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Our Expert Voices conversation on space.

In mathematics, "space" describes a setting where relations between objects imitate real life phenomena: distances, directions, continuity, convergence. In abstract settings, these relations can be warped or decoupled from one another so we can examine the meaning of each one separately. A space can have infinitely many dimensions, the surface of a ball need not be curved, or we can determine directions without being able to measure distances. The "points" in a space can be complicated objects with structure of their own, such as functions or matrices. Their properties are examined indirectly through the geometry of the space they live in. We build sophisticated and productive theories of mathematical spaces that require no knowledge of what the elements of these spaces truly are, only asking that they conform to certain geometric requirements. This might shed light on why we are able to function so well in the universe, developing science and technology, while there are still fundamental questions about the space we live in that remain unanswered. Bottom line: Mathematics works around the unknown, providing sufficient functionality even while the essence may still be under investigation. Other voices in the conversation:

Sean Carroll, theoretical physicist, California Institute of Technology: Space is overrated Bridget Falck, astrophysicist, University of Oslo: Space is a relation between things, not a thing itself David Albert, philosopher, Columbia University: Maybe there is no space

Go deeper

1 hour ago - World

Netanyahu and Israel reluctantly adjust to a post-Trump Washington

Netanyahu (R) and Biden in 2010. Photo: Avi Ohayon/GPO via Getty

Prime Minister Benjamin Netanyahu and his close aides are very nervous about the transition to a new U.S. administration after a four-year honeymoon with Donald Trump. One Israeli official told me it felt like going through detox.

What he's saying: Netanyahu congratulated Biden minutes after he was sworn in, saying in a statement that he looked forward to working together to "continue expanding peace between Israel and the Arab world and to confront common challenges, chief among them the threat posed by Iran."

Updated 2 hours ago - Politics & Policy

Coronavirus dashboard

Illustration: Aïda Amer/Axios

  1. State of play: New coronavirus cases down, but more bad news ahead.
  2. Politics: Biden set to immediately ramp up federal pandemic response with 10 executive actions — Scoop: Joe Biden's COVID-19 bubble.
  3. World: Biden will order U.S. to rejoin World Health OrganizationBiden to bring U.S. into global COVAX initiative for equitable vaccine access.
  4. Vaccine: Amazon offers to help Biden administration with COVID vaccine efforts.
Dion Rabouin, author of Markets
3 hours ago - Economy & Business

First glimpse of the Biden market

Photo: Jonathan Ernst-Pool/Getty Images

Investors made clear what companies they think will be winners and which will be losers in President Joe Biden's economy on Wednesday, selling out of gun makers, pot purveyors, private prison operators and payday lenders, and buying up gambling, gaming, beer stocks and Big Tech.

What happened: Private prison operator CoreCivic and private prison REIT Geo fell by 7.8% and 4.1%, respectively, while marijuana ETF MJ dropped 2% and payday lenders World Acceptance and EZCorp each fell by more than 1%.