Dimensions Are a Social Construct

Out of the 7 (technically 8, might post my midterm “return gift” essay soon) blog posts I’ve written this year, the prevailing trend (although it might be a stretch to consider two posts a 'trend') in their topics has been applied biology and chemistry. And sure, that same number of posts is also matched by the number of low-effort assignments I’ve written on this blog, but that’s beside the point. Between these entries, I’ve also dabbled a little bit with some philosophical mental terrorism disguised as reflective esoterism, and I guess a little bit of parody and satire too.

But there’s one thing that I’ve tried to stay away from as much as possible: math, more specifically abstract quantum physics-y type math. Maybe it’s repressed trauma from the Geometry Honors summer course I took as a stupid 12 year-old with non-existent study habits. It was the only class that I’ve ever gotten a B in, and to be honest, even that was a more generous grade than what I deserved given the lack of effort that I put in.

Or maybe it’s online Physics 2 coming back to haunt me, which I stupidly took as my first AP Science class as a sophomore. The theoretical, variable manipulation-based questions combined with the fact that Brawl Stars was better at capturing my attention than Zoom probably helped contribute to the least deserved 4 in all of College Board history (though my miraculous 4 in AP French is a close second).

But the truth is, the weird sci-fi-sounding science and abstract math have always fascinated me*.
*I don't know if ‘fascinated' is really the right word, I mean ‘fascinated’ in a “a car crash you can’t look away from” kind of way.

(side note: skip to here to get to the research part of this project)


Some of my earliest reading memories involve me going to the Houston Public Library and stockpiling a month’s worth of “A True Book” books so that I could speedrun through them on Saturday mornings.


Looking back, as impressive as finishing 10+ books a week as an 8-year-old may sound, those books were essentially the literary equivalent of the edutainment-type “science content” on Youtube these days. With total word counts less than even my shortest college supplemental essays, these addictive, 25-page bite-sized “books” offered little more than what seemed like “fun-fact”-y pseudo-nuances that really just deceptively coated surface-level information. While I may have gained a decent amount of “general knowledge” reading these books, the reality is that using them as my primary exposure to a number of unfamiliar subjects sort of lulled me into a Dunning-Kruger-like sense of “know-it-all ness”, a mindset that I’m still trying to combat to this day.

 

Like I said, those books seemed to offer easy-to-understand explanations of complex topics, but the removal of that complexity also came at the cost of also removing most of their meaning. I took everything that those books said at face value, which (whether unintentionally or not) gave me an inherently biased lens going into any kind of discussion or further research about those topics. Presenting content in this way served on an ultra-sanitized vanilla platter essentially made me ignore anything that questioned my previous understanding.

But this project isn’t about the impact of dumbed-down content on my mental health. I could probably write another one of these dedicated purely to my deteriorating attention span, seeing as I haven't been able to finish more than 2 full thoughts without reaching for my phone to spend another half hour watching a jumble of YouTube Shorts.


Now that I’ve wasted enough words, what I’ve been trying to get at is that physics is one of those fields that I gas-lit myself into thinking I knew a lot about.


After a few of those library book hauls, I found myself gravitating (haha) toward the space and physics “TRUE books”. Even after I moved from Houston to Naperville (and then eventually here), my curiosity for physics continued to grow. This interest manifested itself in a few more ways than just reading books, as I started to dive into the physics side of Youtube, with channels like Sciencephile the AI, Anton Petrov, Astrum, Styropyro, and Kurzgesagt- In a Nutshell.


In 7th grade, when we did our career project, I even said I wanted to become a theoretical physicist (link).


But when I finally took a “real” theoretical physics class (AP Physics 2), I found myself struggling to stay awake. “Knowing” what a boson or M-string feels cool and all but actually putting in the work to really “know” what they are is definitely not. After the AP test was over, I threw in the towel and happily laid my physics journey to rest.

 
But I’ve decided not to stop while I’m ahead, and to throw my hat back in the ring to wrestle with some physics again for this project.

At first, I was kind of lost since I didn’t really know what I wanted to do, but luckily it didn’t take too long for an idea to come to me.

