if not talking about modern things like HFT with broad using of probability theory (and we obviously are talking about ancient times).
Physics is understandable even with way more simple (and way more ancient) species then humans. For example, an ape can take a stick and use more heavy end to make a more powerful hit. Birds seems to understand physics quite well - starting from setting wings while flying and ending to general intelligence of crows.
And BTW why are you concerned that in the pyramid of knowledge (Biology is a science > Chemistry is a science > Physics is a science > Mathematics is a language) there are three sciences and one a non-science?
Mathematics is a language, but then why are you saying there was no Mathematics before Pythagoras? Obviously Pythagoras didn’t invent language! Long before Pythagoras people had been using language for doing and expressing computation.
Pāṇini did it. The Babylonians did it. It then took us a few thousand years to mechanize that knowledge and invent computers as we know them.
As for physics being “understandable” - I think you are conflating the ability to exploit nature with the ability to understand it.
Physics isn’t something “out there”. Available to birds and apes. It it is the body of knowledge (texts, ideas, concepts, formulas, narratives) instrumental to humans navigating nature.
There would be no physics without humans inventing it just like there would be no language without humans inventing it.
I am not at all concerned about the contents; or the structure of the pyramid. I am simply expressing a fact about the pyramid. That which people call science is not founded upon science. It is founded upon the liberal arts, humanities and social constructs (logic, philosophy, mathematics, computation, language) - the pyramid is founded upon human invention.
> Mathematics is a language, but then why are you saying there was no Mathematics before Pythagoras? Obviously Pythagoras didn’t invent language!
He did invent the language. When Pythagoras used to teach some folks the division (mathematical operation required for Trigonometry which is required for building Egyptian Pyramids) he faced with un-understanding of "why we should learn this silly useless numbers?" Then Pythagoras has invented a music (consonance and dissonance at least) and everyone started to learn Math because most of us can hear that numbers which may lead to either consonance or dissonance.
> you are conflating the ability to exploit nature with the ability to understand it.
Yes you are right, I do not see how can you understand Physics/Nature without exploiting anything. And if you are enough successful to exploit something so why not to claim that I have gained some understanding.
> There would be no physics without humans inventing it just like there would be no language without humans inventing it.
I think two instances of "humans" word are extra, that words don't add anything into the discussion of some mathematical and physical concepts.
And I keep staying on my opinion that: if one fly can do something complicated in controllable experiments set by human (kind of pull this rope and get some sugar) and another fly can learn this queue of actions from the trained fly, that means that after the experiment both flies share some physical knowledge about Nature.
>Yes you are right, I do not see how can you understand Physics/Nature without exploiting anything
I am happy to equate exploitation with understanding, but then I don’t see how you could possibly understand Mathematics without exploiting computation.
The pyramids were built at least 1000 years before Pythagoras was even born. If division and trigonometry was needed to build them then the Egyptians understood and exploited division trigonometry before Pythagoras invented the language to explain/teach division and trigonometry.
It is not at all surprising that nobody else could understand (exploit, compute with) a language Pythagoras made up, but eventually he taught (indoctrinated?) some students on how to use his invention.
To compute with; and exploit any language first you must comprehend its grammar and semantics.
Still! The Babylonians could compute the square root of 2 (in practical terms, obviously they didn’t call it “square root of 2”) to arbitrary precision even without having numbers in their Mathematics.
Overall I don’t think we are disagreeing over anything substantial either way. Computation is the controlled manipulation of matter. Manipulating symbols to do useful things is a form of computation.
A fly may have some knowledge sufficient to exploit nature in the moment, but it doesn’t have the knowledge necessary to encode and communicate its knowledge to its peers. And it certainly can’t communicate its knowledge to generations 2500 (or more) years into the future.
The point about Pythagoras is that he made Math really popular and maybe even enough broad to use it for Liberal Arts. The Egyptians which have build pyramids used to keep all their Mathematics in secret, only priests and some high-rankings could learn from their sources - and for limited set of goals.
What about Babylonians, their math (as well as Egyptian's) were too complicated for writing and (unless Greek's) was experienced some lack of integrity. For example, did Babylonians know that the square root of 2 is irrational? Pythagorians knew that exactly.
For me it is much more handy to consider well-known Pythagoras as father of our omnipotent Mathematics instead of some anonymous Babylonian who does not have an epic story about stealing some knowledge from totalitarian company and presenting it to mortals like Robin Good or Prometheas. And in that formulation I consider omnipotent Mathematics to be younger than Physics which even now has not achieved omnipotency level (hint about Theory of Everything).
And sorry but I have nothing to say should a CS be a part of Liberal Arts.
