apsk32 @apsk32 Twitter profile

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apsk32

@apsk32

4 days

Get off zero. Do it for your family. #bitcoin

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apsk32

@apsk32

6 months

60-second introduction to the bitcoin power law and time contours See it blow through a million, sound on

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apsk32

@apsk32

4 months

This is my favorite bitcoin metric and it tells me that I should be open to $300,000 BTC in 2025. --- As an engineer I look for signals that allow me to measure physical processes. The fact that bitcoin's price has followed a power law for more than 10-years points to a

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apsk32

@apsk32

5 months

In the 2030's, you could retire and support your family with just two bitcoin.

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apsk32

@apsk32

4 months

Bitcoin price fractals based on the power law support and a 4-year cycle period show the potential price action of the current cycle. Cycle tops: 8 Nov 2025 - $227,328 (2021 fractal) 16 Dec 2025 - $271,868 (2017 fractal) 4 Dec 2025 - $193,180 (2013 fractal) Near-term lows:

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apsk32

@apsk32

3 months

If bitcoin's cycle pattern continues, price should remain inside or near this blue cloud. The ETFs pushed us out of the cloud and now we're reverting back. We're 3+ months away from upwards acceleration and we could see prices go up 4x by the end of 2025. --- Many anticipate

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apsk32

@apsk32

2 months

These two bitcoin animations received 2.3M impressions in the last 72 hours! A common saying is that school teaches us math, like cosines and the hypotenuse of a triangle, but we never use it at work. As an engineer I have to use math everyday to calculate satellite orbits and

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apsk32

@apsk32

2 months

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apsk32

@apsk32

4 months

There's a line that bitcoin's price shall not pass. A lower bound on price, a power law. Time contours tell us how long it will be before the support forces current prices upwards. For 12 years, every bear market has returned to this support line. The support passes one

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apsk32

@apsk32

2 months

Michael Saylor's new model is a power law. It's a power law fit of bitcoin's market cap. Blue dots (Saylor) on orange line (power law). I'll drop a link to his spreadsheet in the comments. Check it out for yourself.

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apsk32

@apsk32

3 months

If price follows the same pattern as the last halving, we could see $210k by next Spring.

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apsk32

@apsk32

3 months

If bitcoin is 5 years ahead of the power law support on 1 Oct 2025 then it will be worth $255,000. I chose that date based on previous cycle timings. I use this plot to visualize the cycles and to see if it looks like the pattern is changing. --- If the 4-year price cycles

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apsk32

@apsk32

26 days

I've been meditating on a mountain for a couple of weeks now. My yogi asked me, "What is the source of your anxiety?" I replied by showing him this chart. After a few minutes, he said, "All this tells me is that $250k is in play for Bitcoin in 2025." .. and I began to levitate.

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apsk32

@apsk32

2 months

What's the first thing you notice?

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apsk32

@apsk32

4 months

If this is new to you, this animation might help build intuition.

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apsk32

@apsk32

3 months

Two equations explain bitcoin's price since 2011. Watch the video, I'll show you. --- We don't have to like this, but we need to respect it. A power law equation provides a lower bound and an exponential decay of the peaks provides the upper bound. We can hope it will

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apsk32

@apsk32

3 months

A short explainer animation for my pinned post, the "Bitcoin Power Law Fractal Cloud" plot. Title adjustment from "Fractal" to "Cycle." I'll refine the animation later, but I wanted to get it out before I got busy with other things.

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apsk32

@apsk32

4 months

I say this as a bitcoiner, a believer in where we're headed, as someone fully confident in $1M BTC-USD in the 2030s, as someone who has never sold a sat and has no plans to do so. Let the market puke. Give us that sweet 3-sigma double-backflip blackswan dive to $52k as an

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apsk32

@apsk32

3 months

I'm hoping bitcoin goes above $200k and breaks this exponential fit of the price/support peaks. Too precise to ignore for now.

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apsk32

@apsk32

3 months

the mathematical beauty of #Bitcoin its a network, but it's also a road i want you to see it so you can meet us there

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apsk32

@apsk32

2 months

The purchasing power of Bitcoin's market cap has followed a power law since 2011. If that continues.. Bitcoin will be worth $2.6 million in 10 years.

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apsk32

@apsk32

2 months

Bitcoin could hit $300k in 2025--but it's a stretch. I like my models simple. They don't get any simpler than this one. All I do is calculate the power law support and ask "how long will it be before the current price is under the support line?" That's what "years ahead" means.

