The wave equation contains the entire state of a particle.
From mathematical formulation of quantum mechanics remember that the wave equation is a vector in Hilbert space.
And a single vector can be represented in many different ways in different basis, and two of those ways happen to be the position and the momentum representations.
More importantly, position and momentum are first and foremost operators associated with observables: the position operator and the momentum operator. And both of their eigenvalue sets form a basis of the Hilbert space according to the spectral theorem.
When you represent a wave equation as a function, you have to say what the variable of the function means. And depending on weather you say "it means position" or "it means momentum", the position and momentum operators will be written differently.
This is well shown at: Video "Visualization of Quantum Physics (Quantum Mechanics) by udiprod (2017)".
Furthermore, the position and momentum representations are equivalent: one is the Fourier transform of the other: position and momentum space. Remember that notably we can always take the Fourier transform of a function in due to Carleson's theorem.
Then the uncertainty principle follows immediately from a general property of the Fourier transform: en.wikipedia.org/w/index.php?title=Fourier_transform&oldid=961707157#Uncertainty_principle
In precise terms, the uncertainty principle talks about the standard deviation of two measures.
We can visualize the uncertainty principle more intuitively by thinking of a wave function that is a real flat top bump function with a flat top in 1D. We can then change the width of the support, but when we do that, the top goes higher to keep probability equal to 1. The momentum is 0 everywhere, except in the edges of the support. Then:
- to localize the wave in space at position 0 to reduce the space uncertainty, we have to reduce the support. However, doing so makes the momentum variation on the edges more and more important, as the slope will go up and down faster (higher top, and less x space for descent), leading to a larger variance (note that average momentum is still 0, due to to symmetry of the bump function)
- to localize the momentum as much as possible at 0, we can make the support wider and wider. This makes the bumps at the edges smaller and smaller. However, this also obviously delocalises the wave function more and more, increasing the variance of x
Bibliography:
- www.youtube.com/watch?v=bIIjIZBKgtI&list=PL54DF0652B30D99A4&index=59 "K2. Heisenberg Uncertainty Relation" by doctorphys (2011)
- physics.stackexchange.com/questions/132111/uncertainty-principle-intuition Uncertainty Principle Intuition on Physics Stack Exchange
Someone should package this better for end user "just works after Conda install" image generation, it is currently much more of a library setup.
Tested on Amazon EC2 on a g5.xlarge machine, which has an Nvidia A10G, using the AWS Deep Learning Base GPU AMI (Ubuntu 20.04) image.
First install Conda as per Section "Install Conda on Ubuntu", and then just follow the instructions from the README, notably the Reference sampling script section.This took about 2 minutes and generated 6 images under
git clone https://github.com/runwayml/stable-diffusion
cd stable-diffusion/
git checkout 08ab4d326c96854026c4eb3454cd3b02109ee982
conda env create -f environment.yaml
conda activate ldm
mkdir -p models/ldm/stable-diffusion-v1/
wget -O models/ldm/stable-diffusion-v1/model.ckpt https://huggingface.co/CompVis/stable-diffusion-v-1-4-original/resolve/main/sd-v1-4.ckpt
python scripts/txt2img.py --prompt "a photograph of an astronaut riding a horse" --plmsoutputs/txt2img-samples/samples, includining an image outputs/txt2img-samples/grid-0000.png which is a grid montage containing all the six images in one:
A quick attempt at removing their useless safety features (watermark and NSFW text filter) is:but that produced 4 black images and only two unfiltered ones. Also likely the lack of sexual training data makes its porn suck, and not in the good way.
diff --git a/scripts/txt2img.py b/scripts/txt2img.py
index 59c16a1..0b8ef25 100644
--- a/scripts/txt2img.py
+++ b/scripts/txt2img.py
@@ -87,10 +87,10 @@ def load_replacement(x):
def check_safety(x_image):
safety_checker_input = safety_feature_extractor(numpy_to_pil(x_image), return_tensors="pt")
x_checked_image, has_nsfw_concept = safety_checker(images=x_image, clip_input=safety_checker_input.pixel_values)
- assert x_checked_image.shape[0] == len(has_nsfw_concept)
- for i in range(len(has_nsfw_concept)):
- if has_nsfw_concept[i]:
- x_checked_image[i] = load_replacement(x_checked_image[i])
+ #assert x_checked_image.shape[0] == len(has_nsfw_concept)
+ #for i in range(len(has_nsfw_concept)):
+ # if has_nsfw_concept[i]:
+ # x_checked_image[i] = load_replacement(x_checked_image[i])
return x_checked_image, has_nsfw_concept
@@ -314,7 +314,7 @@ def main():
for x_sample in x_checked_image_torch:
x_sample = 255. * rearrange(x_sample.cpu().numpy(), 'c h w -> h w c')
img = Image.fromarray(x_sample.astype(np.uint8))
- img = put_watermark(img, wm_encoder)
+ # img = put_watermark(img, wm_encoder)
img.save(os.path.join(sample_path, f"{base_count:05}.png"))
base_count += 1 Sponsor Ciro Santilli's work on OurBigBook.com Financial crime preventive measures by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Crazy shady crypto people seem to like Ciro Santilli, so this is in order.
