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tphyahoo2

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Thanks for articulating this.

https://math.andrej.com/2010/03/29/proof-of-negation-and-pro...

also

"It’s fine to use a proof by contradiction to show something doesn’t exist. When the assumption that it does exist leads to a contradiction, then that shows it can’t exist.

It’s not so fine to use a proof by contradiction to show something does exist. Here’s the situation. The assumption that it does not exist leads to a contradiction. What can you conclude from that? You would like say “therefore it exists”. But you haven’t got any idea what it is. You may know it’s out there somewhere, but you have no idea how to find it. It would be better to have a proof that tells you what it is.

That’s a difference between what’s called “classical logic” and “intuitionistic logic”. In classical logic, proof by contradiction is perfectly accepted as a method of deductive logic. In intuitionistic logic, proof by contradiction is accepted to show something doesn’t exist, but is not accepted to show something does exist."

David Joyce, https://www.quora.com/In-math-are-there-any-proofs-that-can-...

"In constructive mathematics, proof by contradiction, while not universally rejected, is treated with caution and often replaced with direct or constructive proofs."

  (gemini llm answer to google query: constructive math contradiction)
"Wiles proved the modularity theorem for semistable elliptic curves, from which Fermat’s last theorem follows using proof by contradiction."
  https://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_Last_Theorem
So, will the Lean formalization of FLT involve translation to a direct or constructive proof? It seems not, I gather the proof will rely on classical not constructive logic.

"3. Proof by Contradiction: The core of the formal proof involves assuming ¬Fermat_Last_Theorem and deriving a contradiction. This contradiction usually arises from building a mathematical structure (like an elliptic curve) based on the assumed solution and then demonstrating that this structure must possess contradictory properties, violating established theorems. 4. Formalizing Contradiction: The contradiction is formalized in Lean by deriving two conflicting statements, often denoted as Q and ¬Q, within the context of the assumed ¬Fermat_Last_Theorem. Since Lean adheres to classical logic, the existence of these conflicting statements implies that the initial assumption (¬Fermat_Last_Theorem) must be false."

(gemini llm answer to google query: Lean formalization of fermat's last theorem "proof by contradiction")

I agree, and this is a reason I am glad bitcoin exists.

My point is that there is nothing stopping bitcoin from being used in a paper cash like way, any more than any other value carrying token.

Bitcoin without government support? Possible, but inconvenient and dangerous. Bitcoin with government support? More nice things.

Currently we are in the "with government support" world, more or less. I hope this continues.

Anyone can issue (paper) cash.

Cash is just a paper IOU for some other thing. With 100 dollar bill, that thing is 100 USD. You could also issue paper for gold backed IOU, or gold itself, or bitcoin.

https://en.wikipedia.org/wiki/Wildcat_banking

Counterfeiting paper is a problem, so you need force against this, and this is why the government is generally involved. But what kind of paper counterfeiting is enforced against, is just a legality. Currently the wost thing to counterfeit is 100 dollar bills. Law could be changed to make it equally bad to counterfeit gold bills, or bitcoin bills.

Saying bitcoin is less private than cash is a category error.

These stories are a way of keeping alive the memory of the victims.

In this case the (alleged) murderer was even tracked down and brought back for a second trial, years later. Songs can keep rage alive for a community.

They're great stories, and it's not strange at all.

Good article.

You can mint new fiat currencies. You can mint new cryptocurrencies. You can issue gold coins diluted with base metals.

But only one cryptocurrency can have the greatest proof of work. Unlike with counterfeit gold, this is easy and cheap to verify. And the cryptocurrency with the greatest proof of work is most secure (against 51% attack) from those who would seek to weaken, control, or destroy it. By its definition, proof of work crypto is a winner-take-almost-all market.

Capital controls are not necessary for a bitcoin dominated world.

I don't think most bitcoin maxis would claim bitcoin can fix capitalism. Any more than gold could fix capitalism.

Hard money is the least bad option. The universe is still cruel, and life is unfair.

The irony is that communist states love gold, and bitcoin.

Venezuela, like usual for marxist states, confiscates valuables from individuals that manage to squirrel some. Bitcoin, bitcoin miners, whatever can be confiscated and operated to provide hard currency for the government.

Beware those who will help you, by denying you freedom.

"If you read the full answer, you would see that his position is that doing that is better than not doing it. If you are correct that it is even more difficult to do so, then his position is that bitcoin is even worse than gold in this regard."

Yes, I did read the full answer. And yes, (according to him) it is.

Yanis is a marxist, as others in this thread point out. Point 10 in communist manifesto, calling for a state central bank, is incompatible with both gold and bitcoin, and pretty much any other form of personal money beyond maybe some petty cash.

""10. A state bank, whose paper issues are legal tender, shall replace all private banks. This measure will make it possible to regulate the credit system in the interest of the people as a whole, and will thus undermine the dominion of the big financial magnates. Further, by gradually substituting paper money for gold and silver coin, the universal means of exchange (that indispensable prerequisite of bourgeois trade and commerce) will be cheapened, and gold and silver will be set free for use in foreign trade. Finally, this measure is necessary in order to bind the interests of the conservative bourgeoisie to the Government."

https://www.marxists.org/archive/marx/works/download/pdf/Man...