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apsk32

@apsk32

25 days

Evolution of the Bitcoin power law

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apsk32

@apsk32

3 months

1.2 bitcoin will retire entire families by 2040. --- "But, what about inflation?" Inflation increases the median US family income, which is accounted for in this analysis. "But, the 4% rule was made for stocks and bonds!" True. If we assume bitcoin will outpace stocks and bonds

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apsk32

@apsk32

2 months

Current power law models don't account for inflation or bitcoin's changing supply. Correcting this increases the 2029 trend value from $300k to $500k, a 66% increase. --- Our current models use bitcoin's spot price as a proxy for the value of the bitcoin network. I think this

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apsk32

@apsk32

3 months

"If you don't believe me or don't get it, I don't have time to try to convince you, sorry." - satoshi

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apsk32

@apsk32

7 months

The evolution of bitcoin's power law, in log-log.

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apsk32

@apsk32

5 months

A study of the 4-year bitcoin cycle

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apsk32

@apsk32

6 months

The bitcoin power law animation passed 500,000 impressions! If you count the reposts from other accounts, it's well over one million. Wow. It feels great that so many people enjoyed the content. Thank you all.

apsk32

@apsk32

6 months

60-second introduction to the bitcoin power law and time contours See it blow through a million, sound on

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apsk32

@apsk32

24 days

If you plot Bitcoin's price over time on a log-log scale, there's clearly a straight line that performs well as a lower bound. A straight line on a log-log plot is indicative of a power law relationship. During periods of hype (e.g., end of 2013, 2017, 2021), the price rises

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apsk32

@apsk32

3 months

If the exponential decay of the price/support peak ratios continue, and if we peak at the end of 2025, then the years ahead of support would equal 3.55 at the cycle peak. The dashed line in each subplots come from the fit of the bitcoin cycle peaks in price/support. Each orange

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apsk32

@apsk32

4 months

Everyone is early. #bitcoin

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apsk32

@apsk32

4 months

Was your favorite bitcoin analyst warning you about a potential downtrend last month? If not, I'd ask you to consider adding a new voice to your timeline. On 9 June 2024, I wrote this article showing how you could use the power law support and 4-year price fractals to forecast

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apsk32

@apsk32

2 months

@100trillionUSD

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apsk32

@apsk32

3 months

A color study of bitcoin's 4-year cycle. --- Will the pattern continue? Has it already broke?

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apsk32

@apsk32

19 days

Over a 4-year period, no one has ever lost money holding Bitcoin. Bitcoin's 4-year compound annual growth rate is trending down. From late 2017 to late 2021, Vanguard's Information Technology ETF outperformed Bitcoin. Bitcoin's 4-year CAGR is currently above 50%. --- The

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apsk32

@apsk32

7 months

Using the power law model to predict bitcoin's price two years in the future.

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apsk32

@apsk32

1 month

On August 1, 2019, the Federal Reserve cut interest rates. One Week Later: Bitcoin was up 20%. Three Months Later: Bitcoin was down 33%. I think we could get a similar pop and drop, but I doubt we go down 33% from here. Bedrock between $45k-$55k and 2025 rewards the survivors.

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apsk32

@apsk32

2 months

My animation is putting in work for @3orovik . 1 million views. Wild numbers, feels bittersweet.

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apsk32

@apsk32

1 month

The Fed's cutting interest rates, the yield curve's uninverting, alts are crushed, bitcoin's stalled, and stocks are looking vulnerable. .. recession .. I don't believe anyone knows if it's coming, or more importantly, when it's coming. The catalysts that trigger a recession

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apsk32

@apsk32

5 months

Those who start saving sooner end up with more bitcoin. I assumed a family started saving 1% of their yearly income each month for two years. In nearly all cases, starting one year later left them with less bitcoin.

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apsk32

@apsk32

2 months

Pulling on the thread that.. fitting bitcoin's price to a power law (r2: 0.9554) is wrong and we should instead.. fit inflation-adjusted market cap (r2: 0.9580). If you've been following along, you know I like to measure deviation from the trend in time. These bands are less

apsk32

@apsk32

2 months

Current power law models don't account for inflation or bitcoin's changing supply. Correcting this increases the 2029 trend value from $300k to $500k, a 66% increase. --- Our current models use bitcoin's spot price as a proxy for the value of the bitcoin network. I think this

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apsk32

@apsk32

5 months

Bitcoin's price over the last twelve years. Each plot in a column has the same price range. Will the cycles continue? See also:

apsk32

@apsk32

5 months

A study of the 4-year bitcoin cycle

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apsk32

@apsk32

4 months

Saving your pay in bitcoin increases your salary. Regardless of which year your family started saving in bitcoin, two things are true. 1) You should have started earlier. 2) You're in profit. (No models here. Historical data only.)

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apsk32

@apsk32

3 months

Families can dramatically increase their effective income by saving 10% of their pay in bitcoin!

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apsk32

@apsk32

4 months

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apsk32

@apsk32

7 months

The evolution of bitcoin's power law.

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apsk32

@apsk32

2 months

Bitcoin rewards families who save for their future, and these families foster stability within their communities.

