I've had a MathAcademy subscription for some time and it's quite good. I'd say it's best at generating problems and using spaced repetition to reinforce learning, but I think it falls short in explaining why something is useful or applicable. I don't know, most math education seems to be "here's an equation and this is how you solve it" and MathAcademy is undoubtedly the best at that, but I wish there were resources that were more like "here's how we discovered this, what we used to do before, why it's useful, and here's some scenarios where you'd use it."
I have so wanted such resources for years. I have found some and should make a list.
The first time the difference between understanding some math, and understanding what the math meant, was after high school Trig. The moment I started manually programming graphics from scratch, the circle as a series of dots, trigonometry transformed in my mind. I can't even say what the difference was - the math was exactly the same - but some larger area of my brain suddenly connected with all the concepts I had already learned.
While ordering the "Mathematica: A Secret World of Intuition and Curiosity" I came across these books, which looked very promising in the "learning formal math by expanding intuition" theme, so I bought them too:
Field Theory For The Non-Physicist, by Ville Hirvonen [0]
Lagrangian Mechanics For The Non-Physicist, by Ville Hirvonen [1]
The Gravity of Math: How Geometry Rules the Universe, by Steve Nadis, Shing-Tung Yau [2]
Vector: A Surprising Story of Space, Time, and Mathematical Transformation, by Robyn Arianrhod [3]
If you're interested in how vector calculus developed, and who was instrumental, all the way from Newton/Leibnitz to Dirac or so, by way of Hamilton, Maxwell, Einstein and others, then Robyn Arianrhod's 'Vector' is brilliant.
But be warned, it gets progressively harder, along with the concepts, so unless you're conversant with tensors, at some point you will have to put on your thinking cap.
I pay people globally through HSBC all the time. Works instantly.
I never understand this argument anyway. If you can't send funds instantly that isn't because the currently itself can't be transferred instantly - it's because for whatever reason you don't have access to a provider that will provide that service. That's a separate problem and can be solved without having to build an entirely new currency / financial system.
That's actually quite worrisome. I don't really think twice about downloading the top result for things like PayPal or local banking apps if I get a new phone, for example.
Takes like these are so moronic it hurts. I just paid an artist across the globe for some icons; the transaction took seconds to resolve and cost me cents to send via SOL. The closest I've come to that is Canada's eTransfer system, but it only works in Canada.
You are ignoring the possibility he got paid in SOL for some other work. Or the possibility the recipient of his SOL can buy dinner using SOL. This is all possible, even if unlikely.
I'm happy the spam and investment FOMO has died down, but crypto has been insanely useful for making payments for me. It's hard to beat nearly instantaneous international payments with tiny fees.
I wouldn't say it's a Ponzi scheme, but I tend to agree that they aren't much different because the price of the stock or crypto only goes up by the demand for said security. The only thing that matters in the end for an investor is that there's someone down the line that will pay me more for my shares than I did. I don't really care if the valuation is based on pure perception (in the case of most crypto or GME) or solid fundamentals. I've been more successful trading on human psychology and pulling profits early than any other approach I've tried.
But this is an argument that can be applied to any continuous trading, on any moving number. You can (spread) bet on cricket scores, weather, oil pipeline capacity, bandwidth, commodity prices, crypto, carbon credits, whatever, and make money if you can "read" the market and the human psychology of others trading in that market.
BUt, if you are a long term investor, rather than a swing or day trader, the fundamentals of the asset are much more important. The supply-side economics of the asset, its liquidity, volatility, correlation with other asset prices, etc, all come into play, and these are very different between crypto, stocks, commodities, bond, et al.
1) I can send large payments effortlessly. I tried to move large sums using eTransfers last year and the friction is just unreal. I don't give a shit about my bank's arbitrary monthly limits
2) Fuck inflation. The fact that I can't park my money without it losing its value over time is asinine. I shouldn't have to be forced to play the market or spend if I don't want to. Just let people save their damn money.
> shouldn't have to be forced to play the market or spend if I don't want to. Just let people save their damn money.
You are always playing the market, and certainly are doing so when you park your wealth in whatever your cryptocurrency of choice is.
Having currency being optimized for use a liquid medium of exchange while other assets are better as a long term store of wealth is much better than having a currency that tries to compromise between competing purposes and ends up doing neither well.
> The fact that I can't park my money without it losing its value over time is asinine
Forcing people to invest or spend their money is the entire point of inflation. For good reason too, decreasing velocity of money is a major cause of recessions, and tightening of liquidity in the money market always leads to high unemployment.
Great comment, because it hits at something fundamental, and something I also think about a lot when considering the state of crypto today.
Point (2) is very axiomatic in its claims:
> The fact that I can't park my money without it losing its value over time is asinine.
Money will always have some relative value to what you can exchange it for. The reason bitcoin's value has kept up with inflation, is because today its price is determined mainly by speculative demand. Not because there's some cosmological guarantee that bitcoin is immune to inflation.
A few examples: one 1btc buys a small car today. Twenty years from now, when the novelty of crypto has worn off, what is providing the guarantee you'll be able to buy another car with 1btc? Or with 10btc you can buy a house today. Will 10btc buy you a house 20 years from now? If not, does it mean btc lost its value, or does it mean land got more valuable?
There's really no known way to park money and expect it to keep value, just because of its inherent properties. We've been trying for 5000 years.
> I shouldn't have to be forced to play the market or spend if I don't want to
Actually, yes, you do have to, at least if you like to preserve wealth, you preserve it by growing it. That's what investing (and it's degenerate cousin, "playing the market") really is.
Point (1) does hint at some intrinsic value of blockchain-technology. I think we'll know in 5-10 years or so, when we've gone through this correction, maybe some more war or something, whether the technologic properties of blockchain are enough to prop up current crypto prices. Consider as a counterpoint: noble metals are amazing technologies, which have provided value for millennia; from mediums of exchange, to stores of wealth, to their use in medical technologies, for mundane applications like for dishware, or spiritual applications in churches or art, for jewelry ... Really, it's absolutely completely mind boggling how long, how broadly, and how consistently gold and silver have provided value to humans. Yet, they've been poor hedges for inflation over the long term, both gold and silver being very speculative assets, worse than stocks or bonds. How is crypto-technology going to be even more fundamentally better? What is so amazing about blockchain that it's going to defy all other asset classes?
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