Any experiment has an abstract result. For example: If throwing a rock from the tower of Pisa gave us result that acceleration of gravity on Earth is 9.8 m/s^2 then that number will be exactly same for throwing any other materials from any other tower on the Earth.
I feel like we have a better definition of math than we do of art. Thus it's a lot easier to accurately declare a thing is not math, than it is to accurately declare a thing is not art.
That is the case, because Engineers have a bad understand of global finance, business and money.
That’s why they don’t understand the problems that crypto is solving.
If you look at the comments here, you’ll see that many comments are saying that crypto isn’t doing anything useful.
However, crypto is literally solving the extreme problem of infinitely printable FIAT money and very slow and expensive cross-border transfers, which might be the most impfactful invention of the last 2 decades.
On top of that, crypto adds transparency, accountability, interoperability, decreases fraud in every possible market.
However, hacker news doesn’t understand that, because they simply don’t global finance, global markets, business and moneys.
Your comment arrogant so I expect you will get badly down voted. It is also fundamentally wrong, so I will comment nevertheless. Maybe I can save some poor soul from this naive ideology.
The question is not really about what are the downsides of FIAT money. All solutions have problems. Even if cryptos could solve all problems that FIAT has, that does not mean it is a better solution to the problem that FIAT solves.
The question is really about what problem money solves in the first place. The foremost purpose of is to distribute resources. Money is a completely social construct that does not have any value itself, all value is derived from the promises of those who have resources make. Real world resources, like oil, are what ultimately matters. As a side note, this is also why the Russian sanctions don't really work as well as some people hope for, and they are ultimately a bad idea.
Anyways, I think it's fair to say say that the current financial system has been extremely successful compared to any earlier financial system, such as the gold standard. Everyone who understands finance even a tiny bit knows that a system with finite money supply like gold does not solve the actual problem the current financial system is solving. It may solve some issues that money has, such as efficiency, transparency, and transfer costs, but as a tool for distributing resources it's useless.
So the comparison you are making is meaningless. Even if those problems would be solved, it won't solve the problem money is actually solving.
On top of that, the problems you mention are not problems of money. They are problems of people, of human nature. New money will not fix them.
Screwdriver (cryptos) and drill driver (fiat schema) both can be used to screw. The proponents of screwdrivers are constantly complaining how drill drivers are clumsy, how you can't safely run around with them, etc. But do you really want back the society where you build houses with screwdrivers? Current fiat schema is just so much more than what you think. I assume you didn't study finance or economics, so it might be hard to understand just how many things have been possible because of fiat currencies. Yes, many crisis too, but it put the rate of innovation and growth into steroids. Thanks to it, we now have time to argue in internet about this kind of worthless matters.
> However, crypto is literally solving the extreme problem of infinitely printable FIAT money
Except crypto does nothing to prevent that; and the printability of fiat money is controlled by a number of systems from historians pointing at what happens if you don’t to international treaty to democratic accountability; and the multitude of different cryptocurrencies means it has an echo of the same problem overall only with no accountability, and even within single currencies it has one-dollar-one-vote rather than one-person-one-vote accountability of a democracy.
> and very slow and expensive cross-border transfers, which might be the most impfactful invention of the last 2 decades.
My banks do this at zero cost. Literally zero. Slowest time it a few minutes to show up as a notification on the other bank, normally it’s about as fast as the time it takes iOS to show a notification banner.
> On top of that, crypto adds transparency, accountability, decreases fraud on nearly every consumer product.
Bank can’t refund you if you get ripped off when there’s no bank.
Halifax (UK), Revolut (Lithiuania at the time), N26 (Germany), plus whoever it is backing up my share trading (I read the small print then promptly forgot it because it didn’t matter).
> However, crypto is literally solving the extreme problem of infinitely printable FIAT money
It might be an extreme problem to you, not to everyone else.
> very slow and expensive cross-border transfers
This has been solved again and again by different companies, be it wise.com or others.
> On top of that, crypto adds transparency, accountability, decreases fraud on nearly every consumer product.
Except for the fact that nobody can get their money back after they have been scamed. There is no authority to complain to or reverse a transaction. Wich makes it useless for the masses.
> which might be the most impfactful invention of the last 2 decades.
This is why people are tired of crypto, it has been over 10 years and it has't really changed anything. Crypto enthusiast think that, but it didn't and it won't.
> It might be an extreme problem to you, not to everyone else.
So mass inflation is only an extremely problem to me? This is probably the most false claim possible.
> This has been solved again and again by different companies, be it wise.com or others
Except they constantly freeze user accounts for no reason.
> Except for the fact that nobody can get their money back after they have been scamed. There is no authority to complain to or reverse a transaction. Wich makes it useless for the masses.