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apsk32

@apsk32

6 months

Bitcoin runs on the rails of a power law

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apsk32

@apsk32

2 months

It's never to late to start saving in bitcoin and you should have started yesterday.

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apsk32

@apsk32

5 months

Three perspectives of the same box.

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apsk32

@apsk32

2 months

The power law of bitcoin's price with time is incongruent with the working theory. Correcting this error identifies a growing divergence in price forecasts. As of today, the difference is $85k vs $74k, ~15%. By 2029, that becomes $394k vs $303k, ~30%. (This post will not

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apsk32

@apsk32

3 months

@CryptoKaleo

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apsk32

@apsk32

4 months

Most of bitcoin's yearly gains happen in just a few days. If you try to time the market, you could miss those big moves. (Less popular, but also true, missing out on the worst couple of days can seriously help your returns.)

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apsk32

@apsk32

25 days

Since May 2022, the power law forecast for January 2028 has decreased by 25%, dropping from $300k to $225k. Since May 2022, the forecast for today has also decreased by 25%, from $100k to $75k. This is a big-picture tool; it shifts and is imprecise. Use it for getting rough

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apsk32

@apsk32

4 months

"How low could bitcoin fall?" "When will price accelerate upwards?" "How high could we reach?" We study the past for clues. --- If bitcoin continues to follow a power law and price continues to follow a 4-year pattern, then these fractals provide us with historical references

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apsk32

@apsk32

4 months

This animation helps to describe the power law support and the 'years ahead of support' measure.

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apsk32

@apsk32

2 months

Today bitcoin and the SP500 fell by 7.5% and 3%. There are only 8 other days where bitcoin and the SP500 fell this far together. 2 of those 8 days happened around the halving in 2020. Those who bought the dip were rewarded with 109% and 375% returns over 6 months. 6 of those 8

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apsk32

@apsk32

5 months

Thanks for having me on your show Fred! If you missed our discussion on bitcoin power laws, you can check it out on Fred's youtube channel. Hope you enjoy!

Fred Krueger

@dotkrueger

5 months

The most epic power law presentation ever from @apsk32

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apsk32

@apsk32

5 months

Buy-and-hold is underrated. Traders and gamblers are usually trying to get back something they lost. There's no need to bring that stress into your home. Just get on the water and let the numbers go up. Converting some of your pay into bitcoin lets you and your family rise

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apsk32

@apsk32

5 months

Experiment results: Bitcoin sell and rebuy scenarios including 20% capital gains tax. *Not financial advice.

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apsk32

@apsk32

6 months

Bitcoin has followed a power law for more than 10 years. The model predicts that one bitcoin will be worth more than $1,000,000 in the 2030s. This model provides a nearly perfect support line for price. The power law, or power function, is simply price=(some constant

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apsk32

@apsk32

5 months

Static frame of bitcoin power law time contours. Added a grid for anyone looking to zoom in. The time contours (0-6 years ahead) are not peak fits! They're reference levels, not a corridor. Time ahead tells us how long it could take to recover. How long it will be before the

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apsk32

@apsk32

2 months

The "Power Law" is a weird name. Law.. Power.. so magnificent. Did you know that the area of a square follows a power law? The area is equal to the length of a side squared. Area=Length^2 The "power" (simply the exponent) is 2. Even y=x is a power law, y=x=x^1, the power

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apsk32

@apsk32

4 months

If the average family saved 10% of their pay in bitcoin, starting January 2020, they would be have turned $39,000 into $131,000.

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apsk32

@apsk32

5 months

Heatmap plot of bitcoin's historical forward return. Think of the x-axis as the date you purchased bitcoin. The y-axis is how long you held that bitcoin. The color is your percentage gain (or loss). Each year in the x- and y-axis are subdivided into 12 cells--one for each

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apsk32

@apsk32

4 months

Some are sad about bitcoin going down. I just see opportunity.

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apsk32

@apsk32

4 months

@BitcoinMagazine This long-term trendline gives me confidence. Stack in peace.

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apsk32

@apsk32

2 months

If you're unfamiliar with the power law fit, here's a 60-second animation that explains it visually. Small caveat, this video fits bitcoin's price, while Saylor's model appears to have fit bitcoin's market cap.

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apsk32

@apsk32

2 months

If MC/GOLD is the real power law, then the fair value today is $129,202. --- Did you know that bitcoin's gold normalized market cap follows a power law and it's a better fit than price? There's a number of quantities you could select with similar r2 values. You have to pick

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apsk32

@apsk32

4 months

As the price of bitcoin falls, your bitcoin denominated income increases. Your job is worth more bitcoin today than it was yesterday and your stacking goals are easier to reach. If you're still buying bitcoin, and if you believe in its long-term trajectory, then today is a good

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apsk32

@apsk32

6 months

If Bitcoin's price crashed, how long could it take to recover? That's what this is.. I made it in frame by frame in python/matlab. Hope you enjoy.

