LessWrong is where I learned about Bitcoin, several years ago, and my greatest regret is that I did not investigate it more as soon as possible, that people here did not yell at me louder that it was important, and to go take a look at it.  In that spirit, I will do so now.

First of all, several caveats:

* You should not go blindly buying anything that you do not understand.  If you don't know about Bitcoin, you should start by reading about its history, read Satoshi's whitepaper, etc.  I will assume that hte rest of the readers who continue reading this have a decent idea of what Bitcoin is.

* Under absolutely no circumstances should you invest money into Bitcoin that you cannot afford to lose.  "Risk money" only!  That means that if you were to lose 100% of you money, it would not particularly damage your life.  Do not spend money that you will need within the next several years, or ever.  You might in fact want to mentally write off the entire thing as a 100% loss from the start, if that helps.

* Even more strongly, under absolutely no circumstances whatsoever will you borrow money in order to buy Bitcoins, such as using margin, credit card loans, using your student loan, etc.  This is very much similar to taking out a loan, going to a casino and betting it all on black on the roulette wheel.  You would either get very lucky or potentially ruin your life.  Its not worth it, this is reality, and there are no laws of the universe preventing you from losing.

* This post is not "investment advice".

* I own Bitcoins, which makes me biased.  You should update to reflect that I am going to present a pro-Bitcoin case.

So why is this potentially a time to buy Bitcoins?  One could think of markets like a pendulum, where price swings from one extreme to another over time, with a very high price corresponding to over-enthusiasm, and a very low price corresponding to despair.  As Warren Buffett said, Mr. Market is like a manic depressive.  One day he walks into your office and is exuberant, and offers to buy your stocks at a high price.  Another day he is depressed and will sell them for a fraction of that. 

The root cause of this phenomenon is confirmation bias.  When things are going well, and the fundamentals of a stock or commodity are strong, the price is driven up, and this results in a positive feedback loop.  Investors receive confirmation of their belief that things are going good from the price increase, confirming their bias.  The process repeats and builds upon itself during a bull market, until it reaches a point of euphoria, in which bad news is completely ignored or disbelieved in.

The same process happens in reverse during a price decline, or bear market.  Investors receive the feedback that the price is going down => things are bad, and good news is ignored and disbelieved.  Both of these processes run away for a while until they reach enough of an extreme that the "smart money" (most well informed and intelligent agents in the system) realizes that the process has gone too far and switches sides. 

Bitcoin at this point is certainly somewhere in the despair side of the pendulum.  I don't want to imply in any way that it is not possible for it to go lower.  Picking a bottom is probably the most difficult thing to do in markets, especially before it happens, and everyone who has claimed that Bitcoin was at a bottom for the past year has been repeatedly proven wrong.  (In fact, I feel a tremendous amount of fear in sticking my neck out to create this post, well aware that I could look like a complete idiot weeks or months or years from now and utterly destroy my reputation, yet I will continue anyway).

First of all, lets look at the fundamentals of Bitcoin.  On one hand, things are going well. 

Use of Bitcoin (network effect):

One measurement of Bitcoin's value is the strenght of its network effect.  By Metcalfe's law, the value of a network is proporitonal to the square of the number of nodes in the network. 

http://en.wikipedia.org/wiki/Metcalfe%27s_law

Over the long term, Bitcoin's price has generally followed this law (though with wild swings to both the upside and downside as the pendulum swings). 

In terms of network effect, Bitcoin is doing well.

Bitcoin transactions are hitting all time highs:  (28 day average of number of transactions).

https://blockchain.info/charts/n-transactions-excluding-popular?timespan=2year&showDataPoints=false&daysAverageString=28&show_header=true&scale=0&address=

Number of Bitcoin addresses are hitting all time highs:

https://blockchain.info/charts/n-unique-addresses?timespan=2year&showDataPoints=false&daysAverageString=28&show_header=true&scale=0&address=

Merchant adoption continues to hit new highs:

BitPay/Coinbase continue to report 10% monthly growth in the number of merchants that accept Bitcoin.