It was a busy Saturday at work. Usually, I’m on the pizza side of the kitchen, but that day one of our line cooks had called in sick, so I was on boxing and oven. It's stormy days like that Saturday that seem to make residents of Troy and Clawson incredibly horny for Italian food. After our first rush of orders, we ran out of grilled chicken, so I quickly grabbed a new one from the walk-in, dusting it with flour and drizzling it with oil before tossing it into the oven.

Normally, we cook the chicken for about 5 minutes on one side before flipping them and putting them back in for another 2 minutes. This is because the recommended temperature for chicken to be cooked to is 165°F since that is the temperature at which the average population density of microbes like the Samonellas experience a 7-log reduction (99.99999 % die) instantaneously (Juneja V. K. et al.). But because we were swamped with orders, that chicken was cooking on borrowed time and the Door-Dashers were getting restless, so I had to take that shit out asap.


Now before you accuse me of almost giving all our customers salmonella, there’s something important you need to know about 7 log reductions (or killing bacteria in general). The amount of microbes that are killed isn't just a function of temperature, but a function of time as well. I probed the chicken when I pulled it out and the fattest piece was at like 150°F, so according to the USDA, the chicken was fine because the heat from the sauce and pasta, as well as additional carry-over cooking would probably kill most of the bacteria just the same as if I had left the chicken in there for the full time.

For some reason, (probably because I was studying the Voltage vs Time graphs for my inductors quiz in Physics C), I was thinking about the properties of dimensions. More specifically dimensions in space-time. The 3 dimensions in space (what we commonly call x, y and z) are pretty intuitive, but the 4th dimension of time is initially something that seems kind of foreign. I mean, space is measured in meters and time is measured in seconds, so how is time even similar to space?

I remember I heard that Einstein’s explanation essentially boiled down to this: you can move back and forth in space, and you can theoretically move back and forth in time. You can move in one direction in one spatial dimension while independently moving in another spatial dimension. Similarly, you can move in a spatial dimension independent of your movement in time. You can also create relationships between time with respect to spatial dimensions. Thus, time is a dimension.

But if being able to move back and forth in “something” is the only qualification for it being a dimension, then why aren’t things like temperature a dimension? I mean if you have an object, it can get heated and cooled just as easily as it can be moved up and down. You can graph temperature with respect to time the same way you can position, I mean that's literally what a weather map is. 

So isn’t temperature a dimension?


Hell, what even is a dimension?



My first instinct when I came up with this question was just to Google it, but even Googling in this case doesn’t really produce any sort of meaningful answer. The Wikipedia blurb that pops up describing what a dimension is only explains the word’s use in math and physics, doesn’t really translate over to the other uses of dimensions. When a character in a sci-fi movie talks about moving into a 'pocket dimension', or when a chemist uses dimensional analysis to solve a problem, it seems like they aren’t even talking about the same general concept, much less the same word.

There’s a quote from the preface of Mark Fennell’s Understanding Dimensions in Physics and Metaphysics that I think describes this dilemma pretty well:

“The word ‘Dimensions’ is used in a variety of different contexts, with a variety of different meanings…[m]any times [however], the people in the discussion do not realize that they are talking about different things. The result is a series of misunderstandings, being passed along in discussions, due to the various assumptions of each person when he hears the word ‘dimension’”(Fennell 5).

In this book, Fennel breaks down the word “dimension” and explains its different 'definitions' in 7 distinct concepts:

1. Classical Dimensions 

2. Physical Attribute Dimensions in Equations 

3. Combined Attribute Dimensions from Multiple Objects

4. Compounded Physical Attributes into Other Variables

5. Metaphysical Realms as Dimensions

6. Larger Scale Perspective Dimensions (Metaphysical or Physical)

7. Graphical Dimensions which Exist Only on Paper

So I guess this is my answer, right? Dimension is a word that has at least like 7 different meanings, and each meaning is used in its own way. But after reading what Fennell has to say and doing further research online, I think I might have a more satisfying, yet esoteric answer for the true definition of dimensions.

Dimensions are a social construct.

Yes, dimensions are like genders*. And I hope that by the end of this you’ll come to the same conclusion.
*note to clarify gender ≠ biological sex yada yada, I don’t want to get into the whole debate 

Dimensions just are a tool that we use to understand the world around us.