Of course there is, all the exchanges have to comply by with law enforcement and that’s what they are doing. This way, since the transactions are all public and can be traced endlessly it’s very difficult to evade law enforcement through scams.
You don't seem to understand what ultimately causes inflation. Not a surprise, as you don't understand money either.
Inflation happens because central banks have been trying to fix structural problems by printing more money, and this time it didn't work out. Sometimes it has worked. If they didn't do that, the problems would still be there. If we didn't have the possibility to print more money, we couldn't even try out if that helps. Ultimately, the structural problems would be worse if financial system was ran on cryptos.
No, if that wasn’t an option, then the root causes such as wasteful spending, not holding politicians accountable, student loan crisis wouldn’t even happen in the first place, because those that are committing those misdeeds currently are the same that are printing the money.
None of those are root causes of inflation in most nations. Hyperinflation perhaps (but even then a collapse in economic output with fixed money supply can mess you up), but normal inflation is put into a deliberate low-but-not-zero level to encourage spending over saving.
> So mass inflation is only an extremely problem to me? This is probably the most false claim possible.
Of course inflation is a problem, but saying crypto could solve it is not true. But even if it could, why would anybody who cares about inflation use crypto, when the value fluctuates so much?
> Except they constantly freeze user accounts for no reason.
And crypto exchanges disappear with all your money. I am not saying there are no problems, just that this problem (simple currency exchange) is solved.
> Of course there is, all the exchanges have to comply by with law enforcement and that’s what they are doing. This way, since the transactions are all public and can be traced endlessly it’s very difficult to evade law enforcement through scams.
So instead of a bank I have a "exchange". All my transactions are public (which is not a positive) and if someone exchanges cryptos from bitcoin to monero then you are still fu*ed.
But ignoring all things we said. All crypto enthusiasts have one important saying: "Not your keys not your crypto". Go ahead and try to explain to someone, how to safely secure their keys and that all their money is bound to them. That if lost/stolen, they have nothing. Crypto makes things (for the avg. user) less secure, more complicated without any benefit. If you fear the government or have specific reasons, go ahed use it, nobody is saying there are no use-cases, just that it's not a useful system for the masses.
The EU did more to solve that issue than crypto ever did.
15'000€ in under 10 seconds, for free, across the entire SEPA zone.
Converting fiat into crypto, transferring it, converting it back still takes far longer. And keeping money as crypto isn't a working solution, because the currencies are so volatile.
Not every crypto solution adds transparency and accountability, look at monero or mixers in other chains.
And then there's the issue with deflation. Inflation is something valuable, because it means doing something today is valued more than what you've done in the past. It encourages people to spend money, to do something with it, instead of saving it forever.
Art gets stolen from Deviant Art etc every day, as it has been for decades. The NFT ecosystem makes it super easy for people to look at listed art and ensure that the proper artist is getting paid. If they fail to do their due diligence, then the NFT they paid for is worthless. The system seems to be working just fine.
NFTs don't prevent theft of IP, nothing does. What it does do is prevent people from effectively profiting off IP theft.
Isn’t one of the points about “slow” social that you don’t need to read 50 posts a day? I would be happy checking in once a week, the same day I am going to post my update.
Yes but it will be an empty desert with anything below 10m users, because only then would an average user would have 100 friends and 10 posts per week.
I would be happy with one, or two posts a day...I only need 5 friends to post a week, at 10 I always have something to read, at 50 friends I am positively awash...
Introverts are a big crowd - a fact the socialites like Zuckerberg tend to forget. This will easily grow...
> You also need to let users upload their contact list otherwise you won’t be able to build your social graph.
In the context of legislation like GDPR and CCPA is this even legal in some jurisdictions any more? Genuinely not sure so any insight gratefully received.
3rd paragraph, although parent may have a typo - rather than 300 - 800 it says 300 - 500
In practice, most strategic nuclear warheads today are in the 300-500 kT range, with tactical weapons being smaller. If we take the American W88 (455 kT) as representative of this range
Your comment is exactly why we shouldn't censor people and the consequence of getting filtered uncontested MSM and Oligarch scrubbed news , if you are insinuating there was an insurrection.
If anyone has become radicalized its the tech oligarch, hollywood, MSM and BOTH the democrat and republican party.
They do nothing but promote hatred , intolerance, and violence among the people in order to keep them fighting with each other.
A Twitter with unlimited speech will become a racist and propaganda hellscape.
Imagine Trump will be brought back on Twitter, he’ll radicalize 40% of Americans into QAnon disciples and try to topple the United States government again. He’ll have thousands like him joining in in spreading mass amounts of fake news exactly like the Russian propaganda machine.
You’ll see extreme science denial, a boatload of new Covid myths, drinking bleach, Ivermectin, Covid is just the flu propaganda all over again, just 5 times worse.
