areyousure

The paper explicitly states that n is greater than 2, but the issue is whether a,b,c can be 0.

I have wanted one general application of this idea in a spreadsheet. Specifically, I track some of my running, including speed (pace), distance, and time. Under different circumstances, I have exactly two of the three available and I want the third to be computed, but it varies which. I have found it fairly difficult to implement this kind of data entry in Google Spreadsheets and Excel, even know conceptually it's a very simple constraint "a*b=c" where I know some two variables.

As a more substantive comment: You may find the thesis "Propagation networks : a flexible and expressive substrate for computation" by Alexey Radul interesting. https://dspace.mit.edu/handle/1721.1/54635

Vlad Tenev tweeted about it here: https://x.com/vladtenev/status/1994922827208663383

In case anyone is curious, there is a discussion of AI in Section 5 (page 8 of the PDF). This direct link might work: https://arxiv.org/pdf/2511.14653#page=8

The real question is why they’re paying $100K per truck

The test equipment can’t possibly cost more than $100K. That leaves $26.9M of “you’re doing something obviously wrong”.

It seems clear from the original text ("It costs $100,000 per certification") that it's the certification FEE that is $100k. For example, https://ww2.arb.ca.gov/sites/default/files/2024-08/mac202403... includes an individual base fee of $126,358.

Ask four mathematicians whether something is a Commutative Ring or not and they'll all agree.

Amusingly, there are at least 3 different definitions of commutative ring.

The principal issue is whether it must have a 1 (unity, ie a multiplicative inverse). Wikipedia https://en.wikipedia.org/wiki/Commutative_ring as well as most modern sources insist on this.

Britannica https://www.britannica.com/science/ring-mathematics#ref89421... as well as many older sources (such as Noether's original definition and van der Waerden) do not insist that the ring have a 1. Even first-edition Bourbaki didn't have 1!

Finally, if you do have a 1, then sometimes people include the condition that 0 != 1, ie the trivial/zero ring is deemed not a [commutative] ring. This is somewhat hard to find, but is relatively common among people who specifically define the concept of "ring with identity" (eg Zariski+Samuel). I have also found it unqualified (ie, just in the definition of "commutative ring") in the wild, eg in "Handbook of Mathematical Logic" by Barwise or "The Math You Need" by Mack.

(I agree with people like Conrad and Poonen that rings should have a 1. And I guess that the zero ring is in fact a [commutative] ring.)

Suppose we designate a unit line segment, and from that we pick out a line segment of (what we now call) length 2 and separately a rectangle of area 3. To "an ancient" (like Aristotle), does it make sense to add the length and the area to get 5? If you then drew a line segment of length 5, would they say it has the same magnitude?

(My understanding is "no" to both questions.)

You are correct that the Memorandum is rather short.

The promise to seek UN Security Council action is only in case Ukraine is attacked with nuclear weapons.

Sadly, firms abuse odd lot rules to give people terrible prices: https://academiccommons.columbia.edu/doi/10.7916/2y01-1s13/d...

In example 3, the NBBO for stock ABC is 495--500, but there is also an odd lot offer for 497 on exchange. If a Robinhood customer sends a market buy order, then Citadel is allowed to fill it for 499.999 even though it's better to send to the exchange. (And if they then pick up the odd lot themselves, it's easy arbitrage.)

By the way, while you're correct about some of your claims, odd lot executions definitely have to occur within the NBBO. (How could it be otherwise?) Otherwise, in the example above, Citadel would give an even worse price!

My research suggests that the majority of on-exchange trades are odd lots.

For stocks like SPY (those over $500 per share!), the vast majority of orders are odd lots.

This article is many years old and already has data strongly in that direction: https://www.nasdaq.com/articles/odd-facts-about-odd-lots-202...

You can't just go get 2 shares of SPY off the lits, so where dyou think those are coming from?

Why can't you just get 2 shares on an exchange?

In case anyone was curious, I computed some popular margins of victory defined as (%popular vote of winner) - (%popular vote of highest other candidate).

I got the following small margins of victory smaller than the 1.5% in 2024, five of which are positive and five of which are negative.

