Does a Hypothesis have to use maths?

[robinpike]

With regards to the post: Is Mathematics Alone a safe medium for exploring the frontiers of Science. Or should Observation and Hypothesis lead in front ?

 

Here, as an example, is a hypothesis: The electron, proton and photon are made of the same substance.

 

Are people saying that maths is the only method at our disposal to investigate a hypothesis?

 

Because it strikes me that a lot of non mathematical thinking must surely have to precede any output of equations?

 

In the above example, there are lots of observations that can be used, both for and against the hypothesis, so surely they would be discussed before any use of maths?

 

 

[swansont]

There are plenty of scientific questions that don't appear to require math. Are electron, proton and photons made of the same substance? The answer is trivially "no" and you don't need math to say that. But that belies the sources of our information that allow us to provide an answer. Those sources are the theories and experiments that tell us what the properties of those particles are. Invariably there is math there.

 

One might get around math by asking a very general question, one that does not require much investigation. One whose answer adds very little to the body of knowledge. Math allows precision, quantification. That's where the value is. Knowing how long it will take for a thrown rock to hit the ground is more valuable than simply knowing it will eventually hit the ground.

 

As I pointed out in the other thread, the formulation of the question creates a false dichotomy, that it must be one or the other — math or observation/hypothesizing. In reality they are all part of the process.

[Bignose]

Just a general comment on the topic: words and story telling can be incredibly powerful. There are a great many truly awesome works of literature mankind has created. But, take any of those same great works of literature. No small part of what makes them great is that the author's intent and meaning is constantly debated, re-evaluated, and individuals approach the works from their own unique experience.

 

In short, words are fungible, and take on different meanings depending on each individual perspective.

 

Here's my favorite example: If I walked into the room carrying a box, set it down in front of you, and said "Wow, that box is heavy," what does that really mean? What if I were an Olympic class weightlifter? A ballet dancer? And so on. The word "heavy" means different things to different people.

 

This is the great thing about a mathematical prediction and measurement. If I had a model that predicted that the box would require 500 N of force to lift, that 500 N is the same no matter if I were a weightlifter, a ballet dancer, or a toll booth attendant. 500 N is 500 N and only 500 N.

 

Then, when you actually measured the force required to lift the box, if it measured 499.3 N, you know that my model is pretty darn close to reality. 0.14% error to be exact. On the other hand, if it measured 63.8 N to lift, my prediction was pretty awful. Over 87% error.

 

This is the powerful use of mathematics. We don't have to decide which model is better by how 'logical' it sounds, by who is the better debater, by how much authority the model creator has, by how accomplished a history the model creator has, etc. What we have is an objective, clear cut, simple metric to determine the better model: the model that makes predictions the most accurately compared to measurements.

 

To recap, words are great. They make readers experience an incredible range of feelings and emotions. But mathematical predictions allow objective and conclusive comparisons between models and thus eliminates the needs to invoke subjective arguments on which model is superior.

[md65536]

In short, words are fungible, and take on different meanings depending on each individual perspective.

I was thinking something that is also true but along an opposite line of thinking...

 

Many people think that words and maths are mutually exclusive or somehow in conflict with each other.

 

Both words and maths have meaning only because what they represent is consistent. If you use the word "electron" it has meaning because it consistently represents something understandable. Similarly, if I combine 4 baskets with 10 apples each, then the count of apples is reliably and consistently represented by using multiplication. Just like I can't just use made-up words to convey meaning, you can't just use made-up math to describe a hypothesis, or expect that math alone explains how things behave. Either words or math must be carefully chosen to properly represent the meaning. Maths represent many different consistent relationships between many different types of things, that can be symbolically represented, and the consistency of those relationships lets you make conclusions based on the maths. Some words represent relationships too. The consistent relationships of physical aspects of the world are often much more efficiently described with math.

 

Whether using words or maths, the value in either is what meaning (and its quality and quantity) that you can convey.

[timo]

To cut it short, two comments:

1) My guess would be that an archeologist's hypothesis saying "I found traces of blood on this altar-like pile of stones, therefore the culture having built it probably offered sacrifices to its gods" does not involve heavy math.

2) Since those "does science depends on math" questions/claims often tend to actually refer to physics or at least natural sciences rather than "science": Physics can be understood as an attempt to describe nature's behavior by means of numbers and rules connecting these numbers (see also Bignose's post). That's probably what an average person would call "math".

Edited April 13, 2013 by timo

[robinpike]

I think maths in physics is used in a very specific way: in order to predict what things do without necessarily explaining why.

 

In the example above of how much force is required to lift a box, we can have a very accurate mathematical equation that states what force is required to lift a certain weight, without the equation having to explain how the force works, how things obtain weight, how gravity works, what the box is made of etc etc.

 

If someone asks "But how does an object obtain the quality of weight?", this doesn't mean that they are questioning the accuracy of the equation that relates force with weight.

 

This is where a hypothesis seems to be more suitable than maths in explaining why an object does something.

 

For discussion, I gave the example of a hypothesis as "The electron, proton and photon are made of the same substance" and the reply given "The answer is trivially "no" and you don't need math to say that."

 

I can argue back (without using maths as well) that the answer importantly is "Yes", since light can be made using an electron and positron, or light can be made using a proton and an anti-proton.

[newts]

I can argue back (without using maths as well) that the answer importantly is "Yes", since light can be made using an electron and positron, or light can be made using a proton and an anti-proton.

 

Excellent logic. But you need to bear in mind that physics-believers do not believe in logic, they believe in imaginary beings, so they would argue that protons are made of quarks, but electrons are not, therefore your hypothesis is wrong.

Usually a correct theory starts as a hypothesis, and then gets tested mathematically. For instance the idea that the nuclei of atoms are composed of protons. However sometimes the maths actually leads to a new discovery, for instance testing the hypothesis that the nucleus of an atom is composed solely of protons, led directly to the discovery of the neutron.

Edited April 16, 2013 by newts

[Relative]

I think that human logic and observation , should always proceed maths.

[Delta1212]

 

I think that human logic and observation , should always proceed maths.

Math is logic.

[Mellinia]

I think that human logic and observation , should always proceed maths.

I was hoping you meant intuition, but you'll still maths to verify. In which case you don't go down the wrong path.

[ajb]

I think maths in physics is used in a very specific way: in order to predict what things do without necessarily explaining why.

One can argue that physics says noting about "why". Physics gives mathematical systems of equations that can be used to model nature. To me, the closest to "why" is the mathematics. And of course, most concepts in physics have their meaning in mathematics, given your example what is a force if one does not know any mathematics?

 

Math is logic.

Not all of mathematics can be reduce to (formal) logic. There for I argue that mathematics is more than just logic.

[Ophiolite]

To cut it short, two comments:

1) My guess would be that an archeologist's hypothesis saying "I found traces of blood on this altar-like pile of stones, therefore the culture having built it probably offered sacrifices to its gods" does not involve heavy math.

I thought your qualification heavy to be interesting. would you expand on that?

 

Certainly a study that considered the frequency with which blood traces were found on similar 'alters' and an exploration of where on the 'alters' and how much, all subjected to statistical analysis, might lead to confirmation or refutation of the hypothesis.

[kristalris]

Apart from the problem of words being inherently ambiguous and mathematics not being so, mathematics can thus be as precise as is needed. When we talk about mathematics most people tend to hold that it is always properly applied and forget the garbage in problem. Further more mathematics is far more cumbersome to use quickly when working in a field where the data are inherently few and quick decision making is needed. Such as courts of law where some protagonists of mathematics would like to use Bayesian probabilistic nets. Apart from exceptions that won't work IMO. Another problem with mathematics is that not everyone is aware of all the extremely concise conventions it needs. If I remember correctly a psychology test showed that some people see windmills turn to the left even though it was clear in that test they were turning to the right. They concluded that some people are inherently deluded. A reason for this I didn't see mentioned in that test is however that some people are not aware of the convention that you should look above the center in order to ascertain which way the mill is turning. A lot of miss-communication between people trained in mathematics and those who are not stem from this, lack of understanding - on both sides - that the conventions can differ. Further more a language lets you make mistakes and still further science. Science has made great progress via mistakes. I.e. you don't get hung up on details. That again doesn't mean that extreme detail isn't required ultimately.

 

So yes hypothesis don't need mathematics for these reasons even in physics. To state that the apple falls down from the tree is a sufficient hypothesis to be tested. If you subsequently observe it falling upwards that readily proves something worthwhile. That on the other hand doesn't mean to say that subsequently it can be left at that after such a phenomenon has been observed. Ultimately Nature should be described in mathematics in the most concise way possible. I.e. with DM & DE we actually observe the apples falling upwards. That we know this via mathematical analysis doesn't mean that a - way to a - solution for these problems can only be reached via mathematics. Even Einstein didn't start off with mathematics but with a thought experiment.

 

Hypothesis and observation should lead in front, because that is logically the quickest way to achieve progress. You don't wait with testing. If you can test a hypothesis you test it. In science period.

Conventions stating anything different constitute democratic science. Science isn't democratic but primarily'driven by observations & logic and thus ultimately and thus logically not only mathematically driven. (Even though all logic can be put into mathematics, it only takes longer, and not everyone knows mathematics, thus excluding a lot of potential brainpower in order to solve scientific problems.)

Edited May 2, 2013 by kristalris

[swansont]

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Moderator Note

newts's hijack to bash physics has been split http://www.scienceforums.net/topic/74676-is-physics-about-why/

[Bignose]

Not to say that I support newts and his theory, but he's throwing physicists in with creationists and astrologists, and pretending that he's the skeptic of both creationism and astrology.

=Uncool-

I re-read it like 10 times, and I guess I still didn't get that. Whatever, it's truly immaterial to the topic at hand. Edited May 2, 2013 by Bignose