So I think the most intuitive way to explain this is to use some linear algebra.(yeah I know, not exactly the first thing that comes to mind when you picture "intuitive"). Linear algebra is like the season finale of math, tying up all the loose ends It's basically the ultimate cross over. Equations are now the same as vectors, vectors are now the same as matrices, and matrices are anything and everything. It is simultaneously the most abstract and most real math class that I have ever taken.

In linear algebra, a dimension is a vector that is used to travel across a space, called a basis vector (Anton et al). The classic example of this is (and the one that Fennell mentions) is Space-time.

You ever wonder why there’s three spatial dimensions? It’s not because of some fundamental law of the universe or some kind of the result of some kind of crazy math proof, It's just cause it’s the most efficient. The most common basis vectors (which together define the dimensions of 3D space) are î (1,0,0), ĵ (0,1,0), and k̂ (0,0,1). This means any point in 3D space can be represented by a combination of multiple of these 3 vectors. But the thing is, you can do this with any set of 3 linearly independent (math term, basically means not parallel) vectors (see gifs below/watch this), or really any number of vectors if you aren't trying to be efficient.




My point is, dimensions are inherently meaningless. We can call almost anything a dimension. They are only used as a tool in order for us to represent things.

The more specifically you try to “label” something with dimensions, the more meaningless that label is

This idea of representation can be generalized into the application of dimensions in science. Equations (that are using an efficient number of dimensions) in 3D have 3 variables because they are measuring 3 different things, the x, y and z positions. Spatial equations (one’s that describe an object’s position in all 3 dimensions) are useful because they can reveal relationships and trends. This is what algebra is, it is the use of dimensions to measure and relate quantities.

One interesting thing that Fennell notes is that simple equations in physics are not actually simple at all, since they “almost always involve the use of numerous physical attributes which are packed inside” (Fennell 14).

For example, the equation V=IR (Ohm’s law) states that the voltage drop across a resistor is equivalent to the current flowing through it times the resistance of that resistor. This is a very generic formula in physics, and it seems to be fairly straightforward.

However in practice, if you wanted to use this relationship to find the exact value for any one of those variables, you would need to measure a lot more things than just the two other variables in the equation. For example, to find the voltage drop through a resistor, you must figure out the current and the resistance. Well, to measure current, you need to measure the movement of charges, which means you have to measure the change in charge over a period of time. And to measure resistance, you would need to measure the length of the resistor, its cross-sectional area, and its resistivity (which is another value that you would need to experimentally find).

Each one of these measurements can theoretically be changed independent of one another, and they all contribute in some way to the equation, therefore they can all be labeled as dimensions. However, what we’ve done by specifying all these dimensions is we’ve made the original relationship less meaningful, since it is no longer something that can be easily worked with. Thus we go back to Fennell’s idea on the “economy of [dimensions]”( Fennell 13). Like I mentioned before, the reason there’s 3 dimensions in space and not 4 is because we are making a trade off between specific-ness and usefulness. It is not important, nor is it meaningful to impose a dimensional label on something that doesn’t need to be labeled. Some things (and people) don’t necessarily need to be categorized into labels and so we shouldn’t try to assign genders dimensions to them.

From these two ideas, I would say that the definition of dimension is a tool that we use to define and measure characteristics that are immediately useful to a given application.

That’s all fine and dandy but there’s still another problem that I need to address.

“Dimensions” is 2 words

Ok so you know how some people use the term “gender” to mean both/either gender and sex.

Well the same is sort of true for the word “dimension”. Going back to Fennell’s book for a second, the 5th and 6th definitions that he lists have to do with dimensions in metaphysics. 

When I first heard the term “metaphysics” I thought it was all science-y sounding, but as it turns out metaphysics is as close to physics as astrology is to astronomy. Fennell sort of goes on a mini-rant in pages 25-27 about how he believes in both “the physical realm and the spiritual realm”, and how dimensions in this context represent planes of existence beyond our understanding.

While I’m not a hippie that believes in activating their inner chakras or whatever, I do sort of get what Fennell’s is trying to say. His ideas are similar to those in Plato’s Allegory of the Cave, and in this context dimensions are not separate independent values, but rather “realms” which encompass one another (they’re layers). 

