However, this is NOT the case in Special Relativity (or in QM or QFT). Instead, the distance between two points ("events") is (cT1-cT2)^2 - (X1-X2)^2 - (Y1-Y2)^2 - (Z1-Z2)^2. Note that this means that the distance between two different events can be positive, negative, or 0. These are typically called "time-like separated" (for example, two events with the same X,Y,Z coordinates but different T coordinates, such as events happening in the same place on different days); "space-like separated" (for example, two events with the same T coordinate but different X,Y,Z coordinates, such as events happening at the same time in two different places on Earth); or light-like separated (for example, if (cT1-cT2) = (X1 - X2), and Y, Z are the same; these are events that could be connected by a light beam). Here c is the maximum speed limit, what we typically call the speed of light.

This difference in metric has many mathematical consequences in how different points can interact, compared to a regular 4D space. But even beyond those, it makes it very clear that walking to the left or right is not the same as walking forwards or backwards in time.

Edit to add a small note: what I called "the distance" is not exactly that - it's a measure of the vector that connects the two points (specifically, it is the result of its scalar product with itself, v . v). Distance would be the square root of that, with special handling for the negative cases in 3+1D space, but I didn't want to go into these complications.

In pure mathematical terms, the vector space used in special relativity (and in theories compatible with it, such as QM/QFT), while being 4 dimensional, is not R^4, it's not a 4D cartesian vector space.

Specifically, the scalar product of two vectors in R^4 (4D space) is [x1,y1,z1,h1] dot [x2,y2,z2,h2] = x1x2 + y1y2 + z1z2 + h1h2. You can order the coordinates however you like - you could replace x with h in the above and nothing would change.

However, SR space-time is quite different. The scalar product is defined as [x1,y1,z1,t1] dot [x2,y2,z2,t2] = c^2 * t1t2 - x1x2 - y1y2 - z1z2. You can still replace x with y without any change with the result; but you can't replace x with t in the same way. This makes it clear from the base math itself that the time dimension is of a different nature than the 3 space dimensions in this representation. This has a significant impact on how distances are calculated, and how operations like rotations work in this geometry.

Remember resources are limited. We cannot fund everyone who wants it. Society needs to make choices, we are generally okay with a bit of "interesting but unlikely to produce anything important", but most of what we fund needs a return on investment.

Likewise, we assume at an operational level that temperature and barometric pressure are continuous functions (as assumed in Borsuk-Ulam), but it's not something you can conclusively prove aobut reality.