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A second issue is that it is unclear to know what

A second issue is that it is unclear to know what you would accept being "not trivial"

You may have hoped for someone to give an entire course on evolutionary biology to fill up this gap of knowledge of yours but I am afraid it would be way too much work for a single post. If this was your position, then it would be like refusing to accept that earth is a sphere without having yourself explain how GPS data work. We just can't give you an entire course here. So, you will have to either 1) rely on those who know (scientists) or 2) understand the field by yourself and therefore start studying for it.

Good luck!

You may have hoped for someone to give an entire course on evolutionary biology to fill up this gap of knowledge of yours but I am afraid it would be way too much work for a single post. If this was your position, then it would be like refusing to accept that earth is a sphere without having yourself explain how GPS data work. We just can't give you an entire course here. 

So you have two solutions; rely on authority or understand by yourself. If you rely on authority you have two main options; Rely on those that rely on evidence (science) or those that don't rely on evidence and either rely on other forms of justification (justification theory;such as a religious book for example). (either those that work through observations, scientists). You second solution is to understand the field by yourself and therefore start studying for it.

For all reasons explained above, the question cannot be answered, not by lack of evidence, but because the question is unclear. I am therefore voting to close as unclear. Good luck in your investigation of the question.

There are two issues in your question.

A big issue in your question is based upon what you call an observation!

When you say

observed - not deduced

, you highlight the whole issue of what you would consider being an observation.

In science, observations often take complex form. It is not only direct visual observation recorded on a standard camera. It is like asking for, recorded-on-camera evidence that quartz exist. Such evidence don't exist (and cannot exist), yet we know of their existence through other means of observation. It would make no sense for someone to only consider camera recording as valid mean of observation.

Of course, We have never recorded on a camera the evolution of an entire new organ because it takes a lot of time. Yet, evidences are numerous.

This technic of limiting arbitrarily the field of methods that one accepts to recognize as bringing evidence and call "observation" is a common technic from science denier (e.g. flat earth society, creationist). I made a similar point as the one I made here on this post if you want.

How to solve this "What is an observation" problem?

There is only one way to go. It will be for you to be able to understand the forms that observation can take. For this, you will have to learn a little bit about evolutionary biology and evolutionary genetics. For a very short introduction to evolutionary biology, you can have a look at Evo101 by UC Berkeley.

**A second issue is that it is unclear to know what **

When you say

Also not looking for something trivial such as a new/modified enzyme or protein molecule but rather a new organ in a species at least the size of an insect

It is hard to know what you would call a significant enough evolutionary event to be accepted. The risk is that you may define it large enough so that it fundamentally cannot be observed by a mean that you would accept.

For your curiosity, this post talks about evolution of lactose digestion in humans and this post about the evolution of cardio-vascular system.

Somewhat related post

You might want to have a look at post Is evolution a fact? and the link posts in the top voted answer.

Just another comment

random evolution

Calling "evolution" random is really never used in the scientific literature. The fact that you're using it shows what kind of literature you are used to.

There are two main issues in your question that make it hard or fundamentally impossible to answer. The two issues are

• What you would accept being an 'observation'
• What you would accept being significant enough to be an example of interest.

A big issue in your question is based upon what you call an observation!

When you say

observed - not deduced

, you highlight the whole issue of what you would consider being an observation.

In science, observations often take complex form. It is not only direct visual observation recorded on a standard camera. It is like asking for, recorded-on-camera evidence that quartz exist. Such evidence don't exist (and cannot exist), yet we know of their existence through other means of observation. It would make no sense for someone to only consider camera recording as valid mean of observation.

Of course, We have never recorded on a camera the evolution of an entire new organ because it takes a lot of time. Yet, evidences are numerous.

This technic of limiting arbitrarily the field of methods that one accepts to recognize as bringing evidence and call "observation" is a common technic from science denier (e.g. flat earth society, creationist). I made a similar point as the one I made here on this post if you want.

How to solve this "What is an observation" problem?

There is only one way to go. It will be for you to be able to understand the forms that observation can take. For this, you will have to learn a little bit about evolutionary biology and evolutionary genetics. For a very short introduction to evolutionary biology, you can have a look at Evo101 by UC Berkeley.

You may have hoped for someone to give an entire course on evolutionary biology to fill up this gap of knowledge of yours but I am afraid it would be way too much work for a single post. If this was your position, then it would be like refusing to accept that earth is a sphere without having yourself explain how GPS data work. We just can't give you an entire course here. So, you will have to either 1) rely on those who know (scientists) or 2) understand the field by yourself and therefore start studying for it.

A second issue is that it is unclear to know what

When you say

Also not looking for something trivial such as a new/modified enzyme or protein molecule but rather a new organ in a species at least the size of an insect

It is hard to know what you would call a significant enough evolutionary event to be accepted. The risk is that you may define it large enough so that it fundamentally cannot be observed by a mean that you would accept.

For your curiosity, this post talks about evolution of lactose digestion in humans and this post about the evolution of cardio-vascular system.

Somewhat related post

You might want to have a look at post Is evolution a fact? and the link posts in the top voted answer.

Just another comment

random evolution

In the scientific literature, "evolution" is never said to be "random". The fact that you're using this expression shows what kind of literature you are used to.

Good luck!