-7.8% in 1824, 1.4% in 1844, -3% in 1876, 0% in 1880, 0.6% in 1884, -0.8% in 1888, 0.1% in 1960, 0.7% in 1968, -0.5% in 2000, -2.1% in 2016.

In case anyone was curious, the interest being paid on the national debt is of the order of $1 trillion per year, while the amount collected in taxes (federally only) is of the order of $5.5 trillion per year.

For those who didn't understand, this is a search result and its AI response:

https://www.google.com/search?q=no%20soot%20in%20the%20pyram...

In case anyone was curious, Wikipedia calls the California Forestry Association a "timber industry lobbying group".

https://www.mersenne.org/primenet/ suggests 127 PFlop/s average over the last month, which would put it in the top 10 on https://top500.org/lists/top500/2024/06/

I used a random estimate online for computing cost which had 5.6e17 Flops per dollar on A100s gives about a dollar every 4.4 seconds or ~$7 million per year.

Sadly, I do not vouch for the correctness of any part of this, though I did try.

Do operating system accessibility controls help you distinguish the colors? For example, both Windows 10/11 and MacOS have "color filters". https://support.microsoft.com/en-us/ windows/use-color-filters-in-windows-43893e44 b8b3-2e27-1a29-b0c15ef0e5ce https://support.apple.com/ guide/mac-help/change-display-colors-easier-onscreen mchl11ddd4b3/mac

ln(5) ~ 1.6094379 is much closer, differing by about half of a percent of a percent.

Today around 9am (Eastern time), Robinhood retroactively canceled all orders filled(!) between 1:45am and 4am.

That paper does not prove that Sokoban is NP-hard. It does, however, cite an earlier paper proving the stronger result that Sokoban is PSPACE-complete:

Culberson, Joseph. "Sokoban is PSPACE-complete." (1997). https://era.library.ualberta.ca/items/f551dfd8-c8e6-4e78-883...

See also https://erikdemaine.org/papers/NCL_TCS/

In case anyone was curious, the 2011 Virginia earthquake was magnitude 5.8: https://en.wikipedia.org/wiki/2011_Virginia_earthquake

But the terminology is a bit confusing because aerodynamic lift is a byproduct of air being a compressible medium, whereas water is not. Maybe lift means something different when we're talking about water?

A https://en.wikipedia.org/wiki/Hydrofoil is a wing that produces lift in water.

The page https://en.wikipedia.org/wiki/Basilica_of_Saint-Denis states

Although known as the "Basilica of St Denis", the cathedral has not been granted the title of Minor Basilica by the Vatican.

Your number "3.5%" refers to US military spending as a proportion of GDP.

The original number "5%" refered to NASA spending as a proportion of the federal budget.

These baselines currently differ by approximately a factor of 4.

In case anyone is curious, they are welcome to read the following UN Security Council resolution that was vetoed by both China and Russia: https://documents-dds-ny.un.org/doc/UNDOC/GEN/N23/320/92/PDF...

Because many of them work in the city, bringing in a lot of tax revenue for New York (city and state) as well as providing services to the residents.

I think one of the reasons people might be harping on you is because the "Special military operation" started on 2022 February 24, which is 652 days < 1.8 years ago. In particular, even after you add 6 weeks to it, it's still less than 2 years.

I assume you mean T + 6 weeks, where T is the time since the invasion and T is approximately 2 years, even though T + 6 weeks is still less than 2 years?

The wikipedia page for the shootdown incident [4] lists the time as 1349 GMT.

In case anyone is curious, the Wikipedia page mention of this time is as follows: "at 13:49 UTC (49 minutes after take-off), KAL 007 reported that it had reached its Bethel waypoint". Bethel is a city in the U.S. state of Alaska.

Wasn't this in Iranian territorial waters.

In case anyone is curious, the topic of discussion appears to be https://en.wikipedia.org/wiki/USS_Samuel_B._Roberts_(FFG-58)...

All sources appear to indicate that the mine was in international waters.

You probably meant "C" as the final one, instead of "A": https://www.wolframalpha.com/input?i=12+in+base+13