Giving to Ciro Santilli is the worst possible way to launder your money, as donations amounts are clearly publicly disclosed (though not donor identities if they with to remain anonymous), and clear records kept of every donation made (including private note of donor identities if known). Also suspicious donations are promptly reported to the authorities.
Donation refunds upon donor's requests are only made at our discretion, and may be declined, unless required by law of course. This is to reduce the risks of us unknowingly serving as money mules or aiding money laundering.
Ciro Santilli believes that he is not require to report large donations to either:But note that Ciro will preventively report if there are any further suspicious aspects to any donations received.
- charities have to report anonymous donations of £25,000 or more as "serious incident", but Ciro Santilli does not have a registered charity: www.gov.uk/guidance/how-to-report-a-serious-incident-in-your-charity, related: docs.ourbigbook.com/project-governance
- dealers selling goods over 10,000 euros for cash must make a Suspicious Activity Report (SAR) www.gov.uk/guidance/money-laundering-regulations-high-value-dealer-registration. However Ciro Santilli does not sell any goods, only provides services, and services are excluded from the report requirements
Sponsor Ciro Santilli's work on OurBigBook.com 1000 Monero donation by Ciro Santilli 40 Updated 2026-03-28
Ciro Santilli 40 Updated 2026-03-28On 2024-03-18, Ciro Santilli received an anonymous 1000 Monero donation (worth ~126k USD at the time) to his self-custody wallet, which pushed him over his public plea for 100k USD goal to quit his job for one year.
The transaction ID was
5c6af4df39021f3a4a053ef169c9b397e6d6bf6c7e557d3f08e4e1675d7d3eed to self hist custody wallet with address 47kzoCeRMTohJhADejtsGmGimvQKzNsuST7u2aVhAD1VX5WDbh3v1FPUoJoTK3NTJVUgAM3dWCqC4Tmp9KSQaJi6GGYWgYn. This is a roof generated by his Monero wallet: InProofV2AVFBmFhofH4GoG5NsaDutkdNWRTaEhuFgHpHTkpprRmuZ54B8FdUwFp71gqfp2jJpDUrhB3GCzZ2p8CNbh2TW1Z88ShmYWEwtkZFLccEMw9PhH3vWcMVo9mKaRsH3WgJXqq9.Since this donation is so huge, it deserves some comments and a bit of a retrospective. The path to this donation has been an interactive one, and it is described below.
After starting the OurBigBook Project, Ciro started the sponsor Ciro Santilli's work on OurBigBook.com page on cirosantilli.com and setup some donation methods to help support the project, and possibly try to capitalize a bit on Ciro Santilli's Stack Overflow contributions.
His sponsors are absolutely crazy amazing people, but Ciro simply could attract a large enough amount of small sponsors to reach life changing amounts under those circumstances. This is partly due to Video "And I am not and never have been 'familiar' scene from The Big Short (2015)".
As such, Ciro came to realize more and more that the best approach would be to reach out to a smaller number of rich people, given that the things he works on niche, but may appeal to a particularly wealthy tranche of the population: STEM people. Other experiences and ideas that contribute to this realization are:
- the creation of the OurBigBook Fellowship, which as of writing consisted of a single donation. During this exercise, Ciro Santilli gave about 2k USD to help a promising Brazilian student. In doing so, he understood a lot about what goes on inside a "rich person's" head when considering a donation
- it is hard to decide who to donate to and find those people. In part because as soon as you create a public donation system with an application process, people will game the fuck out of it. Perhaps the Lost Horse LLC approach of "they find you" is the best?
- it is basically impossible to donate more than 1% of your net worth if you have a family. Even 1% you may be discouraged about. Perhaps with reason due to previous bad donations they have made.
- the increasing wealth inequality of this world, perhaps one of the greatest problems we now face
Then, whenever a larger donation would come through and surprise Ciro, he would improve his sponsor page statements. First a private 150 USD by an awesome sponsor. Then the 2023-09 ~810$ Bitcoin one. Finally came the 2023-11-20 100 Monero one. And it was that one that pushed Ciro to start his "100k USD = 1 year campaign".