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apsk32

@apsk32

4 months

Thank you to my 10,000 followers, and a special thank you to those who engaged when I had none. ❤️

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apsk32

@apsk32

2 months

If you fumbled your bag, could you ever earn it all back?

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apsk32

@apsk32

5 months

In my pinned post, I animated the bitcoin power law support and time contours. There, I used all available price data to compute the support line. Here, I compute the support line at each time step. The numbers on the right tell you value of the support n years in the future.

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apsk32

@apsk32

4 months

A few people have asked for a tutorial on how to plot bitcoin data with python. This image contains all the code needed to - retrieve bitcoin price data from the Federal Reserve Economic Data (FRED) - compute the number of days since the genesis block - perform linear regression

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apsk32

@apsk32

2 months

@CryptoKaleo All systems nominal

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apsk32

@apsk32

5 months

Bitcoin rewards those who hodl

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apsk32

@apsk32

6 months

To the men and women who endured, happy halving.

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apsk32

@apsk32

2 months

@3orovik The recent drop just puts us back in line with previous cycles. Still feeling great about 2025.

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apsk32

@apsk32

7 months

Raw bitcoin power law fit. Nothing else.

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apsk32

@apsk32

5 months

For most people, your job will bring more money into your home than the returns on your bitcoin. If you have $25k of bitcoin today and bitcoin reaches $1M in 2034, you'll have gained $350k over 10-years. A $70k/yr job brings in $700k every 10-years! Do both.

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apsk32

@apsk32

3 months

Last frame

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apsk32

@apsk32

5 months

abide bitcoin's rising tide

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apsk32

@apsk32

3 months

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apsk32

@apsk32

2 months

"My stack is monotonic and downturns excite me." I don't know if this is the start of a deeper pain cycle, but if it is, remember this: doom brings opportunity

apsk32

@apsk32

4 months

I say this as a bitcoiner, a believer in where we're headed, as someone fully confident in $1M BTC-USD in the 2030s, as someone who has never sold a sat and has no plans to do so. Let the market puke. Give us that sweet 3-sigma double-backflip blackswan dive to $52k as an

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apsk32

@apsk32

2 months

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apsk32

@apsk32

2 months

A version with labels for all you label lovers 😘

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apsk32

@apsk32

1 month

Check out this video by @GameofTrades_ . It does a good job of showing what could happen.. even if we don't know that it will.

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apsk32

@apsk32

3 months

This 60-sec animation is a great place to start for those looking to understand the power law and the 'years ahead of support' metric.

apsk32

@apsk32

4 months

There's a line that bitcoin's price shall not pass. A lower bound on price, a power law. Time contours tell us how long it will be before the support forces current prices upwards. For 12 years, every bear market has returned to this support line. The support passes one

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apsk32

@apsk32

3 months

I'm not on board with the idea that cost of living is causing people to have less kids. My grandparents were poor as dirt and each had 9 or 10 siblings. They didn't have air-conditioning, refrigerators, electricity at the house, cars, they didn't go to college, and they lived in

Preston Pysh

@PrestonPysh

3 months

@PicoPaco17 What a bad take. It address the effect not the cause. The birth rate collapse is because governments use perpetual debasement to offset runaway government spending (wars etc) which eventually makes the cost of having a family too expensive so they start having way less kids.

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apsk32

@apsk32

6 months

Saving $1,337/mo in bitcoin. It's probably too late for lambos and islands, but there's good news here. Assuming bitcoin continues to follow a power law, bitcoin would hit $1M around Oct. 2033. In that time you could have saved 0.724 BTC (worth $724k) with $152k. 4.7x on savings.

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apsk32

@apsk32

5 months

Have you ever been on a long drive and noticed you were 30-min ahead of schedule? Maybe you were going over the speed limit or there was no traffic. That's how you should think of these contours. The support line is the schedule. You can stop for a bit and still arrive on time.

apsk32

@apsk32

6 months

60-second introduction to the bitcoin power law and time contours See it blow through a million, sound on

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apsk32

@apsk32

7 months

Two year price predictions using bitcoin's power law model, in log-log.

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apsk32

@apsk32

2 months

Looking Ahead: What's Your Prediction for Bitcoin's High in 2025? Convince us in the comments!

>$300,000

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$233,000 - $300,000

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$167,000 - $233,000

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apsk32

@apsk32

20 days

@Sina_21st

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apsk32

@apsk32

5 months

I'm joining @dotkrueger live tomorrow at 1p PST to discuss the bitcoin power law. Hope to see you there!

Fred Krueger

@dotkrueger

5 months

I'm going live tomorrow here at 1pm PST with apsk32 on Bitcoin Power Laws. Cue up your Power Law Questions. Later, this week (or next) more Giovani. You can never get enough Power Laws