Prominent companies that began accepting Bitcoin in the past year include: Dell, Overstock, Paypal, Microsoft, etc.

On the other hand, due to the sustained price decline, many Btcoin businesses that started up in the past two years with venture capital funding have shut down.  This is more of an effect of the price decline than a cause however.  In the past month especially there has been a number of bearish news stories, such as Bitpay laying off employees, exchanges Vault of Satoshi and CEX.io deciding to shut down, exchange Bitstamp being hacked and shut down for 3 days, but ultimately is back up without losing customer funds, etc.

The cost to mine a Bitcoin is commonly seen as one indicator of price.   Note that the cost to mine a Bitcoin does not directly determine the *value* or usefulness of a Bitcoin.   I do not believe in the labor theory of value: http://en.wikipedia.org/wiki/Labor_theory_of_value

However, there is a stabilizing effect in commodities, in which over time, the price of an item will often converge towards the cost to produce it due to market forces. 

If a Bitcoin is being priced at a value much greater than the cost (in mining equipment and electricity) to create it, people will invest in mining equipment.  This results in increased 'difficulty' of mining and drives down the amount of Bitcoin that you can create with a particular piece of mining equipment.  (The amount of Bitcoins created is a fixed amount per unit of time, and thus the more mining equipment that exists, the less Bitcoin each miner will get).

If Bitcoin is being priced at a value below the cost to create it, people will stop investing in mining equipment.  This may be a signal that the price is getting too low, and could rise.

Historically, the one period of time where Bitcoin was priced significantly below the cost to produce it was in late 2011.  It was noted on LessWrong.  The price has not currently fallen to quite the same extent as it did back then (which may indicate that it has further to fall), however the current price relative to the mining cost indicates we are very much in the bearish side of the pendulum.

It is difficult to calculate an exact cost to mine a Bitcoin, because this depends on the exact hardware used, your cost of electricity, and a prediction of the future difficulty adjustments that will occur.  However, we can make estimates with websites such as http://www.vnbitcoin.org/bitcoincalculator.php

According to this site, every available Bitcoin miner will never give you back as much money as it cost, factoring in the hardware cost and electricity cost.   Upcoming more efficient miners which have not yet released yet are estimated to pay off in about a year, if difficulty grows extremely slowly, and that is for upcoming technology which has not yet even been released. 

There are two important breakpoints when discussing Bitcoin mining profitability.  The first is the point at which your return is enough that it pays for both the electricity and the hardware.  The second is the point at which you make more than your electricity costs, but cannot recover the hardware cost.

For example, lets say Alice pays $1000 on Bitcoin mining equipment.  Every day, this mining equipment can return $10 worth of Bitcoin, but it costs $5 of electricity to run.  Her gain for the day is $5, and it would take 200 days at this rate before the mining equipment paid for itself.  Once she has made the decision to purchase the mining equipment, the money spent on the miner is a sunk cost.  The money spent on electricity is not a sunk cost, she continues to have the decision every day of whether or not to run her mining equipment.  The optimal decision is to continue to run the miner as long as it returns more than the electricity cost. 

Over time, the payout she will receive from this hardware will decline, as the difficulty of mining Bitcoin increases.  Eventually, her payout will decline below the electricity cost, and she should shut the miner down.  At this point, if her total gain from running the equipment was higher than the hardware cost, it was a good investment.  If it did not recoup its cost, then it was worse than simply spending the money buying Bitcoin on an exchange in the first place.

This process creates a feedback into the market price of Bitcoins.  Imagine that Bitcoin investors have two choices, either they can buy Bitcoins (the commodity which has already been produced by others), or they can buy miners, and produce Bitcoins for themself.   If the Bitcoin price falls sufficiently that mining equipment will not recover its costs over time, investment money that would have gone into miners instead goes into Bitcoin, helping to support the price.  As you can see from mining cost calculators, we have passed this point already.  (In fact, we passed it months ago already).