Finally on Wednesday 2024-03-13, Ciro received an anonymous 10 Monero donation to self-custody wallet. He had clearly stated that one should make a test donation to that wallet before the big one, so 10 Monero felt like it could be the test one. Ciro announced its reception on Sunday March 17, probably having noticed it after the usual weekend check:
Over the next few days, Ciro checked his wallet more often than his previously self imposed once a weekend max, and as expected, he found the big one on a slightly despaired around midnight sleepless night (partly due to parenthood). He was feeling particularly bored and a bit sad with his work life that night. And there it was. 1000 Monero on the wallet. Needless to say, not much sleep was done on that evening!!!
Still of the reaction video after finding out about the big donation around about midnight
. Source. 
The following days were also tense, with Ciro having a trial by fire on selling large amounts of Monero on the UK, which is not trivial as it had been banned from all major exchanges. But he managed. Further notes on that at: www.reddit.com/r/Monero/comments/17arz9f/converting_xmr_to_gbp_in_the_uk/. Ciro also decided to keep about 200 Monero around just for fun as a crazy moonshot.
Another major factor likely Ciro having published his article: Section "Cool data embedded in the Bitcoin blockchain" in 2019. This is something he wrote entirely for fun during an intense 3 week side-time binge in 2019, though some large updates were made later on. It was this article that likely some crypto-dude attention to Ciro Santilli's profile. As of 2024, there is said to be about 20 crypto billionaires, so perhaps there are about 2000 crypto 10 millionaires[ref], which is the minimum net worth for a donation of 100k USD to be feasible (1% mark). And perhaps a reasonable number of them are just nerds who got rich, and want to improve the world. There are two lessons from this:
- follow your instincts, always. If something seems mega fun and quick, do it!
- making money from a few rich people (or entities like organizations) is easier than working for a bunch of poor people, because you have to convince less people. If you reach many poor people however, things are much more stable as you can lose a few customers and still be fine
Another factor in the donation, Ciro Santilli believes, is that many rich people thing that education is bullshit. Many successful people are neurodiverse and as such, it is only natural that a large number of rich people want to improve our educational system, which tends to be the very epitome of "boring and average normality" which Ciro Santilli so much detests. This can also be seen in people such as:
- Michael J. Saylor and his Saylor Academy
- Peter Thiel and his Thiel Fellowship
Announcements:
- pre-announcement before everything was clearly documented online:
- main announcement
Amazing reactions from the Monero Reddit community: www.reddit.com/r/Monero/comments/1brryao/ciro_santilli_received_a_1000_xmr_donation_to/These people have some serious trust issues!!! Perhaps not surprising from a privacy coin community. Ciro's Twitter post: twitter.com/cirosantilli/status/1775961945193017790
geonic_comments:Reaction video is fake. Very bad acting.
Inaeipathycomments:-TrustyDwarf-comments:rbrunner7comments:
Ciro Santilli is very happy to meet people with related interests, he really loves his like-minded online friends. Even if you don't have something a specific goal in mind for the contact, please just say hi.
To contact Ciro publicly about any general subject that is not covered in a more specific GitHub repository, including saying hi or suggestions about his website either:
- create a GitHub issue at: github.com/cirosantilli/cirosantilli.github.io/issues/new or Giscus thread
- at mention Ciro's main Twitter account
For comments about China, first read:
and then create a GitHub issue at: github.com/cirosantilli/china-dictatorship/issues/new
Publicly viewable contact is preferred if possible to more effectively share Ciro's wisdom with the world.
But if you feel more comfortable with private contact, no problem, either:
- email: username
cirosantilliwith provider ProtonMail which has domain nameproton.me. Note that Ciro also controls the Gmail address with that same username, and keep in mind that dots are ignored in Gmail addresses. But ProtonMail preferred because why should we give our private minds to the CIA by default? Push notifications disabled. - Signal: username
cirosantilli.89signal.me/#eu/BuJjV0enXYTOnFFc1FZV5LFcWodL1a2Oy9VZ5uyQU7xrYxqw+npIcaHBqghWudrI. 89 is a reference to Ciro Santilli's birth year 1989. Push notifications enabled, but treat like email unless we are actively chatting back and forth.
For other less good methods that will also likely work, use direct messages of the following profiles from under Section "Accounts controlled by Ciro Santilli":Ciro's Twitter DMs are also open, but note that Ciro receives endless Chinese language SPAM there which Twitter is doing nothing to combat, so it's not as reliable.
- LinkedIn: www.linkedin.com/in/cirosantilli
- Reddit: www.reddit.com/user/cirosantilli
- Facebook: www.facebook.com/cirosantilli
- Telegram: telegram.me/cirosantilli. Note that end-to-end encryption is present on secret chats only, which don't have device sync. Ridiculous.
If you are a privacy freak or are going to tell Ciro state secrets Ciro has this GNU Privacy Guard public key: pubkey.gpg, but it's not something that he has ever really used.
Disqus comments were removed from his website in 2019-05-04, a manual dump is available here, removal rationale at: why Ciro Santilli removed Disqus comments from his website in 2019-05-04.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact