Algebra and its limits
Central to mathematics and science is algebra. The concept of x + y = z is so intrinsic to our mathematical understanding that it has been considered a foundation of much of our modern world. Yet, in 4D maths algebra fails to work, and calculations produce unpredictable results. This brings into question everything we presumed we knew about mathematics and science, and ushers in a whole new understanding of number — hitherto only ever considered a bizarre possibility.
Numbers and mathematics are at the heart of our modern understanding of the universe. From computer technology, science, and even our financial systems, all have been predicated on the assurance that 1+1=2. But what if that was not true?
The implications would be so profound that they would undoubtedly reshape what we consider to be the 'truth'. Algebra is the primary methodology used by science in all equations, appearing to define our universe to an alarming degree of accuracy. Some have postulated 'what would it be like if the laws of mathematics were to change?' — a question most people believe to be an impossibility.
Yet, 4D Maths shows us that algebra is only applicable when the 4D calculator is set to a specific value. This article demonstrates how algebra is not a mathematical truth, but only a certain perception of number that, whilst able to predict scientific phenomena, fails to engage with numbers outside our standard space-time awareness. The result is that mathematics as we know it is only applicable within the nature of our consciousness, ingrained in our particular space-time reality. Only a 4th dimensional approach to number can reveal the deeper truth.
Numbers are far more than mathematics. They are the very thing that limits our awareness of the physical universe, a fact which can only be decoded through 4th dimensional maths.
Everything we know about maths
The concept of algebra has had a long history. From the simplest equation to the most complex mathematical algorithms of our modern age, all have been predicated on the logic of numbers combined with four mathematical operators that produce consistent results. So ingrained is this premise that the notion it might not be true has only been postulated in the farthest reaches of mathematical theory. For most people, the idea that 1+1 does not equal 2 is a logical impossibility. The consistency of algebra permeates so deeply into our understanding of reality that the mere thought of it not being true would be met with ridicule.
However, in the rather remarkable world of 4D maths, that is exactly what we find. The 4D calculator treats every calculation as having three variables: space (an ordinary number, the kind used in standard calculations), time (a calculative function that divides space), and dimension (which is added or subtracted from the result). Mathematics as we know it can be reproduced on this calculator, but only when time and dimension are both set to minus ONE. Change either of those settings, and the result will devolve towards a specific value regardless of the 'space' number used.
If the time and/or dimension numbers are changed, then any number entered as the space value appears to have no effect on the result. This means that any number — including transcendental numbers like e and π — will devolve into the same value.
This begins to alter everything one might have held 'true' in terms of mathematical understanding. After all, algebra has long been the bedrock of logical reasoning. Yet, 4D maths not only challenges this belief — it opens the door to a whole new world of mathematical understanding, one that fundamentally changes how we conceive of number itself.
Notice that only the odd effort values result in the same number as the original space value entered into the calculator. The effort value refers to how many times the calculation is iterated — essentially the number of steps applied in sequence. To understand the significance of this requires delving into the very foundations of what mathematics is — or more accurately, the nature of calculation itself.
What is a calculation?
Numbers and calculation are not the same thing. Consider this example: four apples are placed on a table. When we observe the table we can count them — 1, 2, 3, 4. We use a consecutive number count to establish how many apples are present. Each count takes a moment to complete, and so counting takes time. Furthermore, calculation is intrinsic to our consciousness. If we do not count the apples, it does not mean the number changes. The apples remain four whether observed or not. Counting is a process of number, not the number itself.
This distinction matters. A computer can calculate numbers at a vastly faster rate than a human mind, but it can only process data that is available to it. Speed of calculation does not change the underlying nature of what a number is.
A number exists in space, but a calculation is processed in time.
Science tells us that space and time are one thing. Yet that is not exactly the case. Time is unified, and space is differentiated. We all share a single moment of time we call the present, whereas we never occupy the same space at the same moment in time.
The 4D calculator is based on the simple equation: space divided by time ± dimension.
When we consider this foundation, we notice that the space value appears first. The next value is the time function, which divides the space value. Time is not just a number here — it is a calculative function. We use division because, in our theory of geometric maths, division is the first of the four mathematical functions to occur. Infinite space is divided by time.
When infinity is divided by TWO, it creates a positive and negative infinity. This is the first step toward the differentiation of number, which gives rise to the next mathematical function: addition and subtraction. Once positive and negative infinities are differentiated, the infinity equation comes into effect.
0 ± 1 = ±∞
Zero, acted on by +1 or −1, generates the infinite positive or negative number line. This is the simplest possible foundation for all counting — from a single point of zero, the entire structure of number unfolds through the repeated action of adding or subtracting one.
The nature of addition and subtraction completes the final part of the 4D calculator — the dimension number, which is added to or subtracted from the result.
Once addition and subtraction come into effect, mathematics arrives at the point where algebra can begin to operate. All subsequent 'numbers' are in fact calculations, based on the addition of unit values predicated on the whole number units ZERO, ONE and TWO. From these, all other units including fractions are derived. You can find out more about this new theory of number in our article on the Russell Paradox.
Standard calculations
When the 4D calculator has a time value of −1, normal algebraic equations can be performed by plugging one number line into the other.
The infinity equation at the foundations of all mathematics suggests that a number can only 'exist' if it is contained within two other numbers — the number needs a context. Think of a fence: each post is erected to create a space between it and the next. The fence panels are held between two posts. Similarly, any number needs to exist within the context of a number line.
When we count objects, they are differentiated by the empty space between each one. No matter what number you think of, there will always be another number that is +1 greater and one that is −1 below. This is the nature of the infinity of whole numbers — a process that requires addition and subtraction in order to be manifest.
Multiplication
In 4D maths, multiplication is not a separate operation but a change in the dimension variable. If the dimension is set to 2, then from a spatial number of zero we progress through the complete infinite set in steps of 2 — this is the two times table. If the dimension number is set to 3 we create the three times table. When we multiply two numbers together, we are combining the multiplication tables of each. For example, 7×3 = 21 combines (1×3) with (1×7), with dimension values of 3 and 7 respectively. When we change the space number we are altering the starting point. In reality, all space numbers begin at zero, to which sequential units are added (+1, +1, +1) to form the sequential series. Any point on the number line is predicated on the numbers before it.
To summarise: numbers are spatial and exist whether counted or not. Counting is calculative and is derived from the division of a single infinity into infinitely small parts. Those parts can be manipulated mathematically by adding single units together to identify a value. Values can only be multiplied once they are established in space, time and dimension.
Calculations outside of regular space-time
Having considered the philosophical background to this new theory of number, we can examine what happens when we change the 4D calculator values to any number other than −1.
Take a practical example. What happens when we change the time and dimension value to 2?
One might expect the 4D calculator to produce a number series based on the 2× multiplication table. However, that is not the case. Instead, the space number dissolves towards the number 4.
In the above image, the space number has a value of 1. As we progress through the effort values, the number dissolves to 4. Now let us change the space number to a value greater than 4 and observe the result.
With a space value of 8, the number still dissolves towards 4. In fact, it does not matter which number is entered as the space value — the result will always dissolve towards 4. This includes all negative numbers, fractions, primes, and even transcendental numbers such as e and π.
We can also take the output from the 4D calculator and perform any kind of calculation with a secondary line (a second set of inputs). What becomes apparent is that we have found a mathematical system where the laws of traditional algebra no longer apply. Even the most fundamental mathematical belief — that 1+1=2 — is violated once the time and dimension values are altered from −1 to any other integer.
The disruption this causes to established mathematics is comparable in significance to what quantum physics did at the start of the twentieth century — completely rewriting the rules of the Newtonian world.
Rewriting the rules
At first glance, it might appear that changing the space number has no effect on the result. Approached in the same way as standard maths, one might assume that all numbers resolve to a specific boundary — termed the limit. Mathematics has a tendency to make such assumptions when dealing with concepts such as continued fractions. Take for example the square root of 2.
The standard assumption is that as this calculation is reiterated, it converges ever closer to the limit of root 2. In 4D maths, each number dissolves towards the limit in a completely unique way. For each time and dimension setting outside of −1, there is an infinite set of dissolution number waves — the characteristic pattern by which each individual number approaches its limit, different for every number that exists.
In 4D maths we track the effort value at every step. For example, with Space = 8 and Time/Dimension = 2, the first effort value produces two prime numbers: 3 and 5. This is not random — it reflects the internal structure of 8 within that dimensional setting, a signature that no other number will produce. Each number generates a dissolution wave that is entirely unique to itself.
The idea that a reiterated number can simply be said to equal its limit is not valid in 4D maths. Instead, numbers dissolve towards a boundary without ever actually reaching it. The fractional remainder above or below the limit becomes smaller and smaller at each step but is never fully resolved. That it appears to be resolved is an artefact of rounding. Whilst rounding is an acceptable convention in traditional mathematics, it conceals important information in 4D maths — the remainder becomes a significant factor that can be examined in great detail.
Experimenting with the 4D calculator is the most direct way to observe these dissolution patterns firsthand.
Conclusion
The 4D calculator radically undermines the traditional laws of mathematics. It clearly demonstrates that reiterative functions exhibit specific boundaries towards which all numbers, regardless of their normal categorisation, will dissolve. Since none of the standard axiomatic categories of number can be applied, a whole new set of axioms is needed to qualify even the most basic assumptions of conventional mathematics.
Mathematics has been predicated upon beliefs formulated within 'normal' space-time. 4D maths shatters those beliefs by allowing us to calculate the dissolution of number waves, rather than treating numbers as fixed points on a line. When we consider the implications, we realise that number, calculation, and the structure of number space are fundamentally different from what is normally believed.
FAQ
Isn't multiplication simply produced by repeated addition?
Multiplication is not solely produced by addition — rather, it is the process of addition that makes multiplication possible. Order matters in the emergence of number. Without a sequential number series, there are no values on which to base the multiplicative function. 4D axioms propose that division comes first: dividing infinity creates positive and negative infinite number sets, which allow for addition and subtraction. Only once division and addition/subtraction are established can multiplication emerge. Read more in our article on the numbers of creation.
If we can multiply lines from two 4D calculators, does algebra still hold?
Algebra represents a number as a variable such as x. However, if all numbers dissolve towards the same value regardless of what x is, then x could technically be any number whatsoever. In the example above — time and dimension set to 2 — every space value dissolves towards 4, making x effectively range across the entire number line. Each line dissolves in its own unique way, so meaningful comparison requires tracking boundaries at specific effort values. As effort approaches infinity the required precision increases without bound, making direct algebraic comparison untenable. Explore this further in zero begins and ends all numbers.