This definition isn’t just limited to pseudo-science and 2,500 year old literature though. Going back to linear alge(bruh), there’s a concept known as vector spaces. A vector space is “an arbitrary non-empty set of objects on which operations are defined” (Anton et al). An example of a common vector space is the set of natural numbers (whole numbers from 1 to ∞+). You can do things like add and multiply natural numbers, so they are a vector space.

But what’s interesting about the vector space of natural numbers is that they belong to another, larger vector space. This is the space of whole numbers (0 to ∞+). This vector space belongs to the vector space of integers, which belongs to the vector space of rational numbers, which (along with the vector space of irrational numbers) belongs to the vector space of all real numbers. This phenomenon is known as subspaces in linear algebra ("whole numbers are a subspace of real numbers”).

In astrophysics, dimensions can refer to different perspectives or scales. Fennell’s explanation for this idea is fairly straightforward:

“Think of each of these levels: atom, basketball, Earth, Solar System, Galaxy. Each level is a broader scale. Each level is a Higher Dimension. lf you live on an atom, then you see other atoms. Each other atom is different [from] yours, but on an equal scale. Then go up in perspective. The ball, which is a large collection of atoms. On this ball you see other balls. You can also look downward at atoms, or broader to see the planet around you..we can continue this process. As a planet, we see other planets…[a]lso note that from each of these perspectives we can look three directions: equal, higher, and lower. As a basketball, we can see other balls of approximately…equal size. Yet we can also see atoms which are much smaller. Looking the other way, we can see Earth and Galaxy which are much larger...Therefore, one way to use the word "Dimension", in the Metaphysical context, is to note at which level of scale we exist. There is always a higher level, and there is always a lower level, from the perspective [of] where we are at the moment"(Fennell 26).

See what I mean, these definitions don’t really match up with the previous definition of dimensions that I previously established. Thus, I think that if we want to be a more inclusive and progressive society, we need to use a second word when referring to these dated and bigoted uses of the word gender dimensions 🙄.

I mean look at the Java coding language. Even it has two different words for these two ideas. My first definition of dimensions is essentially the Java equivalent of parameters, arguments that are passed into functions in order to do something. Parameters are variables that can be changed and measured and can independently affect a relationship.

On the other hand, an array or ArrayList in Java is like the second definition of dimensions. Arrays and ArrayLists are basically tools that store values. However, you can store arrays and ArrayLists in each other, creating multidimensional arrays.

So if a stupid coding language can differentiate between gender and sex these uses of dimensions, why can't we? 

But jokes aside, what I’ve really learned is that

Dimensions are what you want them to be

Going back to my original question about why things like temperature aren’t dimensions, it turns out I’m not the only idiot who’s asked that. According to Google, there are two reasons. One is that temperature is an “intrinsic scalar”.

Temperature, and other quantities like charge and mass, can’t exist without an object since they are properties of objects, while space and time technically can, hence why they are not “intrinsic”.

The other reason applies to some intrinsic scalars other than temperature. Other properties of objects, such as charge, cannot be their own “fundamental” dimensions since they are derived from other properties of objects. According to the International System of Units, charge and most other properties of objects can be derived from a set of 7 fundamental units. This is why things like speed aren’t really a dimension, they are just relationships between two or more other dimensions. Calculus tells us that speed is the magnitude of the rate of change in a positional dimension with respect to the time dimension.

But this answer doesn’t really sit right with me. Aren’t positions in space scalars too? The only way you can define a value in a dimension to be a vector (a non-scalar) is if you define a direction for that value in respect to another dimension. Therefore, if I was measuring temperature in relation to time, I could make a “temperature vector”. And since Kelvin (the unit for temperature) is a fundamental unit like seconds and meters, it isn’t a relationship between two "fundamental dimensions". So temperature should be a dimension, but it isn’t.

But this whole argument is kind of stupid. It completely ignores the purpose of dimensions. Intrinsic or not, the usefulness of dimensions is purely dependent on the context in which they are used. Even things like time and position, which are things that everyone agrees are dimensions, aren't worth measuring on their own. Yes, time will continue to move forward even when we cease to exist, when traces of our existence cease to exist, and even when the matter in the universe ceases to exist. But is that point in time even worth measuring? What is the reason for measuring space unless it is in relation to something that we prescribe meaning, something that we as people feel is worth measuring? The meaning of dimensions is what we make of them.

Works Cited