The second breakpoint is when the Bitcoin price falls so low that it falls below the electricity cost of running mining equipment.  We have passed this point for many of the less efficient ways to mine.  For example, Cointerra recently shut down its cloud mining pool because it was losing money.  We have not yet passed this point for more recent and efficient miners, but we are getting fairly close to it. Crossing this point has occurred once in Bitcoin's history, in late 2011 when the price bottomed out near $2, before giving birth to the massive bull run of 2012-2013 in which the price rose by a factor of 500.

Market Sentiment: 

I was not active in Bitcoin back in 2011, so I cannot compare the present time to the sentiment at the November 2011 bottom.  However, sentiment currently is the worst that I have seen by a significant margin. Again, this does not mean that things could not get much, much worse before they get better!  After all, sentiment has been growing worse for months now as the price declines, and everyone who predicted that it was as bad as it could get and the price could not possibly go below $X has been wrong.  We are in a feedback loop which is strongly pumping bearishness into all market participants, and that feedback loop can continue and has continued for quite a while.

A look at market indicators tells us that Bitcoin is very, very oversold, almost historically oversold.  Again, this does not mean that it could not get worse before it gets better. 

As I write this, the price of Bitcoin is $230.  For perspective, this is down over 80% from the all time high of $1163 in November 2013.  It is still higher than the roughly $100 level it spent most of mid 2013 at.

* The average price of a Bitcoin since the last time it moved is $314.

https://www.reddit.com/r/BitcoinMarkets/comments/2ez90b/and_the_average_bitcoin_cost_basis_is/

The current price is a multiple of .73 of this price.  This is very low historically, but not the lowest it has ever ben.  THe lowest was about .39 in late 2011. 

* Short interest (the number of Bitcoins that were borrowed and sold, and must be rebought later) hit all time highs this week, according to data on the exchange Bitfinex, at more than 25000 Bitcoins sold short:

http://www.bfxdata.com/swaphistory/totals.php

* Weekly RSI (relative strength index), an indicator which tells if a stock or commodity is 'overbought' or 'oversold' relative to its history, just hit its lowest value ever.

Many indicators are telling us that Bitcoin is at or near historical levels in terms of the depth of this bear market.  In percentage terms, the price decline is surpassed only by the November 2011 low.  In terms of length, the current decline is more than twice as long as the previous longest bear market.

To summarize: At the present time, the market is pricing in a significant probability that Bitcoin is dying.

But there are some indicators (such as # of transactions) which say it is not dying.  Maybe it continues down into oblivion, and the remaining fundamentals which looked bullish turn downwards and never recover.  Remember that this is reality, and anything can happen, and nothing will save you.

Given all of this, we now have a choice.  People have often compared Bitcoin to making a bet in which you have a 50% chance of losing everything, and a 50% chance of making multiples (far more than 2x) of what you started with. 

There are times when the payout on that bet is much lower, when everyone is euphoric and has been convinced by the positive feedback loop that they will win.  And there are times when the payout on that bet is much higher, when everyone else is extremely fearful and is convinced it will not pay off. 

This is a time to be good rationalists, and investigate a possible opportunity, comparing the present situation to historical examples, and making an informed decision.   Either Bitcoin has begun the process of dying, and this decline will continue in stages until it hits zero (or some incredibly low value that is essentially the same for our purposes), or it will live.  Based on the new all time high being hit in number of transactions, and ways to spend Bitcoin, I think there is at least a reasonable chance it will live.  Enough of a chance that it is worth taking some money that you can 100% afford to lose, and making a bet.  A rational gamble that there is a decent probability that it will survive, at a time when a large number of others are betting that it will fail.

And then once you do that, try your hardest to mentally write it off as a complete loss, like you had blown the money on a vacation or a consumer good, and now it is gone, and then wait a long time.