Communist Manifesto, Demands of the Communist Party in Germany / 10 Demands

"Given all this, you may be puzzled to hear me call myself a Marxist. But, in truth, Karl Marx was responsible for framing my perspective of the world we live in, from my childhood to this day. This is not something that I often volunteer to talk about in “polite society” because the very mention of the M-word switches audiences off. But I never deny it either. After a few years of addressing audiences with whom I do not share an ideology, a need has crept up on me to talk about Marx’s imprint on my thinking. To explain why, while an unapologetic Marxist, I think it is important to resist him passionately in a variety of ways. To be, in other words, erratic in one’s Marxism."

https://www.theguardian.com/news/2015/feb/18/yanis-varoufaki...

Lots of weasel room here. But basically, Varoufakis doesn't believe people should have personal financial freedom. And he makes a good case for it!

But no thanks.

Even if this untraceability / unstoppability was possible, it might not be as revolutionary as you'd think.

It's sort of the same problem as email with pgp. You not only have to secure your email, you also have to secure your counterparty and anyone he forwards your email to. Money is like that as well.

So even if monero wins, or bitcoin becomes like monero, there'd still be tax.

There was tax under gold. Bitcoin isn't about ending tax.

I think a bitcoin economy in stablestate would have about the same amount of lending as a gold economy under the gold standard. There is enough history during gold standard periods to have some idea how this would be.

https://en.wikipedia.org/wiki/Gold_standard

These times weren't perfect, but no time ever is.

In short there would be less lending than under fiat with MMT, but certainly not zero lending. On the plus side, much more stability, and no hyperinflations, ever.

Seems worth it to me.

We may well see this scenario play out in our lives.

Countries with free speech and no capital controls, ie the west, bitcoinize.

Countries with controlled internet and capital controls, ie china, act like fiatland.

Who wins the war. It's not an easy question. It's not an obvious answer.

But it's true. You can't have both.

*****

One reason to hope for the west over fiatland in a conflict is, defense contractors and soldiers and police would rather get paid in a hard currency.

So at some point fiatland may just collapse.

That doesn't mean no more wars.

Bitcoin country 1 can tax and borrow, and wage war against Bitcoin country 2, who can do the same.

I never subscribed to bitcoin equals forever peace. Bitcoin doesn't cure cancer either, or wash your car.

But the extent of the taxing and borrowing is at least constrained.

"In practice, most people dealing with Bitcoin are dealing with it through ~banks~ exchanges which gave them a Bitcoin denominated IOU; and which may or may not be engaging in fractional reserve banking."

You're not wrong. Most people do it with IOUs, ie exchanges. But most people, don't have most of the bitcoin.

"Crypto Exchanges Hold 6.6% of Bitcoin Supply – One of the Lowest in History"

https://bitcoinke.io/2021/09/percentage-of-bitcoins-on-excha...

I'd like this number to be even lower. And as more exchanges (and governments) default, I expect it will be.

"* hard to store securely - I'd class this as a point for Gold."

fair to debate, a lot does get lost because people lose paper backups. but is this really harder than gold? I think it's largely unfamiliarity that will improve with time.

"* expensive to transact with at a distance - As opposed to Bitcoin, which is just expensive to transact; and gets more expensive the more people use it, as there is a finite amount of transactions per unit time."

if you don't understand how lightning works, of course you will believe this. lots of fud right now. encourage you to kick the tires here, and actually install a lightning wallet and see. as a retail guy, you can start selling slurpees via lightning, today.

https://medium.com/coinmonks/strike-partners-with-shopify-bl...

no it's not perfect, but it is non custodial. now imagine you are in venezuela or weimar germany.

Yanis was talking about the government central bank, under a time of stress.

Without force, will the government have enough credit?

This is what allows the big re-armaments before / during a war, btw. See for instance Hjalmar Schacht's mefo bills in

https://en.wikipedia.org/wiki/German_rearmament

In this case stealth rather than force but same principle. It's also a lot harder to do stealth with a non-inflating currency that has proof of reserves.

Governments certainly will attempt to issue IOUs backed by bitcoin. And some people will accept them.

If you are willing to trust your bitcoin to an exchange, as many people are, you should certainly be willing to trust your government.

But a lot of people hold their bitcoin offline, in hardware wallets, in cold storage. It's not that hard.

Another feature that bitcoin has, that gold does not, is proof of reserves. Barely any exchanges do this, but this will change with time.

Proof of reserves pretty much makes bitcoin IOUs for the government useless. You can't cheat by printing more.

I think far fewer people will trust their government with bitcoin under a bitcoin standard, than trusted their government with gold under a gold standard.

Particularly after a few governments default.

I discuss this more in depth at

https://web.archive.org/web/20210116135412/https://taaalk.co... (long)

Yanis:

"The Gold Standard is, indeed, a great source of insight into how dangerously primitive Bitcoin maximalist thinking is. Suppose Bitcoin were to take over from fiat currencies. What would banks do? They would lend in Bitcoin, of course. This means that overdraft facilities would emerge allowing lenders to buy goods and services with Bitcoins that do not yet exist. What would governments do? At moments of stress, they would have to issue units of account linked to Bitcoin (as they did under the Gold Exchange Standard during the interwar period)."

The reason governments could do this with gold is that gold is easy to counterfeit, hard to store securely, and expensive to transact with at a distance. So it makes sense to keep it all in a giant vault (a bank, or central bank) and trust the vaultkeeper to issue ious and transact in those.

But bitcoin does not suffer from these defects.

I don't think Yanis understands this.

https://nassimtaleb.org/2016/09/intellectual-yet-idiot/